browning

explanation blue bibcodes open ADS page with paths to full text

Author name code: browning
ADS astronomy entries on 2022-09-14
author:"Browning, Philippa"

---------------------------------------------------------
Title: Oscillatory reconnection and waves driven by merging magnetic
flux ropes in solar flares
Authors: Stewart, J.; Browning, P. K.; Gordovskyy, M.
2022MNRAS.513.5224S Altcode: 2022arXiv220503106S
Oscillatory reconnection is a process that has been suggested to
underlie several solar and stellar phenomena, and is likely to play
an important role in transient events such as flares. Quasi-periodic
pulsations in flare emissions may be a manifestation of oscillatory
reconnection, but the underlying mechanisms remain uncertain. In
this paper, we present 2D magnetohydrodynamic simulations of two
current-carrying magnetic flux ropes with an out-of-plane magnetic
field undergoing oscillatory reconnection in which the two flux ropes
merge into a single flux rope. We find that oscillatory reconnection
can occur intrinsically without an external oscillatory driver during
flux rope coalescence, which may occur both during large-scale coronal
loop interactions and the merging of plasmoids in fragmented current
sheets. Furthermore, we demonstrate that radially propagating non-linear
waves are produced in the aftermath of flux rope coalescence, due to the
post-reconnection oscillations of the merged flux rope. The behaviour
of these waves is found to be almost independent of the initial
out-of-plane magnetic field. It is estimated that the waves emitted
through merging coronal loops and merging plasmoids in loop-top current
sheets would have a typical phase speed of 90 and 900 km s-1,
respectively. It is possible that the properties of the waves emitted
during flux rope coalescence could be used as a diagnostic tool to
determine physical parameters within a coalescing region.

---------------------------------------------------------
Title: Pulsations of microwave emission from a solar flare in a
twisted loop caused by intrinsic magnetohydrodynamic oscillations
Authors: Smith, Christopher; Gordovskyy, M.; Browning, P. K.
2022MNRAS.511.2880S Altcode: 2022arXiv220108419S; 2022MNRAS.tmp..227S
We present results revealing microwave pulsations produced in a
model of a flaring twisted solar coronal loop, without any external
oscillatory driver. Two types of oscillations are identified: slowly
decaying oscillations with a period of about 70-75 s and amplitude
of about 5-10 per cent seen in loops both with and without energetic
electrons, and oscillations with a period of about 40 s and amplitude of
a few tens of per cent observed only in loops with energetic electrons
for about 100 s after the onset of fast energy release. We interpret
the longer-period oscillations as the result of a standing kink mode
modulating the average magnetic field strength in the loop, whilst
the short-period intermittent oscillations associated with energetic
electrons are likely to be produced by fast variations of the electric
field, which produces energetic electrons in this scenario. The slowly
decaying oscillations can explain the quasi-periodic pulsations often
observed in the flaring corona.

---------------------------------------------------------
Title: Sizes and Shapes of Sources in Solar Metric Radio Bursts
Authors: Gordovskyy, Mykola; Kontar, Eduard P.; Clarkson, Daniel L.;
Chrysaphi, Nicolina; Browning, Philippa K.
2022ApJ...925..140G Altcode: 2021arXiv211107777G
Metric and decametric radio emissions from the Sun are the only direct
source of information about the dynamics of nonthermal electrons
in the upper corona. In addition, the combination of spectral and
imaging (sizes, shapes, and positions) observations of low-frequency
radio sources can be used as a unique diagnostic tool to probe plasma
turbulence in the solar corona and inner heliosphere. The geometry of
the low-frequency sources and its variation with frequency are still
not understood, primarily due to the relatively low spatial resolution
available for solar observations. Here we report the first detailed
multifrequency analysis of the sizes of solar radio sources observed
by the Low Frequency Array. Furthermore, we investigate the source
shapes by approximating the derived intensity distributions using
2D Gaussian profiles with elliptical half-maximum contours. These
measurements have been made possible by a novel empirical method for
evaluating the instrumental and ionospheric effects on radio maps
based on known source observations. The obtained deconvolved sizes
of the sources are found to be smaller than previous estimations,
and often show higher ellipticity. The sizes and ellipticities of the
sources inferred using 2D Gaussian approximation, and their variation
with frequency are consistent with models of anisotropic radio-wave
scattering in the solar corona.

---------------------------------------------------------
Title: The high-energy Sun - probing the origins of particle
acceleration on our nearest star
Authors: Matthews, S. A.; Reid, H. A. S.; Baker, D.; Bloomfield, D. S.;
Browning, P. K.; Calcines, A.; Del Zanna, G.; Erdelyi, R.; Fletcher,
L.; Hannah, I. G.; Jeffrey, N.; Klein, L.; Krucker, S.; Kontar, E.;
Long, D. M.; MacKinnon, A.; Mann, G.; Mathioudakis, M.; Milligan,
R.; Nakariakov, V. M.; Pesce-Rollins, M.; Shih, A. Y.; Smith, D.;
Veronig, A.; Vilmer, N.
2021ExA...tmp..135M Altcode:
As a frequent and energetic particle accelerator, our Sun provides
us with an excellent astrophysical laboratory for understanding
the fundamental process of particle acceleration. The exploitation
of radiative diagnostics from electrons has shown that acceleration
operates on sub-second time scales in a complex magnetic environment,
where direct electric fields, wave turbulence, and shock waves all
must contribute, although precise details are severely lacking. Ions
were assumed to be accelerated in a similar manner to electrons, but
γ-ray imaging confirmed that emission sources are spatially separated
from X-ray sources, suggesting distinctly different acceleration
mechanisms. Current X-ray and γ-ray spectroscopy provides only a basic
understanding of accelerated particle spectra and the total energy
budgets are therefore poorly constrained. Additionally, the recent
detection of relativistic ion signatures lasting many hours, without
an electron counterpart, is an enigma. We propose a single platform
to directly measure the physical conditions present in the energy
release sites and the environment in which the particles propagate and
deposit their energy. To address this fundamental issue, we set out
a suite of dedicated instruments that will probe both electrons and
ions simultaneously to observe; high (seconds) temporal resolution
photon spectra (4 keV - 150 MeV) with simultaneous imaging (1 keV -
30 MeV), polarization measurements (5-1000 keV) and high spatial and
temporal resolution imaging spectroscopy in the UV/EUV/SXR (soft X-ray)
regimes. These instruments will observe the broad range of radiative
signatures produced in the solar atmosphere by accelerated particles.

---------------------------------------------------------
Title: Transport of energetic particles from reconnecting current
sheets in flaring corona to the heliosphere
Authors: Browning, Philippa; Gordovskyy, Mykola; Inoue, Satashi;
Kontar, Eduard; Kusano, Kanya; Vekstein, Gregory
2021EGUGA..2315163B Altcode:
In this study, we inverstigate the acceleration of electrons and ions
at current sheets in the flaring solar corona, and their transport
into the heliosphere. We consider both generic solar flare models and
specific flaring events with a data-driven approach. The aim is to
answer two questions: (a) what fraction of particles accelerated in
different flares can escape into the heliosphere?; and (b) what are
the characteristics of the particle populations propagating towards
the chromosphere and into the heliosphere?We use a combination of
data-driven 3D magnetohydrodynamics simulations with drift-kinetic
particle simulations to model the evolution of the magnetic field
and both thermal and non-thermal plasma and to forward-model
observable characteristics. Particles are accelerated in current
sheets associated with flaring reconnection. When applied to a
specific flare, the model successfully predicts observed features
such as the location and relative intensity of hard X-ray sources
and helioseismic source locations. This confirms the viability of
the approach.Using these MHD-particle models, we will show how the
magnetic field evolution and particle transport processes affect the
characteristics of both energetic electrons and ions in the the inner
corona and the heliosphere. The implications for interpretation of in
situ measurements of energetic particles by Solar Orbiter and Parker
Solar Probe will be discussed.

---------------------------------------------------------
Title: Sizes of solar radio sources observed by LOFAR
Authors: Gordovskyy, Mykola; Kontar, Eduard; Clarkson, Daniel;
Browning, Philippa
2021EGUGA..2315852G Altcode:
Decametric radio emission provides a unique insight into the physics
of solar and heliospheric plasmas. Along with dynamic spectra, the
spatial characteristics of the emission sources observed in solar
radio bursts yield important information about the behaviour of
high-energy non-thermal electrons, and the state of thermal plasma in
the upper solar corona. Recently, it has been shown that sizes and
locations of radio sources in the 10-100 MHz range can be used as a
diagnostic tool for plasma turbulence in the upper corona and inner
heliosphere. However, observations in this spectral range can be
strongly affected by limited spatial resolution of the instrument,
as well as by the effect of the Earth's ionosphere on radio wave
propagation.We describe a new method for correcting radio intensity
maps for instrumental and ionospheric effects using observations of
a known radio source at an arbitrary location in the sky. Based on
this method, we derive sizes and areas of the emission sources in the
solar radio bursts observed by the Low-Frequency Array (LOFAR) in 30-45
MHz range. It is shown that the sizes of sources are of the order of
ten arcminutes and decrease with increasing frequency. Overall, we
find that the sizes and their variation, as well as the shapes of the
sources in the considered events are consistent with the theoretical
models of turbulent radio-wave scattering in the solar corona developed
by Kontar et al. 2019 (Astrophys.J., 884, 122).

---------------------------------------------------------
Title: Forward Modeling of Particle Acceleration and Transport in
an Individual Solar Flare
Authors: Gordovskyy, Mykola; Browning, Philippa K.; Inoue, Satoshi;
Kontar, Eduard P.; Kusano, Kanya; Vekstein, Grigory E.
2020ApJ...902..147G Altcode: 2020arXiv200910130G
The aim of this study is to generate maps of the hard X-ray emission
produced by energetic electrons in a solar flare and compare them
with observations. The ultimate goal is to test the viability of the
combined MHD/test-particle approach for data-driven modeling of active
events in the solar corona and their impact on the heliosphere. Based
on an MHD model of X-class solar flare observed on 2017 September 8,
we calculate trajectories of a large number of electrons and protons
using the relativistic guiding-center approach. Using the obtained
particle trajectories, we deduce the spatial and energy distributions of
energetic electrons and protons, and calculate bremsstrahlung hard X-ray
emission using the "thin-target" approximation. Our approach predicts
some key characteristics of energetic particles in the considered
flare, including the size and location of the acceleration region,
energetic particle trajectories and energy spectra. Most importantly,
the hard X-ray bremsstrahlung intensity maps predicted by the model
are in good agreement with those observed by RHESSI. Furthermore, the
locations of proton and electron precipitation appear to be close to
the sources of helioseismic response detected in this flare. Therefore,
the adopted approach can be used for observationally driven modeling
of individual solar flares, including manifestations of energetic
particles in the corona, as well as the inner heliosphere.

---------------------------------------------------------
Title: Predicting the time variation of radio emission from MHD
simulations of a flaring T-Tauri star
Authors: Waterfall, C. O. G.; Browning, P. K.; Fuller, G. A.;
Gordovskyy, M.; Orlando, S.; Reale, F.
2020MNRAS.496.2715W Altcode: 2020MNRAS.tmp.1811W; 2020arXiv200605570W
We model the time-dependent radio emission from a disc accretion event
in a T-Tauri star using 3D, ideal magnetohydrodynamic simulations
combined with a gyrosynchrotron emission and radiative transfer
model. We predict for the first time, the multifrequency (1-1000 GHz)
intensity and circular polarization from a flaring T-Tauri star. A flux
tube, connecting the star with its circumstellar disc, is populated
with a distribution of non-thermal electrons that is allowed to decay
exponentially after a heating event in the disc and the system is
allowed to evolve. The energy distribution of the electrons, as well
as the non-thermal power-law index and loss rate, are varied to see
their effect on the overall flux. Spectra are generated from different
lines of sight, giving different views of the flux tube and disc. The
peak flux typically occurs around 20-30 GHz and the radio luminosity is
consistent with that observed from T-Tauri stars. For all simulations,
the peak flux is found to decrease and move to lower frequencies with
elapsing time. The frequency-dependent circular polarization can
reach 10 $-30{{\ \rm per\ cent}}$ but has a complex structure that
evolves as the flare evolves. Our models show that observations of the
evolution of the spectrum and its polarization can provide important
constraints on physical properties of the flaring environment and
associated accretion event.

---------------------------------------------------------
Title: Using the Stokes V widths of Fe I lines for diagnostics of
the intrinsic solar photospheric magnetic field
Authors: Gordovskyy, M.; Shelyag, S.; Browning, P. K.; Lozitsky, V. G.
2020A&A...633A.136G Altcode: 2019arXiv191203340G
 Aims: The goal of this study is to explore a novel method
for the solar photospheric magnetic field diagnostics using Stokes
V widths of different magnetosensitive Fe I spectral lines. Methods: We calculate Stokes I and V profiles of several Fe I
lines based on a one-dimensional photospheric model VAL C using the
NICOLE radiative transfer code. These profiles are used to produce
calibration curves linking the intrinsic magnetic field values with the
widths of blue peaks of Stokes V profiles. The obtained calibration
curves are then tested using the Stokes profiles calculated for
more realistic photospheric models based on magnetohydrodynamic of
magneto-convection. Results: It is shown that the developed
Stokes V widths method can be used with various optical and
near-infrared lines. Out of six lines considered in this study,
Fe I 6301 line appears to be the most effective: it is sensitive
to fields over ∼200 G and does not show any saturation up to ∼2
kG. Other lines considered can also be used for the photospheric field
diagnostics with this method, however, only in narrower field value
ranges, typically from about 100 G to 700-1000 G. Conclusions:
The developed method can be a useful alternative to the classical
magnetic line ratio method, particularly when the choice of lines
is limited.

---------------------------------------------------------
Title: Determining whether the squashing factor, Q, would be a good
indicator of reconnection in a resistive MHD experiment devoid of
null points
Authors: Reid, J.; Parnell, C. E.; Hood, A. W.; Browning, P. K.
2020A&A...633A..92R Altcode:
The squashing factor of a magnetic field, Q, is commonly used as an
indicator of magnetic reconnection, but few studies seek to evaluate
how reliable it is in comparison with other possible reconnection
indicators. By using a full, self-consistent, three-dimensional,
resistive magnetohydrodynamic experiment of interacting magnetic strands
constituting a coronal loop, Q and several different quantities are
determined. Each is then compared with the necessary and sufficient
condition for reconnection, namely the integral along a field line
of the component of the electric field parallel to the magnetic
field. Among the reconnection indicators explored, we find the squashing
factor less successful when compared with alternatives, such as Ohmic
heating. In a reconnecting magnetic field devoid of null points, our
work suggests that Q, being a geometric measure of the magnetic field,
is not a reliable indicator of the onset or a diagnostic of the location
of magnetic reconnection in some configurations.

---------------------------------------------------------
Title: Anisotropic Radio-wave Scattering and the Interpretation of
Solar Radio Emission Observations
Authors: Kontar, Eduard P.; Chen, Xingyao; Chrysaphi, Nicolina;
Jeffrey, Natasha L. S.; Emslie, A. Gordon; Krupar, Vratislav;
Maksimovic, Milan; Gordovskyy, Mykola; Browning, Philippa K.
2019ApJ...884..122K Altcode: 2019arXiv190900340K
The observed properties (i.e., source size, source position, time
duration, and decay time) of solar radio emission produced through
plasma processes near the local plasma frequency, and hence the
interpretation of solar radio bursts, are strongly influenced by
propagation effects in the inhomogeneous turbulent solar corona. In
this work, a 3D stochastic description of the propagation process
is presented, based on the Fokker-Planck and Langevin equations
of radio-wave transport in a medium containing anisotropic electron
density fluctuations. Using a numerical treatment based on this model,
we investigate the characteristic source sizes and burst decay times
for Type III solar radio bursts. Comparison of the simulations with
the observations of solar radio bursts shows that predominantly
perpendicular density fluctuations in the solar corona are required,
with an anisotropy factor of ∼0.3 for sources observed at around 30
MHz. The simulations also demonstrate that the photons are isotropized
near the region of primary emission, but the waves are then focused by
large-scale refraction, leading to plasma radio emission directivity
that is characterized by a half width at half maximum of about 40°
near 30 MHz. The results are applicable to various solar radio bursts
produced via plasma emission.

---------------------------------------------------------
Title: Frequency-Distance Structure of Solar Radio Sources Observed
by LOFAR
Authors: Gordovskyy, Mykola; Kontar, Eduard; Browning, Philippa;
Kuznetsov, Alexey
2019ApJ...873...48G Altcode:
Low-frequency radio observations make it possible to study the
solar corona at distances up to 2-3 R ⊙. Frequency of
plasma emission is a proxy for electron density of the emitting
plasma and, therefore, observations of solar radio bursts can be
used to probe the density structure of the outer corona. In this
study, positions of solar radio sources are investigated using the
Low-Frequency Array (LOFAR) spectral imaging in the frequency range
30-50 MHz. We show that there are events where apparent positions
of the radio sources cannot be explained using the standard coronal
density models. Namely, the apparent heliocentric positions of the
sources are 0.1-0.7 R ⊙ further from the Sun compared
with the positions predicted by the Newkirk model, and these shifts
are frequency-dependent. We discuss several possible explanations for
this effect, including enhanced plasma density in the flaring corona,
as well as scattering and refraction of the radio waves.

---------------------------------------------------------
Title: Forced magnetic reconnection and plasmoid
coalescence. I. Magnetohydrodynamic simulations
Authors: Potter, M. A.; Browning, P. K.; Gordovskyy, M.
2019A&A...623A..15P Altcode: 2019arXiv190102392P
Context. Forced magnetic reconnection, a reconnection event triggered by
external perturbation, should be ubiquitous in the solar corona. Energy
released during such cases can be much greater than that which
was introduced by the perturbation. The exact dynamics of magnetic
reconnection events are determined by the structure and complexity of
the reconnection region: the thickness of reconnecting layers, the field
curvature; the presence, shapes and sizes of magnetic islands. It is
unclear how the properties of the external perturbation and the initial
current sheet affect the reconnection region properties, and thereby
the reconnection dynamics and energy release profile. Aims:
We investigate the effect of the form of the external perturbation
and initial current sheet on the evolution of the reconnection region
and the energy release process. Chiefly we explore the non-linear
interactions between multiple, simultaneous perturbations, which
represent more realistic scenarios. Future work will use these results
in test particle simulations to investigate particle acceleration
over multiple reconnection events. Methods: Simulations
are performed using Lare2d, a 2.5D Lagrangian-remap solver for the
visco-resistive MHD equations. The model of forced reconnection is
extended to include superpositions of sinusoidal driving disturbances,
including localised Gaussian perturbations. A transient perturbation
is applied to the boundaries of a region containing a force-free
current sheet. The simulation domain is sufficiently wide to allow
multiple magnetic islands to form and coalesce. Results: Island
coalescence contributes significantly to energy release and involves
rapid reconnection. Long wavelength modes in perturbations dominate
the evolution, without the presence of which reconnection is either
slow, as in the case of short wavelength modes, or the initial current
sheet remains stable, as in the case of noise perturbations. Multiple
perturbations combine in a highly non-linear manner: reconnection is
typically faster than when either disturbance is applied individually,
with multiple low-energy events contributing to the same total energy
release.

---------------------------------------------------------
Title: Combining MHD and kinetic modelling of solar flares
Authors: Gordovskyy, Mykola; Browning, Philippa; Pinto, Rui F.
2019AdSpR..63.1453G Altcode: 2018arXiv180905751G
Solar flares are explosive events in the solar corona, representing
fast conversion of magnetic energy into thermal and kinetic energy,
and hence radiation, due to magnetic reconnection. Modelling is
essential for understanding and predicting these events. However,
self-consistent modelling is extremely difficult due to the vast
spatial and temporal scale separation between processes involving
thermal plasma (normally considered using magnetohydrodynamic (MHD)
approach) and non-thermal plasma (requiring a kinetic approach). In
this mini-review we consider different approaches aimed at bridging the
gap between fluid and kinetic modelling of solar flares. Two types of
approaches are discussed: combined MHD/test-particle (MHDTP) models,
which can be used for modelling the flaring corona with relatively
small numbers of energetic particles, and hybrid fluid-kinetic methods,
which can be used for modelling stronger events with higher numbers
of energetic particles. Two specific examples are discussed in more
detail: MHDTP models of magnetic reconnection and particle acceleration
in kink-unstable twisted coronal loops, and a novel reduced-kinetic
model of particle transport in converging magnetic fields.

---------------------------------------------------------
Title: Modelling the radio and X-ray emission from T-Tauri flares
Authors: Waterfall, C. O. G.; Browning, P. K.; Fuller, G. A.;
Gordovskyy, M.
2019MNRAS.483..917W Altcode: 2018MNRAS.tmp.2737W
T-Tauri stars are known for their high levels of magnetic activity and
variability. Both classical and weak-line T-Tauri stars are overluminous
in the radio compared with the well-established Güdel-Benz relation
between radio and X-ray luminosity for solar and main sequence
stellar flares. We show that there is little difference in the
observational properties of classical T-Tauri stars and weak-line
T-Tauri stars. We then model a typical T-Tauri - circumstellar
disc system magnetosphere to predict the radio emission from flares
associated with the circumstellar disc and accretion events. We assume
that energetic electrons are generated in a large-scale magnetic flux
tube due to a reconnection event with the accretion disc field at 4
R⊙. Our standard model, with a dipolar magnetic field
with a strength of 2 kG at the stellar surface and non-thermal and
thermal densities of 2.5 × 1011 cm-3 and 5.0
× 1011 cm-3 respectively, produces both X-ray
and radio emission consistent with observations (logLX =
30.5, logLR = 16.3). Varying the model parameters, we can
reproduce the observed range of radio and X-ray emission. The peak radio
luminosity and the frequency of this peak (which occurs at &gt;10 GHz
and possibly beyond 100 GHz for some sets of parameters) depend on the
fraction of non-thermal particles and may be used as a diagnostic of
this quantity. The surface field strength was varied from 0.5 to 7 kG,
with the peak flux increasing by over three orders of magnitude. The
models provide a framework for constraining the properties of these
sources and to guide and interpret future observations.

---------------------------------------------------------
Title: Analysis of unresolved photospheric magnetic field structure
using Fe I 6301 and 6302 lines
Authors: Gordovskyy, M.; Shelyag, S.; Browning, P. K.; Lozitsky, V. G.
2018A&A...619A.164G Altcode: 2018arXiv180806862G
Context.Early magnetographic observations indicated that the magnetic
field in the solar photosphere has an unresolved small-scale
structure. Near-infrared and optical data with extremely high
spatial resolution show that these structures have scales of a few
tens of kilometres, which are not resolved in the majority of solar
observations. Aims.The goal of this study is to establish the effect of
the unresolved photospheric magnetic field structure on Stokes profiles
observed with relatively low spatial resolution. Ultimately, we aim
to develop methods for fast estimation of the photospheric magnetic
filling factor and line-of-sight gradient of the photospheric magnetic
field, which can be applied to large observational data sets. Methods.We
exploit 3D magnetohydrodynamic models of magneto-convection developed
using the MURAM code. Corresponding profiles of Fe I 6301.5 and
6302.5 Å spectral lines are calculated using the NICOLE radiative
transfer code. The resulting I and V Stokes [x, y, λ] cubes with a
reduced spatial resolution of 150 km are used to calculate magnetic
field values as they would be obtained in observations with the Solar
Optical Telescope (SOT) onboard Hinode or the Helioseismic and Magnetic
Imager (HMI) onboard the Solar Dynamic Observatory (SDO) mission. 
Results: Three different methods of magnetic filling factor estimation
are considered: the magnetic line ratio method, the Stokes V width
method, and a simple statistical method. We find that the statistical
method and the Stokes V width method are sufficiently reliable for
fast filling factor estimations. Furthermore, we find that the Stokes
I ± V bisector splitting gradient can be used for fast estimation of
the line-of-sight gradient of the photospheric magnetic field.

---------------------------------------------------------
Title: Three-dimensional magnetic reconnection in a collapsing
coronal loop system
Authors: O'Flannagain, Aidan M.; Maloney, Shane A.; Gallagher, Peter
T.; Browning, Philippa; Refojo, Jose
2018A&A...617A...9O Altcode: 2018arXiv180609365O
Context. Magnetic reconnection is believed to be the primary mechanism
by which non-potential energy stored in coronal magnetic fields is
rapidly released during solar eruptive events. Unfortunately, owing
to the small spatial scales on which reconnection is thought to
occur, it is not directly observable in the solar corona. However,
larger scale processes, such as associated inflow and outflow, and
signatures of accelerated particles have been put forward as evidence
of reconnection. Aims: Using a combination of observations
we explore the origin of a persistent Type I radio source that
accompanies a coronal X-shaped structure during its passage across
the disk. Of particular interest is the time range around a partial
collapse of the structure that is associated with inflow, outflow,
and signatures of particle acceleration. Methods: Imaging radio
observations from the Nançay Radioheliograph were used to localise the
radio source. Solar Dynamics Observatory (SDO) AIA extreme ultraviolet
(EUV) observations from the same time period were analysed, looking for
evidence of inflows and outflows. Further mpole magnetic reconstructions
using SDO HMI observations allowed the magnetic connectivity associated
with the radio source to be determined. Results: The Type I
radio source was well aligned with a magnetic separator identified
in the extrapolations. During the partial collapse, gradual (1 km
s-1) and fast (5 km s-1) inflow phases and fast
(30 km s-1) and rapid (80-100 km s-1) outflow
phases were observed, resulting in an estimated reconnection rate
of ∼0.06. The radio source brightening and dimming was found to be
co-temporal with increased soft X-ray emission observed in both Reuven
Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and Geostationary
Operational Environmental Satellite (GOES). Conclusions:
We interpret the brightening and dimming of the radio emission
as evidence for accelerated electrons in the reconnection region
responding to a gradual fall and rapid rise in electric drift velocity,
in response to the inflowing and outflowing field lines. These results
present a comprehensive example of 3D null-point reconnection. The movies associated to Figs. 2 and 3 are available at <A
href="https://www.aanda.org/10.1051/0004-6361/201732122/olm">https://www.aanda.org/</A>

---------------------------------------------------------
Title: Coronal energy release by MHD avalanches: continuous driving
Authors: Reid, J.; Hood, A. W.; Parnell, C. E.; Browning, P. K.;
Cargill, P. J.
2018A&A...615A..84R Altcode:
Previous work has confirmed the concept of a magnetohydrodynamic (MHD)
avalanche in pre-stressed threads within a coronal loop. We undertook
a series of full, three-dimensional MHD simulations in order to create
three threads by twisting the magnetic field through boundary motions
until an instability ensues. We find that, following the original
instability, one unstable thread can disrupt its neighbours with
continued driving. A "bursty" heating profile results, with a series
of ongoing energy releases, but no evident steady state. For the first
time using full MHD, we show that avalanches are a viable mechanism
for the storing and release of magnetic energy in the solar corona,
as a result of photospheric motions.

---------------------------------------------------------
Title: Spatial and frequency structure of solar LOFAR radio sources
Authors: Gordovskyy, Mykola; Browning, Philippa; Kontar, Eduard;
Kuznetsov, Alexey
2018EGUGA..2013823G Altcode:
We investigate frequency-position structure of radio sources in solar
type III and type IV bursts in the frequency range 30-50 MHz observed
by LOFAR. These sources are produced by fundamental and harmonic plasma
emission induced by propagating suprathermal electrons. Therefore, the
frequency is a proxy for the electron density in the emitting plasma,
and these observations can be used to estimate the plasma density in the
outer corona. Our analysis indicates that coronal plasma, which produces
the emission, is denser and has larger hydrodynamic scale height (i.e.,
it is less stratified or more uniform) compared to Newkirk's density
model. We interpret this as the result of local plasma gradients
induced by plasma motion in the corona above solar active regions.

---------------------------------------------------------
Title: Flare particle acceleration resulting from the interaction
of twisted coronal flux ropes
Authors: Threlfall, James; Hood, Alan; Browning, Philippa
2018EGUGA..20.5145T Altcode:
Solar flares are highly explosive events which release significant
quantities of energy (upto 10^32 ergs) from specific magnetic
configurations in the solar atmosphere. As part of this process, flares
produce unique signatures across the entire electromagnetic spectrum,
from radio to ultra-violet (UV) and X-ray wavelengths, over extremely
short length and timescales. Many of the observed signals are indicative
of strong particle acceleration, where highly energised electron and
proton populations rapidly achieve MeV/GeV energies and therefore form
a significant fraction of the energy budget of each event. It is almost
universally accepted that magnetic reconnection plays a fundamental role
(on some level) in the acceleration of particles to such incredible
energies. I will briefly summarise a recent investigation of non-thermal
particle behaviour in a three-dimensional (3D) magnetohydrodynamical
(MHD) model of unstable multi-threaded flaring coronal loops. Using the
test-particle approach, I will describe how particle orbits respond
to the reconnection and fragmentation in MHD simulations wherein the
onset of the kink instability in a single loop thread can lead to the
destabilisation and fragmentation of other loop threads. I will also
compare the test particle energy distributions and final positions
with other theoretical particle acceleration models in the context of
observed energetic particle populations during solar flares.

---------------------------------------------------------
Title: Flare particle acceleration in the interaction of twisted
coronal flux ropes
Authors: Threlfall, J.; Hood, A. W.; Browning, P. K.
2018A&A...611A..40T Altcode: 2018arXiv180102907T
Aim. The aim of this work is to investigate and characterise non-thermal
particle behaviour in a three-dimensional (3D) magnetohydrodynamical
(MHD) model of unstable multi-threaded flaring coronal loops. 
Methods: We have used a numerical scheme which solves the relativistic
guiding centre approximation to study the motion of electrons and
protons. The scheme uses snapshots from high resolution numerical MHD
simulations of coronal loops containing two threads, where a single
thread becomes unstable and (in one case) destabilises and merges
with an additional thread. Results: The particle responses to
the reconnection and fragmentation in MHD simulations of two loop
threads are examined in detail. We illustrate the role played by
uniform background resistivity and distinguish this from the role of
anomalous resistivity using orbits in an MHD simulation where only one
thread becomes unstable without destabilising further loop threads. We
examine the (scalable) orbit energy gains and final positions recovered
at different stages of a second MHD simulation wherein a secondary loop
thread is destabilised by (and merges with) the first thread. We compare
these results with other theoretical particle acceleration models in the
context of observed energetic particle populations during solar flares.

---------------------------------------------------------
Title: Comparison of methods for modelling coronal magnetic fields
Authors: Goldstraw, E. E.; Hood, A. W.; Browning, P. K.; Cargill, P. J.
2018A&A...610A..48G Altcode: 2017arXiv171107458G
 Aims: Four different approximate approaches used to model the
stressing of coronal magnetic fields due to an imposed photospheric
motion are compared with each other and the results from a full
time-dependent magnetohydrodynamic (MHD) code. The assumptions used
for each of the approximate methods are tested by considering large
photospheric footpoint displacements. Methods: We consider a
simple model problem, comparing the full non-linear MHD, determined
with the Lare2D numerical code, with four approximate approaches. Two
of these, magneto-frictional relaxation and a quasi-1D Grad-Shafranov
approach, assume sequences of equilibria, whilst the other two methods,
a second-order linearisation of the MHD equations and Reduced MHD,
are time dependent. Results: The relaxation method is very
accurate compared to full MHD for force-free equilibria for all
footpoint displacements, but has significant errors when the plasma
β0 is of order unity. The 1D approach gives an extremely
accurate description of the equilibria away from the photospheric
boundary layers, and agrees well with Lare2D for all parameter
values tested. The linearised MHD equations correctly predict the
existence of photospheric boundary layers that are present in the
full MHD results. As soon as the footpoint displacement becomes
a significant fraction of the loop length, the RMHD method fails
to model the sequences of equilibria correctly. The full numerical
solution is interesting in its own right, and care must be taken for
low β0 plasmas if the viscosity is too high.

---------------------------------------------------------
Title: Polarisation of microwave emission from reconnecting twisted
coronal loops
Authors: Gordovskyy, M.; Browning, P. K.; Kontar, E. P.
2017A&A...604A.116G Altcode: 2016arXiv161102237G
Context. Magnetic reconnection and particle acceleration due to the
kink instability in twisted coronal loops can be a viable scenario
for confined solar flares. Detailed investigation of this phenomenon
requires reliable methods for observational detection of magnetic twist
in solar flares, which may not be possible solely through extreme UV
and soft X-ray thermal emission. Polarisation of microwave emission in
flaring loops can be used as one of the detection criteria. Aims:
The aim of this study is to investigate the effect of magnetic twist in
flaring coronal loops on the polarisation of gyro-synchrotron microwave
(GSMW) emission, and determine whether it could provide a means for
magnetic twist detection. Methods: We consider time-dependent
magnetohydrodynamic and test-particle models developed using the LARE3D
and GCA codes to investigate twisted coronal loops that relax after kink
instability. Synthetic GSMW emission maps (I and V Stokes components)
are calculated using GX simulator. Results: It is found that
flaring twisted coronal loops produce GSMW radiation with a gradient
of circular polarisation across the loop. However, these patterns
may be visible only for a relatively short period of time owing to
fast magnetic reconfiguration after the instability. Their visibility
also depends on the orientation and position of the loop on the solar
disk. Typically, it would be difficult to see these characteristic
polarisation patterns in a twisted loop seen from the top (I.e. close
to the centre of the solar disk), but easier in a twisted loop seen
from the side (I.e. observed very close to the limb).

---------------------------------------------------------
Title: A relaxation model of coronal heating in multiple interacting
flux ropes
Authors: Hussain, A. S.; Browning, P. K.; Hood, A. W.
2017A&A...600A...5H Altcode:
Context. Heating the solar corona requires dissipation of stored
magnetic energy, which may occur in twisted magnetic fields. Recently
published numerical simulations show that the ideal kink instability in
a twisted magnetic thread may trigger energy release in stable twisted
neighbours, and demonstrate an avalanche of heating events. 
Aims: We aim to construct a Taylor relaxation model for the energy
release from two flux ropes and compare this with the outcomes of the
simulations. We then aim to extend the model to large numbers of flux
ropes, allowing the possibility of modelling a heating avalanche, and
calculation of the energy release for ensembles of twisted threads with
varying twist profiles. Methods: The final state is calculated
by assuming a helicity-conserving relaxation to a minimum energy
state. Multiple scenarios are examined, which include kink-unstable flux
ropes relaxing on their own, as well as stable and unstable flux ropes
merging into a single rope as a result of magnetic reconnection. We
consider alternative constraints that determine the spatial extent
of the final relaxed state. Results: Good agreement is found
between the relaxation model and the magnetohydrodynamic simulations,
both for interactions of two twisted threads and for a multi-thread
avalanche. The model can predict the energy release for flux ropes
of varying degrees of twist, which relax individually or which merge
through reconnection into a single flux rope. It is found that the
energy output of merging flux ropes is dominated by the energy of the
most strongly twisted rope. Conclusions: The relaxation approach
provides a very good estimate of the energy release in an ensemble of
twisted threads of which one is kink-unstable.

---------------------------------------------------------
Title: Magnetic reconnection in twisted magnetic fields in solar
flares - heating, particle acceleration and observational signatures
Authors: Browning, Philippa K.
2017psio.confE..65B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Plasma motions and non-thermal line broadening in flaring
twisted coronal loops
Authors: Gordovskyy, M.; Kontar, E. P.; Browning, P. K.
2016A&A...589A.104G Altcode: 2015arXiv150806412G
Context. Observation of coronal extreme ultra-violet (EUV) spectral
lines sensitive to different temperatures offers an opportunity to
evaluate the thermal structure and flows in flaring atmospheres. This,
in turn, can be used to estimate the partitioning between the thermal
and kinetic energies released in flares. Aims: Our aim is to
forward-model large-scale (50-10 000 km) velocity distributions to
interpret non-thermal broadening of different spectral EUV lines
observed in flares. The developed models allow us to understand
the origin of the observed spectral line shifts and broadening,
and link these features to particular physical phenomena in flaring
atmospheres. Methods: We use ideal magnetohydrodynamics
(MHD) to derive unstable twisted magnetic fluxtube configurations
in a gravitationally stratified atmosphere. The evolution of these
twisted fluxtubes is followed using resistive MHD with anomalous
resistivity depending on the local density and temperature. The model
also takes thermal conduction and radiative losses in the continuum
into account. The model allows us to evaluate average velocities
and velocity dispersions, which would be interpreted as non-thermal
velocities in observations, at different temperatures for different
parts of the models. Results: Our models show qualitative and
quantitative agreement with observations. Thus, the line-of-sight
(LOS) velocity dispersions demonstrate substantial correlation
with the temperature, increasing from about 20-30 km s-1
around 1 MK to about 200-400 km s-1 near 10-20 MK. The
average LOS velocities also correlate with velocity dispersions,
although they demonstrate a very strong scattering compared to the
observations. We also note that near footpoints the velocity dispersions
across the magnetic field are systematically lower than those along the
field. We conclude that the correlation between the flow velocities,
velocity dispersions, and temperatures are likely to indicate that
the same heating mechanism is responsible for heating the plasma,
its turbulisation, and expansion/evaporation.

---------------------------------------------------------
Title: Energy Release in Driven Twisted Coronal Loops
Authors: Bareford, M. R.; Gordovskyy, M.; Browning, P. K.; Hood, A. W.
2016SoPh..291..187B Altcode: 2015arXiv150601312B; 2015SoPh..tmp..177B
We investigate magnetic reconnection in twisted magnetic fluxtubes,
representing coronal loops. The main goal is to establish the
influence of the field geometry and various thermodynamic effects on
the stability of twisted fluxtubes and on the size and distribution of
heated regions. In particular, we aim to investigate to what extent
the earlier idealised models, based on the initially cylindrically
symmetric fluxtubes, are different from more realistic models,
including the large-scale curvature, atmospheric stratification,
thermal conduction and other effects. In addition, we compare the
roles of Ohmic heating and shock heating in energy conversion during
magnetic reconnection in twisted loops. The models with straight
fluxtubes show similar distribution of heated plasma during the
reconnection: it initially forms a helical shape, which subsequently
becomes very fragmented. The heating in these models is rather uniformly
distributed along fluxtubes. At the same time, the hot plasma regions
in curved loops are asymmetric and concentrated close to the loop
tops. Large-scale curvature has a destabilising influence: less twist
is needed for instability. Footpoint convergence normally delays the
instability slightly, although in some cases, converging fluxtubes
can be less stable. Finally, introducing a stratified atmosphere gives
rise to decaying wave propagation, which has a destabilising effect.

---------------------------------------------------------
Title: An MHD Avalanche in a Multi-threaded Coronal Loop.
Authors: Hood, A. W.; Cargill, P. J.; Browning, P. K.; Tam, K. V.
2016ApJ...817....5H Altcode: 2015arXiv151200628H
For the first time, we demonstrate how an MHD avalanche might occur
in a multithreaded coronal loop. Considering 23 non-potential magnetic
threads within a loop, we use 3D MHD simulations to show that only one
thread needs to be unstable in order to start an avalanche even when the
others are below marginal stability. This has significant implications
for coronal heating in that it provides for energy dissipation with
a trigger mechanism. The instability of the unstable thread follows
the evolution determined in many earlier investigations. However,
once one stable thread is disrupted, it coalesces with a neighboring
thread and this process disrupts other nearby threads. Coalescence with
these disrupted threads then occurs leading to the disruption of yet
more threads as the avalanche develops. Magnetic energy is released in
discrete bursts as the surrounding stable threads are disrupted. The
volume integrated heating, as a function of time, shows short spikes
suggesting that the temporal form of the heating is more like that of
nanoflares than of constant heating.

---------------------------------------------------------
Title: Thermal and non-thermal emission from reconnecting twisted
coronal loops
Authors: Pinto, R. F.; Gordovskyy, M.; Browning, P. K.; Vilmer, N.
2016A&A...585A.159P Altcode: 2015arXiv150601251P
Context. Twisted magnetic fields should be ubiquitous in the solar
corona, particularly in flare-producing active regions where the
magnetic fields are strongly non-potential. The magnetic energy
contained in such twisted fields can be released during solar
flares and other explosive phenomena. It has recently been shown
that reconnection in helical magnetic coronal loops results in
plasma heating and particle acceleration distributed within a large
volume, including the lower coronal and chromospheric sections of
the loops. Hence, the magnetic reconnection and particle acceleration
scenario involving magnetic helicity can be a viable alternative to
the standard flare model, where particles are accelerated only in
a small volume located in the upper corona. Aims: The key
goal of this study is to investigate the links and observational
signatures of plasma heating and particle acceleration in kink-unstable
twisted coronal loops. Methods: We used a combination of
magnetohydrodynamic (MHD) simulations and test-particle methods. These
simulations describe the development of kink instability and magnetic
reconnection in twisted coronal loops using resistive compressible
MHD and incorporate atmospheric stratification and large-scale loop
curvature. The resulting distributions of hot plasma let us estimate
thermal X-ray emission intensities. With the electric and magnetic
fields we obtained, we calculated electron trajectories using the
guiding-centre approximation. These trajectories combined with the
MHD plasma density distributions let us deduce synthetic hard X-ray
bremsstrahlung intensities. Results: Our simulations emphasise
that the geometry of the emission patterns produced by hot plasma in
flaring twisted coronal loops can differ from the actual geometry
of the underlying magnetic fields. In particular, the twist angles
revealed by the emission threads (soft X-ray thermal emission; SXR)
are consistently lower than the field-line twist present at the onset
of the kink instability. Hard X-ray (HXR) emission that is due to the
interaction of energetic electrons with the stratified background is
concentrated at the loop foot-points in these simulations, even though
the electrons are accelerated everywhere within the coronal volume
of the loop. The maximum of the HXR emission consistently precedes
that of SXR emission, with the HXR light curve being approximately
proportional to the temporal derivative of the SXR light curve.

---------------------------------------------------------
Title: Reduced drift-kinetics with thermal velocity distribution
across magnetic field
Authors: Gordovskyy, Mykola; Browning, Philippa
2016arXiv160200341G Altcode:
The goal of this study is to develop an approximate self-consistent
description of particle motion in strongly magnetised solar corona. We
derive a set of reduced drift-kinetic equations based on the assumption
that the gyro-velocity distribution is Maxwellian. The equations are
tested using simple 1D models.

---------------------------------------------------------
Title: Coronal heating in multiple magnetic threads
Authors: Tam, K. V.; Hood, A. W.; Browning, P. K.; Cargill, P. J.
2015A&A...580A.122T Altcode: 2015arXiv150700259T
Context. Heating the solar corona to several million degrees requires
the conversion of magnetic energy into thermal energy. In this paper,
we investigate whether an unstable magnetic thread within a coronal
loop can destabilise a neighbouring magnetic thread. Aims:
By running a series of simulations, we aim to understand under what
conditions the destabilisation of a single magnetic thread can also
trigger a release of energy in a nearby thread. Methods: The 3D
magnetohydrodynamics code, Lare3d, is used to simulate the temporal
evolution of coronal magnetic fields during a kink instability and
the subsequent relaxation process. We assume that a coronal magnetic
loop consists of non-potential magnetic threads that are initially in
an equilibrium state. Results: The non-linear kink instability
in one magnetic thread forms a helical current sheet and initiates
magnetic reconnection. The current sheet fragments, and magnetic
energy is released throughout that thread. We find that, under certain
conditions, this event can destabilise a nearby thread, which is a
necessary requirement for starting an avalanche of energy release in
magnetic threads. Conclusions: It is possible to initiate an
energy release in a nearby, non-potential magnetic thread, because the
energy released from one unstable magnetic thread can trigger energy
release in nearby threads, provided that the nearby structures are
close to marginal stability.

---------------------------------------------------------
Title: Solar and Heliospheric Physics with the Square Kilometre Array
Authors: Nakariakov, V.; Bisi, M. M.; Browning, P. K.; Maia,
D.; Kontar, E. P.; Oberoi, D.; Gallagher, P. T.; Cairns, I. H.;
Ratcliffe, H.
2015aska.confE.169N Altcode: 2015PoS...215E.169N; 2015arXiv150700516N
The fields of solar radiophysics and solar system radio physics,
or radio heliophysics, will benefit immensely from an instrument
with the capabilities projected for SKA. Potential applications
include interplanetary scintillation (IPS), radio-burst tracking,
and solar spectral radio imaging with a superior sensitivity. These
will provide breakthrough new insights and results in topics of
fundamental importance, such as the physics of impulsive energy
releases, magnetohydrodynamic oscillations and turbulence, the
dynamics of post-eruptive processes, energetic particle acceleration,
the structure of the solar wind and the development and evolution of
solar wind transients at distances up to and beyond the orbit of the
Earth. The combination of the high spectral, time and spatial resolution
and the unprecedented sensitivity of the SKA will radically advance
our understanding of basic physical processes operating in solar and
heliospheric plasmas and provide a solid foundation for the forecasting
of space weather events.

---------------------------------------------------------
Title: Recent advances in coronal heating
Authors: De Moortel, Ineke; Browning, Philippa
2015RSPTA.37340269D Altcode: 2015arXiv151000977D
The solar corona, the tenuous outer atmosphere of the Sun, is orders of
magnitude hotter than the solar surface. This 'coronal heating problem'
requires the identification of a heat source to balance losses due to
thermal conduction, radiation and (in some locations) convection. The
review papers in this Theo Murphy meeting issue present an overview
of recent observational findings, large- and small-scale numerical
modelling of physical processes occurring in the solar atmosphere
and other aspects which may affect our understanding of the proposed
heating mechanisms. At the same time, they also set out the directions
and challenges which must be tackled by future research. In this brief
introduction, we summarize some of the issues and themes which reoccur
throughout this issue.

---------------------------------------------------------
Title: Notes on Magnetohydrodynamics of Magnetic Reconnection in
Turbulent Media
Authors: Browning, Philippa; Lazarian, Alex
2014mpcp.book..249B Altcode: 2014mcp..book..249B
Astrophysical fluids have very large Reynolds numbers and therefore
turbulence is their natural state. Magnetic reconnection is an important
process in many astrophysical plasmas, which allows restructuring
of magnetic fields and conversion of stored magnetic energy into
heat and kinetic energy. Turbulence is known to dramatically change
different transport processes and therefore it is not unexpected that
turbulence can alter the dynamics of magnetic field lines within the
reconnection process. We shall review the interaction between turbulence
and reconnection at different scales, showing how a state of turbulent
reconnection is natural in astrophysical plasmas, with implications for
a range of phenomena across astrophysics. We consider the process of
magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit
and discuss how turbulence—both externally driven and generated
in the reconnecting system—can make reconnection independent
on the microphysical properties of plasmas. We will also show how
relaxation theory can be used to calculate the energy dissipated in
turbulent reconnecting fields. As well as heating the plasma, the
energy dissipated by turbulent reconnection may cause acceleration of
non-thermal particles, which is briefly discussed here.

---------------------------------------------------------
Title: Accelerated particles and their observational signatures from
confined solar flares in twisted coronal loops
Authors: Browning, Philippa; Kontar, Eduard; Vilmer, Nicole;
Gordovskyy, Mykola; Pinto, Rui; Bian, Nicolas
2014cosp...40E.416B Altcode:
Twisted magnetic fields provide a reservoir of free magnetic energy,
and are ubiquitous in the solar corona. Recent theoretical studies
suggest that the onset of the kink instability in twisted coronal loops
may generate fragmented current sheets throughout the loop, leading
to fast magnetic reconnection which dissipates magnetic energy. This
provides a viable model for small self-contained flares. Using a
combination of 3D MHD and guiding-centre test-particle simulations,
incorporating collisions with the background plasma, we study
the kinetics of non-thermal particles accelerated during magnetic
reconnection in a flaring twisted coronal loop. It is shown that this
model can provide the number of high-energy electrons and acceleration
efficiency comparable with those obtained from observations of small
flares. We consider various geometries: including idealised cylindrical
loop models, as well as, more realistically, curved loops. The effects
of gravitational stratification, which has very significant effects
on the non-thermal particles through collisions, are included. The
calculated loop temperatures and densities, and the energy spectra and
pitch-angles of the accelerated particles, are used to forward-model
the emission in both Soft X-rays and Hard X-rays, predicting spatial
distributions and temporal evolution, as well as radio emission arising
from cyclotron/synchrotron radiation. These properties may be compared
with observations.

---------------------------------------------------------
Title: Particle acceleration and transport in reconnecting twisted
loops in a stratified atmosphere
Authors: Gordovskyy, M.; Browning, P. K.; Kontar, E. P.; Bian, N. H.
2014A&A...561A..72G Altcode: 2015arXiv150106418G
Context. Twisted coronal loops should be ubiquitous in the solar
corona. Twisted magnetic fields contain excess magnetic energy, which
can be released during magnetic reconnection, causing solar flares. Aims: The aim of this work is to investigate magnetic reconnection,
and particle acceleration and transport in kink-unstable twisted coronal
loops, with a focus on the effects of resistivity, loop geometry and
atmospheric stratification. Another aim is to perform forward-modelling
of bremsstrahlung emission and determine the structure of hard X-ray
sources. Methods: We use a combination of magnetohydrodynamic
(MHD) and test-particle methods. First, the evolution of the kinking
coronal loop is considered using resistive MHD model, incorporating
atmospheric stratification and loop curvature. Then, the obtained
electric and magnetic fields and density distributions are used to
calculate electron and proton trajectories using a guiding-centre
approximation, taking into account Coulomb collisions. 
Results: It is shown that electric fields in twisted coronal loops
can effectively accelerate protons and electrons to energies up to
10 MeV. High-energy particles have hard, nearly power-law energy
spectra. The volume occupied by high-energy particles demonstrates
radial expansion, which results in the expansion of the visible
hard X-ray loop and a gradual increase in hard X-ray footpoint
area. Synthesised hard X-ray emission reveals strong footpoint sources
and the extended coronal source, whose intensity strongly depends on
the coronal loop density.

---------------------------------------------------------
Title: Microphysics of Cosmic Plasmas: Hierarchies of Plasma
Instabilities from MHD to Kinetic
Authors: Brown, M. R.; Browning, P. K.; Dieckmann, M. E.; Furno, I.;
Intrator, T. P.
2014mpcp.book..281B Altcode: 2014mcp..book..281B
In this article, we discuss the idea of a hierarchy of instabilities
that can rapidly couple the disparate scales of a turbulent plasma
system. First, at the largest scale of the system, L, current carrying
flux ropes can undergo a kink instability. Second, a kink instability in
adjacent flux ropes can rapidly bring together bundles of magnetic flux
and drive reconnection, introducing a new scale of the current sheet
width, ℓ, perhaps several ion inertial lengths (δ i )
across. Finally, intense current sheets driven by reconnection electric
fields can destabilize kinetic waves such as ion cyclotron waves as
long as the drift speed of the electrons is large compared to the ion
thermal speed, v D ≫v i . Instabilities
such as these can couple MHD scales to kinetic scales, as small as
the proton Larmor radius, ρ i .

---------------------------------------------------------
Title: Simulations of energy release and particle acceleration in
forced magnetic reconnection in solar flare current sheets
Authors: Browning, Philippa; Gordovskyy, Mykola
2014cosp...40E.415B Altcode:
Solar flares are a release of stored magnetic energy through magnetic
reconnection. The electric fields associated with reconnection are
a strong candidate for explaining the origin of the large numbers
of non-thermal electrons and ions which are produces in flares. A
useful model for large-scale current sheets in solar flares is forced
magnetic reconnection, triggered by a boundary disturbance, in a
force-free current sheet. A chain of magnetic islands is generated,
where particles may be trapped, as well as remaining open field lines
which allow particles to escape to the solar surface or into the
heliosphere. We present results both from test particle codes coupled
to magnetohydrodynamic simulations, and particle-in-cell codes, and
compare the results of the two approaches with regard to the energy
spectra and spatial locations of both ions and electrons.

---------------------------------------------------------
Title: The origins of space weather: recent advances in understanding
solar flares
Authors: Browning, Philippa
2014cosp...40E.414B Altcode:
“Space weather” events affecting the terrestrial magnetosphere have
their origins in explosive events in the solar atmosphere, notably solar
flares. Solar flares may affect the magnetosphere through EUV/X-ray
radiation and energetic charged particles (both ions and electrons)
, as well as the production of Coronal Mass Ejections (CMEs). A brief
overview of our current theoretical and observational understanding of
solar flares will be given, focusing on the generation of radiation,
particles and CMEs. Recent new models of the acceleration of charged
particles by magnetic reconnection in large-scale current sheets solar
flares will be described, showing how populations of both trapped and
escaping non-thermal particles are generated - the latter propagating
into the heliosphere. Test particle and particle-in-cell modelling allow
prediction of the time evolution of energy spectra and pitch angles of
energetic particles, and their spatial distributions. Smaller, confined
flares may occur due to instabilities in twisted magnetic loops. Recent
modelling of the heating and particle acceleration in unstable twisted
loops will be described, using a coupled magnetohydrodynamic and test
particle approach. The time dependence of the radiation in EUV and soft
X-rays, due to plasma heating, as well as the Hard X-rays associated
with the non-thermal particles are forward-modelled, allowing comparison
with data from SDO and RHESSI, and radio instruments.

---------------------------------------------------------
Title: Models of Fine Structure in Coronal Loops
Authors: Browning, Philippa; Gordovskyy, Mykola
2014cosp...40E.413B Altcode:
Modelling based on the magnetohydrodynamic (MHD) equations shows
that fine structure naturally arises in coronal loops. Magnetic
reconnection may occur in narrow current structures, leading to
efficient dissipation of stored magnetic energy and heating of the
coronal plasma. An overview of such models will be presented, and
the relevance to recent observations will be considered. One approach
proposes that complex motions in the photosphere lead to braiding of the
field and the formation of current sheets in the corona. Alternatively,
even very simple footpoint motions, in the form of rotations, can
lead to kink instabilities which inevitably generate fine structure
in the form of current sheets. The results of 3D MHD simulations
of unstable twisted loops will be presented, including recent
results which consider realistic curved loops in a gravitationally
stratified atmosphere, showing how a network of fragmented current
sheet arises. Forward-modelling of the observable properties of fine
structure in unstable twisted loops will be described, together with
the implications for heating of the coronal plasma. The generation of
fine structure leads to significant modelling challenges, including
a need to include physics beyond MHD, and a brief discussion of some
of these issues will be given.

---------------------------------------------------------
Title: Two-fluid simulations of driven reconnection in the mega-ampere
spherical tokamak
Authors: Stanier, A.; Browning, P.; Gordovskyy, M.; McClements, K. G.;
Gryaznevich, M. P.; Lukin, V. S.
2013PhPl...20l2302S Altcode: 2013arXiv1308.2855S
In the merging-compression method of plasma start-up, two flux-ropes
with parallel toroidal current are formed around in-vessel poloidal
field coils, before merging to form a spherical tokamak plasma. This
start-up method, used in the Mega-Ampere Spherical Tokamak (MAST),
is studied as a high Lundquist number and low plasma-beta magnetic
reconnection experiment. In this paper, 2D fluid simulations are
presented of this merging process in order to understand the underlying
physics, and better interpret the experimental data. These simulations
examine the individual and combined effects of tight-aspect ratio
geometry and two-fluid physics on the merging. The ideal self-driven
flux-rope dynamics are coupled to the diffusion layer physics,
resulting in a large range of phenomena. For resistive MHD simulations,
the flux-ropes enter the sloshing regime for normalised resistivity
η ≲10-5. In Hall-MHD, three regimes are found for the
qualitative behaviour of the current sheet, depending on the ratio of
the current sheet width to the ion-sound radius. These are a stable
collisional regime, an open X-point regime, and an intermediate regime
that is highly unstable to tearing-type instabilities. In toroidal
axisymmetric geometry, the final state after merging is a MAST-like
spherical tokamak with nested flux-surfaces. It is also shown that the
evolution of simulated 1D radial density profiles closely resembles the
Thomson scattering electron density measurements in MAST. An intuitive
explanation for the origin of the measured density structures is
proposed, based upon the results of the toroidal Hall-MHD simulations.

---------------------------------------------------------
Title: Notes on Magnetohydrodynamics of Magnetic Reconnection in
Turbulent Media
Authors: Browning, Philippa; Lazarian, Alex
2013SSRv..178..325B Altcode: 2013SSRv..tmp...92B
Astrophysical fluids have very large Reynolds numbers and therefore
turbulence is their natural state. Magnetic reconnection is an important
process in many astrophysical plasmas, which allows restructuring
of magnetic fields and conversion of stored magnetic energy into
heat and kinetic energy. Turbulence is known to dramatically change
different transport processes and therefore it is not unexpected that
turbulence can alter the dynamics of magnetic field lines within the
reconnection process. We shall review the interaction between turbulence
and reconnection at different scales, showing how a state of turbulent
reconnection is natural in astrophysical plasmas, with implications for
a range of phenomena across astrophysics. We consider the process of
magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit
and discuss how turbulence—both externally driven and generated
in the reconnecting system—can make reconnection independent
on the microphysical properties of plasmas. We will also show how
relaxation theory can be used to calculate the energy dissipated in
turbulent reconnecting fields. As well as heating the plasma, the
energy dissipated by turbulent reconnection may cause acceleration of
non-thermal particles, which is briefly discussed here.

---------------------------------------------------------
Title: Microphysics of Cosmic Plasmas: Hierarchies of Plasma
Instabilities from MHD to Kinetic
Authors: Brown, M. R.; Browning, P. K.; Dieckmann, M. E.; Furno, I.;
Intrator, T. P.
2013SSRv..178..357B Altcode: 2013SSRv..tmp...80B
In this article, we discuss the idea of a hierarchy of instabilities
that can rapidly couple the disparate scales of a turbulent plasma
system. First, at the largest scale of the system, L, current carrying
flux ropes can undergo a kink instability. Second, a kink instability in
adjacent flux ropes can rapidly bring together bundles of magnetic flux
and drive reconnection, introducing a new scale of the current sheet
width, ℓ, perhaps several ion inertial lengths ( δ i )
across. Finally, intense current sheets driven by reconnection electric
fields can destabilize kinetic waves such as ion cyclotron waves as
long as the drift speed of the electrons is large compared to the ion
thermal speed, v D ≫ v i . Instabilities
such as these can couple MHD scales to kinetic scales, as small as
the proton Larmor radius, ρ i .

---------------------------------------------------------
Title: Effect of Collisions and Magnetic Convergence on Electron
Acceleration and Transport in Reconnecting Twisted Solar Flare Loops
Authors: Gordovskyy, M.; Browning, P. K.; Kontar, E. P.; Bian, N. H.
2013SoPh..284..489G Altcode: 2012SoPh..tmp..225G; 2015arXiv150106436G
We study a model of particle acceleration coupled with an MHD model
of magnetic reconnection in unstable twisted coronal loops. The kink
instability leads to the formation of helical currents with strong
parallel electric fields resulting in electron acceleration. The motion
of electrons in the electric and magnetic fields of the reconnecting
loop is investigated using a test-particle approach taking into account
collisional scattering. We discuss the effects of Coulomb collisions and
magnetic convergence near loop footpoints on the spatial distribution
and energy spectra of high-energy electron populations and possible
implications on the hard X-ray emission in solar flares.

---------------------------------------------------------
Title: Coronal heating by the partial relaxation of twisted loops
Authors: Bareford, M. R.; Hood, A. W.; Browning, P. K.
2013A&A...550A..40B Altcode: 2012arXiv1211.3855B
Context. Relaxation theory offers a straightforward method for
estimating the energy that is released when continual convective
driving causes a magnetic field to become unstable. Thus, an
upper limit to the heating caused by ensembles of nanoflaring
coronal loops can be calculated and checked against the level of
heating required to maintain observed coronal temperatures (T ≳
106 K). Aims: We present new results obtained
from nonlinear magnetohydrodynamic (MHD) simulations of idealised
coronal loops. All of the initial loop configurations discussed are
known to be linearly kink unstable. The purpose of this work is to
determine whether or not the simulation results agree with Taylor
relaxation, which will require a modified version of relaxation theory
applicable to unbounded field configurations. In addition, we show
for two cases how the relaxation process unfolds. Methods: A
three-dimensional (3D) MHD Lagrangian-remap code is used to simulate
the evolution of a line-tied cylindrical coronal loop model. This
model comprises three concentric layers surrounded by a potential
envelope; hence, being twisted locally, each loop configuration is
distinguished by a piecewise-constant current profile, featuring three
parameters. Initially, all configurations carry zero-net-current
fields and are in ideally unstable equilibrium. The simulation
results are compared with the predictions of helicity-conserving
relaxation theory. Results: For all simulations, the change in
helicity is no more than 2% of the initial value; also, the numerical
helicities match the analytically-determined values. Magnetic energy
dissipation predominantly occurs via shock heating associated with
magnetic reconnection in distributed current sheets. The energy release
and final field profiles produced by the numerical simulations are
in agreement with the predictions given by a new model of partial
relaxation theory: the relaxed field is close to a linear force free
state; however, the extent of the relaxation region is limited, while
the loop undergoes some radial expansion. Conclusions: The
results presented here support the use of partial relaxation theory,
specifically, when calculating the heating-event distributions produced
by ensembles of kink-unstable loops. The energy release increases with
relaxation radius; but, once the loop has expanded by more than 50%,
further expansion yields little more energy. We conclude that the
relaxation methodology may be used for coronal heating studies.

---------------------------------------------------------
Title: Magnetic reconnection and particle acceleration in twisted
coronal loops
Authors: Gordovskyy, M.; Browning, P.
2012AGUFMSH43B2153G Altcode:
We consider models of magnetic reconnection and particle acceleration
occurring in twisted coronal loops. In this scenario, a potential
field over bipolar magnetic region is twisted by photospheric rotation
yielding an unstable nearly force-free magnetic loop with the strong
field convergence near foot-points. The kink instability results in
drastic increase of the current density, which, in turn, leads to
magnetic reconnection. Appearance of strong electric field with very
fragmented structure results in particle acceleration. Based on this
3D time-dependent MHD model, proton and electron motion is considered
using the relativistic guiding centre motion equations and taking into
account Coulomb collisions. We derive spectral and spatial distribution
of HXR emission and discuss possible observational implications.

---------------------------------------------------------
Title: Particle Acceleration at Reconnecting 3D Null Points
Authors: Stanier, A.; Browning, P.; Gordovskyy, M.; Dalla, S.
2012AGUFMSH51A2208S Altcode:
Hard X-ray observations from the RHESSI spacecraft indicate that a
significant fraction of solar flare energy release is in non-thermal
energetic particles. A plausible acceleration mechanism for these are
the strong electric fields associated with reconnection, a process that
can be particularly efficient when particles become unmagnetised near
to null points. This mechanism has been well studied in 2D, at X-points
within reconnecting current sheets; however, 3D reconnection models
show significant qualitative differences and it is not known whether
these new models are efficient for particle acceleration. We place
test particles in analytic model fields (eg. Craig and Fabling 1996)
and numerical solutions to the the resistive magnetohydrodynamic (MHD)
equations near reconnecting 3D nulls. We compare the behaviour of these
test particles with previous results for test particle acceleration in
ideal MHD models (Dalla and Browning 2005). We find that the fan model
is very efficient due to an increasing "guide field" that stabilises
particles against ejection from the current sheet. However, the spine
model, which was the most promising in the ideal case, gives weak
acceleration as the reconnection electric field is localised to a
narrow cylinder about the spine axis.

---------------------------------------------------------
Title: Editorial: How JGR works
Authors: Lysak, R. L.; Fujimoto, M.; Browning, P.
2012JGRA..11710001L Altcode: 2012JGRA..11710001.
No abstract at ADS

---------------------------------------------------------
Title: Solar particle acceleration at reconnecting 3D null points
Authors: Stanier, A.; Browning, P.; Dalla, S.
2012A&A...542A..47S Altcode: 2012arXiv1201.4846S
Context. The strong electric fields associated with magnetic
reconnection in solar flares are a plausible mechanism to accelerate
populations of high energy, non-thermal particles. One such reconnection
scenario, in a fully 3D geometry, occurs at a magnetic null point. Here,
global plasma motion can give rise to strong currents in the spine
axis or fan plane. Aims: We aim to understand the mechanism of
charged particle energy gain in both the external drift region and the
diffusion region associated with 3D magnetic reconnection. In doing so
we aim to evaluate the efficiency of resistive spine and fan models for
particle acceleration, and find possible observables for each. 
Methods: We used a full orbit test particle approach to study proton
trajectories within electromagnetic fields that are exact solutions
to the steady and incompressible magnetohydrodynamic equations. We
studied the acceleration physics of single particle trajectories
and found energy spectra from many particle simulations. The scaling
properties of the accelerated particles with respect to field and plasma
parameters was investigated. Results: For fan reconnection,
strong non-uniform electric drift streamlines can accelerate the
bulk of the test particles. The highest energy gain is for particles
that enter the current sheet, where an increasing "guide field"
stabilises particles against ejection. The energy is only limited by
the total electric potential energy difference across the fan current
sheet. The spine model has both slow external electric drift speed
and weak energy gain for particles reaching the current sheet. Conclusions: The electromagnetic fields of fan reconnection can
accelerate protons to the high energies observed in solar flares,
gaining up to 0.1 GeV for anomalous values of resistivity. However,
the spine model, which gave a harder energy spectrum in the ideal
case, is not an efficient accelerator after pressure constraints in
the resistive model are included.

---------------------------------------------------------
Title: Magnetic Relaxation and Particle Acceleration in a Flaring
Twisted Coronal Loop
Authors: Gordovskyy, M.; Browning, P. K.
2012SoPh..277..299G Altcode:
In the present work we aim to study particle acceleration in twisted
coronal loops. For this purpose, an MHD model of magnetic reconnection
in a linearly unstable twisted magnetic fluxtube is considered. Further,
the electric and magnetic fields obtained in the MHD simulations are
used to calculate proton and electron trajectories in the guiding-centre
approximation. It is shown that particle acceleration in such a
model is distributed rather uniformly along the coronal loop and the
high-energy population remains generally neutral. It also follows from
the model that the horizontal cross-section of the volume occupied by
high-energy particles near the loop footpoints increases with time,
which can be used as an observational proxy.

---------------------------------------------------------
Title: Solar Particle Acceleration Radiation and Kinetics (SPARK). A
mission to understand the nature of particle acceleration
Authors: Matthews, Sarah A.; Williams, David R.; Klein, Karl-Ludwig;
Kontar, Eduard P.; Smith, David M.; Lagg, Andreas; Krucker, Sam;
Hurford, Gordon J.; Vilmer, Nicole; MacKinnon, Alexander L.; Zharkova,
Valentina V.; Fletcher, Lyndsay; Hannah, Iain G.; Browning, Philippa
K.; Innes, Davina E.; Trottet, Gerard; Foullon, Clare; Nakariakov,
Valery M.; Green, Lucie M.; Lamoureux, Herve; Forsyth, Colin; Walton,
David M.; Mathioudakis, Mihalis; Gandorfer, Achim; Martinez-Pillet,
Valentin; Limousin, Olivier; Verwichte, Erwin; Dalla, Silvia; Mann,
Gottfried; Aurass, Henri; Neukirch, Thomas
2012ExA....33..237M Altcode: 2011ExA...tmp..124M
Energetic particles are critical components of plasma populations
found throughout the universe. In many cases particles are accelerated
to relativistic energies and represent a substantial fraction of
the total energy of the system, thus requiring extremely efficient
acceleration processes. The production of accelerated particles
also appears coupled to magnetic field evolution in astrophysical
plasmas through the turbulent magnetic fields produced by diffusive
shock acceleration. Particle acceleration is thus a key component
in helping to understand the origin and evolution of magnetic
structures in, e.g. galaxies. The proximity of the Sun and the range
of high-resolution diagnostics available within the solar atmosphere
offers unique opportunities to study the processes involved in particle
acceleration through the use of a combination of remote sensing
observations of the radiative signatures of accelerated particles, and
of their plasma and magnetic environment. The SPARK concept targets the
broad range of energy, spatial and temporal scales over which particle
acceleration occurs in the solar atmosphere, in order to determine how
and where energetic particles are accelerated. SPARK combines highly
complementary imaging and spectroscopic observations of radiation from
energetic electrons, protons and ions set in their plasma and magnetic
context. The payload comprises focusing-optics X-ray imaging covering
the range from 1 to 60 keV; indirect HXR imaging and spectroscopy
from 5 to 200 keV, γ-ray spectroscopic imaging with high-resolution
LaBr3 scintillators, and photometry and source localisation
at far-infrared wavelengths. The plasma environment of the regions
of acceleration and interaction will be probed using soft X-ray
imaging of the corona and vector magnetography of the photosphere
and chromosphere. SPARK is designed for solar research. However,
in addition it will be able to provide exciting new insights into the
origin of particle acceleration in other regimes, including terrestrial
gamma-ray flashes (TGF), the origin of γ-ray bursts, and the possible
existence of axions.

---------------------------------------------------------
Title: Relaxation and Heating Triggered by Nonlinear Kink Instability:
Application to Solar Flares and Coronal Heating
Authors: Browning, Philippa K.; Bareford, Michael R.; Gordovskyy,
Mykola
2012ASSP...33...69B Altcode: 2012msdp.book...69B
Energy release and particle acceleration in kink-unstable twisted
coronal loops are discussed. If the magnetic field in a coronal loop is
sufficiently strongly twisted, it may become unstable to the ideal kink
instability. We present results of 3D MHD simulations which show that
in the nonlinear phase of the instability, current sheets form in which
magnetic reconnection rapidly dissipates magnetic energy. In the later
phase, the current sheet fragments. The energy release is well-modelled
by a helicity conserving relaxation to a minimum energy state. We
exploit this in order to calculate a distribution of energy-release
events, and show how this is relevant to the solar coronal heating
problem. Using test particle approach coupled with 3D MHD simulations,
we also show how the electric fields associated with the fragmented
currents sheet can efficiently accelerate charged particles. This has
implications for the origin of high-energy particles in solar flares.

---------------------------------------------------------
Title: Acceleration of charged particles in solar flares by magnetic
reconnection in twisted coronal loops
Authors: Browning, P.; Gordovskyy, M.
2011AGUFMSH51E..04B Altcode:
A coronal loop twisted by photospheric footpoint motions may become
unstable to the ideal kink mode. Numerical simulations show that,
in the nonlinear phase of this instability, current sheets develop,
leading to magnetic reconnection and energy dissipation - this is
manifest as a confined flare. The electric fields associated with
these fragmented current sheets are an efficient accelerator of
charged particles. Test particle simulations, coupled to 3D MHD
simulations, are used to determine the time-evolution of particle
populations, and show that the loop quickly fills with high-energy
ions and electrons. Firstly, we consider the evolution of loops whose
initial magnetic field configuration is kink-unstable, consisting
of a one-dimensional twisted flux tube. Then, we model loops with
initially purely-axial field, which become twisted as a result of slow
footpoint motions and thus become unstable; this model also includes
the effects of flux tube expansion from the footpoints to the loop
apex. Results are also presented showing the effects of collisions
in the denser chromospheric plasma near the loop footpoints. Thus,
transport is considered along with acceleration. Properties such as
energy spectra and pitch-angle distributions are calculated, as well
as spatial and temporal variations of particle properties, which may
be compared with data.

---------------------------------------------------------
Title: The Flare-Energy Distributions Generated by Kink-Unstable
Ensembles of Zero-Net-Current Coronal Loops
Authors: Bareford, M. R.; Browning, P. K.; Van der Linden, R. A. M.
2011SoPh..273...93B Altcode: 2011SoPh..tmp..338B; 2011arXiv1103.5378B
It has been proposed that the million-degree temperature of
the corona is due to the combined effect of barely detectable
energy releases, called nanoflares, that occur throughout the solar
atmosphere. Unfortunately, the nanoflare density and brightness implied
by this hypothesis means that conclusive verification is beyond present
observational abilities. Nevertheless, we investigate the plausibility
of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD)
model that can derive the energy of a nanoflare from the nature of
an ideal kink instability. The set of energy-releasing instabilities
is captured by an instability threshold for linear kink modes. Each
point on the threshold is associated with a unique energy release;
thus we can predict a distribution of nanoflare energies. When the
linear instability threshold is crossed, the instability enters a
nonlinear phase as it is driven by current sheet reconnection. As the
ensuing flare erupts and declines, the field transitions to a lower
energy state, which is modelled by relaxation theory; i.e., helicity is
conserved and the ratio of current to field becomes invariant within
the loop. We apply the model so that all the loops within an ensemble
achieve instability followed by energy-releasing relaxation. The result
is a nanoflare energy distribution. Furthermore, we produce different
distributions by varying the loop aspect ratio, the nature of the path
to instability taken by each loop and also the level of radial expansion
that may accompany loop relaxation. The heating rate obtained is just
sufficient for coronal heating. In addition, we also show that kink
instability cannot be associated with a critical magnetic twist value
for every point along the instability threshold.

---------------------------------------------------------
Title: Recent Advances in Understanding Particle Acceleration
Processes in Solar Flares
Authors: Zharkova, V. V.; Arzner, K.; Benz, A. O.; Browning, P.;
Dauphin, C.; Emslie, A. G.; Fletcher, L.; Kontar, E. P.; Mann, G.;
Onofri, M.; Petrosian, V.; Turkmani, R.; Vilmer, N.; Vlahos, L.
2011SSRv..159..357Z Altcode: 2011SSRv..tmp..156Z; 2011SSRv..tmp..249Z; 2011SSRv..tmp..232Z;
2011arXiv1110.2359Z; 2011SSRv..tmp..278Z
We review basic theoretical concepts in particle acceleration,
with particular emphasis on processes likely to occur in regions of
magnetic reconnection. Several new developments are discussed, including
detailed studies of reconnection in three-dimensional magnetic field
configurations (e.g., current sheets, collapsing traps, separatrix
regions) and stochastic acceleration in a turbulent environment. Fluid,
test-particle, and particle-in-cell approaches are used and results
compared. While these studies show considerable promise in accounting
for the various observational manifestations of solar flares, they
are limited by a number of factors, mostly relating to available
computational power. Not the least of these issues is the need to
explicitly incorporate the electrodynamic feedback of the accelerated
particles themselves on the environment in which they are accelerated. A
brief prognosis for future advancement is offered.

---------------------------------------------------------
Title: Particle Acceleration by Magnetic Reconnection in a Twisted
Coronal Loop
Authors: Gordovskyy, Mykola; Browning, Philippa K.
2011ApJ...729..101G Altcode:
Photospheric motions may lead to twisted coronal magnetic fields which
contain free energy that can be released by reconnection. Browning
&amp; Van der Linden suggested that such a relaxation event may be
triggered by the onset of ideal kink instability. In the present work,
we study the evolution of a twisted magnetic flux tube with zero net
axial current following Hood et al. Based on the obtained magnetic
and electric fields, proton and electron trajectories are calculated
using the test-particle approach. We discuss resulting particle
distributions and possible observational implications, for example,
for small solar flares.

---------------------------------------------------------
Title: Acceleration of charged particles by reconnection by small
solar flares in twisted loops
Authors: Browning, P.; Gordovskyy, M.
2010AGUFMSH33B1845B Altcode:
Solar flares produce large numbers of high energy ions and
electrons. The primary energy release in solar flares is almost
certainly magnetic reconnection, and the electric fields associated
with reconnection are a strong candidate as a mechanism for particle
acceleration. Test particle studies are a very useful tool to
understanding this process, and particle acceleration in idealized
steady 2D geometries has been widely studied with this approach. We
extend this to consider both time-dependent and 3D fields, coupling
a test particle approach with 3D MHD simulations of reconnecting
fields. Time-dependent fields are used, so that the time evolution of
the energy spectra and other properties can be explored. Results are
presented for particle acceleration in fields arising in reconnecting
current sheets which arise in the nonlinear phase of kink instability
of a twisted coronal loop (Hood et al; Astron Astrophys. 506, 913 ,
2009). This models small solar flares occurring in single loops. We
compare behaviour in the early phase, which has a single monolithic
helical current sheet, with the later phase, in which the current
sheet structure is turbulent and fragmented, which allows particles
to undergo multiple accelerations. In the turbulent phase, particles
are accelerated throughout the loop volume, which mitigates some
of the problems associated with the highly localised acceleration
region postulated in the "standard flare model". We present results
for the energy spectra, spatial distribution and pitch angles of the
accelerated particles, and explore how these depend on the properties
of the twisted coronal loop.

---------------------------------------------------------
Title: A nanoflare distribution generated by repeated relaxations
triggered by kink instability
Authors: Bareford, M. R.; Browning, P. K.; van der Linden, R. A. M.
2010A&A...521A..70B Altcode: 2010arXiv1005.5249B
Context. It is thought likely that vast numbers of nanoflares
are responsible for the corona having a temperature of millions
of degrees. Current observational technologies lack the resolving
power to confirm the nanoflare hypothesis. An alternative approach
is to construct a magnetohydrodynamic coronal loop model that has
the ability to predict nanoflare energy distributions. Aims:
This paper presents the initial results generated by a coronal loop
model that flares whenever it becomes unstable to an ideal MHD kink
mode. A feature of the model is that it predicts heating events with a
range of sizes, depending on where the instability threshold for linear
kink modes is encountered. The aims are to calculate the distribution
of event energies and to investigate whether kink instability can
be predicted from a single parameter. Methods: The loop is
represented as a straight line-tied cylinder. The twisting caused by
random photospheric motions is captured by two parameters, representing
the ratio of current density to field strength for specific regions of
the loop. Instability onset is mapped as a closed boundary in the 2D
parameter space. Dissipation of the loop's magnetic energy begins during
the nonlinear stage of the instability, which develops as a consequence
of current sheet reconnection. After flaring, the loop evolves to the
state of lowest energy where, in accordance with relaxation theory, the
ratio of current to field is constant throughout the loop and helicity
is conserved. Results: There exists substantial variation in the
radial magnetic twist profiles for the loop states along the instability
threshold. These results suggest that instability cannot be predicted by
any simple twist-derived property reaching a critical value. The model
is applied such that the loop undergoes repeated episodes of instability
followed by energy-releasing relaxation. Hence, an energy distribution
of the nanoflares produced is collated. This paper also presents the
calculated relaxation states and energy releases for all instability
threshold points. Conclusions: The final energy distribution
features two nanoflare populations that follow different power laws. The
power law index for the higher energy population is more than sufficient
for coronal heating. Appendices are only available in electronic
form at <A href="http://www.aanda.org">http://www.aanda.org</A>

---------------------------------------------------------
Title: Scaling of particle acceleration in 3D reconnection at
null points
Authors: Browning, P. K.; Dalla, S.; Peters, D.; Smith, J.
2010A&A...520A.105B Altcode:
Context. The strong electric fields associated with magnetic
reconnection are likely to be responsible for the presence of
high energy protons and electrons observed in solar flares. There
is much evidence for 3D reconnection in the solar corona, and
we discuss particle acceleration at 3D reconnection sites. The
simplest configuration for 3D reconnection is at a 3D null point,
where reconnection can take place in spine and fan modes. 
Aims: The aim is to understand the properties of accelerated particles
generated by 3D magnetic reconnection, using a test particle approach,
and thus contribute to understanding the origin of high energy protons
and electrons in solar flares. We analyse the properties of electrons
in the magnetic configuration we previously used to study protons. In
addition, we discuss the dependence of the particle properties on
the parameters of the reconnection, such as strengths of electric
and magnetic fields. Methods: A theoretical framework is
presented which can be used to interpret particle acceleration at 3D
null points, and which shows how strong acceleration can arise. We
also use a test particle approach to calculate particle trajectories
in simple model 3D reconnecting nulls. A modified guiding-centre
approach is used for electrons, whilst the full equation of motion
is solved for protons. Results: Most particle acceleration
takes place when particles closely approach the spine or fan, and
we have derived scalings for the sizes of the localised regions in
which strong acceleration occurs. The energy spectra of protons and
electrons are compared, and it is shown that the spatial distribution
of accelerated electrons differs from protons. A significant number of
trapped, high-energy particles can be generated, which may be observed
as coronal HXR sources. The effectiveness of acceleration increases
with the electric-field magnitude, and decreases with magnetic-field
magnitude. Conclusions: Both protons and electrons can be
effectively accelerated at 3D reconnecting null points. The particle
properties depend on the geometry and field parameters, so that,
in principle, the field configuration may be inferred from observed
properties of particles.

---------------------------------------------------------
Title: Particle acceleration in a transient magnetic reconnection
event
Authors: Gordovskyy, M.; Browning, P. K.; Vekstein, G. E.
2010A&A...519A..21G Altcode:
Context. In the present paper, we investigate particle acceleration
by direct electric field in solar flares. Aims: Proton and
electron kinetics are considered based on MHD simulations of magnetic
reconnection, with the aim of determining the properties of accelerated
particles in a time-dependent reconnecting event model. Methods:
At first, we considered several two-dimensional numerical models
of forced reconnection in the initially force-free Harris current
sheet. The electric and magnetic fields from these models were then
used to study proton and electron motion with the guiding centre,
test particle approach. Results: It is shown that protons and
electrons can be accelerated to very high energies up to tens of MeV
in the present model. The energy spectra for both particle species are
combinations of exponential and rather hard power-law shapes. Also,
protons and electrons are ejected from the CS in different directions.

---------------------------------------------------------
Title: Particle Acceleration in Fragmenting Periodic Reconnecting
Current Sheets in Solar Flares
Authors: Gordovskyy, M.; Browning, P. K.; Vekstein, G. E.
2010ApJ...720.1603G Altcode:
Proton and electron acceleration in a fragmenting periodic current
sheet (CS) is investigated, based on the forced magnetic reconnection
scenario. The aim is to understand the role of CS fragmentation
in high-energy beam generation in solar flares. We combine
magnetohydrodynamics and test-particle models to consider particle
trajectories consistent with a time-dependent reconnection model. It
is shown that accelerated particles in such a model form two distinct
populations. Protons and electrons moving in open magnetic field
have energy spectra that are a combination of the initial Maxwellian
distribution and a power-law high-energy (E&gt;20 keV) part. The second
population contains particles moving in a closed magnetic field around
O-points. These particles move predominantly along the guiding field
and their energies fall within quite a narrow range between ~1 MeV and
~10 MeV. It is also found that particles moving in an open magnetic
field have a considerably wider pitch-angle distribution.

---------------------------------------------------------
Title: Magnetic reconnection in the solar atmosphere: from proposal
to paradigm
Authors: Cargill, Peter; Parnell, Clare; Browning, Philippa; de
Moortel, Ineke; Hood, Alan
2010A&G....51c..31C Altcode:
MEETING REPORT On 13 November 2009, the RAS hosted a discussion meeting
to commemorate the formal retirement of Prof. Eric Priest. Here Peter
Cargill, Clare Parnell, Philippa Browning, Ineke de Moortel and Alan
Hood examine how magnetic reconnection has evolved over the past
50 years from an important but controversial proposal, to a general
paradigm.

---------------------------------------------------------
Title: Microflare Activity Driven by Forced Magnetic Reconnection
Authors: Jess, D. B.; Mathioudakis, M.; Browning, P. K.; Crockett,
P. J.; Keenan, F. P.
2010ApJ...712L.111J Altcode: 2010arXiv1002.3792J
High cadence, multiwavelength, optical observations of a solar active
region, obtained with the Swedish Solar Telescope, are presented. Two
magnetic bright points are seen to separate in opposite directions
at a constant velocity of 2.8 km s-1. After a separation
distance of ≈4400 km is reached, multiple Ellerman bombs are
observed in both Hα and Ca-K images. As a result of the Ellerman
bombs, periodic velocity perturbations in the vicinity of the magnetic
neutral line, derived from simultaneous Michelson Doppler Imager data,
are generated with amplitude ±6 km s-1 and wavelength
≈1000 km. The velocity oscillations are followed by an impulsive
brightening visible in Hα and Ca-K, with a peak intensity enhancement
of 63%. We interpret these velocity perturbations as the magnetic field
deformation necessary to trigger forced reconnection. A time delay of
≈3 minutes between the Hα-wing and Ca-K observations indicates that
the observed magnetic reconnection occurs at a height of ~200 km above
the solar surface. These observations are consistent with theoretical
predictions and provide the first observational evidence of microflare
activity driven by forced magnetic reconnection.

---------------------------------------------------------
Title: Particle acceleration by magnetic reconnection in unstable
twisted coronal loop
Authors: Gordovskyy, Mykola; Browning, Philippa; Vekstein, Grigory
2010cosp...38.2994G Altcode: 2010cosp.meet.2994G
Photospheric motions may result in twisting of a coronal loop magnetic
field. Such a field configuration contains free energy that may be
released by reconnection with the magnetic field relaxing to the linear
force-free configuration. Browning &amp; Van der Linden (2003) suggested
that such a relaxation event may be triggered by onset of ideal kink
instability. In the present work we study the evolution of a twisted
magnetic fluxtube with zero net ax-ial current following Browning et
al. (2008). Further, proton and electron trajectories are investigated
using the test-particle approach consistently with the time-dependent
reconnec-tion model. We discuss temporal evolution of proton and
electron energy spectra and possible observational implications.

---------------------------------------------------------
Title: Coronal heating by magnetic reconnection in loops with zero
net current
Authors: Hood, A. W.; Browning, P. K.; van der Linden, R. A. M.
2009A&A...506..913H Altcode:
Context: The paper is concerned with heating of the solar corona
by nanoflares: a superposition of small transient events in which
stored magnetic energy is dissipated by magnetic reconnection. It is
proposed that heating occurs in the nonlinear phase of an ideal kink
instability, where magnetic reconnection leads to relaxation to a state
of minimum magnetic energy. Aims: The aim is to investigate the
nonlinear aspects of magnetic relaxation on a current loop with zero
net axial current. The dynamical processes leading to the establishment
of a relaxed state are explored. The efficiency of loop heating is
investigated. Methods: A 3D magnetohydrodynamic numerical code
is used to simulate the evolution of coronal loops which are initially
in ideally unstable equilibrium. The initial states have zero net
current. The results are interpreted by comparison both with linear
stability analysis and with helicity-conserving relaxation theory. Results: The disturbance due to the unstable mode is strongly radially
confined when the loop carries zero net current. Strong current sheets
are still formed in the nonlinear phase with dissipation of magnetic
energy by fast reconnection. The nonlinear development consists first
of reconnection in a large scale current sheet, which forms near
the quasi-resonant surface of the equilibrium field. Subsequently,
the current sheet extends and then fragments, leading to multiple
reconnections and effective relaxation to a constant α field. Conclusions: Magnetic reconnection is triggered in the nonlinear
phase of kink instability in loops with zero net current. Initially,
reconnection occurs in a single current sheet, which then fragments
into multiple reconnection sites, allowing almost full relaxation
to the minimum energy state. The loop is heated to high temperatures
throughout its volume.

---------------------------------------------------------
Title: Particle Acceleration in a Model of a Turbulent Reconnecting
Plasma: A Fractional Diffusion Approach
Authors: Bian, N. H.; Browning, P. K.
2008ApJ...687L.111B Altcode:
High-energy charged particles are produced during solar flares. These
may be accelerated by the strong electric fields associated with the
magnetic reconnection process which is the source of energy release in
flares. A simple model of random acceleration of charged particles due
to fragmented electric fields is considered for the case of a turbulent
reconnecting plasma in which the fluctuating electric field is highly
localized and its magnitude distributed according to power laws. The
statistical properties of the acceleration process are expressed in
terms of a fractional diffusion equation in velocity space, whose
solution displays a power-law tail related only to the statistics of
the electric field.

---------------------------------------------------------
Title: Particle trajectories and acceleration during 3D fan
reconnection
Authors: Dalla, S.; Browning, P. K.
2008A&A...491..289D Altcode: 2008arXiv0811.1144D
Context: The primary energy release in solar flares is almost certainly
due to magnetic reconnection, making this a strong candidate as a
mechanism for particle acceleration. While particle acceleration in 2D
geometries has been widely studied, investigations in 3D are a recent
development. Two main classes of reconnection regimes at a 3D magnetic
null point have been identified: fan and spine reconnection Aims:
Here we investigate particle trajectories and acceleration during
reconnection at a 3D null point, using a test particle numerical code,
and compare the efficiency of the fan and spine regimes in generating
an energetic particle population. Methods: We calculated the
time evolution of the energy spectra. We discuss the geometry of
particle escape from the two configurations and characterise the
trapped and escaped populations. Results: We find that fan
reconnection is less efficent than spine reconnection in providing seed
particles to the region of strong electric field where acceleration
is possible. The establishment of a steady-state spectrum requires
approximately double the time in fan reconnection. The steady-state
energy spectrum at intermediate energies (protons 1 keV to 0.1 MeV) is
comparable in the fan and spine regimes. While in spine reconnection
particle escape takes place in two symmetric jets along the spine,
in fan reconnection no jets are produced and particles escape in the
fan plane, in a ribbon-like structure.

---------------------------------------------------------
Title: Heating the corona by nanoflares: simulations of energy
release triggered by a kink instability
Authors: Browning, P. K.; Gerrard, C.; Hood, A. W.; Kevis, R.; van
der Linden, R. A. M.
2008A&A...485..837B Altcode:
Context: The heating of solar coronal plasma to millions of
degrees is likely to be due to the superposition of many small
energy-releasing events, known as nanoflares. Nanoflares dissipate
magnetic energy through magnetic reconnection. Aims: A model has
been recently proposed in which nanoflare-like heating naturally arises,
with a sequence of dissipation events of various magnitudes. It is
proposed that heating is triggered by the onset of ideal instability,
with energy release occurring in the nonlinear phase due to fast
magnetic reconnection. The aim is to use numerical simulations to
investigate this heating process. Methods: Three-dimensional
magnetohydrodynamic numerical simulations of energy release are
presented for a cylindrical coronal loop model. Initial equilibrium
magnetic-field profiles are chosen to be linearly unstable, with a
two-layer parameterisation of the current profile. The results are
compared with calculations of linear instability, with line-tying,
which are extended to account for a potential field layer surrounding
the loop. The energy release is also compared with predictions that
the field relaxes to a state of minimum magnetic energy with conserved
magnetic helicity (a constant α force-free field). Results:
The loop initially develops a helical kink, whose structure and
growth rate are generally in accordance with linear stability theory,
and subsequently a current sheet forms. During this phase, there is
a burst of kinetic energy while the magnetic energy decays. A new
relaxed equilibrium is established that corresponds quite closely to
a constant α field. The fraction of stored magnetic energy released
depends strongly on the initial current profile, which agrees with the
predictions of relaxation theory. Conclusions: Energy dissipation
events in a coronal loop are triggered by the onset of ideal kink
instability. Magnetic energy is dissipated, leading to large or small
heating events according to the initial current profile.

---------------------------------------------------------
Title: The way forward for coronal heating
Authors: De Moortel, Ineke; Browning, Philippa; Bradshaw, Stephen J.;
Pintér, Balázs; Kontar, Eduard P.
2008A&G....49c..21D Altcode:
Ineke De Moortel, Philippa K Browning, Stephen J Bradshaw, Balázs
Pintér and Eduard P Kontar consider approaches to the longstanding
and enigmatic problem of coronal heating, as presented at the RAS
discussion meeting on 11 January 2008.

---------------------------------------------------------
Title: Coronal heating by nanoflares: a model based on Taylor
relaxation following kink instability
Authors: van der Linden, Ronald; Browning, Philippa; Hood, Alan
2008cosp...37.3285V Altcode: 2008cosp.meet.3285V
In this work we present progress on a recently proposed model in
which coronal heating is generated by nanoflares, with a sequence
of dissipation events of various magnitudes according to the initial
current profile. In this model it was proposed that heating is triggered
by the onset of ideal instability, with energy release occurring in
the nonlinear phase due to fast magnetic reconnection. As a proof of
principle, the model was applied to a simplified representation of
coronal loops consisting of two regions of constant-alpha force-free
magnetic fields joined together at an interface. By adding an
evolutionary scenario, the field evolves until it reaches the stability
threshold, after which a kink instability sets in with resistive
dissipation of the magnetic energy. The distribution of nanoflares
energies can be obtained in a straightforward way by using the Taylor
relaxation principle, whereby the field evolves to the lowest energy
state under the constraint of conservation of helicity (a constant-alpha
field). This heating process has also been verified for a number of
cases using numerical simulations. These studies showed that the loop
initially develops a helical kink, whose structure and growth rate are
generally in accordance with linear stability theory, and subsequently
a current sheet forms, which leads to a burst of kinetic energy whilst
magnetic energy decays. A new relaxed equilibrium is established which
corresponds quite closely to a constant-alpha field. The fraction of
stored magnetic energy released depends strongly on the initial current
profile, and this is in agreement with the predictions of relaxation
theory. It is discussed how observational data of loop structure and
footpoint motions could be used to apply this model so as to generate
a nanoflare distribution.

---------------------------------------------------------
Title: Jets of energetic particles generated by magnetic reconnection
at a three-dimensional magnetic null
Authors: Dalla, Silvia; Browning, Philippa K.
2007HiA....14...98D Altcode:
Magnetic reconnection is a candidate mechanism for particle acceleration
in a variety of astrophysical contexts. It is now widely accepted that
reconnection plays a key role in solar flares, and reconstructions of
coronal magnetic fields indicate that three-dimensional (3D) magnetic
null points can be present during flares. We investigate particle
acceleration during spine reconnection at a 3D magnetic null point,
using a test particle numerical code. We observe efficient particle
acceleration and find that two energetic populations are produced:
a trapped population of particles that remain in the vicinity of the
null, and an escaping population, which leave the configuration in two
symmetric jets along field lines near the spine. While the parameters
used in our simulation aim to represent solar coronal plasma conditions
of relevance for acceleration in flares, the fact that the 3D spine
reconnection configuration naturally results in energetic particle jets
may be of importance in other astrophysical situations. We also compare
the results obtained for the spine reconnection regime with those for
the other possible mode of 3D reconnection, fan reconnection. We find
that in the latter case energetic particle jets are not produced,
though acceleration is observed.

---------------------------------------------------------
Title: Proton acceleration by 3D magnetic reconnection in solar flares
Authors: Browning, P. K.; Dalla, S.
2007AGUSMSH22A..03B Altcode:
High energy charged particles are an important feature of solar
activity such as flares, and indeed non thermal particles play a
significant role in flare energy balance. Magnetic reconnection is the
primary energy release mechanism in flares, and the strong DC electric
fields associated with this reconnection may well be the origin of
the high energy charged particles. Whilst particle acceleration has
been widely studied for 2D configurations, little is known about 3D
configurations. We investigate particle acceleration using a test
particle approach, in the simplest 3D reconnection configuration, a
3D magnetic null point. Two modes of reconnection are possible: with
a strong current filament along the "spine" field line connecting to
the null, or with a sheet current at the "fan" plane of field lines
emerging from the null. Using simple model fields, incorporating
intiially only thee ideal reconnection region outside the current
sheet (or filament), particle trajectories are investigated and the
energy spectra and spatial distribution of accelerated particles are
determined. We consider and compare fan and spine reconnection, and
determine how the properties of the accelerated particles depend on
the parameters of the reonnecting field. We also present preliminary
results using more realistic, self consistent model fields.

---------------------------------------------------------
Title: Particle acceleration at 3D magnetic reconnection sites .
Authors: Browning, P.; Dalla, S.
2007MmSAI..78..255B Altcode:
It is proposed that the direct electric fields associated with
magnetic reconnection may be responsible for accelerating high energy
charged particles which are observed in solar flares. We investigate
charged particle acceleration using a test particle approach,
with electromagnetic fields arising from a simple model of magnetic
reconnection at a 3D magnetic null point for both spine and fan modes
of reconnection.

---------------------------------------------------------
Title: Jets of Energetic Particles Generated by Magnetic Reconnection
at a Three-Dimensional Magnetic Null
Authors: Dalla, S.; Browning, P. K.
2006IAUJD...1E..14D Altcode:
Magnetic reconnection is a candidate mechanism for particle acceleration
in a variety of astrophysical contexts. It is now widely accepted that
reconnection plays a key role in solar flares, and reconstructions of
coronal magnetic fields indicate that three-dimensional (3D) magnetic
null points can be present during flares. We investigate particle
acceleration during spine reconnection at a 3D magnetic null point,
using a test particle numerical code. We observe efficient particle
acceleration and find that two energetic populations are produced:
a trapped population of particles that remain in the vicinity of the
null, and an escaping population, which leave the configuration in two
symmetric jets along field lines near the spine. While the parameters
used in our simulation aim to represent solar coronal plasma conditions
of relevance for acceleration in flares, the fact that the 3D spine
reconnection configuration naturally results in energetic particle jets
may be of importance in other astrophysical situations. We also compare
the results obtained for the spine reconnection regime with those for
the other possible mode of 3D reconnection, fan reconnection. We find
that in the latter case energetic particle jets are not produced,
though acceleration is observed.

---------------------------------------------------------
Title: Jets of Energetic Particles Generated by Magnetic Reconnection
at a Three-dimensional Magnetic Null
Authors: Dalla, S.; Browning, P. K.
2006ApJ...640L..99D Altcode:
We investigate particle acceleration during magnetic reconnection at a
three-dimensional magnetic null point, in the spine reconnection regime,
using a test particle numerical code. We observe efficient particle
acceleration and find that two energetic populations are produced:
a trapped population of particles that remain in the vicinity of the
null and an escaping population, which leave the configuration in two
symmetric jets along field lines near the spine. While the parameters
used in our simulation aim to represent solar coronal plasma conditions
of relevance for acceleration in flares, the fact that the reconnection
configuration we studied naturally results in energetic particle jets
may be of importance in other astrophysical contexts.

---------------------------------------------------------
Title: Particle Acceleration at Three-Dimensional Reconnection Sites
in Solar Flares
Authors: Browning, P. K.; Dalla, S.
2005ESASP.600E..40B Altcode: 2005dysu.confE..40B; 2005ESPM...11...40B
No abstract at ADS

---------------------------------------------------------
Title: a Model of Nanoflare Energies Based on Relaxation Theory
Authors: Browning, P. K.; van der Linden, R.; Gerrard, C.; Kevis,
R.; Hood, A.
2005ESASP.600E..82B Altcode: 2005dysu.confE..82B; 2005ESPM...11...82B
No abstract at ADS

---------------------------------------------------------
Title: On Solar Coronal Heating by Forced Magnetic Reconnection
Authors: Jain, R.; Browning, P.; Kusano, K.
2005ESASP.596E..23J Altcode: 2005ccmf.confE..23J
No abstract at ADS

---------------------------------------------------------
Title: Solar and Fusion Plasmas
Authors: Browning, Philippa
2005AIPC..795Q.198B Altcode:
The poster describes work I have published with co-authors in
theoretical and experimental studies of plasmas: both in the laboratory,
with relevance to magnetically confined fusion, and naturally occurring,
in the Sun's atmosphere (the corona). In the case of fusion plasmas,
recent work on recombining plasmas in a linear plasma device, the ULS,
is described, which develops understanding of the processes by which
detachment is obtained in a tokamak divertor. Results of experimental
studies of recombining plasmas are presented, interpreted through 1D
plasma models and collisional-radiative models. In the case of the
solar corona, we discuss coronal heating by magnetic reconnection. The
question of how the solar corona is heated to temperatures of millions
of degrees is a major outstanding problem in astrophysics. Some recent
results of numerical simulation of forced magnetic reconnection
are presented, focusing on the energy release, and we describe
how relaxation theory can be used to calculate heating by multiple
reconnection events. The presence of high-energy charged particles
is an important diagnostic of magnetic reconnection, and models of
particle acceleration by reconnecting fields are also presented.

---------------------------------------------------------
Title: Particle acceleration at a three-dimensional reconnection
site in the solar corona
Authors: dalla, S.; Browning, P. K.
2005A&A...436.1103D Altcode:
We study test particle trajectories in the vicinity of
a three-dimensional (3D) magnetic null point during spine
reconnection. Particles are injected into the steady-state non-uniform
magnetic and electric fields derived by Priest &amp; Titov (1996),
and the equations of motion numerically integrated. We use input
parameters typical of the solar corona, for which reconnection has
been suggested as the fundamental mechanism responsible for particle
acceleration in flare events. We show that substantial acceleration
is possible in the 3Dspine reconnection configuration, in the strong
electric field regime. The energy gain is strongly dependent on
the location of injection into the simulation box, as was the case
in 2DX-point configurations. In our 3Dgeometry, we first vary the
location of injection within a plane through the spine, and derive
an analytical value for the injection angle for which maximum energy
gain is achieved. Secondly we vary the azimuthal location of particle
injection and show that as one moves away from the plane with maximum
electric field magnitude, higher final energies can be achieved,
though this requires substantially longer times.

---------------------------------------------------------
Title: Particle acceleration at a 3D reconnection site
Authors: dalla, S.; Browning, P. K.
2005AGUSMSM23B..06D Altcode:
We study test particle trajectories in the vicinity of
a three-dimensional (3D) magnetic null point during spine
reconnection. Particles are injected into the steady-state non-uniform
magnetic and electric fields derived by Priest and Titov (1996),
and the equations of motion numerically integrated. We use input
parameters typical of the solar corona, for which reconnection has
been suggested as the fundamental mechanism responsible for particle
acceleration in flare events. We show that substantial acceleration
is possible in the 3D spine reconnection configuration, in the strong
electric field regime. The energy gain is strongly dependent on the
location of injection into the simulation box, as was the case in
2D X-point configurations. In our 3D geometry, we first vary the
location of injection within a plane through the spine, and derive
an analytical value for the injection angle for which maximum energy
gain is achieved. Secondly we vary the azimuthal location of particle
injection and show that as one moves away from the plane with maximum
electric field magnitude, higher final energies can be achieved, though
this requires substantially longer times. We also discuss application
of our trajectory code to the study of particle acceleration during
reconnection in the Earth's magnetotail.

---------------------------------------------------------
Title: Solar coronal heating by forced magnetic reconnection:
Multiple reconnection events
Authors: Jain, Rekha; Browning, Philippa; Kusano, K.
2005PhPl...12a2904J Altcode:
Magnetic reconnection is a strong candidate for a coronal heating
mechanism, and heating by forced magnetic reconnection is investigated
here. Two dimensional, nonlinear magnetohydrodynamic simulations are
used to investigate forced magnetic reconnection in a compressible
plasma. The reconnection occurs when a sheared force-free field is
perturbed by a slow disturbance (pulse) at the boundary which is
representative of the solar corona where the reconnection is induced
by the photospheric motions. The case of driving by successive pulses,
which generate a series of heating events which may interact with each
other, is considered. This is in order to model the heating of the
corona by a series of nanoflare events. For small perturbations, the
simulation results are consistent with the previous analytic theory
based on linear approach where a current sheet is formed initially
at the resonant surface followed by reconnection and then release of
magnetic energy. For large amplitude perturbations, or close to the
threshold for tearing instability, the system exhibits strong nonlinear
aspects. Following the second driving pulse, the current sheet expands
along the separatrix before relaxing to a reconnective equilibrium and
releasing even more magnetic energy for the same amplitude perturbation.

---------------------------------------------------------
Title: Coronal Heating by Forced Magnetic Reconnection with
Multi-Pulse Driving
Authors: Browning, P. K.; Jain, R.
2004ESASP.575..474B Altcode: 2004soho...15..474B
No abstract at ADS

---------------------------------------------------------
Title: Particle Acceleration at a 3d Reconnection Site
Authors: dalla, S.; Browning, P. K.
2004ESASP.575..222D Altcode: 2004soho...15..222D
No abstract at ADS

---------------------------------------------------------
Title: Coronal Heating by Nanoflares: a Reconnection Model
Authors: Browning, P. K.; van der Linden, R.; Gerrard, C.; Kevis,
R.; Hood, A.
2004ESASP.575..210B Altcode: 2004soho...15..210B
No abstract at ADS

---------------------------------------------------------
Title: Solar coronal heating by relaxation events
Authors: Browning, P. K.; Van der Linden, R. A. M.
2003A&A...400..355B Altcode:
A coronal heating model is proposed which predicts heating by a series
of discrete events of various energies, analogous to the observed range
of events from large scale flares through various transient brightening
phenomena down to the often discussed “nanoflares”. We suggest that
an energy release event occurs when a field becomes linearly unstable
to ideal MHD modes, with dissipation during the nonlinear phase of such
an instability due to reconnection in fine-scale structures such as
current sheets. The energy release during this complex dynamic period
can be evaluated by assuming the field relaxes to a minimum energy state
subject to the constraint of helicity conservation. A model problem is
studied: a cylindrical coronal loop, with a current profile generated by
slow twisting of the photospheric footpoints parameterised by two values
of alpha (the ratio of current density to field strength). Different
initial alpha profiles, corresponding to different footpoint twisting
profiles, lead to energy release events of a wide range of magnitudes,
but our model predicts an observationally realistic minimum size for
these events.

---------------------------------------------------------
Title: A solar coronal heating model: multi-energy relaxation events
Authors: Browning, P. K.; van der Linden, R. A. M.
2002ESASP.508..263B Altcode: 2002soho...11..263B
A coronal heating model is proposed which predicts heating by a
series of events of various energies, analogous to flares and the
often discussed "nanoflares". We suggest that an energy release
event occurs when a field becomes unstable to ideal MHD modes, with
dissipation during the nonlinear phase of such an instability due
to fine-scale structures such as current sheets. The energy release
during this complex dynamic period can be evaluated by assuming the
field relaxes to a minimum energy state subject to the constraint
of helicity conservation. A model problem is studied: a cylindrical
coronal loop, with a current profile generated by slow twisting of the
photospheric footpoints parametrised by two values of α (the ratio
of current density to field strength). Different initial α profiles,
corresponding to different footpoint twisting profiles, lead to energy
release events of a wide range of magnitudes.

---------------------------------------------------------
Title: Particle acceleration at an X-type reconnection site with a
parallel magnetic field
Authors: Browning, P. K.; Vekstein, G. E.
2001JGR...10618677B Altcode:
The acceleration of charged particles at a two-dimensional magnetic
reconnection site is investigated. The magnetic field has an X-type
neutral point, while reconnection is driven by a uniform transverse
electric field; the effect of including a uniform magnetic field
component parallel to the driving electric field and transverse to
the plane of the X point is studied. We focus on the adiabatic motion
of strongly magnetized particles, a valid assumption everywhere for
sufficiently strong parallel magnetic fields but one which excludes
a region around the neutral point for weaker fields. The regime of
interest is fast driven reconnection, in which the electric drift
is strong. The trajectories of particles and their dependence
on the magnitude of the parallel magnetic field component are
investigated. Particles can be accelerated along the magnetic field
lines both because of the coupling of the perpendicular electric drift
with the parallel motion, which occurs in an inhomogeneous magnetic
field, and the direct acceleration by the electric field. The energy
spectra of particles leaving the reconnection site are also calculated.

---------------------------------------------------------
Title: A Cosmic Ray Signature of Equatorial Coronal Holes
Authors: Bromage, B. J. I.; Browning, P. K.; Clegg, J. R.
2001SSRv...97...13B Altcode:
The evolution of open field regions on the Sun over the last cycle is
illustrated by observations of coronal holes in SOHO EIT images. The
development of a large equatorial coronal hole near solar minimum is
discussed, indicating the processes which led to the appearance of
open field regions at low latitude. The observed cosmic ray signature
is presented and interpreted in terms of the passage of the Earth
through the streamer belt, which at this time had become distorted
by the coronal hole and associated active region. The times when such
equatorial coronal holes might be expected to directly influence cosmic
ray counts in this way are seen to be limited to the approach to solar
minimum, around minimum and the approach to maximum.

---------------------------------------------------------
Title: Particle Acceleration in Collisionless Magnetic Reconnection
Authors: Browning, P. K.; Vekstein, G. E.
2001IAUS..203..555B Altcode:
Magnetic reconnection is a process of fundamental importance in the
solar atmosphere, particularly in flares and in coronal heating. The
acceleration of charged particles is a key diagnostic of reconnection,
and we investigate this process in the framework of collisionless
reconnection, relevant to hot tenuous plasmas where the length
scale of the reconnection region is less than the particle mean
free paths. We consider a steady reconnection scenario, with a two
dimensional X-point magnetic field geometry, and an inductive electric
field generating an inflow of particles. The aim is to investigate the
effect of adding a uniform field component transverse to the plane of
the X-point field. Test particles trajectories are studied, and the
energy spectra of the accelerated particles leaving the reconnection
site are determined. The interesting parameter regime is when there
is both significant direct acceleration, due to the component of the
magnetic field parallel to the driving electric field, and parallel
acceleration generated through the interaction of the electric drift
motion with the inhomogeneous magnetic field.

---------------------------------------------------------
Title: The linear force-free field in a spherical shell using a new
method to determine the coefficients of the eigenfunction expansion
Authors: Clegg, J. R.; Browning, P. K.; Laurence, P.; Bromage,
B. J. I.; Stredulinsky, E.
2000A&A...361..743C Altcode:
The linear force-free field of a plasma in between spherical
shells is found allowing for inhomogeneous boundary conditions. A
three-dimensional solution is found by analysis and used as a benchmark
to test a solution in terms of an expansion of eigenfunctions where
the coefficients are determined by a new method. Alternative methods
are also applied in the context of the spherical shell example and
used to illustrate some mathematical constraints that can affect their
validity. The solution is used to model the solar coronal field in the
presence of a large low-latitude coronal hole; SOHO-MDI data provide
the inner boundary conditions.

---------------------------------------------------------
Title: Energy dissipation and helicity in coronal loops of variable
cross-section
Authors: Lothian, R. M.; Browning, P. K.
2000SoPh..194..205L Altcode:
A model is developed to describe a coronal loop, which may originate
from a photospheric source of smaller size than the coronal radius of
the loop. The energy and relative helicity of the loop are evaluated,
as are two alternative estimates of the energy available for coronal
heating. Both of these estimates are strongly dependent on the size of
the photospheric footprint of the loop. A coronal heating rate is then
deduced, based on a nanoflare-type scenario, where slowly accumulated
energy is rapidly released as heat. An explicit calculation is carried
out for one particular choice of loop length and coronal radius, with
dissipation timescale and photospheric radius as parameters. Two main
conclusions are reached. Firstly, the proposed mechanism can make a
significant contribution to coronal heating. Secondly, the mechanism
is more effective for a more concentrated photospheric flux source.

---------------------------------------------------------
Title: Structure of a Large low-Latitude Coronal Hole
Authors: Bromage, B. J. J.; Alexander, D.; Breen, A.; Clegg, J. R.;
Del Zanna, G.; DeForest, C.; Dobrzycka, D.; Gopalswamy, N.; Thompson,
B.; Browning, P. K.
2000SoPh..193..181B Altcode:
Coronal holes on the Sun are the source of high-speed solar wind
streams that produce magnetic disturbances at the Earth. A series
of multi-wavelength, multi-instrument observations obtained during
the 1996 `Whole Sun Month' campaign examined a large coronal hole in
greater detail than ever before. It appeared on the Sun in August, and
extended from the north pole to a large active region in the southern
hemisphere. Its physical and magnetic structure and subsequent evolution
are described.

---------------------------------------------------------
Title: Asymmetries Across a Coronal Hole Extension
Authors: Clegg, J. R.; Browning, P. K.; del Zanna, G.; Bromage,
B. J. I.
1999ESASP.448.1159C Altcode: 1999ESPM....9.1159C; 1999mfsp.conf.1159C
No abstract at ADS

---------------------------------------------------------
Title: Modeling the coronal magnetic field, with a new method for
obtaining boundary conditions on the farside of the Sun
Authors: Clegg, J. R.; Bromage, B. J. I.; Browning, P. K.
1999JGR...104.9831C Altcode:
A novel technique is presented that aids the reconstruction of solar
coronal magnetic fields by augmenting the visible solar surface boundary
conditions with an estimate of the simultaneous conditions on the
far side of the Sun. In converting from line-of-sight measurements,
two alternative assumptions are considered: (1) ignore the plasma beta
differences between corona and photosphere and so find a radial field
component that is consistent with an overlying potential (or force free)
field corona; and (2) characterize the change in beta by a boundary
layer, matching the coronal field to the photosphere where the field,
seen in projection, is taken to be wholly radial. The radial magnetic
field (or radial field component) over the unseen hemisphere of the
Sun is deduced from information held within a time series of the Solar
and Heliospheric Observatory Michelson Doppler imager photospheric
magnetograms centered on the time of interest and combined with a full
disc of visible data for that time. Comparison is made with the more
usual synoptic map boundary conditions to test the time sensitivity
of the problem. Several methods of extrapolation to the far side are
assessed using data centered on an observation at the end of August
1996, when a large equatorial coronal hole was present on one side of
the Sun. The corresponding magnetic field equilibrium in the corona
is found, assuming a simple potential approximation, which employs
an outer “source surface” in addition to the derived inner boundary
condition. Together with the inherent assumption that the evolution of
the global field is slow, the validity of the technique is confirmed
by the self-consistency of the results.

---------------------------------------------------------
Title: The Solar Magnetic Field as a Coronal Hole Extension Forms:
Effects of Magnetic Helicity and Boundary Conditions
Authors: Clegg, J. R.; Bromage, B. J. I.; Browning, P. K.
1999SSRv...87..145C Altcode:
An analytical solution is presented for linear force fields within a
spherical shell, representing the solar corona. Allowing for a global
magnetic helicity, we find magnetic fields over the entire corona with
realistic inner boundary conditions obtained from transformation and
extrapolation of photospheric magnetograms and considering alternative
outer boundary conditions. Such fields are found for the well known
coronal hole extension event of August 1996.

---------------------------------------------------------
Title: Force Free Models of Relaxed and Partially Relaxed Coronal
Magnetic Fields
Authors: Browning, P. K.; Lothian, R. M.; Clegg, J. R.
1998ASPC..155...95B Altcode: 1998sasp.conf...95B
No abstract at ADS

---------------------------------------------------------
Title: Magnetic Reconnection and Dynamos in Laboratory Plasmas
Authors: Browning, P. K.
1998ASSL..229...73B Altcode: 1998opaf.conf...73B
No abstract at ADS

---------------------------------------------------------
Title: Acceleration of Particles in Collisionles Magnetic Reconnection
Authors: Browning, P. K.; Vekstein, G.
1998ASSL..229..313B Altcode: 1998opaf.conf..313B
No abstract at ADS

---------------------------------------------------------
Title: Field-Aligned Particle Acceleration in Collisionless Magnetic
Reconnection
Authors: Vekstein, G. E.; Browning, P. K.
1996ASPC..111..308V Altcode: 1997ASPC..111..308V
Specific field-aligned acceleration of charged particles originates
from the coupling between the electric drift and longitudinal motion
in a non-uniform magnetic field. As a result, initially slow particles
entering the reconnection site of an X-type magnetic geometry can
leave the latter as substantially accelerated jets directed along the
magnetic separatrices.

---------------------------------------------------------
Title: Coronal Magnetic Field Equilibrium with Discrete Flux Sources
Authors: Lothian, R. M.; Browning, P. K.
1995SoPh..161..289L Altcode:
A model of the equilibrium structure of the coronal magnetic field
is developed, taking account of the fact that field lines are rooted
in the photosphere, where field is concentrated into isolated flux
tubes. The field is force-free, described by ∇ ×B =αB, withα
constant; this field has special physical significance, being the
state of mininum energy after small-scale reconnections, and is also
mathematically convenient in that the principle of superposition can
be used to construct complex geometries. First a model of a single loop
is presented, with a flux source and sink pair at the photosphere; both
point flux tubes and finite radius flux tubes are considered. Then more
complex topologies with multiple sources and sinks are investigated. It
is shown that significant topology changes arise for different values
ofα, indicating the possibility that there can be energy changes
through magnetic reconnection if the field evolves ideally and then
relaxes to a linear state.

---------------------------------------------------------
Title: Book Review: Physics of the plasma universe / Springer-Verlag,
1992
Authors: Browning, P. K.
1993Ap&SS.206..318B Altcode: 1993Ap&SS.206..318P
No abstract at ADS

---------------------------------------------------------
Title: Small-scale activity and coronal heating.
Authors: Browning, P. K.
1992AnGeo..10..324B Altcode: 1992AnG....10..324B
It is generally accepted that the corona is heated magnetically, with
the energy source being photospheric motions. The author considers
only slow footpoint motions: these cause the coronal field to evolve
quasi-statically, building up free magnetic energy which can dissipate
as heat. The dissipation requires small-scale processes such as
reconnection in thin current sheets. Three theories are considered. (1)
The question of current sheet formation is discussed, (2) an approach to
quantifying heating rates, using driven relaxation theory, is described,
and (3) recent developments invoking turbulent cascades are outlined.

---------------------------------------------------------
Title: Reconnection, current sheets and relaxation.
Authors: Browning, P. K.
1992mrpa.work...29B Altcode:
A tutorial introduction to the basic concepts of reconnection, covering
both "spontaneous" and "driven" modes is given. Then the question of the
formation of current sheets - the potential locations for reconnection -
is discussed. The dynamics of a field with reconnection occurring in
many sites are considered, and it is shown that the global magnetic
helicity is an appropriate invariant; the significance of this quantity
is explained, and the reasons for its conservation are discussed.

---------------------------------------------------------
Title: Energy relations in reconnection.
Authors: Browning, P. K.
1992mrpa.work..177B Altcode:
Spheromak, a laboratory experiment in which reconnection is integral
to setting-up the magnetic field configuration, is described, and the
application of relaxation theory to this device is outlined. Both the
Spheromak and the solar corona have external energy input as well as
relaxation, and the properties of such driven systems are discussed.

---------------------------------------------------------
Title: Mechanisms of solar coronal heating
Authors: Browning, P. K.
1991PPCF...33..539B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The creation of the magnetic environment for prominence
formation in a coronal arcade
Authors: Amari, T.; Démoulin, P.; Browning, P.; Hood, A.; Priest, E.
1991A&A...241..604A Altcode:
The possibility of prominence formation in sheared coronal arcades is
investigated. The creation of a dip at the summit of field lines is
a likely requirement before a prominence can form; then dense plasma
can be supported against gravity by the Lorentz force. It is proved
that, in fact, no shear profile can create a dip in a two-dimensional
force-free arcade if the photospheric field is bipolar. However,
numerical investigations show that shearing an arcade can induce very
flat field lines. It is investigated, in order of magnitude, how this
flattening of the field can increase the free fall time of a dense
plasma. Also, the interaction between shear and twist is analyzed; the
critical twist needed to have a dip is a decreasing function of shear.

---------------------------------------------------------
Title: Relaxed states in a spheromak with inhomogeneous boundary
fields
Authors: Dixon, A. M.; Browning, P. K.; Bevir, M. K.; Gimblett, C. G.;
Priest, E. R.
1990JPlPh..43..357D Altcode:
In this paper we consider force-free equilibrium solutions of the MHD
equations in a spherical geometry for the case in which magnetic flux
crosses the boundary of the containing vessel. The main motivation is
to model more faithfully actual spheromak experiments in the laboratory,
for which boundaries are unlikely to be magnetic surfaces. We show how a
general inhomogeneous boundary field may be constructed from individual
components. In particular, we consider the cases of a boundary field
of dipolar form and one of quadrupolar form. We then go on to discuss
solutions for fields embedded in point or ring electrodes using the
‘general solution’, some of which can be used to model experiments
such as the PS-1- or CTX-type spheromaks.

---------------------------------------------------------
Title: Twisted flux ropes in the solar corona
Authors: Browning, P. K.
1990GMS....58..219B Altcode:
Loop structures, which are essentially magnetic flux tubes, often
with twist, are common in the solar corona. This paper considers the
magnetic equilibrium of twisted coronal loops. Ignoring curvature,
as a loop is twisted at the photospheric footpoints, longitudinal
structure develops with the center of the loop tending to expand
radially. Results of a 2D numerical code show that nearly all of
the expansion occurs in narrow boundary layers near the photosphere,
and most of the loop is approximately a straight cylinder.

---------------------------------------------------------
Title: A generalization of the Woltjer minimum-energy principle
Authors: Dixon, A. M.; Berger, M. A.; Priest, E. R.; Browning, P. K.
1989A&A...225..156D Altcode:
The theorem of Woltjer (1958) for the minimization of the magnetic
energy of a magnetic structure is extended to include the case of
a free boundary subjected to external magnetic or plasma pressure
forces. The case where the boundary is not a magnetic surface is also
treated. Applications to a finite cylindrical flux tube and a spheromak
are given to illustrate the theory. It is also shown how the theory
may be applied to the construction of stationary Euler flows.

---------------------------------------------------------
Title: The shape of twisted, line-tied coronal loops
Authors: Browning, P. K.; Hood, A. W.
1989SoPh..124..271B Altcode:
The magnetostatic equilibrium of a coronal loop in response to slow
twisting of the photospheric footpoints is investigated. A numerical
code is used to solve the full non-linear 2-D axisymmetric problem,
extending earlier linearised models which assume weak twist and large
aspect ratio. It is found that often the core of the loop tends to
contract into a region of strong longitudinal field while the outer
part expands. It is shown that, away from the photospheric footpoints,
the equilibrium is very well approximated by a straight 1-D cylindrical
model. This idea is used to develop a simple method for prescribing
the footpoint angular displacement and calculating the equilibrium.

---------------------------------------------------------
Title: Magnetohydrodynamics in solar coronal and laboratory plasmas:
A comparative study
Authors: Browning, P. K.
1988PhR...169..329B Altcode:
In this review we discuss the application of MHD theory to plasma in
two contexts: the solar atmosphere and magnetically confined fusion
experiments. The MHD equations are set up, and their relevance to the
two systems discussed. It is shown that in both cases the resistivity
is small, and the magnetic field is strong, so that similar physical
behaviour should be expected. Three areas of research with relevance
to both systems are described, the basic theory and some recent
developments being outlined. These are magnetostatic equilibrium,
linear stability theory and wave propagation, and relaxation of magnetic
fields and helicity conservation.

---------------------------------------------------------
Title: Helicity injection and relaxation in a solar-coronal magnetic
loop with a free surface
Authors: Browning, P. K.
1988JPlPh..40..263B Altcode:
A solar-coronal magnetic loop is rooted in the photosphere, where
motions shuffle the footpoints of the field, generating currents in
the corona. The dissipation of these currents provides a possible
mechanism for heating the solar corona. A theory is described based on
a generalization of Taylor's hypothesis, predicting that as the loop is
twisted up, it relaxes towards a minimum-energy state V × B = μB. The
footpoint motions inject helicity as well as energy, and the evolution
is determined through a helicity-injection equation. The loop is
modelled as a straight magnetic-flux tube, with twisting motions at the
ends, confined by a constant external pressure at the curved surface,
which is a free boundary. The problem of the loop evolution in response
to given footpoint motions is solved, and an interesting example of
multiple equilibria arises. The heating rate is calculated for an
almost-potential loop. The model may also be regarded as representing
a laboratory experiment: in particular, a simple idealization of a
spheromak, with the footpoint motions replaced by an applied voltage.

---------------------------------------------------------
Title: Magnetic relaxation in solar and laboratory plasmas
Authors: Browning, P. K.
1988PPCF...30....1B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Coronal heating by relaxation in a sunspot magnetic field
Authors: Dixon, A. M.; Browning, P. K.; Priest, E. R.
1988GApFD..40..293D Altcode:
The heating by resistive turbulence of solar coronal magnetic fields is
evaluated by means of the Taylor-Heyvaerts hypothesis, which enables one
to calculate the evolution of the magnetic helicity and magnetic field
in the corona in response to prescribed motions of the photospheric
footpoints. The relationship between the photospheric velocity field and
the helicity generation rate is considered for a coronal arcade and the
energy release is proved to be positive definite in general. Also, the
evolution and dissipation is determined for the axisymmetric magnetic
field above a single sunspot which is being twisted up from below.

---------------------------------------------------------
Title: Coronal Evolution and Heating by Magnetic Reconnection in
Closely Packed Flux Tubes
Authors: Browning, P. K.
1987sman.work..173B Altcode:
It is now widely accepted that the solar corona is heated to
temperatures of more than 106K by a magnetic mechanism,
with energy supplied by motions of the photospheric footpoints of the
coronal magnetic field. One approach to heating by reconnection has
been developed by Parker (1972, 1982, 1983). While Parker suggests that
the field will reconnect and release heat, the ultimate state of the
field and the amount of energy released are yet to be determined. The
author's aim is to develop an alternative approach to answer these
questions, using some recent developments in coronal heating theory
which is outlined here.

---------------------------------------------------------
Title: The Shape of Buoyant Coronal Loops in a Magnetic Field and
the Eruption of Coronal Transients and Prominences
Authors: Browning, P. K.; Priest, E. R.
1986SoPh..106..335B Altcode:
The equilibrium and non-equilibrium properties of a coronal loop
embedded in a stratified isothermal atmosphere are investigated. The
shape of the loop is determined by a balance between magnetic tension,
buoyancy, and external pressure gradients. The footpoints of the loop
are anchored in the photosphere; if they are moved too far apart, no
equilibrium is possible and the loop erupts upwards. This critical
separation is independent of the pressure differential between the
loop and the external medium if the loop has enhanced magnetic field,
but varies if instead the loop pressure is increased. The maximum width
is proportional to the larger of the gravitational scale-height and the
length-scale of the ambient field. In some circumstances, it is shown
that multiple solutions exist for the tube path. These results may be
relevant to the eruption of prominences during the preflare phase of
two-ribbon flares and to the onset of coronal loop transients. Such
eruptions may occur if the footpoint separation, internal pressure or
internal magnetic field are too great.

---------------------------------------------------------
Title: Coronal heating in closely-packed flux tubes: a
Taylor-Heyvaerts relaxation theory.
Authors: Browning, P. K.; Sakurai, T.; Priest, E. R.
1986A&A...158..217B Altcode:
The aim of this paper is to take a more quantitative and detailed look
at dissipation in an array of closely-packed flux tubes. An initially
potential coronal loop is investigated, whose footpoints are twisted
up by cellular photospheric motions, forming a network of twisted flux
tubes. The motions are assumed to be slow compared with the reconnection
time-scale, so that the stressed field reconnects and dissipates some
of its energy as heat. The generalised Taylor's hypothesis is used
to investigate the effects of reconnection on the flux tubes and to
determine the efficiency of the dissipation. A basic mathematical
model is set up and the procedure for calculating the evolution is
outlined. The authors investigate the response of the field to the
footpoint motions and evaluate the heating produced. The results are
discussed, applications to the coronal heating problem are considered,
and the predictions are compared with the known heating requirements
of the corona.

---------------------------------------------------------
Title: Heating of coronal arcades by magnetic tearing turbulence,
using the Taylor-Heyvaerts hypothesis
Authors: Browning, P. K.; Priest, E. R.
1986A&A...159..129B Altcode:
The heating of the solar corona by direct currents, which are dissipated
by magnetic reconnection, is studied. The coronal field responds to slow
photospheric motions by evolving through a series of equilibria, which
may be unstable to resistive modes. According to a generalization of
Taylor's hypothesis (Heyvaerts and Priest, 1984), the field reconnects
and relaxes to a linear force-free state (satisfying Delta X B = alpha
B), where the parameter alpha is uniform. During the relaxation process,
the field reconnects and dissipates some magnetic energy as heat. The
value of alpha at each time and the energy released during relaxation
may be determined from the evolution of magnetic helicity. Two theorems
concerning this method are proved: First, the invariance of the method
with respect to gauge transformations of the vector potential is
discussed, and it is shown that the helicity evolution equation in any
gauge predicts the same evolution of the field. Second, it is shown
that the energy release always vanishes in the limit of infinitely
fast reconnection. It is found that similar footpoint motions heat an
arcade more efficiently if it is already strongly sheared, such as
in a rapidly evolving active region. The general conclusion is that
tearing turbulence is a viable heating mechanism for the solar corona.

---------------------------------------------------------
Title: Coronal heating in closely packed flux tubes: a
Taylor-Heyvaerts relaxation theory.
Authors: Browning, P. K.; Sakurai, T.; Priest, E. R.
1985MPARp.181.....B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Heating of coronal loops by tearing turbulence.
Authors: Browning, P. K.
1984ESASP.220..129B Altcode: 1984ESPM....4..129B
The heating of a coronal loop by reconnection, in response to slow
photospheric motions is discussed. It is shown that the method is
invariant to the choice of gauge. General evolution equations of a
coronal loop, modelled as a straight cylinder, are then derived. For
solid body motions, it is shown that α is constant in time, and the
heating is calculated.

---------------------------------------------------------
Title: The Magnetic Non-Equilibrium of Buoyant Flux Tubes in the
Solar Corona
Authors: Browning, P. K.; Priest, E. R.
1984SoPh...92..173B Altcode:
The equilibrium shape of a slender flux tube in the stratified solar
atmosphere is studied. The path is determined by a balance between the
downwards magnetic tension, which depends on the curvature of the loop,
and the upwards buoyancy force. Previous results for untwisted slender
tubes are extended to include twisted tubes embedded in an external
magnetic field.

---------------------------------------------------------
Title: Global magnetohydrostatic fields in stellar atmosphere
Authors: Browning, P. K.; Priest, E. R.
1984GApFD..28..141B Altcode:
The equilibrium properties of the magnetic field of an axisymmetric star
are studied. A family of analytical solutions to the magnetohydrostatic
equations is found, which are used to model the slow evolution of the
field through a series of equilibria. Firstly, a model is set up for
a force-free dipole-like field, which has a toroidal field component;
it is found that, as such a field is twisted up, a critical point is
reached, at which the field topology changes. If the twist is increased
beyond this point, there is no physically reasonable equilibrium. Next,
an untwisted magnetostatic dipole-like field is studied, with
an increasing pressure differential between pole and equator. A
critical point again occurs when the pressure differential becomes
too large. Finally a force-free quadrupole-like field is modelled,
which is being twisted up, for example by differential rotation;
this has similar properties to the dipole-like field. In each case,
it is suggested that, when the critical point is reached, the field
will no longer evolve smoothly, but will change catastrophically to a
new stable, releasing energy. Such an event could represent the onset
of a stellar flare or some other dynamic stellar process.

---------------------------------------------------------
Title: Kelvin-Helmholtz instability of a phased-mixed Alfven wave
Authors: Browning, P. K.; Priest, E. R.
1984A&A...131..283B Altcode:
The development of the Kelvin-Helmholtz instability at the velocity
antinodes of a standing Alfven wave is studied. The problem is
investigated at large times, when the velocity profile has a sinusoidal
form, and at the onset of instability. At large times it is found
that the growth rates of the sinusoidal profile are much smaller, and
that the most unstable wavelengths are about 12 times the phase-mixed
velocity inhomogeneity length scale, whereas for the square wave, short
waves are the most unstable. In a temporally local stability analysis,
a critical time is found after which the instability grows significantly
within one Alfven wave period. This critical time is related to the
dimensionless wave frequency Omega1 = (k-parallel)(a)/M,
where k-parallel is the Alfven wavenumber and M is the magnetic Mach
number. The growth rate of the instability is determined as a function
of time for several values of Omega1, and the critical time
is found at which the growth rate is equal to the wave frequency. It
is shown that the instability develops within very few wave periods,
thus it is expected that a shear Alfven wave would rapidly be disrupted
by Kelvin-Helmholtz instability.

---------------------------------------------------------
Title: Inhomogeneous magnetic fields in the solar atmosphere
Authors: Browning, Philippa K.
1984PhDT.......210B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The structure of twisted magnetic flux tubes
Authors: Browning, P. K.; Priest, E. R.
1983ApJ...266..848B Altcode:
The basic physics of untwisted flux tubes confined by an external
plasma pressure has been developed by Parker (1979). However,
observations indicate that in many situations on the sun flux tubes
are twisted. There is, for instance, evidence for helical structures
in erupting prominences. It is, therefore, important to extend the
results already found for untwisted tubes to include the effects of
twist. The present investigation is concerned with the structure of
a thick twisted flux tube in an inhomogeneous atmosphere. Previous
work on untwisted flux tubes and straight cylindrical twisted tubes is
generalized, in order to describe the properties of twisted flux tubes
confined by a varying external pressure. The governing equations are
nonlinear, and, if the confining pressure is specified, they define a
free surface problem. This problem is solved analytically in certain
limiting cases, for which the complete structure of the field is
found. Two exact solutions for force-free fields are studied in detail.

---------------------------------------------------------
Title: The structure of untwisted magnetic flux tubes
Authors: Browning, P. K.; Priest, E. R.
1982GApFD..21..237B Altcode:
The equilibrium structure of an axisymmetric magnetic flux tube confined
by an external pressure pe(Z) that varies along the length of the tube
is studie. In the past, most work has concentrated on slender flux
tubes, where the effects of transverse structure and radial fields are
neglected. Here the aim is to explore the properties of thick tubes,
in order to see to what extent the slender tube theory is valid. The
main results are: