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Author name code: botha
ADS astronomy entries on 2022-09-14
author:"Botha, Gert J.J."
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Title: The Independence of Oscillatory Reconnection Periodicity from
the Initial Pulse
Authors: Karampelas, Konstantinos; McLaughlin, James A.; Botha,
Gert J. J.; Régnier, Stéphane
2022ApJ...933..142K Altcode: 2022arXiv220701980K
Oscillatory reconnection can manifest through the interaction between
the ubiquitous MHD waves and omnipresent null points in the solar
atmosphere and is characterized by an inherent periodicity. In the
current study, we focus on the relationship between the period
of oscillatory reconnection and the strength of the wave pulse
initially perturbing the null point, in a hot coronal plasma. We
use the PLUTO code to solve the fully compressive, resistive MHD
equations for a 2D magnetic X-point. Using wave pulses with a wide
range of amplitudes, we perform a parameter study to obtain values
for the period, considering the presence and absence of anisotropic
thermal conduction separately. In both cases, we find that the
resulting period is independent of the strength of the initial
perturbation. The addition of anisotropic thermal conduction only
leads to an increase in the mean value for the period, in agreement
with our previous study. We also consider a different type of initial
driver and we obtain an oscillation period matching the independent
trend previously mentioned. Thus, we report for the first time on
the independence between the type and strength of the initializing
wave pulse and the resulting period of oscillatory reconnection in a
hot coronal plasma. This makes oscillatory reconnection a promising
mechanism to be used within the context of coronal seismology.
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Title: Oscillatory Reconnection of a 2D X-point in a hot coronal
plasma
Authors: Karampelas, Konstantinos; Botha, Gert J. J.; Regnier,
Stephane; Mclaughlin, James A.
2022cosp...44.2559K Altcode:
Oscillatory reconnection (a relaxation mechanism with periodic changes
in connectivity) has been proposed as a potential physical mechanism
underpinning several periodic phenomena in the solar atmosphere
including, but not limited to, quasi-periodic pulsations (QPPs)
and flows. In the past, this mechanism had been extensively studied
numerically for 2D and 3D simulations of null points in cold plasma. In
our latest studies, we have expanded our understanding of oscillatory
reconnection, by considering for the first time hot, coronal plasma. We
will be presenting our latest results, from numerically solving the
fully-compressive, resistive MHD equations for a 2D magnetic X-point
under coronal conditions using the PLUTO code. We report on the
resulting oscillatory reconnection including its periodicity and decay
rate, by tracking the evolution of the current density profile at the
null point. We also consider, for the first time, the effect of adding
anisotropic thermal conduction to the mechanism, and how it simplifies
the spectrum of the oscillation profile and increases its decay rate,
while still allowing the mechanism to manifest. Finally, we reveal how
the equilibrium magnetic field strength, density distribution and the
amplitude of the initial perturbation relate to the decay rate, and
period of oscillatory reconnection, opening the tantalising possibility
of utilizing oscillatory reconnection as a seismological tool.
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Title: Using Oscillatory Reconnection of a 2D X-point as a tool for
coronal seismology.
Authors: Karampelas, Konstantinos; Botha, Gert J. J.; Regnier,
Stephane; Mclaughlin, James A.
2022cosp...44.2487K Altcode:
The mechanism of oscillatory reconnection of a null point has been
one of the proposed mechanisms behind phenomena like quasi-periodic
pulsations (QPPs). The manifestation of this mechanism through the
interaction of the ubiquitous waves with null points in the solar
atmosphere opens the possibility of utilizing oscillatory reconnection
as a tool for coronal seismology. In the past, the first steps had
been taken, by connecting the length of the initial current sheet
with the period of oscillatory reconnection, and by identifying a
linear regime where the period is affected by resistivity. Our recent
numerical studies have expanded upon these findings, by considering
plasma at coronal conditions, with the addition of anisotropic
thermal conduction. We have performed a series of parameter studies
with the use of the PLUTO code, which reveal a relation between the
equilibrium magnetic field strength and density distribution with
the period and decay rate of oscillatory reconnection. In addition,
we see an independence of the oscillation period from the type and
strength of the external wave pulse, which perturbs the null from its
initial equilibrium state. This allows us to formulate an empirical
formula connecting these four quantities, opening the way in using
oscillatory reconnection for coronal seismology.
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Title: Oscillatory Reconnection of a 2D X-point in a Hot Coronal
Plasma
Authors: Karampelas, Konstantinos; McLaughlin, James A.; Botha,
Gert J. J.; Régnier, Stéphane
2022ApJ...925..195K Altcode: 2021arXiv211205712K
Oscillatory reconnection (a relaxation mechanism with periodic changes
in connectivity) has been proposed as a potential physical mechanism
underpinning several periodic phenomena in the solar atmosphere,
including, but not limited to, quasi-periodic pulsations (QPPs). Despite
its importance, however, the mechanism has never been studied within
a hot, coronal plasma. We investigate oscillatory reconnection in a
one million Kelvin plasma by solving the fully-compressive, resistive
MHD equations for a 2D magnetic X-point under coronal conditions using
the PLUTO code. We report on the resulting oscillatory reconnection
including its periodicity and decay rate. We observe a more complicated
oscillating profile for the current density compared to that found for
a cold plasma, due to mode-conversion at the equipartition layer. We
also consider, for the first time, the effect of adding anisotropic
thermal conduction to the oscillatory reconnection mechanism, and
we find this simplifies the spectrum of the oscillation profile
and increases the decay rate. Crucially, the addition of thermal
conduction does not prevent the oscillatory reconnection mechanism
from manifesting. Finally, we reveal a relationship between the
equilibrium magnetic field strength, decay rate, and period of
oscillatory reconnection, which opens the tantalising possibility of
utilizing oscillatory reconnection as a seismological tool.
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Title: Observing solar wind turbulence in the corona with ground-based
radio telescopes
Authors: Toit Strauss, Du; Botha, Gert; Chibueze, James; Kontar,
Eduard; Engelbrecht, Eugene; Lotz, Stefan; Wicks, Robert; Krupar,
Vratislav; Bale, Stuart; Maharaj, Shimul; Jeffrey, Natasha; Nel,
Amore; Steyn, Ruhann; van den Berg, Jabus
2021EGUGA..2314180T Altcode:
When point-like galactic and extragalactic radio sources are observed
through the solar corona by ground-based radio telescopes, plasma
density fluctuations in the turbulent solar wind scatter these photons,
leading to an observed broadening and/or elongation of such sources. By
observing this broadening for several sources, over several days, we
can get information about e.g. the wavenumber and radial dependence
of solar wind density fluctuations at very small scales (~30m - 8km)
inside the Alfven radius, thereby capturing details of the turbulence
dissipation range. Here, we present very initial results of such a
study with the MeerKAT radio telescope in South Africa (being, of
course, a precursor to the much larger Square Kilometer Array, SKA),
discuss the preliminary results, and compare these with theoretical
estimates and previous observations.
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Title: A chromospheric resonance cavity in a sunspot mapped with
seismology
Authors: Jess, David B.; Snow, Ben; Houston, Scott J.; Botha, Gert
J. J.; Fleck, Bernhard; Krishna Prasad, S.; Asensio Ramos, Andrés;
Morton, Richard J.; Keys, Peter H.; Jafarzadeh, Shahin; Stangalini,
Marco; Grant, Samuel D. T.; Christian, Damian J.
2020NatAs...4..220J Altcode: 2019NatAs...4..220J; 2019NatAs.tmp..502J
Sunspots are intense collections of magnetic fields that pierce through
the Sun's photosphere, with their signatures extending upwards into the
outermost extremities of the solar corona<SUP>1</SUP>. Cutting-edge
observations and simulations are providing insights into the
underlying wave generation<SUP>2</SUP>, configuration<SUP>3,4</SUP> and
damping<SUP>5</SUP> mechanisms found in sunspot atmospheres. However,
the in situ amplification of magnetohydrodynamic waves<SUP>6</SUP>,
rising from a few hundreds of metres per second in the photosphere to
several kilometres per second in the chromosphere<SUP>7</SUP>, has,
until now, proved difficult to explain. Theory predicts that the
enhanced umbral wave power found at chromospheric heights may come
from the existence of an acoustic resonator<SUP>8-10</SUP>, which
is created due to the substantial temperature gradients experienced
at photospheric and transition region heights<SUP>11</SUP>. Here,
we provide strong observational evidence of a resonance cavity
existing above a highly magnetic sunspot. Through a combination of
spectropolarimetric inversions and comparisons with high-resolution
numerical simulations, we provide a new seismological approach to
mapping the geometry of the inherent temperature stratifications across
the diameter of the underlying sunspot, with the upper boundaries of the
chromosphere ranging between 1,300 ± 200 km and 2,300 ± 250 km. Our
findings will allow the three-dimensional structure of solar active
regions to be conclusively determined from relatively commonplace
two-dimensional Fourier power spectra. The techniques presented are
also readily suitable for investigating temperature-dependent resonance
effects in other areas of astrophysics, including the examination of
Earth-ionosphere wave cavities<SUP>12</SUP>.
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Title: 3D WKB solution for fast magnetoacoustic wave behaviour within
a separatrix dome containing a coronal null point
Authors: McLaughlin, James A.; Thurgood, Jonathan O.; Botha, Gert
J. J.; Wiggs, Joshua A.
2019MNRAS.484.1390M Altcode: 2019MNRAS.tmp..133M
The propagation of the fast magnetoacoustic wave is studied within a
magnetic topology containing a 3D coronal null point whose fan field
lines form a dome. The topology is constructed from a magnetic dipole
embedded within a global uniform field. This study aims to improve the
understanding of how magnetohydrodynamics (MHD) waves propagate through
inhomogeneous media, specifically in a medium containing an isolated 3D
magnetic null point. We consider the linearized MHD equations for an
inhomogeneous, ideal, cold plasma. The equations are solved utilizing
the WKB approximation and Charpit's Method. We find that for a planar
fast wave generated below the null point, the resultant propagation is
strongly dependent upon initial location and that there are two main
behaviours: the majority of the wave escapes the null (experiencing
different severities of refraction depending upon the interplay with the
equilibrium Alfvén-speed profile) or, alternatively, part of the wave
is captured by the coronal null point (for elements generated within
a specific critical radius about the spine and on the z = 0 plane). We
also generalize the magnetic topology and find that the height of the
null determines the amount of wave that is captured. We conclude that
for a wavefront generated below the null point, nulls at a greater
height can trap proportionally less of the corresponding wave energy.
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Title: Predictions of DKIST/DL-NIRSP Observations for an Off-limb
Kink-unstable Coronal Loop
Authors: Snow, B.; Botha, G. J. J.; Scullion, E.; McLaughlin, J. A.;
Young, P. R.; Jaeggli, S. A.
2018ApJ...863..172S Altcode: 2018arXiv180704972S
Synthetic intensity maps are generated from a 3D kink-unstable flux
rope simulation using several DKIST/DL-NIRSP spectral lines to make
a prediction of the observational signatures of energy transport and
release. The reconstructed large field-of-view intensity mosaics and
single tile sit-and-stare high-cadence image sequences show detailed,
fine-scale structure and exhibit signatures of wave propagation,
redistribution of heat, flows, and fine-scale bursts. These fine-scale
bursts are present in the synthetic Doppler velocity maps and can be
interpreted as evidence for small-scale magnetic reconnection at the
loop boundary. The spectral lines reveal the different thermodynamic
structures of the loop, with the hotter lines showing the loop
interior and braiding and the cooler lines showing the radial edges
of the loop. The synthetic observations of DL-NIRSP are found to
preserve the radial expansion, and hence the loop radius can be
measured accurately. The electron number density can be estimated
using the intensity ratio of the Fe XIII lines at 10747 and 10798
Å. The estimated density from this ratio is correct to within ±10%
during the later phases of the evolution; however, it is less accurate
initially when line-of-sight density inhomogeneities contribute to the
Fe XIII intensity, resulting in an overprediction of the density by
≈30%. The identified signatures are all above a conservative estimate
for instrument noise and therefore will be detectable. In summary, we
have used forward modeling to demonstrate that the coronal off-limb
mode of DKIST/DL-NIRSP will be able to detect multiple independent
signatures of a kink-unstable loop and observe small-scale transient
features including loop braiding/twisting and small-scale reconnection
events occurring at the radial edge of the loop.
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Title: Onset of 2D magnetic reconnection in the solar photosphere,
chromosphere, and corona
Authors: Snow, B.; Botha, G. J. J.; McLaughlin, J. A.; Hillier, A.
2018A&A...609A.100S Altcode: 2017arXiv171100683S
<BR /> Aims: We aim to investigate the onset of 2D time-dependent
magnetic reconnection that is triggered using an external (non-local)
velocity driver located away from, and perpendicular to, an
equilibrium Harris current sheet. Previous studies have typically
utilised an internal trigger to initiate reconnection, for example
initial conditions centred on the current sheet. Here, an external
driver allows for a more naturalistic trigger as well as the study
of the earlier stages of the reconnection start-up process. <BR />
Methods: Numerical simulations solving the compressible, resistive
magnetohydrodynamic (MHD) equations were performed to investigate the
reconnection onset within different atmospheric layers of the Sun,
namely the corona, chromosphere and photosphere. <BR /> Results: A
reconnecting state is reached for all atmospheric heights considered,
with the dominant physics being highly dependent on atmospheric
conditions. The coronal case achieves a sharp rise in electric field
(indicative of reconnection) for a range of velocity drivers. For the
chromosphere, we find a larger velocity amplitude is required to trigger
reconnection (compared to the corona). For the photospheric environment,
the electric field is highly dependent on the inflow speed; a sharp
increase in electric field is obtained only as the velocity entering
the reconnection region approaches the Alfvén speed. Additionally,
the role of ambipolar diffusion is investigated for the chromospheric
case and we find that the ambipolar diffusion alters the structure
of the current density in the inflow region. <BR /> Conclusions: The
rate at which flux enters the reconnection region is controlled by
the inflow velocity. This determines all aspects of the reconnection
start-up process, that is, the early onset of reconnection is dominated
by the advection term in Ohm's law in all atmospheric layers. A lower
plasma-β enhances reconnection and creates a large change in the
electric field. A high plasma-β hinders the reconnection, yielding a
sharp rise in the electric field only when the velocity flowing into
the reconnection region approaches the local Alfvén speed.
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Title: Observational Signatures of a Kink-unstable Coronal Flux Rope
Using Hinode/EIS
Authors: Snow, B.; Botha, G. J. J.; Régnier, S.; Morton, R. J.;
Verwichte, E.; Young, P. R.
2017ApJ...842...16S Altcode: 2017arXiv170505114S
The signatures of energy release and energy transport for a
kink-unstable coronal flux rope are investigated via forward
modeling. Synthetic intensity and Doppler maps are generated from
a 3D numerical simulation. The CHIANTI database is used to compute
intensities for three Hinode/EIS emission lines that cover the
thermal range of the loop. The intensities and Doppler velocities at
simulation-resolution are spatially degraded to the Hinode/EIS pixel
size (1″), convolved using a Gaussian point-spread function (3″),
and exposed for a characteristic time of 50 s. The synthetic images
generated for rasters (moving slit) and sit-and-stare (stationary
slit) are analyzed to find the signatures of the twisted flux and the
associated instability. We find that there are several qualities of a
kink-unstable coronal flux rope that can be detected observationally
using Hinode/EIS, namely the growth of the loop radius, the increase in
intensity toward the radial edge of the loop, and the Doppler velocity
following an internal twisted magnetic field line. However, EIS cannot
resolve the small, transient features present in the simulation,
such as sites of small-scale reconnection (e.g., nanoflares).
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Title: 3D WKB solution for fast magnetoacoustic wave behaviour around
an X-line
Authors: McLaughlin, J. A.; Botha, G. J. J.; Régnier, S.; Spoors,
D. L.
2016A&A...591A.103M Altcode: 2016arXiv160702379M
Context. We study the propagation of a fast magnetoacoustic wave in
a 3D magnetic field created from two magnetic dipoles. The magnetic
topology contains an X-line. <BR /> Aims: We aim to contribute to the
overall understanding of MHD wave propagation within inhomogeneous
media, specifically around X-lines. <BR /> Methods: We investigate the
linearised, 3D MHD equations under the assumptions of ideal and cold
plasma. We utilise the WKB approximation and Charpit's method during
our investigation. <BR /> Results: It is found that the behaviour
of the fast magnetoacoustic wave is entirely dictated by the local,
inhomogeneous, equilibrium Alfvén speed profile. All parts of the
wave experience refraction during propagation, where the magnitude of
the refraction effect depends on the location of an individual wave
element within the inhomogeneous magnetic field. The X-line, along
which the Alfvén speed is identically zero, acts as a focus for the
refraction effect. There are two main types of wave behaviour: part
of the wave is either trapped by the X-line or escapes the system, and
there exists a critical starting region around the X-line that divides
these two types of behaviour. For the set-up investigated, it is found
that 15.5% of the fast wave energy is trapped by the X-line. <BR />
Conclusions: We conclude that linear, β = 0 fast magnetoacoustic waves
can accumulate along X-lines and thus these will be specific locations
of fast wave energy deposition and thus preferential heating. The work
here highlights the importance of understanding the magnetic topology
of a system. We also demonstrate how the 3D WKB technique described
in this paper can be applied to other magnetic configurations.
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Title: Chromospheric seismology above sunspot umbrae
Authors: Snow, B.; Botha, G. J. J.; Régnier, S.
2015A&A...580A.107S Altcode: 2015arXiv150707371S
Context. The acoustic resonator is an important model for explaining
the three-minute oscillations in the chromosphere above sunspot
umbrae. The steep temperature gradients at the photosphere and
transition region provide the cavity for the acoustic resonator,
which allows waves to be both partially transmitted and partially
reflected. <BR /> Aims: In this paper, a new method of estimating
the size and temperature profile of the chromospheric cavity above a
sunspot umbra is developed. <BR /> Methods: The magnetic field above
umbrae is modelled numerically in 1.5D with slow magnetoacoustic
wave trains travelling along magnetic fieldlines. Resonances are
driven by applying the random noise of three different colours -
white, pink, and brown - as small velocity perturbations to the upper
convection zone. Energy escapes the resonating cavity and generates
wave trains moving into the corona. Line-of-sight integration is also
performed to determine the observable spectra through SDO/AIA. <BR />
Results: The numerical results show that the gradient of the coronal
spectra is directly correlated with the chromosperic temperature
configuration. As the chromospheric cavity size increases, the
spectral gradient becomes shallower. When line-of-sight integration
is performed, the resulting spectra demonstrate a broadband of excited
frequencies that is correlated with the chromospheric cavity size. The
broadband of excited frequencies becomes narrower as the chromospheric
cavity size increases. <BR /> Conclusions: These two results provide
a potentially useful diagnostic for the chromospheric temperature
profile by considering coronal velocity oscillations.
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Title: Simulation of the observed coronal kink instability and its
implications for the SDO/AIA
Authors: Srivastava, A. K.; Botha, G. J. J.; Arber, T. D.; Kayshap, P.
2013AdSpR..52...15S Altcode: 2013arXiv1301.2927S
Srivastava et al. (2010) have observed a highly twisted coronal loop,
which was anchored in AR10960 during the period 04:43 UT-04:52 UT on
4 June 2007. The loop length and radius are approximately 80 Mm and 4
Mm, with a twist of 11.5 π. These observations are used as initial
conditions in a three dimensional nonlinear magnetohydrodynamic
simulation with parallel thermal conduction included. The initial
unstable equilibrium evolves into the kink instability, from which
synthetic observables are generated for various high-temperature
filters of SDO/AIA. These observables include temporal and spatial
averaging to account for the resolution and exposure times of SDO/AIA
images. Using the simulation results, we describe the implications of
coronal kink instability as observables in SDO/AIA filters.
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Title: Formation of magnetic flux tubes in cylindrical wedge geometry
Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E.
2012GApFD.106..701B Altcode:
Three-dimensional (3D) MHD numerical simulations have not been able to
demonstrate convincingly the spontaneous formation of large vertical
flux tubes. Two-dimensional (2D) magnetoconvection in axisymmetric
cylinders forms a central magnetic flux tube surrounded by annular
convection rings. To study the robustness of this type of solution in
three dimensions, the nonlinear resistive MHD equations are solved
numerically in a 3D cylindrical wedge from an initially uniform
vertical magnetic field. It is shown that the 2D result is retrieved
for small domain radii. However, for larger radii the central axis
loses its importance and in this case many convection cells form in
the numerical domain. Magnetic flux is captured between cells where
flow converges and the reduced amount of flux that congregates at the
central axis is eroded by the surrounding convection.
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Title: Observation and Simulation of Coronal Kink Instability
Authors: Srivastava, Abhishek K.; Botha, G. J. J.; Arber, T. D.
2012cosp...39.1881S Altcode: 2012cosp.meet.1881S
No abstract at ADS
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Title: Observational Signatures of the Coronal Kink Instability with
Thermal Conduction
Authors: Botha, G. J. J.; Arber, T. D.; Srivastava, Abhishek K.
2012ApJ...745...53B Altcode: 2011arXiv1111.0456B
It is known from numerical simulations that thermal conduction
along magnetic field lines plays an important role in the evolution
of the kink instability in coronal loops. This study presents the
observational signatures of the kink instability in long coronal loops
when parallel thermal conduction is included. The three-dimensional
nonlinear magnetohydrodynamic equations are solved numerically to
simulate the evolution of a coronal loop that is initially in an
unstable equilibrium. The loop has length 80 Mm, width 8 Mm, and
an initial maximum twist of Φ = 11.5π, where Φ is a function of
the radius. The initial loop parameters are obtained from a highly
twisted loop observed in the Transition Region and Coronal Explorer
(TRACE) 171 Å wave band. Synthetic observables are generated from
the data. These observables include spatial and temporal averaging to
account for the resolution and exposure times of TRACE images. Parallel
thermal conduction reduces the maximum local temperature by up to an
order of magnitude. This means that different spectral lines are formed
and different internal loop structures are visible with or without
the inclusion of thermal conduction. However, the response functions
sample a broad range of temperatures. The result is that the inclusion
of parallel thermal conductivity does not have as large an impact on
observational signatures as the order of magnitude reduction in the
maximum temperature would suggest; the net effect is a blurring of
internal features of the loop structure.
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Title: Coronal Kink Instability With Parallel Thermal Conduction
Authors: Botha, Gert J. J.; Arber, Tony D.; Hood, Alan W.; Srivastava,
A. K.
2012csem.conf....7B Altcode:
Thermal conduction along magnetic field lines plays an important
role in the evolution of the kink instability in coronal loops. In
the nonlinear phase of the instability, local heating occurs due
to reconnection, so that the plasma reaches high temperatures. To
study the effect of parallel thermal conduction in this process, the
3D nonlinear magnetohydrodynamic (MHD) equations are solved for an
initially unstable equilibrium. The initial state is a cylindrical loop
with zero net current. Parallel thermal conduction reduces the local
temperature, which leads to temperatures that are an order of magnitude
lower than those obtained without thermal conduction. This process
is important on the timescale of fast MHD phenomena; it reduces the
kinetic energy released by an order of magnitude. The impact of this
process on observational signatures is presented. Synthetic observables
are generated that include spatial and temporal averaging to account
for the resolution and exposure times of TRACE images. It was found
that the inclusion of parallel thermal conductivity does not have as
large an impact on observables as the order of magnitude reduction
in the maximum temperature would suggest. The reason is that response
functions sample a broad range of temperatures, so that the net effect
of parallel thermal conduction is a blurring of internal features of
the loop structure.
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Title: Nonlinear Three-dimensional Magnetoconvection around Magnetic
Flux Tubes
Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E.
2011ApJ...731..108B Altcode:
Magnetic flux in the solar photosphere forms concentrations from small
scales, such as flux elements, to large scales, such as sunspots. This
paper presents a study of the decay process of large magnetic flux
tubes, such as sunspots, on a supergranular scale. Three-dimensional
nonlinear resistive magnetohydrodynamic numerical simulations are
performed in a cylindrical domain, initialized with axisymmetric
solutions that consist of a well-defined central flux tube and an
annular convection cell surrounding it. As the nonlinear convection
evolves, the annular cell breaks up into many cells in the azimuthal
direction, allowing magnetic flux to slip between cells away from the
central flux tube (turbulent erosion). This lowers magnetic pressure
in the central tube, and convection grows inside the tube, possibly
becoming strong enough to push the tube apart. A remnant of the central
flux tube persists with nonsymmetric perturbations caused by the
convection surrounding it. Secondary flux concentrations form between
convection cells away from the central tube. Tube decay is dependent
on the convection around the tube. Convection cells forming inside the
tube as time-dependent outflows will remove magnetic flux. (This is
most pronounced for small tubes.) Flux is added to the tube when flux
caught in the surrounding convection is pushed toward it. The tube
persists when convection inside the tube is sufficiently suppressed
by the remaining magnetic field. All examples of persistent tubes
have the same effective magnetic field strength, consistent with the
observation that pores and sunspot umbrae all have roughly the same
magnetic field strength.
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Title: Chromospheric Resonances above Sunspot Umbrae
Authors: Botha, G. J. J.; Arber, T. D.; Nakariakov, V. M.; Zhugzhda,
Y. D.
2011ApJ...728...84B Altcode:
Three-minute oscillations are observed in the chromosphere above
sunspot umbrae. One of the models used to explain these oscillations
is that of a chromospheric acoustic resonator, where the cavity
between the photosphere and transition region partially reflects
slow magnetoacoustic waves to form resonances in the lower sunspot
atmosphere. We present a phenomenological study that compares simulation
results with observations. The ideal magnetohydrodynamic equations
are used with a uniform vertical magnetic field and a temperature
profile that models sunspot atmospheres above umbrae. The simulations
are initialized with a single broadband pulse in the vertical
velocity inside the convection zone underneath the photosphere. The
frequencies in the spectrum of the broadband pulse that lie below
the acoustic cutoff frequency are filtered out so that frequencies
equal and above the acoustic cutoff frequency resonate inside
the chromospheric cavity. The chromospheric cavity resonates with
approximately three-minute oscillations and is a leaky resonator, so
that these oscillations generate traveling waves that propagate upward
into the corona. Thus, there is no requirement that a narrowband
three-minute signal is present in the photosphere to explain the
narrowband three-minute oscillations in the chromosphere and corona. The
oscillations in the chromospheric cavity have larger relative amplitudes
(normalized to the local sound speed) than those in the corona and
reproduce the intensity fluctuations of observations. Different umbral
temperature profiles lead to different peaks in the spectrum of the
resonating chromospheric cavity, which can explain the frequency shift
in sunspot oscillations over the solar cycle.
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Title: Thermal conduction effects on the kink instability in
coronal loops
Authors: Botha, G. J. J.; Arber, T. D.; Hood, A. W.
2011A&A...525A..96B Altcode:
Context. Heating of the solar corona by nanoflares, which are small
transient events in which stored magnetic energy is dissipated by
magnetic reconnection, may occur as the result of the nonlinear
phase of the kink instability (Hood et al. 2009). Because of
the high temperatures reached through these reconnection events,
thermal conduction cannot be ignored in the evolution of the kink
instability. <BR /> Aims: To study the effect of thermal conduction
on the nonlinear evolution of the kink instability of a coronal
loop. To assess the efficiency of loop heating and the role of thermal
conduction, both during the kink instability and for the long time
evolution of the loop. <BR /> Methods: Numerically solve the 3D
nonlinear magnetohydrodynamic equations to simulate the evolution
of a coronal loop that is initially in an unstable equilibrium. The
initial state has zero net current. A comparison is made of the time
evolution of the loop with thermal conduction and without thermal
conduction. <BR /> Results: Thermal conduction along magnetic field
lines reduces the local temperature. This leads to temperatures that
are an order of magnitude lower than those obtained in the absence
of thermal conductivity. Consequently, different spectral lines
are activated with and without the inclusion of thermal conduction,
which have consequences for observations of solar corona loops. The
conduction process is also important on the timescale of the fast
magnetohydrodynamic phenomena. It reduces the kinetic energy released
by an order of magnitude. <BR /> Conclusions: Thermal conduction plays
an essential role in the kink instability of coronal loops and cannot
be ignored in the forward modelling of such loops.
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Title: Effect of Solar Chromospheric Neutrals on Equilibrium Field
Structures
Authors: Arber, T. D.; Botha, G. J. J.; Brady, C. S.
2009ApJ...705.1183A Altcode:
Solar coronal equilibrium fields are often constructed by
nonlinear force-free field (NLFFF) extrapolation from photospheric
magnetograms. It is well known that the photospheric field is not
force-free and the correct lower boundary for NLFFF construction
ought to be the top of the chromosphere. To compensate for this,
pre-filtering algorithms are often applied to the photospheric data
to remove the non-force-free components. Such pre-filtering models,
while physically constrained, do not address the mechanisms that may be
responsible for the field becoming force-free. The chromospheric field
can change through, for example, field expansion due to gravitational
stratification, reconnection, or flux emergence. In this paper, we study
and quantify the effect of the chromospheric neutrals on equilibrium
field structures. It is shown that, depending on the degree to which
the photospheric field is not force-free, the chromosphere will change
the structure of the equilibrium field. This is quantified to give an
estimate of the change in α profiles one might expect due to neutrals
in the chromosphere. Simple scaling of the decay time of non-force-free
components of the magnetic field due to chromospheric neutrals is also
derived. This is used to quantify the rate at which, or equivalent at
which height, the chromosphere is expected to become force-free.
---------------------------------------------------------
Title: Numerical simulations of rotating axisymmetric sunspots
Authors: Botha, G. J. J.; Busse, F. H.; Hurlburt, N. E.; Rucklidge,
A. M.
2008MNRAS.387.1445B Altcode: 2008MNRAS.tmp..702B; 2008arXiv0804.4429B
A numerical model of axisymmetric convection in the presence of
a vertical magnetic flux bundle and rotation about the axis is
presented. The model contains a compressible plasma described by
the non-linear MHD equations, with density and temperature gradients
simulating the upper layer of the Sun's convection zone. The solutions
exhibit a central magnetic flux tube in a cylindrical numerical domain,
with convection cells forming collar flows around the tube. When the
numerical domain is rotated with a constant angular velocity, the plasma
forms a Rankine vortex, with the plasma rotating as a rigid body where
the magnetic field is strong, as in the flux tube, while experiencing
sheared azimuthal flow in the surrounding convection cells, forming
a free vortex. As a result, the azimuthal velocity component has its
maximum value close to the outer edge of the flux tube. The azimuthal
flow inside the magnetic flux tube and the vortex flow is prograde
relative to the rotating cylindrical reference frame. A retrograde
flow appears at the outer wall. The most significant convection cell
outside the flux tube is the location for the maximum value of the
azimuthal magnetic field component. The azimuthal flow and magnetic
structure are not generated spontaneously, but decay exponentially in
the absence of any imposed rotation of the cylindrical domain.
---------------------------------------------------------
Title: Numerical simulations of convection around magnetic features
in the solar convection zone
Authors: Botha, Gert; Rucklidge, Alastair; Hurlburt, Neal
2008cosp...37..354B Altcode: 2008cosp.meet..354B
On the solar surface, magnetic flux elements collect in regions of
converging flow and grow in field strength to become pores. In order to
investigate convection around these magnetic flux tubes, we initialize
a cylindrical simulation with an axisymmetric solution consisting of
a flux tube surrounded by an inflowing collar flow. This is allowed
to evolve using the 3D nonlinear magnetohydrodynamic equations for
compressible resistive flow. The axisymmetric collar flow breaks into
convection cells around the flux tube that are highly dynamic. Through
vigorous convection they change the shape of the central magnetic flux
tube, but do not succeed in destroying its integrity. We relate our
calculation to recent helioseismic measurements of subsurface flows.
---------------------------------------------------------
Title: Nonaxisymmetric Instabilities of Convection around Magnetic
Flux Tubes
Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E.
2007ApJ...662L..27B Altcode:
On the surface of the Sun, magnetic flux elements collect in regions
of converging flow, grow in field strength, and become pores, which
have been observed to exhibit nonaxisymmetric structure over a range of
scales. Around a fully developed sunspot, as well as the fine scale of
the penumbra, the moat sometimes shows a clearly observable spokelike
structure at low azimuthal wavenumbers. We investigate the formation
of azimuthal structure by computing the linear stability properties of
fully nonlinear axisymmetric magnetoconvection, which takes the form of
a central flux tube surrounded by a convecting field-free region. We
find steady and oscillatory instabilities with a preferred azimuthal
wavenumber. The unstable modes are concentrated in the convecting
region close to the outer edge of the flux tube. The instability is
driven by convection and is not a magnetic fluting instability.
---------------------------------------------------------
Title: Numerical simulations of sunspots
Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E.
2007IAUS..239..507B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Differential rotation and angular momentum
Authors: Botha, G. J. J.; Evangelidis, E. A.
2007IAUS..239..451B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Reply to comment on “Relativistic Landau resonances”
Authors: Botha, G. J. J.; Evangelidis, E. A.
2007JGRA..112.5206B Altcode: 2007JGRA..11205206B
No abstract at ADS
---------------------------------------------------------
Title: Numerical Simulations of Rotating Sunspots
Authors: Botha, G. J. J.; Rucklidge, A. M.; Busse, F. H.; Hurlburt,
N. E.
2006ESASP.617E..53B Altcode: 2006soho...17E..53B
No abstract at ADS
---------------------------------------------------------
Title: Converging and diverging convection around axisymmetric
magnetic flux tubes
Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E.
2006MNRAS.369.1611B Altcode: 2006MNRAS.tmp..605B
A numerical model of idealized sunspots and pores is presented, where
axisymmetric cylindrical domains are used with aspect ratios (radius
versus depth) up to 4. The model contains a compressible plasma with
density and temperature gradients simulating the upper layer of the
Sun's convection zone. Non-linear magnetohydrodynamic equations are
solved numerically and time-dependent solutions are obtained where the
magnetic field is pushed to the centre of the domain by convection
cells. This central magnetic flux bundle is maintained by an inner
convection cell, situated next to it and with a flow such that there
is an inflow at the top of the numerical domain towards the flux
bundle. For aspect ratio 4, a large inner cell persists in time, but
for lower aspect ratios it becomes highly time dependent. For aspect
ratios 2 and 3 this inner convection cell is smaller, tends to be
situated towards the top of the domain next to the flux bundle, and
appears and disappears with time. When it is gone, the neighbouring
cell (with an opposite sense of rotation, i.e. outflow at the top)
pulls the magnetic field away from the central axis. As this happens
a new inner cell forms with an inflow which pushes the magnetic field
towards the centre. This suggests that to maintain their form, both
pores and sunspots need a neighbouring convection cell with inflow at
the top towards the magnetic flux bundle. This convection cell does not
have to be at the top of the convection zone and could be underneath
the penumbral structure around sunspots. For an aspect ratio of 1,
there is not enough space in the numerical domain for magnetic flux and
convection to separate. In this case the solution oscillates between
two steady states: two dominant convection cells threaded by magnetic
field and one dominant cell that pushes magnetic flux towards the
central axis.
---------------------------------------------------------
Title: Relativistic Landau resonances
Authors: Evangelidis, E. A.; Botha, G. J. J.
2005JGRA..110.2216E Altcode: 2005JGRA..11002216E
The possible interactions between plasma waves and relativistic charged
particles are considered. An electromagnetic perturbation in the plasma
is formulated as an elliptically polarized wave, and the collisionless
plasma is described by a distribution in phase space, which is realized
in cylindrical coordinates. The linearized Vlasov equation is solved
in the semi-relativistic limit, to obtain the distribution function in
the rest frame of the observer. The perturbed currents supported by
the ionized medium are then calculated, so that an expression can be
written for the total amount of energy available for transfer through
the Landau mechanism. It is found that only certain modes of the
perturbed current are available for this energy transfer. The final
expressions are presented in terms of Stokes parameters, and applied
to the special cases of a thermal as well as a nonthermal plasma. The
thermal plasma is described by a Maxwellian distribution, while two
nonthermal distributions are considered: the kappa distribution and
a generalized Weibull distribution.
---------------------------------------------------------
Title: Cylindrical linear force-free magnetic fields with toroidal
flux surfaces
Authors: Botha, G. J. J.; Evangelidis, E. A.
2004MNRAS.350..375B Altcode:
A linear force-free field solution is presented in cylindrical
coordinates, formulated in terms of trigonometric and Bessel
functions. A numerical exploration has revealed that this solution
describes magnetic field lines that meander in Cartesian space, as well
as field lines that lie on toroidal flux surfaces. These tori are in
(or close to) the plane perpendicular to the cylindrical axis. Nested
tori, as well as tori with shells that have finite thickness, were
found. The parameter space of the solution shows that the tori exist
within a bounded range of values.
---------------------------------------------------------
Title: Cylindrical Solutions of Force Free Magnetic Fields
Authors: Botha, G. J. J.; Evangelidis, E. A.
2004IAUS..219..743B Altcode: 2003IAUS..219E.148B
A general method for the solution of force free magnetic fields in
cylindrical coordinates is presented and a solution is formulated as
a combination of trigonometric and Bessel functions. The numerical
exploration has revealed the existence of trapped and untrapped orbits
in the sense that they remain (or not) inside a specific part of space
volume. Most interestingly orbits have been identified that wind on
toroidal surfaces perpendicular to the z-axis.
---------------------------------------------------------
Title: Alfvén Wave-Charged Particle Interactions through Landau
Damping
Authors: Evangelidis, E. A.; Botha, G. J. J.
2004IAUS..219..748E Altcode: 2003IAUS..219E.147E
The possibility of Landau damping of energetic particles in resonance
with Alfven waves was first raised in the context of pulsar envelopes
some decades ago. Today due to satellite observations there is a
renewed interest in the topic as one of the possible mechanisms for
transfer of energy in the solar atmosphere and solar wind. We therefore
analyze the interaction of elliptically polarised Alfven waves with a
semi-relativistic collisionless charged particle distribution by using
the linearised Vlasov equation. Taking into consideration developments
in the theory of Bessel functions we write the results in a concise
form. The transfer of energy is thus expressed in terms of particle
parameters as well as the Stokes parameter which is associated with
the total energy of the wave. The frequency of the Alfven wave must
be comparable with or larger than that of the cyclotron frequency
in order to play an efficient role in the absorption or emission of
the energy of the charged particle in agreement with the theorem of
energy conservation. The role of the relative velocity of the particles
against the Alfven velocity is elucidated in a natural way as a result
of relativistic considerations.
---------------------------------------------------------
Title: A new family of solutions of the force-free field equation
Authors: Evangelidis, E. A.; Botha, G. J. J.
2003SoPh..213...69E Altcode:
A new family of solutions has been found for force-free magnetic fields
and Beltrami flows, which admits a complete classification in terms of
the eigenvalues of the problem. In the absence of boundary values to
determine them uniquely, the eigenvalues correspond to the entire set
of real numbers, except for zero. The eigenvalues are degenerate in
that each eigenvalue has many eigensolutions associated with it. For
each eigensolution we have been able to identify sets of equilibrium
or null points and lines. The linear mappings of these null points
and lines are all unstable. Finally, we derive the first integral of
energy associated with this family of solutions.
---------------------------------------------------------
Title: A new family of solutions of the force free field equation
Authors: Evangelidis, E. A.; Botha, G. J. J.
2002ESASP.505..401E Altcode: 2002solm.conf..401E; 2002IAUCo.188..401E
A new family of solutions has been found for force free magnetic fields
and Beltrami flows, which admits a complete classification in terms of
the eigenvalues of the problem. In the absence of boundary values to
determine them uniquely, the eigenvalues correspond to the entire set of
real numbers, except for zero. The eigenvalues are degenerate in that
each eigenvalue has many eigensolutions associated with it. For each
eigensolution we have been able to identify dense sets of equilibrium
or null points and lines. We present a linear analysis of the magnetic
field line configurations around these null points and lines, and derive
the first integral of energy associated with this family of solutions.
---------------------------------------------------------
Title: Photoionized Plasma Calculations using Laboratory and
Astrophysical Models
Authors: Phillips, M. E.; Keenan, F. P.; Rose, S. J.; Botha, G. J. J.;
Foord, M. E.; Heeter, R. F.; Ferland, G. J.
2001ASPC..247..123P Altcode: 2001scpp.conf..123P
No abstract at ADS
---------------------------------------------------------
Title: A. Cylindrical Formulation of Force Free Magnetic Fields
Authors: Evangelidis, E. A.; Botha, G. J. J.
2001IAUS..203..270E Altcode:
It is shown that the behaviour of force free magnetic fields is
governed by the existence of a first integral of energy. We give its
explicit expression and we identify the parametric space where these
fields are ergodic or non-ergodic. We further compare results based
on toroidal geometries with results based on cylindrical geometries,
to show the modification due to toroidal curvature.
---------------------------------------------------------
Title: A developed stage of Alfvén wave phase mixing
Authors: Botha, G. J. J.; Arber, T. D.; Nakariakov, V. M.; Keenan,
F. P.
2000A&A...363.1186B Altcode:
Alfvén wave phase mixing is an extensively studied mechanism for
dissipating wave energy in an inhomogeneous medium. It is common in the
vast majority of phase mixing papers to assume that even though short
scale lengths and steep gradients develop as a result of phase mixing,
nonlinear wave coupling does not occur. However, weakly nonlinear
studies have shown that phase mixing generates magnetoacoustic
modes. Numerical results are presented which show the nonlinear
generation of magnetosonic waves by Alfvén wave phase mixing. The
efficiency of the effect is determined by the wave amplitude, the
frequency of the Alfvén waves and the gradient in the background
Alfvén speed. Weakly nonlinear theory has shown that the amplitude
of the fast magnetosonic wave grows linearly in time. The simulations
presented in this paper extend this result to later times and show
saturation of the fast magnetosonic component at amplitudes much lower
than that of the Alfvén wave. For the case where Alfvén waves are
driven at the boundary, simulating photospheric footpoint motion,
a clear modulation of the saturated amplitude is observed. All the
results in this paper are for a low amplitude (<= 0.1), single
frequency Alfvén wave and a uniform background magnetic field in
a two dimensional domain. For this simplified geometry, and with a
monochromatic driver, we concluded that the nonlinear generation of
fast modes has little effect on classical phase mixing.
---------------------------------------------------------
Title: Extreme ultraviolet emission lines of Nixii in laboratory
and solar spectra
Authors: Keenan, F. P.; Botha, G. J. J.; Matthews, A.; Lawson, K. D.;
Coffey, I. H.
2000MNRAS.318...37K Altcode:
Wavelengths for emission lines arising from
3s<SUP>2</SUP>3p<SUP>5</SUP>-3s3p<SUP>6</SUP> and
3s<SUP>2</SUP>3p<SUP>5</SUP>-3s<SUP>2</SUP>3p<SUP>4</SUP>3d
transitions in Nixii have been measured in extreme ultraviolet
spectra of the Joint European Torus (JET) tokamak. The
3s<SUP>2</SUP>3p<SUP>5</SUP> <SUP>2</SUP>P<SUB>1/2</SUB>-
3s<SUP>2</SUP>3p<SUP>4</SUP>(<SUP>3</SUP>P)3d
<SUP>2</SUP>D<SUB>3/2</SUB> line is found to lie at 152.90+/-0.02Å,
a significant improvement over the previous experimental determination
of 152.95+/-0.5Å. This new wavelength is in good agreement with a solar
identification at 152.84+/-0.06Å, confirming the presence of this line
in the solar spectrum. The Nixii feature at 152.15Å may be a result
only of the 3s<SUP>2</SUP>3p<SUP>5</SUP> <SUP>2</SUP>P<SUB>3/2</SUB>-
3s<SUP>2</SUP>3p<SUP>4</SUP>(<SUP>3</SUP>P)3d
<SUP>2</SUP>D<SUB>5/2</SUB> transition, rather than a blend of this
line with 3s<SUP>2</SUP>3p<SUP>5</SUP> <SUP>2</SUP>P<SUB>3/2</SUB>-
3s<SUP>2</SUP>3p<SUP>4</SUP>(<SUP>3</SUP>P)3d
<SUP>2</SUP>P<SUB>1/2</SUB>, as previously
suggested. Unidentified emission lines at 295.32 and
317.61Å in solar flare spectra from the Skylab mission are
tentatively identified as the 3s<SUP>2</SUP>3p<SUP>5</SUP>
<SUP>2</SUP>P<SUB>3/2</SUB>-3s3p<SUP>6</SUP>
<SUP>2</SUP>S<SUB>1/2</SUB> and 3s<SUP>2</SUP>3p<SUP>5</SUP>
<SUP>2</SUP>P<SUB>1/2</SUB>-3s3p<SUP>6</SUP> <SUP>2</SUP>S<SUB>1/2</SUB>
transitions in Nixii, which have laboratory wavelengths of 295.33 and
317.50Å, respectively. Additional support for these identifications
is provided by the line intensity ratio for the solar features, which
shows good agreement between theory and observation.
---------------------------------------------------------
Title: The structure of force-free magnetic fields
Authors: Evangelidis, E. A.; Vaughan, L. L.; Botha, G. J. J.
2000SoPh..193...17E Altcode:
Incontrovertible evidence is presented that the force-free magnetic
fields exhibit strong stochastic behavior. Arnold's solution is
given with the associated first integral of energy. A subset of the
solution is shown to be non-ergodic whereas the full solution is shown
to be ergodic. The first integral of energy is applied to the study
of these fields to prove that the equilibrium points of such magnetic
configurations are saddle points. Finally, the potential function of
the first integral of energy is shown to be a member of the Helmholtz
family of solutions. Numerical results corroborate the theoretical
conclusions and demonstrate the robustness of the energy integral,
which remains constant for arbitrarily long computing times.
