Author name code: litvinenko
ADS astronomy entries on 2022-09-14
author:"Litvinenko, Yuri E."
------------------------------------------------------------------------
Title: A perturbative approach to a nonlinear advection-diffusion
equation of particle transport
Authors: Walter, D.; Fichtner, H.; Litvinenko, Y.
Bibcode: 2022icrc.confE.139W
Altcode: 2022PoS...395E.139W
No abstract at ADS
Title: Electric resistivity of partially ionized plasma in the lower
solar atmosphere
Authors: Chae, Jongchul; Litvinenko, Yuri E.
Bibcode: 2021RAA....21..232C
Altcode:
The lower solar atmosphere is a gravitationally stratified layer of
partially ionized plasma. We calculate the electric resistivity in the
solar photosphere and chromosphere, which is the key parameter that
controls the rate of magnetic reconnection in a Sweet-Parker current
sheet. The calculation takes into account the collisions between ions
and hydrogen atoms as well as the electron-ion collisions and the
electron-hydrogen atom collisions. We find that under the typical
conditions of the quiet Sun, electric resistivity is determined
mostly by the electron-hydrogen atom collisions in the photosphere,
and mostly by the ion-hydrogen collisions, i.e. ambipolar diffusion, in
the chromosphere. In magnetic reconnection events with strong magnetic
fields, the ambipolar diffusion, however, may be insignificant because
the heating by the reconnection itself may lead to the full ionization
of hydrogen atoms. We conclude that ambipolar diffusion may be the most
important source of electric resistivity responsible for the magnetic
flux cancelation and energy release in chromospheric current sheets
that can keep a significant fraction of neutral hydrogen atoms.
Title: A perturbative approach to a nonlinear advection-diffusion
equation of particle transport
Authors: Walter, Dominik; Fichtner, Horst; Litvinenko, Yuri
Bibcode: 2020PhPl...27h2901W
Altcode:
We explore analytical techniques for modeling the nonlinear cosmic ray
transport in various astrophysical environments which is of significant
current research interest. While nonlinearity is most often described by
coupled equations for the dynamics of the thermal plasma and the cosmic
ray transport or for the transport of the plasma waves and the cosmic
rays, we study the case of a single but nonlinear advection-diffusion
equation. The latter can be approximately solved analytically or
semi-analytically, with the advantage that these solutions are easy to
use and, thus, can facilitate a quantitative comparison to data. In the
present study, we extend our previous work in a twofold manner. First,
instead of employing an integral method to the case of pure nonlinear
diffusion, we apply an expansion technique to the advection-diffusion
equation. We use the technique systematically to analyze the effect of
nonlinear diffusion for the cases of constant and spatially varying
advection combined with time-varying source functions. Second, we
extend the study from the one-dimensional, Cartesian geometry to the
radially symmetric case, which allows us to treat more accurately the
nonlinear diffusion problems on larger scales away from the source.
Title: Linear Acoustic Waves in a Nonisothermal
Atmosphere. II. Photospheric Resonator Model of Three-minute Umbral
Oscillations
Authors: Chae, Jongchul; Kang, Juhyung; Litvinenko, Yuri E.
Bibcode: 2019ApJ...883...72C
Altcode:
The velocity oscillations observed in the chromosphere of sunspot
umbrae resemble a resonance in that their power spectra are sharply
peaked around a period of about three minutes. In order to describe
the resonance that leads to the observed 3-minute oscillations, we
propose the photospheric resonator model of acoustic waves in the solar
atmosphere. The acoustic waves are driven by the motion of a piston
at the lower boundary, and propagate in a nonisothermal atmosphere
that consists of the lower layer (photosphere), where temperature
rapidly decreases with height, and the upper layer (chromosphere),
where temperature slowly increases with height. We have obtained
the following results: (1) The lower layer (photosphere) acts as
a leaky resonator of acoustic waves. The bottom end is established
by the piston, and the top end by the reflection at the interface
between the two layers. (2) The temperature minimum region partially
reflects and partially transmits acoustic waves of frequencies around
the acoustic cutoff frequency at the temperature minimum. (3) The
resonance occurs in the photospheric layer at one frequency around this
cutoff frequency. (4) The waves escaping the photospheric layer appear
as upward-propagating waves in the chromosphere. The power spectrum of
the velocity oscillation observed in the chromosphere can be fairly well
reproduced by this model. The photospheric resonator model was compared
with the chromospheric resonator model and the propagating wave model.
Title: A Maximum Entropy Argument for the Slopes of Power-law Particle
Spectra in Solar Flares
Authors: Litvinenko, Yuri E.
Bibcode: 2019ApJ...880...20L
Altcode:
The maximum entropy formalism is used to infer the spectral index of
power-law particle spectra in the heliosphere. The entropy-maximization
argument by Brown et al. is revisited and generalized by relaxing the
assumption of a particle spectrum extending to an infinite energy. The
results for particle spectra with a finite upper cutoff energy are
shown to be qualitatively different from those for spectra extending to
infinity. The dependence of the predicted spectral index on the upper
cutoff energy is determined. The relevance of the predicted values of
the spectral index to the observed spectra of accelerated electrons
in solar flares and ion tails in the solar wind is discussed.
Title: Power-law spectra of energetic electrons in solar flares from
the maximum entropy and dimensional considerations
Authors: Litvinenko, Y. E.
Bibcode: 2019AdSpR..63.1466L
Altcode:
The maximum entropy formalism and dimensional analysis are used to
derive a power-law spectrum of accelerated electrons in impulsive
solar flares, where the particles can contain a significant fraction
of the total flare energy. Entropy considerations are used to derive
a power-law spectrum for a particle distribution characterised by
its order of magnitude of energy. The derivation extends an earlier
one-dimensional argument to the case of an isotropic three-dimensional
particle distribution. Dimensional arguments employ the idea that the
spectrum should reflect a balance between the processes of energy
input into the corona and energy dissipation in solar flares. The
governing parameters are suggested on theoretical grounds and shown to
be consistent with solar flare observations. The flare electron flux,
differential in the non-relativistic electron kinetic energy E, is
predicted to scale as E-3 . This scaling is in agreement
with RHESSI measurements of the hard X-ray flux that is generated by
deka-keV electrons, accelerated in intense solar flares.
Title: Flows and magnetic field structures in reconnection regions
of simulations of the solar atmosphere: Do flux pile-up models work?
Authors: Shelyag, S.; Litvinenko, Y. E.; Fedun, V.; Verth, G.;
González-Avilés, J. J.; Guzmán, F. S.
Bibcode: 2018A&A...620A.159S
Altcode: 2018arXiv180900587S
Aims: We study the process of magnetic field annihilation
and reconnection in simulations of magnetised solar photosphere
and chromosphere with magnetic fields of opposite polarities and
constant numerical resistivity.
Methods: Exact analytical
solutions for reconnective annihilations were used to interpret the
features of magnetic reconnection in simulations of flux cancellation
in the solar atmosphere. We used MURaM high-resolution photospheric
radiative magneto-convection simulations to demonstrate the presence of
magnetic field reconnection consistent with the magnetic flux pile-up
models. Also, a simulated data-driven chromospheric magneto-hydrodynamic
simulation is used to demonstrate magnetic field and flow structures,
which are similar to the theoretically predicted ones.
Results:
Both simulations demonstrate flow and magnetic field structures
roughly consistent with accelerated reconnection with magnetic flux
pile-up. The presence of standard Sweet-Parker type reconnection is
also demonstrated in stronger photospheric magnetic fields.
Title: Linear Acoustic Waves in a Nonisothermal Atmosphere. I. Simple
Nonisothermal Layer Solution and Acoustic Cutoff Frequency
Authors: Chae, Jongchul; Litvinenko, Yuri E.
Bibcode: 2018ApJ...869...36C
Altcode:
We investigate the behavior of acoustic waves in a nonisothermal
atmosphere based on the analytical solution of the wave
equation. Specifically, we consider acoustic waves propagating upwardly
in a simple nonisothermal layer where temperature either increases or
decreases monotonically with height. We present the solutions for both
velocity fluctuation and pressure fluctuation. In these solutions,
either velocity or pressure is spatially oscillatory in one part of
the layer and nonoscillatory in the other part, with the two parts
being smoothly connected to one another. Since the two parts transmit
the same amount of wave energy in each frequency, it is unreasonable to
identify the oscillating solution with the propagating solution and the
nonoscillating solution with the nonpropagating solution. The acoustic
cutoff frequency is defined as the frequency that separates the solution
that is spatially oscillatory for both velocity and pressure and the
solution that is not oscillatory for either velocity or pressure. The
cutoff frequency is found to be the same as the Lamb frequency at the
bottom in the temperature-decreasing layer but higher than this in the
temperature-increasing layer. Based on the transmission efficiency
introduced to quantify the wave propagation, we suggest that the
acoustic cutoff frequency should be understood as the center of the
frequency band where the transition from low acoustic transmission to
high transmission takes place, rather than as the frequency sharply
separating the propagating solution and the nonpropagating solution.
Title: Nonlinear Effects in Three-minute Oscillations of the Solar
Chromosphere. II. Measurement of Nonlinearity Parameters at Different
Atmospheric Levels
Authors: Chae, Jongchul; Cho, Kyuhyoun; Song, Donguk; Litvinenko,
Yuri E.
Bibcode: 2018ApJ...854..127C
Altcode:
Recent theoretical studies suggest that the nonlinearity of three-minute
velocity oscillations at each atmospheric level can be quantified
by the two independent parameters—the steepening parameter and the
velocity amplitude parameter. For the first time, we measured these
two parameters at different atmospheric levels by analyzing a set of
spectral lines formed at different heights of sunspots ranging from
the temperature minimum to the transition region. The spectral data
were taken by the Fast Imaging Solar Spectrograph of the Goode Solar
Telescope, and by the Interface Region Imaging Spectrograph. As a
result, from the wavelet power spectra of the velocity oscillations
at different heights, we clearly identified the growth of the
second harmonic oscillations associated with the steepening of the
velocity oscillation, indicating that higher-frequency oscillations
of periods of 1.2 to 1.5 minutes originate from the nonlinearity
of the three-minute oscillations in the upper chromosphere. We also
found that the variation of the measured nonlinearity parameters is
consistent with the theoretical expectation that the nonlinearity of
the three-minute oscillations increases with height, and shock waves
form in the upper chromosphere. There are, however, discrepancies as
well between theory and observations, suggesting the need to improve
both theory and the measurement technique.
Title: Nonlinear Effects in Three-minute Oscillations of the Solar
Chromosphere. I. An Analytical Nonlinear Solution and Detection of
the Second Harmonic
Authors: Chae, Jongchul; Litvinenko, Yuri E.
Bibcode: 2017ApJ...844..129C
Altcode:
The vertical propagation of nonlinear acoustic waves in an isothermal
atmosphere is considered. A new analytical solution that describes a
finite-amplitude wave of an arbitrary wavelength is obtained. Although
the short- and long-wavelength limits were previously considered
separately, the new solution describes both limiting cases within a
common framework and provides a straightforward way of interpolating
between the two limits. Physical features of the nonlinear waves
in the chromosphere are described, including the dispersive nature
of low-frequency waves, the steepening of the wave profile, and
the influence of the gravitational field on wavefront breaking and
shock formation. The analytical results suggest that observations of
three-minute oscillations in the solar chromosphere may reveal the
basic nonlinear effect of oscillations with combination frequencies,
superposed on the normal oscillations of the system. Explicit
expressions for a second-harmonic signal and the ratio of its amplitude
to the fundamental harmonic amplitude are derived. Observational
evidence of the second harmonic, obtained with the Fast Imaging Solar
Spectrograph, installed at the 1.6 m New Solar Telescope of the Big
Bear Observatory, is presented. The presented data are based on the
time variations of velocity determined from the Na I D2
and Hα lines.
Title: Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion
Model
Authors: Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik
Bibcode: 2017ApJ...841...57L
Altcode:
We investigate analytically and numerically the transport of cosmic rays
following their escape from a shock or another localized acceleration
site. Observed cosmic-ray distributions in the vicinity of heliospheric
and astrophysical shocks imply that anomalous, superdiffusive transport
plays a role in the evolution of the energetic particles. Several
authors have quantitatively described the anomalous diffusion scalings,
implied by the data, by solutions of a formal transport equation with
fractional derivatives. Yet the physical basis of the fractional
diffusion model remains uncertain. We explore an alternative model
of the cosmic-ray transport: a nonlinear diffusion equation that
follows from a self-consistent treatment of the resonantly interacting
cosmic-ray particles and their self-generated turbulence. The nonlinear
model naturally leads to superdiffusive scalings. In the presence of
convection, the model yields a power-law dependence of the particle
density on the distance upstream of the shock. Although the results
do not refute the use of a fractional advection-diffusion equation,
they indicate a viable alternative to explain the anomalous diffusion
scalings of cosmic-ray particles.
Title: Analytical description of nonlinear acoustic waves in the
solar chromosphere
Authors: Litvinenko, Yuri E.; Chae, Jongchul
Bibcode: 2017A&A...599A..15L
Altcode:
Aims: Vertical propagation of acoustic waves of finite
amplitude in an isothermal, gravitationally stratified atmosphere is
considered.
Methods: Methods of nonlinear acoustics are used to
derive a dispersive solution, which is valid in a long-wavelength limit,
and a non-dispersive solution, which is valid in a short-wavelength
limit. The influence of the gravitational field on wave-front breaking
and shock formation is described. The generation of a second harmonic
at twice the driving wave frequency, previously detected in numerical
simulations, is demonstrated analytically.
Results: Application
of the results to three-minute chromospheric oscillations, driven
by velocity perturbations at the base of the solar atmosphere, is
discussed. Numerical estimates suggest that the second harmonic signal
should be detectable in an upper chromosphere by an instrument such as
the Fast Imaging Solar Spectrograph installed at the 1.6-m New Solar
Telescope of the Big Bear Observatory.
Title: Sunspot and Starspot Lifetimes in a Turbulent Erosion Model
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2017ApJ...834..108L
Altcode: 2016arXiv161103920L
Quantitative models of sunspot and starspot decay predict the timescale
of magnetic diffusion and may yield important constraints in stellar
dynamo models. Motivated by recent measurements of starspot lifetimes,
we investigate the disintegration of a magnetic flux tube by nonlinear
diffusion. Previous theoretical studies are extended by considering
two physically motivated functional forms for the nonlinear diffusion
coefficient D: an inverse power-law dependence D ∝ B-ν
and a step-function dependence of D on the magnetic field magnitude
B. Analytical self-similar solutions are presented for the power-law
case, including solutions exhibiting “superfast” diffusion. For the
step-function case, the heat-balance integral method yields approximate
solutions, valid for moderately suppressed diffusion in the spot. The
accuracy of the resulting solutions is confirmed numerically, using a
method which provides an accurate description of long-time evolution by
imposing boundary conditions at infinite distance from the spot. The
new models may allow insight into the differences and similarities
between sunspots and starspots.
Title: The Telegraph Approximation for Focused Cosmic-Ray Transport
in the Presence of Boundaries
Authors: Litvinenko, Yuri E.; Effenberger, Frederic; Schlickeiser,
Reinhard
Bibcode: 2015ApJ...806..217L
Altcode: 2015arXiv150505134L
Diffusive cosmic-ray transport in nonuniform large-scale magnetic
fields in the presence of boundaries is considered. Reflecting and
absorbing boundary conditions are derived for a modified telegraph
equation with a convective term. Analytical and numerical solutions
of illustrative boundary problems are presented. The applicability
and accuracy of the telegraph approximation for focused cosmic-ray
transport in the presence of boundaries are discussed, and potential
applications to modeling cosmic-ray transport are noted.
Title: Comments on Magnetic Reconnection Models of Canceling Magnetic
Features on the Sun
Authors: Litvinenko, Yuri E.
Bibcode: 2015JKAS...48..187L
Altcode:
No abstract at ADS
Title: Modeling Sunspot and Starspot Decay by Turbulent Erosion
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2015ApJ...800..130L
Altcode: 2015arXiv150101699L
Disintegration of sunspots (and starspots) by fluxtube erosion,
originally proposed by Simon and Leighton, is considered. A moving
boundary problem is formulated for a nonlinear diffusion equation that
describes the sunspot magnetic field profile. Explicit expressions
for the sunspot decay rate and lifetime by turbulent erosion are
derived analytically and verified numerically. A parabolic decay law
for the sunspot area is obtained. For moderate sunspot magnetic field
strengths, the predicted decay rate agrees with the results obtained
by Petrovay and Moreno-Insertis. The new analytical and numerical
solutions significantly improve the quantitative description of sunspot
and starspot decay by turbulent erosion.
Title: Analytical Solutions of a Fractional Diffusion-advection
Equation for Solar Cosmic-Ray Transport
Authors: Litvinenko, Yuri E.; Effenberger, Frederic
Bibcode: 2014ApJ...796..125L
Altcode: 2014arXiv1410.1223L
Motivated by recent applications of superdiffusive transport models
to shock-accelerated particle distributions in the heliosphere, we
analytically solve a one-dimensional fractional diffusion-advection
equation for the particle density. We derive an exact Fourier transform
solution, simplify it in a weak diffusion approximation, and compare
the new solution with previously available analytical results and with
a semi-numerical solution based on a Fourier series expansion. We apply
the results to the problem of describing the transport of energetic
particles, accelerated at a traveling heliospheric shock. Our analysis
shows that significant errors may result from assuming an infinite
initial distance between the shock and the observer. We argue that the
shock travel time should be a parameter of a realistic superdiffusive
transport model.
Title: On the Solution of the Continuity Equation for Precipitating
Electrons in Solar Flares
Authors: Emslie, A. Gordon; Holman, Gordon D.; Litvinenko, Yuri E.
Bibcode: 2014ApJ...792....5E
Altcode:
Electrons accelerated in solar flares are injected into the surrounding
plasma, where they are subjected to the influence of collisional
(Coulomb) energy losses. Their evolution is modeled by a partial
differential equation describing continuity of electron number. In a
recent paper, Dobranskis & Zharkova claim to have found an "updated
exact analytical solution" to this continuity equation. Their solution
contains an additional term that drives an exponential decrease in
electron density with depth, leading them to assert that the well-known
solution derived by Brown, Syrovatskii & Shmeleva, and many others
is invalid. We show that the solution of Dobranskis & Zharkova
results from a fundamental error in the application of the method of
characteristics and is hence incorrect. Further, their comparison of the
"new" analytical solution with numerical solutions of the Fokker-Planck
equation fails to lend support to their result. We conclude that
Dobranskis & Zharkova's solution of the universally accepted and
well-established continuity equation is incorrect, and that their
criticism of the correct solution is unfounded. We also demonstrate
the formal equivalence of the approaches of Syrovatskii & Shmeleva
and Brown, with particular reference to the evolution of the electron
flux and number density (both differential in energy) in a collisional
thick target. We strongly urge use of these long-established, correct
solutions in future works.
Title: The Diffusion Approximation versus the Telegraph Equation
for Modeling Solar Energetic Particle Transport with Adiabatic
Focusing. I. Isotropic Pitch-angle Scattering
Authors: Effenberger, Frederic; Litvinenko, Yuri E.
Bibcode: 2014ApJ...783...15E
Altcode: 2014arXiv1410.1225E
The diffusion approximation to the Fokker-Planck equation is
commonly used to model the transport of solar energetic particles
in interplanetary space. In this study, we present exact analytical
predictions of a higher order telegraph approximation for particle
transport and compare them with the corresponding predictions of
the diffusion approximation and numerical solutions of the full
Fokker-Planck equation. We specifically investigate the role of the
adiabatic focusing effect of a spatially varying magnetic field on
an evolving particle distribution. Comparison of the analytical and
numerical results shows that the telegraph approximation reproduces the
particle intensity profiles much more accurately than does the diffusion
approximation, especially when the focusing is strong. However, the
telegraph approximation appears to offer no significant advantage over
the diffusion approximation for calculating the particle anisotropy. The
telegraph approximation can be a useful tool for describing both
diffusive and wave-like aspects of the cosmic-ray transport.
Title: The Telegraph Approximation and Solar Energetic Particle
Intensity and Anisotropy Profiles
Authors: Effenberger, Frederic; Litvinenko, Yuri E.
Bibcode: 2014cosp...40E.781E
Altcode:
Diffusion type approximations are a common tool in the transport
modelling of energetic particles originating at the Sun. For a
spatially varying magnetic field and in situations where the pitch
angle distribution of the particles is not completely isotropic,
i.e. especially at early times during a solar event, an approximation to
the more general Fokker-Planck transport equation has to take effects
of focusing and anisotropy into account. In this study, we compare
exact analytic results of the higher order telegraph approximation
for focused transport to stochastic numerical solutions of the full
Fokker-Planck model. On the basis of space- and time profiles of
the particle intensity and anisotropy, we find that the telegraph
approximation has some significant advantages in cases where the
focusing is strong. Furthermore, it resolves the well known problem
of causality of the plain diffusion model.
Title: Erratum: "A Numerical Study of Diffusive Cosmic-Ray Transport
with Adiabatic Focusing" (2013,
ApJ, 765, 31)
Authors: Litvinenko, Yuri E.; Noble, P. L.
Bibcode: 2013ApJ...776..140L
Altcode:
No abstract at ADS
Title: An Exact Solution for Magnetic Annihilation in a Curved
Current Sheet
Authors: Litvinenko, Yuri E.
Bibcode: 2013ApJ...774..155L
Altcode:
An exact magnetohydrodynamic solution is presented for steady
magnetic annihilation (merging) in an incompressible resistive viscous
plasma. The merging, driven by an axisymmetric stagnation flow on a
cylinder, takes place in a curved current sheet that is perpendicular
to the plane in which the plasma flow stagnates. The new solution
extends earlier models of flux pileup merging in a flat current sheet,
driven by stagnation-point flows. The new solution remains valid in
the presence of both the isotropic and anisotropic (parallel) plasma
viscosity. The geometry of the solution may make it useful in modeling
the photospheric flux cancellation on the Sun.
Title: The telegraph equation for cosmic-ray transport with weak
adiabatic focusing
Authors: Litvinenko, Y. E.; Schlickeiser, R.
Bibcode: 2013A&A...554A..59L
Altcode:
Time-dependent solutions of a spatial diffusion equation are often used
to describe the transport of solar energetic particles, accelerated in
large solar flares. Approximate analytical solutions of the diffusion
approximation can complement and guide detailed numerical solutions of
the Fokker-Planck equation for the particle distribution function. The
accuracy of the diffusion approximation is limited, however, because the
signal propagation speed is infinite in the diffusion limit. An improved
description of cosmic-ray transport is provided by the telegraph
equation, characterised by a finite signal propagation speed. We
derive the telegraph equation for the particle density, taking into
account adiabatic focusing in a large-scale interplanetary magnetic
field in a weak focusing limit. As an illustration, we calculate a
propagating pulse solution of the telegraph equation, determine the
rise time when the maximum particle intensity is reached at a given
distance from the Sun, and compare the results with those obtained in
the diffusion approximation. In comparison with the diffusion equation,
the telegraph equation predicts an asymmetrical shape of the pulse and
a shorter rise time. These potentially significant differences suggest
that the more accurate telegraph equation should be used in analysis of
the solar energetic particle data, at least to quantify the accuracy of
the focused diffusion model. Appendix A is available in electronic
form at http://www.aanda.org
Title: A Numerical Study of Diffusive Cosmic-Ray Transport with
Adiabatic Focusing
Authors: Litvinenko, Yuri E.; Noble, P. L.
Bibcode: 2013ApJ...765...31L
Altcode:
Focused particle transport in a nonuniform large-scale magnetic
field is investigated numerically in the case of isotropic pitch-angle
scattering. Evolving particle density profiles and distribution moments
are computed from solutions of a system of stochastic differential
equations, equivalent to the original Fokker-Planck equation for
the particle distribution. Conflicting analytical predictions for
the transport coefficients in the diffusion limit, independently
calculated by Beeck & Wibberenz and Shalchi, are compared with
the numerical results. The reasons for the discrepancies among the
analytical and numerical treatments, as well as the general limitations
of the diffusion model, are discussed. The telegraph equation, derived
in a higher-order expansion of the particle distribution function,
is shown to describe the particle transport much more accurately than
the diffusion model, especially ahead of a moving density pulse.
Title: Modeling Focused Acceleration of Cosmic-Ray Particles by
Stochastic Methods
Authors: Armstrong, C. K.; Litvinenko, Yuri E.; Craig, I. J. D.
Bibcode: 2012ApJ...757..165A
Altcode:
Schlickeiser & Shalchi suggested that a first-order Fermi
mechanism of focused particle acceleration could be important in
several astrophysical applications. In order to investigate focused
acceleration, we express the Fokker-Planck equation as an equivalent
system of stochastic differential equations. We simplify the system for
a set of physically motivated parameters, extend the analytical theory,
and determine the evolving particle distribution numerically. While
our numerical results agree with the focused acceleration rate
of Schlickeiser & Shalchi for a weakly anisotropic particle
distribution, we establish significant limitations of the analytical
approach. Momentum diffusion is found to be more significant than
focused acceleration at early times. Most critically, the particle
distribution rapidly becomes anisotropic, leading to a much slower
momentum gain rate. We discuss the consequences of our results for
the role of focused acceleration in astrophysics.
Title: Rates of Magnetic Flux Cancellation Measured with Hinode/SOT
Authors: Park, S.; Chae, J.; Litvinenko, Y. E.
Bibcode: 2012ASPC..454...59P
Altcode:
The specific cancellation rate of canceling magnetic features,
defined as the rate of flux cancellation divided by the interface
length, is an observational quantity of magnetic reconnection model
in the low atmosphere. This value gives an accurate estimate of the
electric field in the reconnecting current sheet. We have measured
the specific rates using the magnetograms taken by the Solar Optical
Telescope (SOT)/Hinode. As a result, the specific rates determined
with SOT turned out to be systematically higher —about four times—
than those based on the data obtained by the Michelson Doppler Imager
(MDI) aboard the SOHO. This higher value is mainly due to the higher
resolution and better sensitivity of the SOT, resulting in magnetic
fluxes up to five times larger than those obtained from the MDI. The
higher rates of flux cancellation correspond to either faster inflows
or stronger magnetic fields of the inflow region in the current sheet,
which may have important consequences for the physics of photospheric
magnetic reconnection.
Title: Time-dependent particle acceleration in a Fermi reservoir
Authors: Litvinenko, Y. E.
Bibcode: 2012A&A...544A..94L
Altcode:
Context. A steady model was presented by Burn, in which energy
conservation is used to constrain the parameters of stochastic Fermi
acceleration. A steady model, however, is unlikely to be adequate for
particle acceleration in impulsive solar flares.
Aims: This paper
describes a time-dependent model for particle acceleration in a Fermi
reservoir
Methods: The calculation is based on the original
formulation of stochastic acceleration by Fermi, with additional
physically motivated assumptions about the turbulent and particle energy
densities within the reservoir, that are similar to those of the steady
analysis. The problem is reduced to an integro-differential equation
that possesses an analytical solution.
Results: The model
predicts the formation of a power-law differential energy spectrum
N(E) ~ E-2, that is observable outside the reservoir. The
predicted spectral index is independent of the parameters of the
model. The results may help in understanding particle acceleration in
solar flares and other astrophysical applications.
Title: Effects of Non-isotropic Scattering, Magnetic Helicity, and
Adiabatic Focusing on Diffusive Transport of Solar Energetic Particles
Authors: Litvinenko, Yuri E.
Bibcode: 2012ApJ...752...16L
Altcode:
Transport of solar energetic particles in interplanetary space is
analyzed. A new systematic derivation of the diffusion approximation
is given, which incorporates the effects of non-isotropic scattering,
magnetic helicity, and adiabatic focusing in a non-uniform large-scale
magnetic field. The derivation is based on a system of stochastic
differential equations, equivalent to the Fokker-Planck equation, and
the new method is a generalization of the Smoluchowski approximation
in the theory of the Brownian motion. Simple, physically transparent
expressions for the transport coefficients are derived. Different
results of earlier treatments of the problem are related to the
assumptions regarding the evolving particle distribution.
Title: Inflow Reconnection Solutions in Incompressible Visco-resistive
Plasmas
Authors: Craig, I. J. D.; Litvinenko, Yuri E.
Bibcode: 2012ApJ...747...16C
Altcode:
The development of a visco-resistive length scale for the thickness of
a reconnecting current sheet would have significant consequences for
the physics of magnetic reconnection in solar flares. In this paper,
planar magnetic reconnection in an incompressible visco-resistive
plasma is investigated analytically and numerically. Relaxation
simulations are performed in an "open" geometry that allows material
to enter and exit the reconnection volume. Solutions of two types are
identified depending on the strength of the external flow that drives
the reconnection. For sufficiently strong flows separate resistive and
viscous layers develop in the reconnection region. In this case merging
rates are found to be largely independent of viscosity. However,
when the flow is too weak to produce a localized current layer,
an equilibrium lacking any small-scale structure is obtained. The
central conclusion is that neither of these steady-state solutions
provide evidence of a visco-resistive length scale.
Title: The Parallel Diffusion Coefficient and Adiabatic Focusing of
Cosmic-Ray Particles
Authors: Litvinenko, Yuri E.
Bibcode: 2012ApJ...745...62L
Altcode:
In this paper, the problem of focused particle transport is revisited. A
description in terms of a system of stochastic differential equations,
completely equivalent to the Fokker-Planck equation, is suggested. The
coefficient for spatial diffusion parallel to the mean magnetic
field is calculated. The case of isotropic pitch angle scattering
and weak focusing is analyzed in detail. The disagreement between a
recent analysis by Shalchi and other treatments of the same problem
is discussed.
Title: Viscous effects in time-dependent planar reconnection
Authors: Armstrong, C. K.; Craig, I. J. D.; Litvinenko, Y. E.
Bibcode: 2011A&A...534A..25A
Altcode:
Context. Viscous dissipation is expected to play a significant part in
energy release in solar flares, yet the role of viscosity in a weakly
resistive plasma of the solar corona remains unclear.
Aims: We
attempt to clarify the role of viscous effects in magnetic reconnection
by performing simulations of reconnection in planar periodic geometry in
an incompressible viscous resistive plasma.
Methods: We consider
magnetic reconnection, driven by large-scale vortical flows. We use
both the classical shear viscosity and the Braginskii form for the ion
parallel viscosity in a magnetised plasma. We determine the scalings
of the current sheet parameters and the global rates of resistive and
viscous dissipation. We use steady-state exact solutions and scaling
arguments to interpret the numerical results.
Results: We show
that, regardless of the form of viscosity, the resistive non-viscous
analytical solutions for flux pile-up merging provide a very good
approximation of the numerical results in the reconnecting current
sheet. We find no evidence for a visco-resistive scale. Numerical
results for a highly sheared magnetic field, however, appear to deviate
from the analytical predictions in the case of the Braginskii viscosity.
Title: Focused Acceleration of Cosmic-ray Particles in Non-uniform
Magnetic Fields
Authors: Litvinenko, Yuri E.; Schlickeiser, R.
Bibcode: 2011ApJ...732L..31L
Altcode:
The Fokker-Planck equation for cosmic-ray particles in a spatially
varying guide magnetic field in a turbulent plasma is analyzed. An
expression is derived for the mean rate of change of particle momentum,
caused by the effect of adiabatic focusing in a non-uniform guide
field. Results of an earlier diffusion-limit analysis are confirmed,
and the physical picture is clarified by working directly with the
Fokker-Planck equation. A distributed first-order Fermi acceleration
mechanism is identified, which can be termed focused acceleration. If
the forward- and backward-propagating waves have equal polarizations,
focused acceleration operates when the net cross helicity of an
Alfvénic slab turbulence is either negative in a diverging guide
field or positive in a converging guide field. It is suggested that
focused acceleration can contribute to the formation of the anomalous
cosmic-ray spectrum at the heliospheric termination shock.
Title: Regular Versus Diffusive Photospheric Flux Cancellation
Authors: Litvinenko, Yuri E.
Bibcode: 2011ApJ...731L..39L
Altcode:
Observations of photospheric flux cancellation on the Sun imply that
cancellation can be a diffusive rather than regular process. A criterion
is derived, which quantifies the parameter range in which diffusive
photospheric cancellation should occur. Numerical estimates show that
regular cancellation models should be expected to give a quantitatively
accurate description of photospheric cancellation. The estimates rely
on a recently suggested scaling for a turbulent magnetic diffusivity,
which is consistent with the diffusivity measurements on spatial scales
varying by almost two orders of magnitude. Application of the turbulent
diffusivity to large-scale dispersal of the photospheric magnetic flux
is discussed.
Title: Energy Losses by Anisotropic Viscous Dissipation in Transient
Magnetic Reconnection
Authors: Craig, I. J. D.; Litvinenko, Yuri E.
Bibcode: 2010ApJ...725..886C
Altcode:
Global energy losses associated with transient magnetic reconnection in
a viscous resistive plasma are examined. The Braginskii stress tensor
is used to model the plasma viscosity for conditions typical of the
solar corona. Analytic arguments are used to show that the large-scale
advective flows associated with magnetic merging are likely to generate
significant viscous losses. It is pointed out that the development
of a visco-resistive reconnection scale, predicted for the classical
shear viscosity, is not expected in the more realistic case of the
Braginskii viscosity. Numerical simulations of planar coalescence
merging show that viscous losses should easily dominate resistive
losses for physically plausible parameters in flaring regions. Our
computations imply that flare-like rates exceeding 1029
erg s-1 can be achieved under plausible coronal conditions.
Title: Evolution of the Axial Magnetic Field in Solar Filament
Channels
Authors: Litvinenko, Yuri E.
Bibcode: 2010ApJ...720..948L
Altcode:
Formation of solar filament channels by photospheric magnetic
reconnection is considered. A magnetohydrodynamic model for magnetic
merging, driven by converging convective motions in the photosphere,
is presented. Evolution of the axial magnetic field in a channel is
analyzed. An exact time-dependent analytical solution for the field
profile in a steady stagnation-point flow is derived. The maximum
magnetic field in the channel is determined, and its dependence on
the reconnection inflow speed is discussed. The quantitative results
show that the maximum axial magnetic field in a forming channel is
an indicator of the photospheric reconnection rate, in agreement with
recent solar observations and laboratory experiments.
Title: Rates of Photospheric Magnetic Flux Cancellation Measured
with Hinode
Authors: Park, Soyoung; Chae, Jongchul; Litvinenko, Yuri E.
Bibcode: 2009ApJ...704L..71P
Altcode:
Photospheric magnetic flux cancellation on the Sun is generally
believed to be caused by magnetic reconnection occurring in the
low solar atmosphere. Individual canceling magnetic features are
observationally characterized by the rate of flux cancellation. The
specific cancellation rate, defined as the rate of flux cancellation
divided by the interface length, gives an accurate estimate of the
electric field in the reconnecting current sheet. We have determined
the specific cancellation rate using the magnetograms taken by the
Solar Optical Telescope (SOT) aboard the Hinode satellite. The specific
rates determined with SOT turned out to be systematically higher than
those based on the data taken by the Michelson Doppler Imager (MDI)
aboard the Solar and Heliospheric Observatory. The median value of
the specific cancellation rate was found to be 8 × 106
G cm s-1—a value four times that obtained from the MDI
data. This big difference is mainly due to a higher angular resolution
and better sensitivity of the SOT, resulting in magnetic fluxes up
to five times larger than those obtained from the MDI. The higher
rates of flux cancellation correspond to either faster inflows or
stronger magnetic fields of the reconnection inflow region, which may
have important consequences for the physics of photospheric magnetic
reconnection.
Title: Anisotropic viscous dissipation in three-dimensional magnetic
merging solutions
Authors: Craig, I. J. D.; Litvinenko, Y. E.
Bibcode: 2009A&A...501..755C
Altcode:
Aims: We consider viscous and resistive energy dissipation in the
flaring solar corona.
Methods: We compute energy dissipation
rates, associated with magnetic merging in three dimensions. We
examine an exact 3D solution for steady magnetic merging in a viscous
resistive incompressible plasma. We use the Braginskii stress tensor
to model viscous effects and derive scalings for the resistive and
viscous dissipation rates. We evaluate the dissipation rates for typical
parameters of solar active regions.
Results: Large-scale advective
flows required to sustain resistive current sheets are shown to be
associated with significant viscous losses. For plausible dimensionless
resistivities (inverse Lundquist numbers), whether classical η ≤
10-14 or anomalous η ≤ 10-8, viscous loss
rates greatly exceed the resistive loss rates of the current layer and
can approach flare-like rates of 1028 erg s-1 .
Title: Analytical Description of Steady Magnetic Reconnection in
Hall Magnetohydrodynamics
Authors: Litvinenko, Yuri E.
Bibcode: 2009ApJ...694.1464L
Altcode:
Steady magnetic reconnection in the framework of incompressible Hall
magnetohydrodynamics is considered. The principal role of the Hall
effect in the formation of the structure of the reconnecting current
sheet is emphasized. Analytical expressions for the velocity and the
magnetic field in the sheet are derived, based on the approximation
of a weak two dimensionality of the planar components of the
solution. The analytical solution illustrates key features of Hall
magnetic reconnection, including the reconnection rate enhancement and
the sheet thinning due to the Hall effect, the presence of a quadrupolar
axial (out-of-the-plane) magnetic field that controls the geometry
of the reconnecting planar magnetic field, and the dynamical coupling
of the axial and planar components of the solution, with the coupling
strength that is proportional to the ion skin depth. Scalings for the
sheet thickness, width, and the reconnection inflow and outflow speeds
in terms of the electric resistivity and the axial magnetic field are
determined. Implications of the results for fast magnetic reconnection
in a weakly collisional plasma of the solar corona are discussed.
Title: Signatures of Sweet-Parker magnetic reconnection in the
solar chromosphere
Authors: Litvinenko, Y. E.; Chae, J.
Bibcode: 2009A&A...495..953L
Altcode:
Aims: Predicted and observed signatures of magnetic reconnection in
the solar chromosphere are discussed.
Methods: Compressible
reconnection scalings for the Sweet-Parker current sheet in the
chromosphere are derived, which generalize earlier treatments by
including both the Lorentz force and the pressure gradient in the
reconnection outflow as possible drivers of reconnection jets. The
theoretical scalings were tested against the measured speed,
density, and temperature of an extreme-ultraviolet jet, observed
with TRACE. Model predictions for the reconnection jet parameters as
functions of height above the solar photosphere were computed.
Results: The predicted variation of reconnection jet parameters with
height appears to correspond to the observed wide range of parameters
of chromospheric jet-like features.
Title: Estimating the size of the cosmic-ray halo using particle
distribution moments
Authors: Litvinenko, Y. E.
Bibcode: 2009A&A...496..129L
Altcode:
Context: Particle transport in many astrophysical problems can be
described either by the Fokker-Planck equation or by an equivalent
system of stochastic differential equations.
Aims: It is shown
that the latter method can be applied to the problem of defining
the size of the cosmic-ray galactic halo.
Methods: Analytical
expressions for the leading moments of the pitch-angle distribution of
relativistic particles are determined. Particle scattering and escape
are analyzed in terms of the moments.
Results: In the case of an
anisotropic distribution, the first moment leads to an expression for
the halo size, identified with the particle escape from the region of
strong scattering. Previous studies are generalized by analyzing the
case of a strictly isotropic initial distribution. A new expression
for the variance of the distribution is derived, which illustrates the
anisotropization of the distribution.
Conclusions: Stochastic
calculus tools allow one to analyze physically motivated forms for the
scattering rate, so that a detailed realistic model can be developed.
Title: Determination of Magnetic Diffusivity from High-Resolution
Solar Magnetograms
Authors: Chae, Jongchul; Litvinenko, Yuri E.; Sakurai, Takashi
Bibcode: 2008ApJ...683.1153C
Altcode:
The magnetic diffusivity in the solar photosphere is determined by
applying a new method to the magnetic induction equation. The magnetic
field evolution is specified by a time sequence of high-resolution
magnetograms of plage regions, taken by Hinode/SOT and SOHO/MDI. The
mean value of magnetic diffusivity determined from SOT magnetograms with
the smallest pixel size of 116 km is about 0.87 +/- 0.08 km2
s-1. This is the smallest value that has been empirically
determined so far. High-resolution and full-disk MDI magnetograms with
the pixel sizes of 440 and 1400 km yielded larger values of 4.4 +/-
0.4 and 18 +/- 7.4 km2 s-1, respectively. The
measured diffusivity values at different length scales are consistent
with a turbulent cascade that ends at a resistive dissipation scale of
about 30 km. The results suggest that turbulent magnetic diffusivity
should be taken into account in the analysis of the observed rate of
magnetic flux cancellation in the photosphere.
Title: Influence of the Hall effect on the reconnection rate at
line-tied magnetic X-points
Authors: Craig, I. J. D.; Litvinenko, Y. E.
Bibcode: 2008A&A...484..847C
Altcode:
Context: The role of the Hall term in magnetic reconnection at
line-tied planar magnetic X-points is explored.
Aims: The goal
is to determine the reconnection scaling laws and to investigate
how the reconnection rate depends on the size of the system in Hall
magnetohydrodynamics (MHD).
Methods: The evolution of reconnective
disturbances is determined numerically by solving the linearized
compressible Hall MHD equations. Scaling laws are derived for the decay
rate as a function of the dimensionless resistivity and ion inertial
length.
Results: Although the Hall effect leads to an increase
in the decay rate, this increase is shown to be moderated in larger
systems. A key finding is that the Hall term contribution to the decay
rate, normalized by the resistive decay rate, scales inversely with the
system size L, approximately as L-2.
Conclusions: The
evidence suggests that decay rate enhancements due to Hall effects in
line-tied X-points are weakened for large-scale systems. The result may
have important implications for modeling energy release in large-scale
astrophysical plasma environments, such as solar flares.
Title: Determination of Magnetic Diffusivity from High Resolution
Solar Magnetograms
Authors: Chae, Jongchul; Litvinenko, Yuri E.; Sakurai, Takashi
Bibcode: 2008cosp...37..482C
Altcode: 2008cosp.meet..482C
The magnetic diffusivity in the solar photosphere is determined by
applying a model of magnetic induction to high resolution magnetograms
of plage regions, taken by HINODE/SOT and SOHO/MDI. The mean value
of magnetic diffusivity determined from SOT magnetograms with the
smallest pixel size of 116 km is about 0.84±0.34 km2 s-1 . This is
the smallest value that has been empirically determined so far. High
resolution and full-disk MDI magnetograms with the pixel sizes of 440
and 1400 km yielded larger values of 4.5±1.4 km2 s-1 and 13±10 km2
s-1 , respectively. The measured diffusivity values at different length
scales are consistent with a turbulent cascade that ends at a resistive
dissipation scale of about 25 km. The results suggest that turbulent
magnetic diffusivity should be taken into account in the analysis of
the observed rate of magnetic flux cancellation in the photosphere.
Title: Wave Energy Dissipation by Anisotropic Viscosity in Magnetic
X-Points
Authors: Craig, I. J. D.; Litvinenko, Yuri E.
Bibcode: 2007ApJ...667.1235C
Altcode:
The viscous dissipation of axial field disturbances in planar magnetic
X-points is examined. It is emphasized that an accurate treatment
requires a nonisotropic tensor viscosity whose components are governed
by the local magnetic field. Numerical solutions are constructed, which
compare the buildup of viscous forces using the tensor formulation
against a simplified model based on conventional shear viscosity. The
scaling of the global energy-loss rate with the viscosity coefficient
is shown to follow Pν~ν1/3 for both the
traditional shear viscosity and the Braginskii bulk viscosity. This
suggests that viscous wave dissipation can occur quite rapidly, in a few
tens of Alfvén times. The results imply that large-scale disturbances,
generated by magnetic reconnection in the solar corona, should dissipate
in a time on the order of a few minutes and significantly contribute
to coronal heating.
Title: Flux Pile-up Magnetic Reconnection in the Solar Photosphere
Authors: Litvinenko, Yuri E.; Chae, Jongchul; Park, So-Young
Bibcode: 2007ApJ...662.1302L
Altcode:
Magnetic reconnection in the temperature minimum region of the
solar photosphere, observationally manifested as canceling magnetic
features, is considered. Flux pile-up reconnection in the Sweet-Parker
current sheet is analyzed. It is shown that the standard Sweet-Parker
reconnection rate in the photosphere is too slow to explain the observed
cancellation. Flux pile-up reconnection scalings, however, are shown
to be in agreement with the speeds of canceling magnetic fragments,
magnetic fields in the fragments, and the rates of magnetic flux
cancellation, derived from SOHO MDI data. Pile-up factors in the range
between 1 and 5 and local reconnecting magnetic fields of a few hundred
G are calculated for the analyzed canceling features. The analysis
shows that flux pile-up is a likely mechanism for adjusting the local
parameters of reconnecting current sheets in the photosphere and for
sustaining the reconnection rates that are determined by large-scale
supergranular flows. The upward mass flux in the reconnection jet,
associated with a large canceling feature, is predicted to exceed
1015 g hr-1. Hence, cancellation in a few
photospheric patches over several hours can lead to the formation of
a solar filament in the corona.
Title: Recent Results of the 2005 LWS TR&T Focus Team for Solar
Energetic Particles
Authors: Desai, M. I.; Cohen, C. M.; Smith, C. W.; Lee, M. A.;
Litvinenko, Y.; Reames, D. V.; Ng, C. K.; Tylka, A. J.; Kota, J.;
Giacalone, J.; Jokipii, J. R.; Sokolov, I.; Gombosi, T.; Roussev,
I. I.; Li, G.; Zank, G. P.; Tessein, J.
Bibcode: 2006AGUFMSH23C..03D
Altcode:
Shock waves driven by coronal mass ejections are presently believed
to be responsible for producing large gradual solar energetic
particle (SEP) events that can pose significant radiation hazard
for humans and technological systems near Earth. However, our
present ability to accurately predict various properties of SEP
events (e.g., peak intensities, energy spectra, and composition)
is somewhat limited. Reliable prediction of these properties depends
on a multitude of observational and theoretical cross-disciplinary
studies that include: (1) Understanding and modeling the initiation and
propagation of fast CMEs and the evolution of shock characteristics
as they travel through the corona and interplanetary medium, (2)
Characterizing the ambient coronal and solar wind plasma, the solar
and interplanetary magnetic field, and the suprathermal ion population
through which the CMEs and their shocks propagate en route to Earth,
and (3) Developing a detailed understanding of particle injection and
acceleration at CME-driven shocks and their subsequent transport out
to 1 AU. Such studies are being routinely conducted both, individually
and collectively by members of the 2005 LWS TR&T Focus Team for
SEPs. In this talk we will summarize the SEP Team's ongoing efforts,
highlight the key new results, and discuss some of the main scientific
challenges that we need to overcome in order to improve current
understanding of the physical processes occurring in large SEP events.
Title: Three-dimensional fan magnetic reconnection and particle
acceleration in the solar corona
Authors: Litvinenko, Y. E.
Bibcode: 2006A&A...452.1069L
Altcode:
Aims.Particle acceleration by the reconnection electric field
in three-dimensional magnetic geometries in the solar corona is
discussed. The acceleration times, defined by the particle escape from
the vicinity of a magnetic null, and the corresponding energy gains
are calculated.
Methods: .An exact global magnetohydrodynamic
solution for fan magnetic reconnection is used to constrain the magnetic
and electric fields in the vicinity of the null. Expressions for the
particle acceleration times and energy gains are derived by applying
the WKB approximation to the equation of motion in nonrelativistic
and ultrarelativistic limits.
Results: .It is shown that the
energies of the accelerated particles can be limited by the particle
escape from the null rather than by the total electric potential at
the reconnection site. For typical coronal parameters, the finite
escape time limits proton energies if the Lundquist number is less
than 1012 and electron energies if the Lundquist number is
less than 1018.
Conclusions: .Particle acceleration
by the electric field, associated with fan magnetic reconnection in
solar flares, can explain proton energies of the order of a few MeV
and electron energies of the order of a few hundred keV in the case of
classical electric resistivity. Energies up to a few hundred MeV can be
reached if the resistivity at the reconnection site is turbulent. These
estimates agree with typical solar flare observations.
Title: A Simple Dynamical Model for Filament Formation in the
Solar Corona
Authors: Litvinenko, Y.
Bibcode: 2005AGUFMSH13A0276L
Altcode:
Filament formation in the solar corona is considered in the case
of a slowly evolving force-free magnetic field. The strong-field
approximation is used, which takes into account the magnetohydrodynamic
equations of motion, induction, and compressibility. Methods for
solving the relevant equations are presented and applied to filament
modeling. A three-dimensional calculation is presented, which uses
linear force-free magnetic fields. The boundary conditions are chosen to
resemble the qualitative linkage model for the formation of filaments,
suggested by Martens and Zwaan (2001). Consistent with this model,
dense formations, reminiscent of filament pillars, are shown to appear
in the corona above the region of converging and canceling magnetic
bipoles. The results demonstrate the principal role of magnetic field
in the dynamical processes of dense plasma accumulation and support
in filaments. The model can be useful for clarifying the role of flux
emergence in coronal mass ejection initiation.
Title: A Simple Dynamical Model for Filament Formation in the
Solar Corona
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2005ApJ...630..587L
Altcode:
Filament formation in the solar atmosphere is considered. In the limit
of sub-Alfvénic but supersonic motion, plasma flow in the solar corona
is driven via the induction equation by a slow evolution of force-free
magnetic fields. Methods for solving the relevant magnetohydrodynamic
equations are presented and applied to filament modeling in two and
three dimensions. An illustrative two-dimensional example is given,
which is based on a potential magnetic field with a dip. The example
describes the formation of a normal filament between two bipolar
regions on the Sun. Next a detailed three-dimensional calculation is
presented, which uses linear force-free magnetic fields. The boundary
conditions are chosen to resemble the qualitative ``head-to-tail''
linkage model for the formation of filaments, suggested by Martens &
Zwaan. Consistent with this model, dense formations, reminiscent of
filament pillars, are shown to appear in the corona above the region of
converging and canceling magnetic bipoles. The numerical results are
consistent with the principal role of magnetic field in the dynamical
processes of dense plasma accumulation and support in filaments,
advocated by Martens & Zwaan.
Title: Viscous Energy Dissipation by Flux Pile-Up Merging in the
Solar Corona
Authors: Litvinenko, Yuri E.
Bibcode: 2005SoPh..229..203L
Altcode:
Magnetic field annihilation in resistive viscous incompressible plasmas
is analyzed. Anisotropic viscous transport is modeled by the dominant
terms in the Braginskii viscous stress tensor. An analytical solution
for steady-state magnetic merging, driven by vortical plasma flows in
two dimensions, is derived. Resistive and viscous energy dissipation
rates are calculated. It is shown that, except in the limiting case
of zero vorticity, viscous heating can significantly exceed Joule
heating at the merging site. The results strongly suggest that viscous
dissipation can provide a significant fraction of the total energy
release in solar flares, which may have far-reaching implications for
flare models.
Title: Viscous effects in planar magnetic X-point reconnection
Authors: Craig, I. J. D.; Litvinenko, Y. E.; Senanayake, T.
Bibcode: 2005A&A...433.1139C
Altcode:
The impact of viscous dissipation is considered on magnetic reconnection
in closed line-tied magnetic X-points. It is shown that viscous effects
can provide fast energy dissipation for disturbances which do not alter
the initial X-point topology. If the X-point topology is altered, then
the rate of viscous dissipation depends on both the perturbed topology
and the relative magnitudes of viscosity and electric resistivity. New
solutions are demonstrated, which derive from the combination of
resistive and viscous effects. The solutions are characterized by
monotonically decaying modes which are qualitatively different from
the previously known oscillatory modes in nonviscous resistive X-point
reconnection. These results suggest that viscous heating in magnetic
X-points may be an important effect in solar flares.
Title: Particle Acceleration Associated with Three-Dimensional Fan
Magnetic Reconnection
Authors: Litvinenko, Y. E.
Bibcode: 2004ASPC..325..355L
Altcode:
Orbits of charged particles in the current sheet located in the
fan of a magnetic null point are described analytically in both
nonrelativistic and ultrarelativistic limits. An orbit instability
effect is described, which limits the acceleration times and kinetic
energy gains in the reconnection-related electric field. The use of
an analytical self-consistent MHD solution to derive the magnetic
field configuration near the null point leads to constraints on local
parameters in the magnetic reconnection region. As a consequence,
conditions can be identified for efficient particle acceleration in
realistic reconnecting geometries. Applications to particle acceleration
in solar flares are discussed.
Title: Energy Balance in the Corona Over the 22-Year Solar Cycle
Authors: Litvinenko, Y.
Bibcode: 2004AGUFMSH13A1161L
Altcode:
A model for dynamic energy balance in the solar corona over the 11-year
solar cycle is presented. The model predicts that the flaring rate in
the corona should lag behind the solar-cycle related driving because
of the coronal response time of order 9 months. This effect may explain
hysteresis phenomena between solar activity indices. The model can also
incorporate 22-year driving consistent with the Gnevyshev-Ohl rule. The
modified model in principle accounts for the observed variation of
the flaring time lag for odd and even solar cycles.
Title: Numerical Examination of the Stability of an Exact
Two-dimensional Solution For Flux Pile-up Magnetic Reconnection
Authors: Hirose, Shigenobu; Litvinenko, Yuri E.; Tanuma, Syuniti;
Shibata, Kazunari; Takahashi, Masaaki; Tanigawa, Takayuki; Sasaqui,
Takahiro; Noro, Ayato; Uehara, Kazuhiro; Takahashi, Kunio; Taniguchi,
Takashi; Terekhova, Yuliya A.
Bibcode: 2004ApJ...610.1107H
Altcode: 2003astro.ph..9033H
The Kelvin-Helmholtz (KH) and tearing instabilities are likely to
be important for the process of fast magnetic reconnection that is
believed to explain the observed explosive energy release in solar
flares. Theoretical studies of the instabilities, however, typically
invoke simplified initial magnetic and velocity fields that are not
solutions of the governing magnetohydrodynamic (MHD) equations. In
the present study, the stability of a reconnecting current sheet
is examined using a class of exact global MHD solutions for steady
state incompressible magnetic reconnection, discovered by Craig &
Henton. Numerical simulation indicates that the outflow solutions where
the current sheet is formed by strong shearing flows are subject to
the KH instability. The inflow solutions where the current sheet is
formed by a fast and weakly sheared inflow are shown to be tearing
unstable. Although the observed instability of the solutions can be
interpreted qualitatively by applying standard linear results for
the KH and tearing instabilities, the magnetic field and plasma flow,
specified by the Craig-Henton solution, lead to the stabilization of
the current sheet in some cases. The sensitivity of the instability
growth rate to the global geometry of magnetic reconnection may help
in solving the trigger problem in solar flare research.
Title: Robust Scalings in Compressible Flux Pile-Up Reconnection
Authors: Litvinenko, Y. E.; Craig, I. J. D.
Bibcode: 2004AAS...204.3911L
Altcode: 2004BAAS...36..716L
Flux pile-up magnetic reconnection is traditionally considered only
for incompressible plasmas. We use a simple analytical argument to
demonstrate that the pile-up scalings with electric resistivity are
robust when plasma compressibility is taken into account. The argument
makes it possible to understand why the transition from a highly
compressible limit to the incompressible one is difficult to discern in
typical simulations spanning a few decades in resistivity. Flux pile-up
reconnection in a compressible plasma, however, can lead to anomalous
resistivity in the current sheet and flare-like energy release in the
solar corona.
Title: Energy Balance in the Corona over the 22 Year Solar Cycle
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2004SoPh..219..265L
Altcode:
Wheatland and Litvinenko (2001) presented a model for dynamical
energy balance in the flaring solar corona which predicts a time
lag between flare occurrence and the supply of energy to the corona
(`driving'). They also suggested that an observed net lag between
flare numbers and sunspot numbers over cycles 21 and 22 might provide
support for the model. Temmer, Veronig, and Hanslmeier (2003) examined
data for five individual solar cycles (19-23) and confirmed a lag
between flare and sunspot numbers for odd solar cycles, but found no
lag for even cycles. Following the suggestion of Temmer, Veronig, and
Hanslmeier, the energy balance model is here extended to incorporate
22-year driving consistent with the phenomenological Gnevyshev—Ohl
rule. The model is found to exhibit a greater lag for the smaller
(even) cycles, in contradiction with the findings of Temmer, Veronig,
and Hanslmeier. A modification to the model is investigated in which
the flaring rate is proportional to the free energy and to the driving
rate for small driving rates, but is proportional only to the free
energy for large driving rates. The modified model can in principle
account for the observations.
Title: Robust Scalings in Compressible Flux Pile-Up Reconnection
Authors: Litvinenko, Yuri E.; Craig, I. J. D.
Bibcode: 2003SoPh..218..173L
Altcode:
Flux pile-up magnetic reconnection is traditionally considered only
for incompressible plasmas. The question addressed in this paper is
whether the pile-up scalings with resistivity are robust when plasma
compressibility is taken into account. A simple analytical argument
makes it possible to understand why the transition from a highly
compressible limit to the incompressible one is difficult to discern
in typical simulations spanning a few decades in resistivity. From
a practical standpoint, however, flux pile-up reconnection in a
compressible plasma can lead to anomalous electric resistivity in the
current sheet and flare-like energy release of magnetic energy in the
solar corona.
Title: Modeling Vertical Plasma Flows in Solar Filament Barbs
Authors: Litvinenko, Y.
Bibcode: 2003AGUFMSH22A0184L
Altcode:
Speeds of observed flows in quiescent solar filaments are typically
much less than the local Alfvén speed. This is why the flows in
filament barbs can be modeled by perturbing a local magnetostatic
solution describing the balance between the Lorentz force, gravity,
and gas pressure in a barb. Similarly, large-scale filament flows can
be treated as adiabatically slow deformations of a force-free magnetic
equilibrium that describes the global structure of a filament. This
approach reconciles current theoretical models with the puzzling
observational result that some of the flows appear to be neither
aligned with the magnetic field nor controlled by gravity.
Title: SOHO CTOF Observations of Interstellar He+ Pickup
Ion Enhancements in Solar Wind Compression Regions
Authors: Saul, L.; Möbius, E.; Litvinenko, Y.; Isenberg, P.; Kucharek,
H.; Lee, M.; Grünwaldt, H.; Ipavich, F.; Klecker, B.; Bochsler, P.
Bibcode: 2003AIPC..679..778S
Altcode: 2003astro.ph..4366S
We present a recent analysis with 1996 SOHO CELIAS CTOF data, which
reveals correlations of He+ pickup ion fluxes and spectra with the
magnetic field strength and solar wind density. The motivation is to
better understand the ubiquitous large variations in both pickup ion
fluxes and their velocity distributions found in interstellar pickup
ion datasets. We concentrate on time periods of that can be associated
with compression regions in the solar wind. Along with enhancements
of the overall pickup ion fluxes, adiabatic heating and acceleration
of the pickup ions are also observed in these regions. Transport
processes that lead to the observed compressions and related heating
or acceleration are discussed. A shift in velocity space associated
with traveling interplanetary compression regions is observed, and
a simple model presented to explain this phenomenon based on the
conserved magnetic adiabatic moment.
Title: Particle Acceleration by a Time-Varying Electric Field in
Merging Magnetic Fields
Authors: Litvinenko, Yuri E.
Bibcode: 2003SoPh..216..189L
Altcode:
Traditional models for particle acceleration by magnetic reconnection in
solar flares assumed a constant electric field in a steady reconnecting
magnetic field. Although this assumption may be justified during
the gradual phase of flares, the situation is different during the
impulsive phase. Observed rapid variations in flare emissions imply
that reconnection is non-steady and a time-varying electric field
is present in a reconnecting current sheet. This paper describes
exploratory calculations of charged particle orbits in an oscillating
electric field present either at a neutral plane or a neutral line
of two-dimensional magnetic field. A simple analytical model makes
it possible to explain the effects of particle trapping and resonant
acceleration previously noted by Petkaki and MacKinnon in a numerical
simulation. As an application, electron acceleration to X-ray generating
energies in impulsive solar flares is discussed within the context of
the model.
Title: Energies of Electrons Accelerated in Turbulent Reconnecting
Current Sheets in Solar Flares
Authors: Litvinenko, Yuri E.
Bibcode: 2003SoPh..212..379L
Altcode:
Yohkoh observations strongly suggest that electron acceleration in solar
flares occurs in magnetic reconnection regions in the corona above the
soft X-ray flare loops. Unfortunately, models for particle acceleration
in reconnecting current sheets predict electron energy gains in terms
of the reconnection electric field and the thickness of the sheet,
both of which are extremely difficult to measure. It can be shown,
however, that application of Ohm's law in a turbulent current sheet,
combined with energy and Maxwell's equations, leads to a formula for the
electron energy gain in terms of the flare power output, the magnetic
field strength, the plasma density and temperature in the sheet, and
its area. Typical flare parameters correspond to electron energies
between a few tens of keV and a few MeV. The calculation supports the
viewpoint that electrons that generate the continuum gamma-ray and
hard X-ray emissions in impulsive solar flares are accelerated in a
large-scale turbulent current sheet above the soft X-ray flare loops.
Title: Particle Acceleration by Magnetic Reconnection
Authors: Litvinenko, Y. E.
Bibcode: 2003LNP...612..213L
Altcode: 2003ecpa.conf..213L
This is a review of theoretical models for particle acceleration
by DC electric fields in reconnecting current sheets during solar
flares. Particular emphasis is placed on models for collisionless
acceleration in a large-scale reconnecting current sheet with a nonzero
magnetic field and a highly super-Dreicer electric field of order a few
hundred V m-1. Theoretical arguments and observational evidence for such
electric fields are also discussed. An approximate analytical approach
is employed to identify the effects of the electric and magnetic fields
on particle orbits. The magnetic field structure in the sheet is shown
to determine both the electron to proton ratio for the accelerated
particles and their typical energies and spectra. Formulae for the
particle energy gains and acceleration times are presented. Recent
numerical calculations of particle orbits are described, stressing the
use of exact MHD solutions for the magnetic fields and plasma flows
in the sheet. The analytical and numerical results form the basis for
electric field acceleration models in solar flares. In particular,
physical conditions can be identified that lead to either electron
acceleration to gamma-ray energies of a few tens of MeV in electron-rich
flares or the generation of protons with energies up to several GeV
in large gradual events.
Title: Electron acceleration in solar flares
Authors: Litvinenko, Yuri E.
Bibcode: 2003AdSpR..32.2385L
Altcode:
Observations suggest that electron acceleration in impulsive solar
flares occurs in magnetic reconnection regions in the corona above the
soft X-ray flare loops. Acceleration by a super-Dreicer electric field
in a reconnecting current sheet appears to be the most direct way of
producing electrons in the energy range between tens of keV and tens
of MeV. Theoretical models for collisionless particle acceleration in
large-scale current sheets formed in quadrupolar magnetic geometries
are reviewed. Recent calculations of particle orbits and energy gains
are described, stressing the use of global balance relations and exact
MHD solutions for the magnetic fields and plasma flows in the current
sheet. The results support the viewpoint that electrons that generate
the continuum gamma-ray and hard X-ray emissions in impulsive solar
flares are accelerated in a turbulent reconnecting current sheet.
Title: Understanding Solar Flare Waiting-Time Distributions
Authors: Wheatland, M. S.; Litvinenko, Y. E.
Bibcode: 2002SoPh..211..255W
Altcode:
The observed distribution of waiting times Δt between X-ray solar
flares of greater than C1 class listed in the Geostationary Operational
Environmental Satellite (GOES) catalog exhibits a power-law tail
∼(Δt)γ for large waiting times (Δt>10 hours). It is
shown that the power-law index γ varies with the solar cycle. For
the minimum phase of the cycle the index is γ=−1.4±0.1, and
for the maximum phase of the cycle the index is −3.2±0.2. For
all years 1975-2001, the index is −2.2±0.1. We present a simple
theory to account for the observed waiting-time distributions
in terms of a Poisson process with a time-varying rate λ(t). A
common approximation of slow variation of the rate with respect to a
waiting time is examined, and found to be valid for the GOES catalog
events. Subject to this approximation the observed waiting-time
distribution is determined by f(λ), the time distribution of the rate
λ. If f(λ) has a power-law form ∼λα for low rates,
the waiting time-distribution is predicted to have a power-law tail
∼(Δt)−(3+α) (α>−3). Distributions f(λ) are
constructed from the GOES data. For the entire catalog a power-law index
α=−0.9±0.1 is found in the time distribution of rates for low rates
(λ<0.1 hours−1). For the maximum and minimum phases
power-law indices α=−0.1±0.5 and α=−1.7±0.2, respectively,
are observed. Hence, the Poisson theory together with the observed time
distributions of the rate predict power-law tails in the waiting-time
distributions with indices −2.2±0.1 (1975-2001), −2.9±0.5
(maximum phase) and −1.3±0.2 (minimum phase), consistent with the
observations. These results suggest that the flaring rate varies in an
intrinsically different way at solar maximum by comparison with solar
minimum. The implications of these results for a recent model for flare
statistics (Craig, 2001) and more generally for our understanding of
the flare process are discussed.
Title: Particle Acceleration Associated with Three-Dimensional Fan
Magnetic Reconnection
Authors: Litvinenko, Y.
Bibcode: 2002AGUFMSH52A0443L
Altcode:
Particle acceleration associated with three-dimensional magnetic
reconnection is discussed. Orbits of charged particles in the current
sheet located in the fan of a magnetic null point are described
analytically in both nonrelativistic and ultrarelativistic limits. An
orbit instability effect is identified, which limits the acceleration
times and kinetic energy gains in the reconnection-related electric
field. The results are discussed using exact MHD solutions for fan
reconnection, discovered by I.J.D. Craig and co-workers. The use of
an analytical self-consistent MHD solution to derive the magnetic
field configuration near the null point allows one to constrain local
parameters in the magnetic reconnection region. As a consequence,
simple conditions can be identified for effective particle acceleration
in realistic reconnecting geometries. Applications to acceleration
processes in solar flares are discussed.
Title: Particle acceleration by a time-varying electric field in
merging magnetic fields
Authors: Litvinenko, Yuri E.
Bibcode: 2002ESASP.506..327L
Altcode: 2002svco.conf..327L; 2002ESPM...10..327L
Traditional models for particle acceleration in current sheets of solar
flares assumed a constant electric field in the sheet. Although this
assumption may be justified during the gradual phase of the flare, the
situation is different during the impulsive phase when nonsteady plasma
motions and rapid changes in the magnetic field imply rapid reconnection
and a time-varying electric field in the sheet. Rapid reconnection is
likely to be related to a flare-triggering instability such as tearing
or the propagation of a reconnective MHD disturbance toward a magnetic
null point. This paper describes exploratory analytical calculations of
charged particle orbits and energy gains in an oscillating electrtic
field present in the region of magnetic field merging. Applications
to particle acceleration in impulsive solar flares are discussed.
Title: Particle Acceleration Scalings Based on Exact Analytic Models
for Magnetic Reconnection
Authors: Litvinenko, Y.
Bibcode: 2002AAS...200.6810L
Altcode: 2002BAAS...34..756L
Observations suggest that particle acceleration in solar flares occurs
in the magnetic reconnection region above the flare loops. Theoretical
models for particle acceleration by the reconnection electric field,
however, employ heuristic configurations for electric and magnetic
fields in model current sheets, which are not solutions to the MHD
reconnection problem. In the present study particle acceleration is
discussed within the context of a self-consistent MHD reconnection
solution. This has the advantage of allowing poorly constrained local
parameters in the current sheet region to be expressed in terms of the
boundary conditions and electric resistivity of the global solution. The
resulting acceleration model leads to energy gains that are consistent
with those for high-energy particles in solar flares.
Title: Particle Acceleration Scalings Based on Exact Analytic Models
for Magnetic Reconnection
Authors: Craig, I. J. D.; Litvinenko, Yuri E.
Bibcode: 2002ApJ...570..387C
Altcode:
Observations suggest that particle acceleration in solar flares occurs
in the magnetic reconnection region above the flare loops. Theoretical
models for particle acceleration by the reconnection electric field,
however, employ heuristic configurations for electric and magnetic
fields in model current sheets, which are not solutions to the MHD
reconnection problem. In the present study, particle acceleration is
discussed within the context of a self-consistent MHD reconnection
solution. This has the advantage of allowing poorly constrained local
parameters in the current sheet region to be expressed in terms of the
boundary conditions and electric resistivity of the global solution. The
resulting acceleration model leads to energy gains that are consistent
with those for high-energy particles in solar flares. The overall
self-consistency of the approach is discussed.
Title: He+ Interstellar Pickup Ion Anisotropies and Flux Variations
Associated with Solar Wind Structures as Observed by SOHO CELIAS CTOF
Authors: Saul, Lukas; Moebius, Eberhard; Litvinenko, Yuri; Kucharek,
Harald; Feruggia, Charlie; et al.
Bibcode: 2002AGUSMSH31B..04S
Altcode:
Despite a rapidly growing understanding of the interaction of the
Heliosphere with the local interstellar medium (LISM), large unexplained
fluctuations in both the pickup ion flux and their velocity distribution
remain at a variety of time scales. Large variations are commonplace
for the solar wind physicist, however the source population for the
pickup ions (the LISM) is expected to be far more uniform. By comparing
the He+ distribution measured in situ by SOHO CELIAS CTOF with other
solar wind parameters, some of these fluctuations can be explained as
transport phenomenon. We present results from the brief lifetime of
the instrument, in which the pickup ion fluxes are seen to be enhanced
in compression regions, including corotating interaction regions and
coronal mass ejections. In addition, statistical correlations with
the interplanetary magnetic field and other solar wind parameters
have been observed, and will be presented as clues towards a further
understanding of the pickup ion flux variations.
Title: Proton Acceleration in Analytic Reconnecting Current Sheets
Authors: Heerikhuisen, J.; Litvinenko, Yuri E.; Craig, I. J. D.
Bibcode: 2002ApJ...566..512H
Altcode:
Particle acceleration provides an important signature for the magnetic
collapse that accompanies a solar flare. Most particle acceleration
studies, however, invoke magnetic and electric field models that
are analytically convenient rather than solutions of the governing
magnetohydrodynamic equations. In this paper a self-consistent magnetic
reconnection solution is employed to investigate proton orbits,
energy gains, and acceleration timescales for proton acceleration
in solar flares. The magnetic field configuration is derived from
the analytic reconnection solution of Craig and Henton. For the
physically realistic case in which magnetic pressure of the current
sheet is limited at small resistivities, the model contains a single
free parameter that specifies the shear of the velocity field. It
is shown that in the absence of losses, the field produces particle
acceleration spectra characteristic of magnetic X-points. Specifically,
the energy distribution approximates a power law ~E-3/2
nonrelativistically, but steepens slightly at the higher energies. Using
realistic values of the ``effective'' resistivity, we obtain energies
and acceleration times that fall within the range of observational
data for proton acceleration in the solar corona.
Title: Heavy Ion Abundances in Impulsive Solar Flares: Influence of
Pre-Acceleration in a Current Sheet
Authors: Litvinenko, Yuri E.
Bibcode: 2002SoPh..205..341L
Altcode:
Competition between stochastic energy gains and collisional energy
losses is known to lead to preferential acceleration of heavy ions
in flare loops. Ion acceleration in a reconnecting current sheet
is shown to mitigate the influence of collisional energy losses on
stochastic particle acceleration in impulsive solar flares. This effect
decreases the sensitivity of the resulting abundance ratios on initial
ion charge states. The resulting abundances are determined by the fact
that the energy loss rate falls off rapidly with increasing energy. As
an example, the expected Fe/O enhancement ratios are computed and
shown to be comparable with those observed with ACE SEPICA in several
impulsive flares in 1998. One consequence of the model is that the
preferential acceleration of heavy ions can occur only when the plasma
gas pressure is large enough, β≈me/mp, which
may explain the observed correlation between the heavy ion enrichment
and selective 3He acceleration in impulsive flares.
Title: Three-dimensional reconnection at the sun: space observations
and collisionless models
Authors: Somov, B. V.; Kosugi, T.; Litvinenko, Y. E.; Sakao, T.;
Masuda, S.; Oreshina, A. V.; Merenkova, E. Y.
Bibcode: 2002AdSpR..29.1035S
Altcode:
The Yohkoh data on the site and mechanism of magnetic energy
transformation into kinetic and thermal energies of a superhot plasma
at the Sun require new models of reconnection under conditions of
highlyanomalous resistivity, which are similar to that one observed in
toroidal devices performed to study turbulent heating of a collisionless
plasma, and its anomalous heat-conductive cooling. The models
make intelligible the observed properties of the three-dimensional
reconnection in solar flares.
Title: Electron acceleration in solar flares
Authors: Litvinenko, Y.
Bibcode: 2002cosp...34E1430L
Altcode: 2002cosp.meetE1430L
Observations suggest that electron acceleration in solar flares occurs
in the magnetic reconnection region above the flare loops. Acceleration
by a strong (super-Dreicer) electric field in the reconnecting current
sheet appears to be the most direct way of accelerating electrons
in the energy range between tens of keV and tens of MeV. Theoretical
models for collisionless acceleration in a large-scale sheet with a
nonzero magnetic field and a strong electric field are reviewed. The
limitations of traditional models are noted, in particular the use of
heuristic configurations for electric and magnetic fields in model
current sheets, which are not solutions to the MHD reconnection
problem. Recent analytical and numerical calculations of particle
orbits and energy gains are described, stressing the use of global
balance relations and exact MHD solutions for the magnetic fields and
plasma flows in the sheet. Electron acceleration in time-dependent
electric fiel d at magnetic null points is discussed as well, and a
new (well-forgotten) mechanism for particle acceleration in impulsive
electron-rich solar flares is proposed.
Title: A Simple Estimate for the Energies of Electrons Accelerated
in Flare Current Sheets on the Sun
Authors: Litvinenko, Y. E.
Bibcode: 2002mwoc.conf..383L
Altcode:
A major result from Yohkoh is the frequency of hard X-ray
sources above the flare loops. Observations suggest that electron
acceleration in flares occurs in the magnetic reconnection region
above the loop. Unfortunately, models for particle acceleration in
reconnecting current sheets predict electron energy gains in terms
of the reconnection electric field and the thickness of the sheet,
both of which are extremely difficult to measure. It can be shown,
however, that application of Ohm's law in a turbulent current sheet,
combined with energy and Maxwell's equations, leads to a formula for the
electron energy gain in terms of the flare power output, the magnetic
field strength, the plasma density and temperature in the sheet and
its area. Typical flare parameters correspond to electron energies
between a few tens of keV and a few MeV.
Title: A Comparison of Suprathermal Pickup Ion Tails with Solar Wind
Conditions at 1AU
Authors: Saul, L.; Moebius, E.; Litvinenko, Y.; Kucharek, H.; Klecker,
B.; Grunwaldt, H.; Smith, C.; Lepping, R.
Bibcode: 2002cosp...34E2314S
Altcode: 2002cosp.meetE2314S
As interstellar pickup ions are convected outwards in the solar wind,
they are subject to a number of complex transport processes. The
interaction of the pickup ion (PUI) distribution and ambient plasma
waves has been discussed by many authors, and can act to create
wave growth, pitch angle scattering, and statistical acceleration or
velocity space diffusion. Large scale structures in the solar wind
such as compression regions, shocks, and other discontinuities will
also affect the PUI distribution. The ubiquitous tails observed in the
distributions have been the subject of much discussion. We present in
situ He+ measurements from SOHO CTOF taken in 1996, in an effort to
determine the dominant transport effects creating these tails. Schwadron
et al observed PUI tails near corotating interaction regions (CIRs)
and compared tail strengths with the fluctuations of the magnetic field
at Ulysses. The conclusion was that statistical acceleration by waves
may be a stronger effect than the shock acceleration at the borders of
the CIR. We have repeated this analysis here for 1AU, using convected
magnetic fields from WIND MFI, and the preliminary results are the
same. W e also compare the tail strengths with t he fluctuations in
the total PUI flux, which are seen to be correlated with solar wind
parameters . Finally we present PUI data taken at individual CIRs and
compres sion regions, which show episodic acceleration on small space
and time scales. "Statistical acceleration of interstellar pick -u p
ions in co-rotating interaction regions", N.A. Schwadron, L. A. Fisk,
G. Gloeckler, Geophysical Research Letters, Vol.23, No.21, pp 2871-2874,
October 15, 1996
Title: Energy Balance in the Flaring Solar Corona
Authors: Wheatland, M. S.; Litvinenko, Y. E.
Bibcode: 2001AGUFMSH42A0778W
Altcode:
Assuming only that flares derive their energy from a coronal source
and that flaring is the dominant mechanism for depleting that source,
the global coronal response time (time for flares to remove available
coronal energy) is about 9 months. A detailed model for dynamic
energy balance in the solar corona over the solar cycle is presented
to describe how the magnetic free energy in the solar corona varies
in response to changes in the supply of energy to the system and to
changes in the flaring rate. The model predicts that both the flaring
rate and the free energy of the system should lag behind the driving
of the system because of the coronal response time (the model gives a
lag of ~ 11 months). This effect may account for hysteresis phenomena
between certain solar activity indices. For example, analysis of time
series of monthly sunspot numbers and monthly numbers of soft X-ray
flares over the years 1976 to 1999 indicates a tendency for flare
numbers to lag behind sunspot numbers by ~ 6 months.
Title: Acceleration in a current sheet and heavy ion abundances in
impulsive solar flares
Authors: Litvinenko, Yuri E.
Bibcode: 2001AIPC..598..311L
Altcode: 2001sgc..conf..311L
The influence of collisional energy losses on stochastic particle
acceleration in impulsive solar flares is considered in the context
of preferential acceleration of heavy ions. It is shown that ion
pre-acceleration in a reconnecting current sheet mitigates the effect
of collisional energy losses, thus removing a strong sensitivity of the
resulting anomalous abundances on the initial ion charge states. As
an example, the expected Fe/O enhancement factors are computed and
shown to be comparable with those observed with ACE SEPICA in a series
of impulsive flares in 1998. One consequence of the model is that
the preferential acceleration of heavy ions can occur only when the
plasma gas pressure is large enough, β~me/mp, which may explain the
observed correlation between the heavy ion enrichment and selective
3He acceleration in impulsive flares. .
Title: Energy Balance in the Flaring Solar Corona
Authors: Wheatland, M. S.; Litvinenko, Yuri E.
Bibcode: 2001ApJ...557..332W
Altcode:
Assuming only that flares derive their energy from a coronal source
and that flaring is the dominant mechanism for depleting that source,
the global coronal response time (time for flares to remove available
coronal energy) is about 9 months. A detailed model for dynamic
energy balance in the solar corona over the solar cycle is presented
to describe how the magnetic free energy in the solar corona varies
in response to changes in the supply of energy to the system and to
changes in the flaring rate. The model predicts that both the flaring
rate and the free energy of the system should lag behind the driving
of the system because of the coronal response time (the detailed model
gives a lag of ~11 months). This effect may account for hysteresis
phenomena between certain solar activity indices. A specific example is
presented in support of the model. Analysis of time series of monthly
sunspot numbers and monthly numbers of soft X-ray flares over the
years 1976-1999 indicates a tendency for flare numbers to lag behind
sunspot numbers by ~6 months.
Title: Study of Interstellar Neutral Velocity Effects on Helium
Pickup Ion Spectra as Observed with SOHO CELIAS
Authors: Saul, L.; Litvinenko, Y.; Moebius, E.; Rucinski, D.; Bzowski,
M.; Gruenwaldt, H.; Klecker, B.
Bibcode: 2001AGUSM..SH31B05S
Altcode:
Recently, systematic deviations of the He pickup ion cut-off energy
from its nominal value at twice the solar wind speed that are related
to the interstellar gas flow have been found in observations with the
SOHO CELIAS instrument. Using the variation of the cut-off with the
location along the Earth's orbit with respect to the interstellar
flow provides another method to determine the inflow velocity of
neutral interstellar He. Qualitative agreement has been found with
these observations by simply adding the neutral velocity to the cut-off
speed. However, it is noted that the neutral He velocity varies with its
distance from the sun due to the gravitational attraction. Therefore,
a simple velocity shift does not describe the effect on the pickup ion
distribution correctly. Portions of the distribution that are picked
up closer to the sun are affected more strongly than those picked up
closer to the Earth. We will discuss a model that includes evaluation
of the entire neutral gas distribution and the variation of the bulk
velocity as a function of distance from the sun. The model results are
compared with the shape of the pickup ion spectra as observed with SOHO
CELIAS. In our discussion we will separate the slow and predictable
variation of the neutral dis-tribution along the orbit from other
faster time variations of the pickup ion distributions that are seen
with SOHO CELIAS, and discuss possible ramifications.
Title: Dimensional Analysis of Solar Flare Distributions
Authors: Litvinenko, Y.
Bibcode: 2001AGUSM..SP51C08L
Altcode:
Dimensional analysis is used to derive the distribution of solar flare
energies ~ E-3/2 in accordance with recent observational
and numerical results. Several other scalings, notably E ~ t
f2 where t f is the flare duration, are obtained
as well. Dimensional considerations can also be employed to model
the rate of occurrence of solar flares (the flare waiting-time
distribution). An analytical estimate for the mean flaring rate λ
0 is obtained, based on the idea that the rate reflects
a balance between the processes of energy input into the corona and
energy dissipation by flaring. The estimate is shown to be in good
agreement with observations of flares by GOES detectors.
Title: Modeling the Rate of Occurrence of Solar Flares
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2001ApJ...550L.109L
Altcode:
Dimensional considerations are used to analyze the distribution of
times between solar flares (the flare waiting-time distribution). An
analytical estimate for the mean flaring rate λ0
is obtained, based on the idea that the rate reflects a balance
between the processes of energy input into the corona and energy
dissipation by flaring. The estimate is shown to be in good agreement
with observations of flares by Geostationary Operational Environmental
Satellite detectors. The analytic result is confirmed using the master
equation (probability balance equation) formalism. Analysis of time
variation leads to a differential equation describing how the free
energy in the corona changes when the rates of driving of the system
and of flaring vary. This equation may be used to describe the global
energy balance in the corona over the solar cycle.
Title: Interstellar gas flow into the heliosphere
Authors: Möbius, E.; Litvinenko, Y.; Saul, L.; Bzowski, M.;
Rucinski, D.
Bibcode: 2001ohnf.conf..109M
Altcode:
No abstract at ADS
Title: Collisionless Reconnection in the Structure and Dynamics of
Active Regions
Authors: Somov, B. V.; Kosugi, T.; Litvinenko, Y. E.; Sakao, T.;
Masuda, S.; Bogachev, S. A.; Oreshina, A. V.; Merenkova, E. Y.
Bibcode: 2001IAUS..203..558S
Altcode:
New theoretical interpretations are discussed of the Yohkoh data on
the site and mechanism of magnetic energy transformation into thermal
and kinetic energies of superhot plasmas and accelerated particles. We
develop a model that explains observed properties of reconnection in
active regions and in flares. The transition from slow reconnection to
fast one is demonstrated by numerical solutions of the problem taking
into account anomalous resistivity and anomalous heat conduction. The
model also makes intelligible the observed decrease (increase) of the
separation between the double-footpoint hard X-ray sources in the more
impulsive (less impulsive) flares. An accumulation of the reconnected
magnetic flux can explain the observed ascent motion of the coronal
source of hard X rays in flares. We demonstrate some features of
electron and ion acceleration in collapsing magnetic traps.
Title: Aspects of the Global MHD Equilibria and Filament Eruptions
in the Solar Corona
Authors: Litvinenko, Yuri E.; Somov, Boris V.
Bibcode: 2001SSRv...95...67L
Altcode:
This is a review of several promising approaches for analyzing the
accumulation and release of magnetic energy in filament eruptions
and coronal mass ejections in the solar corona. The importance of the
magnetic virial theorem for understanding the role of slowly changing
boundary conditions in the photosphere is stressed. A possible role
of the magnetic expulsion force in the solar filament dynamics is
also discussed.
Title: Flare Energy Release by Flux Pile-up Magnetic Reconnection
in a Turbulent Current Sheet
Authors: Litvinenko, Yuri E.; Craig, I. J. D.
Bibcode: 2000ApJ...544.1101L
Altcode:
The power output of flux pile-up magnetic reconnection is known
to be determined by the total hydromagnetic pressure outside the
current sheet. The maximum energy-release rate is reached for
optimized solutions that balance the maximum dynamic and magnetic
pressures. An optimized solution is determined in this paper for a
current sheet with anomalous, turbulent electric resistivity. The
resulting energy dissipation rate Wa is a strong
function of the maximum, saturated magnetic field Bs:
Wa~B4s. Numerically, Wa
can exceed the power output based on the classical resistivity by more
than 2 orders of magnitude for three-dimensional pile-up, leading to
solar flarelike energy-release rates of the order of 1028
ergs s-1. It is also shown that the optimization prescription
has its physical basis in relating the flux pile-up solutions to the
Sweet-Parker reconnection model.
Title: On the Magnetic Field Orientation and Plasma Flows in Solar
Filament Barbs
Authors: Litvinenko, Yuri E.
Bibcode: 2000SoPh..196..369L
Altcode:
Speeds of vertical flows in quiescent solar filaments are typically much
less than the local Alfvén speed. This is why the flows in filament
barbs can be modeled by perturbing a magnetostatic solution describing
a balance between the Lorentz force, gravity, and gas pressure in a
barb. This approach explains why some of the flows are neither aligned
with the magnetic field nor controlled by gravity. Both the observed
upflows and the magnetic field dips in barbs are likely to be caused
by photospheric magnetic reconnection.
Title: Particle acceleration at sites of magnetic reconnection
Authors: Litvinenko, Yuri E.
Bibcode: 2000AIPC..528...39L
Altcode: 2000atep.conf...39L
Electric fields induced by the changing magnetic field at sites of
magnetic reconnection can efficiently accelerate charged particles in
the solar corona. This review begins with estimates for the electric
field magnitude in flare models and presents some of the theoretical
results for the electron and proton acceleration in reconnecting
current sheets in solar flares. Particular emphasis is placed on
models for collisionless acceleration in a large-scale reconnecting
current sheet with a nonzero magnetic field and a highly super-Dreicer
electric field of order a few V cm-1. Particle orbits in
model current sheets are discussed using an approximate analytical
approach that allows one to identify the effects of both the electric
and magnetic field components on the particle motion. Formulas for the
particle energy gains and acceleration times are presented. Given a
super-Dreicer electric field in the sheet, it is the magnetic field
structure in the sheet that determines both the electron to proton
ratio for the accelerated particles and their typical energies and
spectra. The analytical results form the basis for the electric
field acceleration models in solar flares. In particular, physical
conditions can be identified that lead to either flares in which
electrons primarily generate hard X-rays in the energy range of tens
of keV or flares with unusually large electron fluxes at gamma-ray
energies extending up to a few tens of MeV. .
Title: Particle Acceleration in Reconnecting Current Sheets in
Impulsive Electron-Rich Solar Flares
Authors: Litvinenko, Yuri E.
Bibcode: 2000SoPh..194..327L
Altcode:
Electron and proton acceleration in reconnecting current
sheets in electron-rich solar flares is considered. A significant
three-dimensional magnetic field is assumed in the current sheet where
the particles are accelerated by the DC electric field. The tearing
instability of a pre-flare current sheet leads to the formation of
multiple singular lines of magnetic field where the electric and
magnetic fields are coaligned. Magnetized electrons are shown to
be accelerated to a few tens of MeV before they leave the vicinity
of a singular line. The acceleration time is estimated to be less
than 10−3 s. By contrast, much heavier protons are
unmagnetized and their energy gain is more modest. The model explains
a high electron-to-proton ratio and the unusually intense gamma-ray
continuum above 1 MeV observed in the electron-rich flares.
Title: Electron Acceleration by Strong DC Electric Fields in
Extragalactic Jets
Authors: Litvinenko, Y. E.
Bibcode: 2000IAUS..195..311L
Altcode:
Fast magnetic reconnection in extragalactic jets leads to electron
acceleration by the DC electric field in the reconnecting current
sheet. The maximum electron energy (γ > 106) and the
acceleration time (< 106 s) are determined by the magnetic
field dynamics in the sheet.
Title: The Rate of Flux Pile-up Magnetic Reconnection in the Solar
Corona
Authors: Litvinenko, Y. E.
Bibcode: 2000SPD....31.0278L
Altcode: 2000BAAS...32R.824L
The rate of two-dimensional flux pile-up magnetic reconnection is
known to be severely limited by gas pressure in a low-beta plasma
of the solar corona. For a two-dimensional stagnation point flow
with nonzero vorticity, for example, the rate cannot exceed the
Sweet-Parker scaling. The limitation should be less restrictive,
however, for three-dimensional flux pile-up. This paper examines
the maximum rate of three-dimensional pile-up reconnection in the
approximation of reduced magnetohydrodynamics (RMHD), which is valid
in the solar coronal loops. Gas pressure effects are ignored in RMHD,
but a similar limitation on the rate of magnetic merging exists. Both
the magnetic energy dissipation rate and the reconnection electric field
are shown to increase by several orders of magnitude in RMHD as compared
with strictly two-dimensional pile-up. This is enough to explain small
solar flares and slow coronal transients with energy release rates of
order 1025 - 1026 erg s-1, as well
as heating of quiet coronal loops. Notably, the reconnection electric
field is several orders of magnitude greater than the Dreicer field,
hence it can efficiently accelerate charged particles in flares. This
work was supported by NSF grant ATM-9813933.
Title: Electron Acceleration by Strong DC Electric Fields in Impulsive
Solar Flares
Authors: Litvinenko, Y. E.
Bibcode: 2000ASPC..206..167L
Altcode: 2000hesp.conf..167L
No abstract at ADS
Title: Magnetic reconnection as the cause of a photospheric canceling
feature and mass flows in a filament
Authors: Litvinenko, Yuri E.; Martin, Sara F.
Bibcode: 1999SoPh..190...45L
Altcode:
Magnetic reconnection in the temperature minimum region of the
solar photosphere can account for the canceling magnetic features
on the Sun. Litvinenko (1999a) showed that a reconnection model
explains the quiet-Sun features with the magnetic flux cancelation
rate of order 1017 Mx hr−1. In this paper
the model is applied to cancelation in solar active regions,
which is characterized by a much larger rate of cancelation ∖
ge1019 Mx hr−1. In particular, the evolution
of a photospheric canceling feature observed in an active region on
July 2, 1994 is studied. The theoretical predictions are demonstrated
to be in reasonable agreement with the measured speed of approaching
magnetic fragments, the magnetic field in the fragments, and the flux
cancelation rate, deduced from the combined Big Bear Hα time-lapse
images and videomagnetograms calibrated against the daily NSO/Kitt
Peak magnetogram. Of particular interest is the prediction that
photospheric reconnection should lead to a significant upward mass
flux and the formation of a solar filament. Hα observations indeed
showed a filament that had one of its ends spatially superposed with
the canceling feature.
Title: Coronal Hard X-rays in Solar Flares: Yohkoh Observations
and Interpretation
Authors: Somov, B. V.; Litvinenko, Y. E.; Kosugi, T.; Sakao, T.;
Masuda, S.; Bogachev, S. A.
Bibcode: 1999ESASP.448..701S
Altcode: 1999ESPM....9..701S; 1999mfsp.conf..701S
No abstract at ADS
Title: Magnetic Energy Release in Flux Pile-up Merging
Authors: Litvinenko, Yuri E.; Craig, I. J. D.
Bibcode: 1999SoPh..189..315L
Altcode:
The problem of pressure limitations on the rate of flux pile-up
magnetic reconnection is studied. We first examine the recent
suggestion of Jardine and Allen (1998) for moderating the build-up
of magnetic pressure in the current sheet by considering inflows
with nonzero vorticity. An analytic argument shows, however, that
unbounded magnetic pressures in the limit of small resistivities
can be avoided only at the cost of unphysical dynamic pressures in
the plasma. Hence, the pressure limitation on the reconnection rate
in a low-beta plasma cannot be avoided completely. Nevertheless, we
demonstrate that reconnection can be more rapid in a new solution that
balances the build-up in dynamic pressure against both the plasma and
magnetic pressures. This exact MHD solution has the characteristics
of merging driven by the coalescence instability. The maximum energy
release rate of the model is capable of explaining a modest solar flare.
Title: Direct evidence of the interstellar gas flow velocity in the
pickup ion cut-off as observed with SOHO CELIAS CTOF
Authors: Möbius, E.; Litvinenko, Y.; Grüwaldt, H.; Aellig, M. R.;
Bogdanov, A.; Ipavich, F. M.; Bochsler, P.; Hilchenbach, M.; Judge,
D.; Klecker, B.; Lee, M. A.; Ogawa, H.
Bibcode: 1999GeoRL..26.3181M
Altcode:
He+ pickup ions as observed with SOHO CELIAS CTOF have
been analyzed for the time period DOY 160-190, 1996. During this time
of the year the Earth is on the upwind side of the interstellar gas
flow with respect to the sun. The high-speed cut-off in the frame of
the sun is significantly higher v/Vsw = 2, predicted for
pickup ions. The difference increases with lower solar wind speeds. This
behavior is interpreted as an effect of the local interstellar gas flow
velocity (inflow at large distances including gravitational acceleration
by the sun) on the pickup ion distribution. The neutral velocity is
added to the solar wind velocity in the determination of the pickup
ion cut-off on the upwind side and subtracted on the downwind side of
the gas flow. This new observation will provide a valuable tool to
determine the interstellar gas flow and will thus complement direct
neutral gas measurements.
Title: Electron acceleration by strong DC electric fields in
extragalactic jets
Authors: Litvinenko, Yuri E.
Bibcode: 1999A&A...349..685L
Altcode:
Electron acceleration by fast magnetic reconnection in extragalactic
jets is considered. A significant three-dimensional magnetic field
is assumed in the reconnecting current sheet where the particles are
accelerated by the DC electric field. The character of electron orbits
in the sheet is controled by the magnetic field that determines, in
particular, the electron acceleration lengths < 10(-2) pc, making
the synchrotron losses in the sheet negligible. The model predicts
a power-law electron spectrum extending to TeV energies. With the
reconnection inflow speed of order 0.1 of the Alfvén speed and the
corresponding electric field of order 10(-6) statvolt/cm, a single
current sheet can provide the energy release rate >= 10(42) erg s(-1)
. Because the electrons escape much more efficiently across the sheet
rather than along it, radiation is continuous all along the jet. The
maximum electron energy gamma >= 10(6) and the acceleration time <
10(6) s are determined by the magnetic field dynamics in the sheet.
Title: The rate of flux pile-up magnetic reconnection in reduced MHD
Authors: Litvinenko, Yuri E.
Bibcode: 1999SoPh..188..115L
Altcode:
The rate of two-dimensional flux pile-up magnetic reconnection is known
to be severely limited by gas pressure in a low-beta plasma of the solar
corona. As earlier perturbational calculations indicated, however, the
pressure limitation should be less restrictive for three-dimensional
flux pile-up. In this paper the maximum rate of reconnection is
calculated in the approximation of reduced magnetohydrodynamics (RMHD),
which is valid in the solar coronal loops. The rate is calculated for
finite-magnitude reconnecting fields in the case of a strong axial field
in the loop. Gas pressure effects are ignored in RMHD but a similar
limitation on the rate of magnetic merging exists. Nevertheless, the
magnetic energy dissipation rate and the reconnection electric field
can increase by several orders of magnitude as compared with strictly
two-dimensional pile-up. Though this is still not enough to explain the
most powerful solar flares, slow coronal transients with energy release
rates of order 1025- 1026 erg s−1and
heating of quiet coronal loops are within the compass of the model.
Title: The Pressure Limitations on Flux Pile-Up Magnetic Reconnection
Authors: Litvinenko, Y. E.
Bibcode: 1999AAS...194.3105L
Altcode: 1999BAAS...31..869L
Flux pile-up magnetic reconnection was thought to be able to provide
fast energy dissipation a strongly magnetized plasma, for example, in
solar flares. We examine the problem of the plasma pressure limitations
on the rapidity of flux pile-up reconnection. It is shown that for
a two-dimensional stagnation point flow with nonzero vorticity the
magnetic merging rate cannot exceed the Sweet-Parker scaling in
a low-beta plasma, which is too slow to explain flares. Moreover,
the solution has some undesireable properties such as a diffusion
layer at the external boundary and the massively increasing inflow
speed. The pressure limitation appears to be somewhat less restrictive
for three-dimensional flux pile-up. This work was supported by NSF
grant ATM-9813933.
Title: The Pressure Limitations on Flux Pile-up Reconnection
Authors: Litvinenko, Yuri E.
Bibcode: 1999SoPh..186..291L
Altcode:
The problem of the plasma pressure limitations on the rapidity of
flux pile-up magnetic reconnection is re-examined, following the claim
made by Jardine and Allen (1998) that the limitations can be removed
by relaxing the assumption of zero-vorticity two-dimensional plasma
flows. It is shown that for a two-dimensional stagnation point flow
with nonzero vorticity the magnetic merging rate cannot exceed the
Sweet-Parker scaling in a low-beta plasma. The pressure limitation
appears to be much less restrictive for weak three-dimensional flux
pile-up, provided the perturbation length scale in the third dimension
is much less than the global length scale. The actual reconnection rate
in the latter case, however, is much lower than this upper estimate
unless the current sheet width is also much less than the global scale.
Title: Photospheric Magnetic Reconnection and Canceling Magnetic
Features on the Sun
Authors: Litvinenko, Yuri E.
Bibcode: 1999ApJ...515..435L
Altcode:
Parameters describing quasi-steady reconnecting current sheets in the
plasma of the solar photosphere and chromosphere are computed using
the VAL-C atmospheric model. In particular, the inflow speed for the
Sweet-Parker magnetic reconnection is found for a sheet whose width is
determined by the density scale height. The resulting speed of several
tens of meters per second corresponds closely to the speeds implied
by observations of canceling magnetic features on the Sun. This
and other arguments support photospheric magnetic reconnection as
the cancellation mechanism. The reconnection process should be most
efficient around the temperature minimum region about 600 km above
the lower photospheric boundary.
Title: Analytical results in a cellular automaton model of solar
flare occurrence
Authors: Litvinenko, Yuri E.
Bibcode: 1998A&A...339L..57L
Altcode:
Methods of the branching theory are applied to the Macpherson-MacKinnon
(1997) cellular automation model for the occurrence of solar flares. The
distribution of flare energies is shown to be a power law with the
slope alpha = 3/2 independent of dimensionality D of the model and in
nice agreement with observations, arguing in favor of the model. An
expression for the upper energy cut-off and a condition for the average
flare size to become infinite are derived for an arbitrary D as well,
providing an opportunity for comparing the analytical and numerical
results.
Title: Dimensional Analysis of the Flare Distribution Problem
Authors: Litvinenko, Yuri E.
Bibcode: 1998SoPh..180..393L
Altcode:
Dimensional analysis is used to derive the distribution of solar flare
energies,p(ɛ) = Aɛ-3/2, in accordance with
recent observational and numerical results. Several other scalings,
notably ɛ ∼ τfl2 , where τfl
is the flare duration, are obtained as well.
Title: Interpretation of Particle Acceleration in a Simulation Study
of Collisionless Reconnection
Authors: Litvinenko, Yuri E.
Bibcode: 1997SPD....28.1901L
Altcode: 1997BAAS...29R.923L
A recent simulation study (Horiuchi and Sato, Physics of Plasmas, 4,
277-289, 1997) investigated collisionless magnetic reconnection in
a sheared magnetic field. Existing theoretical models for particle
acceleration in current sheets are used to interpret some of the
simulation results. It is shown how the character of particle
trajectories changes as a function of the longitudinal magnetic
field. The numerical results are found to be consistent with predicted
analytical expressions for values of the electron energy gain, the
acceleration time, and the longitudinal field giving rise to adiabatic
particle motion. The agreement justifies the use of the current sheet
model for explanation of electron acceleration in solar flares. The
simulation also identified an ion acceleration mechanism that will
require additional theoretical study.
Title: A Strong Limitation on the Rapidity of Flux-Pile-Up
Reconnection
Authors: Litvinenko, Y. E.; Forbes, T. G.; Priest, E. R.
Bibcode: 1996SoPh..167..445L
Altcode:
The reconnection rate which can be achieved in the steady-state
flux-pile-up regime is severely limited by the gas pressure of the
plasma. Using the family of solutions obtained previously by Priest and
Forbes, we show that the Alfvén Mach number of the plasma flowing
towards the reconnection site cannot exceed πβe/(8
ln Rme), where βe and Rme are
the plasma β and magnetic Reynolds numbers at large distance. This
limit corresponds to a very weak flux-pile-up, and it is a factor of
βe slower than the maximum Petschek rate. Thus the maximum
flux-pile-up reconnection rate in the corona is at least two orders
of magnitude smaller than the rate implied by flare observations.
Title: A New Model for the Distribution of Flare Energies
Authors: Litvinenko, Yuri E.
Bibcode: 1996SoPh..167..321L
Altcode:
A new model is presented for the distribution of solar (and stellar)
flare energies. Flares are assumed to result from energy release in
multiple reconnecting current sheets (RCSs) in the solar corona. The
model takes into account both the dynamical evolution of separate RCSs
and their interaction by virtue of coalescence. Thus an attempt is
made to generalize previously suggested avalanche and RCS models for
the flare frequency distribution. The number of RCSs is not specified
and the strength of their interaction is governed by a coalescence
parameter. Under quite general assumptions, the resulting distribution
can be approximated by a power law with the slope 3/2 < α <
7/4, as required by numerous observations. A softer distribution of
numerous `nanoflares', responsible for the coronal heating, is also
possible under suitable choice of parameters.
Title: On the formation of the helium-3 spectrum in impulsive
solar flares
Authors: Litvinenko, Yuri E.
Bibcode: 1996AIPC..374..498L
Altcode: 1996hesp.conf..498L
The resonant interaction with oblique electromagnetic ion-cyclotron
waves is the most promising mechanism for selective acceleration of
3He ions in some impulsive solar flares. At the same time,
the properties of the observed particle spectrum remain unexplained,
in particular the spectral steepening or break at energies <10 MeV
that leads to an increase in the effective power-law spectral index at
higher energies. An analytical solution of the Fokker-Planck equation,
describing the resonant wave-particle interaction, shows that the
steepening is unlikely to stem from the action of the acceleration
mechanism alone. It is argued that the Coulomb energy losses at
energies greater than a few MeV may be large enough to provide the
observed spectral break. Its position is determined by the balance
between energy gain by acceleration and energy loss. Therefore, the
position of the break may serve as a diagnostic tool for the study of
the acceleration mechanism.
Title: Particle Acceleration in Reconnecting Current Sheets with a
Nonzero Magnetic Field
Authors: Litvinenko, Yuri E.
Bibcode: 1996ApJ...462..997L
Altcode:
Motion of charged particles in a reconnecting current sheet (RCS) is
considered, taking into account not only the electric field inside it
but also all three components of the magnetic field. A new solution for
the particle trajectory is found for the case of a large longitudinal
magnetic field. It allows one to find the "critical" value of the field,
beyond which the particle motion in the sheet becomes adiabatic. The
longitudinal component in RCSs in the solar atmosphere is likely to
exceed this value (typically 0.1 of the main reconnecting field for
electrons). The longitudinal field tends to counteract the effect of the
transverse magnetic field that serves to rapidly eject the particles
out of the sheet. Hence, a longitudinal component on the order of the
reconnecting component is necessary to explain the electron acceleration
in RCSs up to 10-100 keV during the impulsive phase of solar flares. The
electron acceleration length turns out to be 5 orders of magnitude
smaller than the RCS length, placing strong requirements on the electric
field necessary to accelerate the particles. This indicates that it
is necessary to modify the simplistic runaway acceleration models,
which ignore the magnetic field altogether. Depending upon the magnetic
field structure in the RCS, the energy can reside mainly in electrons
or protons. Thus, the model gives a unified description for different
regimes of particle acceleration in flares.
Title: A New Model for the Distribution of Flare Energies
Authors: Litvinenko, Y. E.
Bibcode: 1996AAS...188.1903L
Altcode: 1996BAAS...28Q.850L
A new model is presented for the distribution of solar (and stellar)
flare energies. Flares are assumed to result from energy release in
multiple reconnecting current sheets (RCSs) in the solar corona. The
model takes into account both the dynamical evolution of separate RCSs
and their interaction by virtue of coalescence. Thus an attempt is
made to generalize previously suggested avalanche and RCS models for
the flare frequency distribution. The number of RCSs is not specified
and the strength of their interaction is governed by a coalescence
parameter. Under quite general assumptions, the resulting distribution
can be approximated by a power law with a slope between 3/2 and 7/4,
as required by numerous observations. A softer distribution of numerous
"nanoflares," responsible for the coronal heating, is also possible
under suitable choice of parameters.
Title: Aspects of particle acceleration in solar flares
Authors: Litvinenko, Yuri Eduardovich
Bibcode: 1996PhDT.......108L
Altcode:
No abstract at ADS
Title: Magnetic Reconnection and Particle Acceleration in the
Solar Corona
Authors: Somov, B. V.; Litvinenko, Y. E.
Bibcode: 1993ASSL..183..603S
Altcode: 1993pssc.symp..603S
No abstract at ADS
Title: Electromagnetic up-pushing force as a possible mechanism for
the equilibrium of prominences
Authors: Litvinenko, Y. E.; Somov, B. V.
Bibcode: 1993AstL...19...27L
Altcode: 1993PAZh...19...65L
The force of electromagnetic up-pushing, which is different from
the well-known magnetic buoyancy force introduced by Parker (1955),
acts on a body immersed into a conducting fluid with electric and
magnetic fields. Dimensional considerations and some exact solutions
of the MHD problem allow us to determine this force in the case of the
large magnetic Reynolds number; that is important for astrophysical
applications. The electromagnetic up-pushing is capable of efficiently
balancing the gravity force in solar prominences and generating fast
vortex flows in their vicinity. The possible observational tests of
the effect are discussed.
Title: Electron acceleration in current sheets of solar flares
Authors: Litvinenko, Y. E.; Somov, B. V.
Bibcode: 1991PAZh...17..835L
Altcode:
A model for electron acceleration in high-temperature turbulent current
sheets is presented. In this model different processes of fast-particle
generation in solar flares are found to have a common cause, namely,
magnetic energy dissipation in a region of magnetic reconnection. The
spectral index of 2-5 and the total number of electrons accelerated
during the main phase of a flare are consistent with observational data.
Title: Solar flares and the virial theorem
Authors: Litvinenko, Y. E.; Somov, B. V.
Bibcode: 1991AZh....68..373L
Altcode:
An expression following from the virial theorem, for the magnetic
energy of a current sheet is considered under preflare conditions in
the solar atmosphere. The false conclusion on the equality of this
energy to the gravitational energy of the current sheet is shown to be
a consequence of unjustified application of the mirror currents model
to the solar atmosphere. Wave processes created by the generation of
electric currents in the corona are discussed. When used correctly,
the virial theorem confirms the possibility that magnetic reconnection
in current sheets can explain the solar flare energetics.
Title: Electron Acceleration in Current Sheets in Solar Flares
Authors: Litvinenko, Y. E.; Somov, B. V.
Bibcode: 1991SvAL...17..353L
Altcode:
No abstract at ADS
Title: Solar Flares and the Virial Theorem
Authors: Litvinenko, Y. E.; Somov, B. V.
Bibcode: 1991SvA....35..183L
Altcode:
No abstract at ADS
Title: Accelerated Electrons and Hard X-Ray Emission of a Solar
Flare in the Reverse Current Model
Authors: Litvinenko, Y. E.; Somov, B. V.
Bibcode: 1990SvA....34..421L
Altcode:
No abstract at ADS