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We investigate the acceleration of charged particles in a time-dependent chaotic magnetic field in this work. In earlier works, it has been demonstrated that in an asymmetric wire-loop current systems (WLCSs), the magnetic field is of chaotic in nature. Furthermore, observations also showed that there exist time-varying current loops and current filaments in solar corona. It is therefore natural to conceive that the magnetic field on the solar surface is chaotic and time-dependent. Here, we develop a numerical model to study the acceleration process of charged particles in a time-varying chaotic magnetic field that is generated by an ensemble of 8 WLCSs. We found that the motion of energetic particles in the system is of diffusive in nature and a power law spectrum can quickly develop. The mechanism examined here may serve as an efficient pre-acceleration mechanism that generates the so-called seed particles for diffusive shock acceleration at a coronal mass ejection (CME) driven shock in large solar energetic particle (SEP) events.

Space satellite observations show that current sheets in the space plasma environment are often characterized by bifurcated structures. In a recent paper a two-fluid model of the bifurcated current sheet was constructed on the basis of the pseudo potential method. A straightforward generalization of Janaki et al.'s two-fluid model to kinetic formalism, however, leads to an unphysical situation of negative particle velocity distribution function occurring over a certain range of velocity space. If one assumes an isotropic background plasma population, however, one can show that a rigorous, physically valid kinetic solution of the bifurcated current sheet can be obtained.

Single and double curl Beltrami magnetic fields are studied numerically in connection with their transport properties, and the results are compared and analyzed by characterizing the magnetic field lines. In the phase space of the single curl Beltrami field, islands of regular field lines are embedded into the chaotic sea, whereas the field lines for certain solutions of the double curl Beltrami field are chaotic over the entire space. Due to the presence of regular islands in phase space, the chaotic trajectories show stickiness phenomena which are characterized by the distribution of a chaotic field line. The dynamical traps in chaotic orbits due to stickiness phenomena are also characterized by the distribution of finite distance Lyapunov exponents. Finally, the recurrence length distribution of chaotic trajectories is plotted to understand their global behaviour.

The magnetic helicity characteristics of fully nonlinear, multi-dimensional Alfven simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulae. Two basic Alfven modes are identified: (1) the plane one-dimensional Alfven simple wave given in standard texts, in which the Alfven wave propagates along the z-axis with wave phase {psi} = k{sub 0}(z - {lambda}t), where k{sub 0} is the wave number and {lambda} is the group velocity of the wave and (2) the generalized Barnes simple Alfven wave in which the wave normal n moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfven wave (1) is analogous to the slab Alfven mode and the generalized Barnes solution (2) is analogous to the two-dimensional mode in Alfvenic, incompressible turbulence. The helicity characteristics of these two basic Alfven modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfven waves are also investigated. Applications to nonlinear Alfvenic fluctuations and structures observed in the solar windmore » are discussed.« less

We have developed an analytic model to describe coupling of plasma and neutral fluids in the partially ionized heliosphere plasma medium. The sources employed in our analytic model are based on a $\kappa$-distribution as opposed to the Maxwellian distribution function. Our model uses the $\kappa$-distribution to analytically model the energetic neutral atoms that result in the heliosphere partially ionized plasma from charge exchange with the protons and subsequently produce a long tail which is otherwise not describable by the Maxwellian distribution. We present our analytic formulation and describe major differences in the sources emerging from these two distinct distributions., Comment: This paper has been accepted in Journal of Plasma Physics. It is in press

We report our recent improvement in non-force-free extrapolation of coronal magnetic field, using vector magnetograms. Based on the principle of minimum (energy) dissipation rate (MDR), a generally non-force-free magnetic field solution is expressed as the superposition of one potential field and two ( constant- α ) linear force-free fields, with distinct α parameters. With a known potential field, the system is reduced to a second-order one that can be solved using one single-layer vector magnetogram. We devise an iteration procedure to determine the potential field, by achieving satisfactory agreement between the MDR-model computed and measured transverse magnetic field vectors on the bottom boundary. We illustrate this approach by applying it to real magnetograph measurement of solar active region AR 10953. We show that the results are satisfactory as judged from the quantitative magnetic field measurement, and the behavior of the derived Lorentz force.

We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys.235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.

The NASA DS1 spacecraft encountered Comet P/Borrelly on September 22, 2001 at a distance of ∼2171 km on the sunward side of the comet. The flyby speed was ∼16.5 km s −1 . Using high temporal resolution (50 μs) absolute electric field amplitude measurements from a ∼1 m dipole antenna, new features of plasma clouds created by cometary dust impacts have been detected. The pulses have 1/ e exponential decays of ∼650 μs duration, exponentially shaped overshoots with rise times of ∼2 ms, and exponential-shaped overshoot decay times of ∼10 ms. Assuming a plasma temperature of 10 4 K, these pulse features have been explained as plasma cloud space charge effects from the electron, proton and heavy ion portions of the clouds passing the antenna. Complex pulse shapes were also detected. These are believed to be due to either plasma cloud scattering off of the spacecraft, or to secondary impacts. Small electric pulses of duration 10–15 ms of cometary origin were detected but are presently unexplained. The electric component of the plasma wave spectra at closest approach had an f −2.4 power law shape from 10 Hz to 1 kHz. The electron cyclotron frequency was approximately 1 kHz. One possible explanation of the wave spectrum is that whistler mode waves associated with phase steepened cometary plasma waves are dispersed, leading to the broad spectrum. Finally, based on the present results, a new type of low-cost, large-area dust detector is proposed.

For a non-relativistic electron–positron plasma the possibility of obtaining a relaxed state is explored. The Euler–Lagrange equations are obtained by minimizing the hyper-resistivity with generalized helicities and magnetofluid energy as the constraints. The relaxed state is shown to be morphologically similar to the steady-state equilibria of the electron–positron plasma system.

A model of vortex with embedded discontinuities in plasma flow is developed in the framework of ideal MHD in a low b plasma. Vortex structures are considered as a result of 2-D evolution of nonlinear shear Alfvén waves in the heliosphere. Physical properties of the solutions and vector fields are analyzed and the observational aspects of the model are discussed. The ratio of normal components to the discontinuity Br /Vr can be close to -2. The alignment between velocity and magnetic field vectors takes place. Spacecraft crossing such vortices will typically observe a pair of discontinuities, but with dissimilar properties. Occurrence rate for different discontinuity types is estimated and agrees with observations in high-speed solar wind stream. Discontinuity crossing provides a backward rotation of magnetic field vector and can be observed as part of a backward arc. The Ulysses magnetometer data obtained in the fast solar wind are compared with the results of theoretical modelling.

The performed magnetohydrodynamic simulations aim to assess the influence of chaotic magnetic field lines on spontaneous generation of current sheets in an evolving viscous magnetofluid with infinite electrical conductivity. Suitable non-force-free initial fields having chaotic magnetic field lines are constructed by superposing two Arnold-Beltrami-Childress magnetic fields. The construction is such that the superposed field is devoid of any three or two-dimensional magnetic nulls, which are potential sites of current sheet development. Consequently, the notion of spontaneity can be attributed to any current sheet generated by the evolving magnetofluid. Moreover, to ensure the development to be spontaneous, the simulations are performed in congruence with Parker's magnetostatic theorem which necessitates an attainment of a terminal quasi-steady state and maintenance of flux-freezing to high fidelity. Importantly, the paper establishes spontaneous onset of volume distributed current sheets to be positively...

The dynamics of charged particles is studied in stationary magnetic fields that are obtained as solutions of nonlinear coupled equations varying in one dimension. The chosen equation can give both regular and chaotic solutions depending on the chosen coupling parameter. For chaotic numerical solution of the equation, rms values of fluctuation are increased by changing the coupling parameter, whereas for regular analytical solution, rms values of fluctuation are increased by changing the amplitude of fluctuation. Energy gain of an ensemble of particles is studied in both cases in the presence of a uniform electric field. Ensemble averaged energy gain is shown to decrease with the increase in rms values of fluctuation in the first case and increase with the increase in rms values of fluctuation in the second case.

Stationary solutions of Vlasov-Maxwell equations are obtained by exploiting the invariants of single particle motion leading to linear or nonlinear functional relations between current and vector potential. For a specific combination of invariants, it is shown that Vlasov-Maxwell equilibria have an associated Hamiltonian that exhibits chaos.

Magnetic field line equations correspond to a Hamiltonian dynamical system, so the features of a Hamiltonian systems can easily be adopted for discussing some essential features of magnetic field lines. The integrability of the magnetic field line equations are discussed by various authors and it can be shown that these equations are, in general, not integrable. We demonstrate several examples of realistic chaotic magnetic fields, produced by asymmetric current configurations. Particular examples of chaotic force-free field and non force-free fields are shown. We have studied, for the first time, the motion of a charged particle in chaotic magnetic fields. It is found that the motion of a charged particle in a chaotic magnetic field is not necessarily chaotic. We also showed that charged particles moving in a time-dependent chaotic magnetic field are energized. Such energization processes could play a dominant role in particle energization in several astrophysical environments including solar corona, solar flares and cosmic ray propagation in space.

The field-reversed configuration (FRC) with a completely null toroidal field and finite plasma beta is shown to result from a relaxation mechanism based on the principle of minimum dissipation of energy.

The principle of minimum energy dissipation rate is utilized to develop a unified model for relaxation in toroidal discharges. The Euler–Lagrange equation for such relaxed states is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar–Kendall (C–K) eigenfunctions analytically continued in the complex domain. The C–K eigenfunctions are hypergeometric functions that are solutions of the scalar Helmholtz equation in toroidal coordinates in the large-aspect-ratio approximation. Equilibria are constructed by assuming the total current J=0 at the edge. This yields the eigenvalues for a given aspect-ratio. The most novel feature of the present model is that solutions allow for tokamak, low-q as well as reversed field pinch-like behavior with a change in the eigenvalue characterizing the relaxed state.

Electrostatic surface waves propagating along the interface between a warm magnetized plasma and vacuum are investigated by deriving the relevant dispersion relations using a fluid model. The general dispersion relation for arbitrary orientation of the magnetic field and the propagation vector is derived in a closed form and certain special cases (when the magnetic field is directed parallel and perpendicular to the boundary surfaces) are analyzed numerically.

Linear dispersion relations of low-frequency electrostatic dust-Bernstein modes have been derived by employing the Vlasov equation for the motions of electrons, ions, and dust particles in a uniformly magnetized dusty plasma. Because of the large mass of the dust grains, the finite Larmor radius effects become significant for dust dynamics giving rise to the existence of extreme low-frequency dust-Bernstein modes. The importance of these low-frequency electrostatic dust-modes on the dust-coagulation and dust-crystallization has also been pointed out.

Classical kinetic theory using Boltzmann statistics shows that the potential distribution φ(r) in the screening cloud surrounding a single test charge at rest within a plasma is governed by a three-dimensional spherically symmetric plasma screening equation ∇2φ(r)=A(exp(+αφ)−exp(−βφ)), r≠0, where A=4πn0e, α=e/Te, β=e/Ti, e=electronic charge, Te=electron temperature, Ti=ion temperature, and n0=electron and ion density at large distances from the charge Q. In this paper it is proved rigorously that any nontrivial solution of the screening equation must have the following property: If φ(r)=potential at a radial distance r and limr→∞ φ(r)=0, then, for any positive integer n, as r→0 either rnφ→+∞ and rnφ′→−∞ or rnφ→−∞ and rnφ′→+∞.

Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabelling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler Poincar\'e variational approach is also used to derive conservation laws associated with fluid relabelling symmetries using Noether's second theorem., Comment: 42 pages, 0 figures

We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients $A=B=C=1$ are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the PDF of kinetic energy is, at late times, close to a Gaussian but with steeper tails., Comment: uses Revtex 4 instead of Revtex 4-1

The dispersion characteristics of the circularly polarized electromagnetic waves propagating along a homogeneous magnetic field in a dusty plasma have been investigated theoretically. The Vlasov equation has been employed to find the response of the magnetized plasma particles where the dust grains form a static background of highly charged and massive centers having certain correlation. It is found that in addition to the usual Landau damping which is negligible in the low temperature approximation, a novel mechanism of damping of the Alfven waves due to the dust comes into play. The modification and damping of the Alfven waves depend on the dust perturbation parameters, unequal densities of plasma particles, the average correlation length of the dust grains, temperature of the plasma and the magnetic field.

We present a numerical simulation of the slow formation of FRC by the merging of two spheromaks with opposite toroidal fluxes. A rather important feature of such a method of formation of FRC should be made explicit. A spheromak is basically a Taylor minimum energy state. On the other hand the FRC with its single component poloidal magnetic field and high plasma beta is decidedly far away from a Taylor state. So a numerical simulation of this process, besides demonstrating the feasibility of such FRC formation, is expected to show the traits in the process of transition from a Taylor state to a non-Taylor state. 5 refs., 2 figs., 1 tab.

[1] Recent satellite observations show that current sheets in the space plasma environment are often characterized by bifurcated structures. The majority of the available models of the bifurcated current sheet in the literature are based upon equilibrium Vlasov-Maxwell kinetic theory. While in principle, kinetic models are more fundamental, investigations based on fluid theory can sometimes be advantageous. For instance, because of its inherent simplicity, fluid models of the current sheet can be used in the detailed nonlocal or global analysis of fluid stability. The present paper puts forth a two-fluid model of the bifurcated current sheet on the basis of the pseudo-potential method. According to the present model, double peaked current sheet is characterized by a transverse non-uniform flow and a profile of plasma density that has a plateau in the region between the current peaks. Further, the plasma pressure tensor associated with such a bifurcated current sheet is shown to be anisotropic and non-gyrotropic.

We present ideas on nonlinear multiple waves in magnetohydrodynamics (MHD). In simple wave solutions, the dependent physical variables (the gas density, fluid velocity, magnetic field induction and gas pressure) depend on one phase variable which can be a function of the space and time variables (x, y, z, t). Double waves are another class of solutions that depend on two independent wave phases. As illustration of these ideas we present examples of double Alfven waves. The solutions possess the usual integrals for Alfven simple waves (the gas density, magnetic pressure, gas pressure and traveling wave velocity or group velocity), and have two independent phases. These waves may well be present in the solar wind. Double wave solutions, involving the other MHD wave modes are also possible.

In large Solar Energetic Particle (SEP) events, ions and electrons are accelerated to GeV/nucleon and keV in energy. These very high energetic particles are likely accelerated at fast coronal shocks. Observations have shown that the seed population (the particles that participate in the shock acceleration process) is not the bulk solar wind, but the suprathermal population. In this work, we propose to investigate a novel pre-acceleration mechanism that may provide the needed seed population for the subsequent shock acceleration in large SEP events. We examine the transport and acceleration of charged particles by chaotic electric and magnetic fields during the pre-eruptive period. It is demonstrated that a realistic chaotic magnetic field can be produced by any asymmetric current configurations - one such configuration is an asymmetric current wire loop system (CWLS). Observational studies have established the existence of current loops and current filaments at the solar surface and simple configurations as CWLSs inevitably exist in solar active regions. This suggests that the magnetic field at an active region is very much chaotic and time variation of these current configurations induces time-varying electric fields. Therefore, charged particles can be naturally accelerated. We outline an approximate model to study the pre-acceleration process of seed particles in a solar active region prior to eruptions by considering the transport and acceleration of charged particles in a time-dependent chaotic magnetic field.

[1] Homotopy formulas are obtained for the magnetic vector potential A, where B = ∇ × A is the magnetic induction, which gives alternative methods for calculating A for a given B, different from the Biot-Savart formulas. The homotopy formulas are used to obtain A for multipole potential fields and other potential fields, which are useful in relative helicity calculations. However, the formulas do not work for monopole and split monopole magnetic fields. In the latter case, there is no global continuous solution for A, but a global discontinuous A can be constructed, which is continuous on two open sets that cover the sphere. The differential and integral forms of the helicity and relative helicity transport equations using both Eulerian and Lagrangian perspectives are discussed. The approach to magnetic helicity and magnetic helicity injection, based on a toroidal-poloidal decomposition of the field, in which the field is represented by Euler potentials is also used in the analysis. The relative magnetic helicity and helicity injection rate for the Parker spiral interplanetary magnetic field, in which there is either a flat current sheet or a warped current sheet in the helioequatorial plane, are discussed. One of the homotopy formulas is used to provide an efficient way to calculate the relative helicity of interplanetary magnetic flux rope configurations observed by the WIND spacecraft.

We derive a generalized linear dispersion relation of waves in a strongly magnetized, compressible, homogeneous and isotropic quasineutral plasma. Starting from a two fluid model, describing distinguishable electron and ion fluids, we obtain a six order linear dispersion relation of magnetized waves that contains effects due to electron and ion inertia, finite plasma beta and angular dependence of phase speed. We investigate propagation characteristics of these magnetized waves in a regime where scale lengths are comparable with electron and ion inertial length scales. This regime corresponds essentially to the solar wind plasma where length scales, comparable with ion cyclotron frequency, lead to dispersive effects. These scales in conjunction with linear waves present a great deal of challenges in understanding the high frequency, small scale dynamics of turbulent fluctuations in the solar wind plasma., Comment: This paper is accepted in the Journal of Plasma Physics

The effects of temperature anisotropy in a weakly relativistic loss cone distribution on absorption of electron cyclotron waves propagating perpendicular to the magnetic field have been studied. The relevant dielectric tensor elements are calculated in terms of the generalized Dnestrovskii functions. The absorption coefficient is determined from the anti‐Hermitian part of the dielectric tensor elements. The expression for absorption coefficient contains the effects of temperature anisotropy, contributions due to finite Larmor radius to all orders, and gyroharmonic overlaps to all orders. Variations in absorption as well as loss cone instability with respect to temperature anisotropy are found both for the ordinary mode around the fundamental harmonic and the extraordinary mode around the second harmonic of electron cyclotron frequency. It is found that with the increase of density and loss cone index, the effect of temperature anisotropy is pronounced.

The effect of Landau damping on nonlinear magnetosonic waves propagating obliquely to the magnetic field in a finite beta plasma has been studied. It has been found that such magnetosonic waves owing to their interaction with resonant particles are governed by a KdV equation with a damping term. This equation has solitary wave solutions whose amplitude decays with time as (1 + τ/τ0)−2. The decay rates of both fast and slow waves have been computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for fast and slow magnetosonic waves. At a certain angle of propagation, the decay rates of both modes are equal in the case of a low beta plasma. The fast mode has a higher damping rate for higher beta and becomes practically nonexistent for nearly perpendicular angles of propagation.

We perform a fully self-consistent 3-D numerical simulation for a compressible, dissipative magneto-plasma driven by large-scale perturbations, that contain a fairly broader spectrum of characteristic modes, ranging from largest scales to intermediate scales and down to the smallest scales, where the energy of the system are dissipated by collisional (Ohmic) and viscous dissipations. Additionally, our simulation includes nonlinear interactions amongst a wide range of fluctuations that are initialized with random spectral amplitudes, leading to the cascade of spectral energy in the inertial range spectrum, and takes into account large scale as well as small scale perturbation that may have been induced by the background plasma fluctuations, also the non adiabatic exchange of energy leading to the migration of energy from the energy containing modes or randomly injected energy driven by perturbations and further dissipated by the smaller scales. Besides demonstrating the comparative decays of total energy and dissipation rate of energy, our results show the existence of a perpendicular component of current, thus clearly confirming that the self-organized state is non-force free., Paper is accepted in Journal of Plasma Physics - In Press

A nonlinear evolution equation governing the two dimensional propagation of fast and slow magnetosonic modes in a warm collisional plasma has been derived. This equation is a combination of Kadomtsev-Petviashvili (K-P) equation and the Burgers equation. The two dimensional K-P equation has two types of solitary wave solutions depending on the sign of the coefficients. One type is the usual planar type, the other is the lump solution. Both types of solitary wave solutions decay with time in the weak collisional limit. The two dimensional features of the amplitude and width of the lump or algebraic soliton have been discussed and the decay rates computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for the fast and the slow waves. At a certain angle of propagation the decay rates of both the modes are equal in the case of low beta plasma. Because of 2-D effects, the slow mode, although it has a lower collisional decay rate than the fast mode,...

Two dimensional shock structures of fast and slow magnetosonic waves, propagating in a dissipative warm magnetized plasma with a flow velocity are studied. The nonlinear evolution equation derived for such plasma, where dissipation is provided by electron ion collisions, is found to be a combination of Kadomtsev Petviashvili and Burger equation. Numerical solutions of this equation are obtained by transforming it to a moving frame of reference. These solutions, with appropriate boundary conditions show the development of shock structures both for fast and slow modes. Dependence of shock strength on plasma beta, angle of inclination of the magnetic field with the direction of flow velocity are shown. The most interesting feature is that, while for slow wave the shock strength persists for all angles of propagation but for the fast wave the shock strength vanishes below a certain critical Mach number and above a certain angle between the propagation vector and flow velocity.

It is known that ponderomotive forces produced by radial gradients in the RF energy can provide an effective stabilizing mechanism and create a stable window to the second stability regime. This problem is reexamined here with the introduction of axisymmetric toroidal rotation which itself is believed to have stabilizing influence on the ballooning modes on most flux surfaces except in the outer region. It is shown that the stabilizing effect is additive and an additional and important observation is that the outer region of the flux surfaces also gets stabilized by RF waves.

The usual theory of plasma relaxation, based on the selective decay of magnetic energy over the (global) magnetic helicity, predicts a force-free state for a plasma. Such a force-free state is inadequate to describe most realistic plasma systems occurring in laboratory and space plasmas as it produces a zero pressure gradient and cannot couple magnetic fields with flow. A different theory of relaxation has been proposed by many authors, based on a well-known principle of irreversible thermodynamics, the principle of minimum entropy production rate which is equivalent to the minimum dissipation rate (MDR) of energy. We demonstrate the applicability of minimum dissipative relaxed states to various self-organized systems of magnetically confined plasma in the laboratory and in the astrophysical context. Such relaxed states are shown to produce a number of basic characteristics of laboratory plasma confinement systems and solar arcade structure., Paper is accepted in JPP 2008

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived. >

We present a newly developed approach to solar coronal magnetic field extrapolation from vector magnetograms, based on the Principle of Minimum Dissipation Rate (MDR). The MDR system was derived from a variational problem that is more suitable for an open and externally driven system, like the solar corona. The resulting magnetic field equation is more general than force-free. Its solution can be expressed as the superposition of two linear (constant-$\alpha$) force-free fields (LFFFs) with distinct $\alpha$ parameters, and one potential field. Thus the original extrapolation problem is decomposed into three LFFF extrapolations, utilizing boundary data. The full MDR-based approach requires two layers of vector magnetograph measurements on solar surface, while a slightly modified practical approach only requires one. We test both approaches against 3D MHD simulation data in a finite volume. Both yield quantitatively good results. The errors in the magnetic energy estimate are within a few percents. In particular, the main features of relatively strong perpendicular current density structures, representative of the non-force freeness of the solution, are well recovered., Comment: submitted to ApJ

We develop an approach to deriving the 3D coronal magnetic field configuration from vector magnetograms, based on the Principle of Minimum Dissipation Rate (MDR). A solution to the system resulted from MDR is generally non‐force free and is expressed as linear superposition of three linear force‐free fields (one is potential) with distinct α parameters. The final solution is thus decomposed into three linear force‐free extrapolations from bottom boundary conditions derived from available vector magnetograms, at both photospheric and chromospheric levels. We illustrate the approach with an analytic test case, and discuss its advantages and limitations.

The heliopause (HP) separates the tenuous hot heliosheath plasma from the relatively dense cool magnetized plasma of the local interstellar medium (LISM). Fluid acceleration in the HP region can therefore drive Rayleigh-Taylor-like and Kelvin-Helmholtz- like instabilities. Charge exchange coupling of plasma ions and primary interstellar neutral atoms provides an effective gravity, suggesting the possibility of Rayleigh Taylor-like (RT-like) instabilities. Shear flow due to the velocity difference between the heliosheath and the interstellar flows drives Kelvin Helmholtz-like (KH-like) modes on the heliopause. Magnetic fields damp the classical KH instability. However, we show that energetic neutral atoms (ENAs) destabilize KH-modes,even in the presence of interplanetary and interstellar magnetic fields. We consider a model that includes a number of effects that are important in the heliosphere such as resonant change exchange between the primary neutrals and the solar wind plasma, ENAs from the inner heliosheath, plasma flows along the heliopause and magnetic fields in the inner and outer heliosheath. We find that the nose region is unstable to RT-like modes for HP parameters, while the shoulder region is unstable to a new instability that has the characteristics of a mixed RT-KH-like mode. These instabilities are not stabilized by typical values of the magnetic fields in the inner and outer heliosheath close to the nose and shoulder regions. Whereas ENAs have a stabilizing influence on the RT instability in the vicinity of the nose region (due to counter streaming), they have a destabilizing influence on the KH instability in the vicinity of the flanks. We find that even in the presence of interplanetary and interstellar magnetic fields, ENAs can drive a new form of KH-like instability on the flanks. An analysis of the collisional and anomalous magnetic field diffusion time scales shows that ideal MHD is an appropriate model at the HP. The interstellar magnetic field therefore drapes over the HP and does not diffuse into the inner heliosheath (IHS). However, RT-like, RT-KH-like, and KH-like instabilities serve to drag outer heliosheath (OHS)/interstellar magnetic field into the IHS, allowing for local reconnection of interplanetary and interstellar magnetic field. Such reconnection may 1) enhance the mixing of plasmas across the heliopause, and 2) provide open magnetic field lines that allow easy ingress of galactic cosmic rays into the heliosphere and easy loss of anomalous cosmic rays.

Electrostatic low frequency surface modes propagating along an interface between a dusty plasma and vacuum with frequencies of the order of the dust plasma frequency are investigated using a fluid model where the dust dynamics and dust charge fluctuations are taken into account. The dispersion properties and damping of these dust acoustic surface modes due to charge fluctuation effects are derived.

[1] We propose a new approach to deriving the local three-dimensional (3D) non-force free coronal magnetic field structure from photospheric vector magnetograph measurements. Based on the Principle of Minimum Dissipation Rate, a general non-force free magnetic field can be expressed as the superposition of two linear (constant-α) force free field. The parameter, α, for each of the two linear force free field, can be determined by optimizing the requirement that the recovered transverse magnetic field components as the superposition of the corresponding components of the two linear force free field agree with the observed ones at the photospheric level. A preliminary test case study of an analytic non-force free field model is presented to illustrate the method. We discuss the difficulties associated with the linear force free field extrapolation and the feasibility of our method.

In our work, we have proposed the arcade structures as minimum dissipative relaxed states (including both the viscous and resistive channels) pertaining to a two-fluid description of the plasma. The obtained relaxed state is non force-free in nature and appropriate to an open system with external drives. The Euler-Lagrange equations are solved in Cartesian coordinates subject to the existing photospheric boundary conditions. The solutions are seen to support flow-containing arcade like magnetic field configurations with inherent dissipative properties that may play an important role in the coronal heating. An interesting feature observed is the generation of different types of arcades with the variation of a single parameter characterizing the relaxed state. Also, recent observations with the LASCO coronagraph on board the SOHO spacecraft suggest that the helmet streamers originating from the sun may have an internal triple-arcade structure. The two-fluid relaxed state obtained here is also seen to support such structures., Comment: 18 pages and seven figures

[1] We examine a method of calculating the magnetic helicity of cylindrical magnetic flux rope of arbitrary cross section from in-situ spacecraft data. First we examine the gauge invariance of the definition of relative helicity by Finn and Antonsen (1985). Two approaches based on Grad-Shafranov equation are then described. A case study is presented to illustrate the method. The results show significant discrepancies from an earlier study utilizing axially symmetric models. We briefly discuss the potential applications for Sun-Earth connection.

[1] The NASA DS1 spacecraft flew past comet P/Borrelly on September 22, 2001, on the sunward side of the comet. Dust impacts were detected by sharp increases (or decreases) in electric fields measured by the plasma wave dipole antennae. Electric pulses from as small as 0.014 Vm−1 to saturation (∼±0.8 Vm−1) were detected. Pulse overshoots were noted in the largest electric pulses. No simultaneous dc magnetic signatures >1 nT were detected in the magnetometer data. Assuming that cometary dust grains propagating in the sunward direction were decelerated by solar radiation pressure, arguments are made that the size of the earliest dust particles detected were probably ∼0.4 μm in radius. Elaboration of the characteristics of these electric pulses and pulse overshoots and their interpretations will be reserved for a subsequent work.

[1] It has been suggested that Magnetic Holes (MHs) are caused by perpendicular proton energization due to the Ponderomotive Force (PF) associated with phase steepened Alfven waves. Here we include particle finite Larmor radius (FLR) effects and the effects of ion gyroharmonics in the PF expression. The general expression for the PF is derived by using the hot plasma dielectric tensor from kinetic theory. The fully kinetic expression has a multiple resonance character which is not revealed in the fluid picture. It will be shown that by including such effects, the expression for the PF will be significantly altered, both at the low frequency and high frequency limit. Also, an explicit analytic expression for the PF keeping only the first order FLR terms is given for conceptual purposes for the readers.

Two electron heating events have been identified on 20 May 1996 when Polar was in the polar cap/polar cusp boundary layer. The electron heating events were located within magnetic holes/cavities/bubbles and were accompanied by nonlinear ± 14 nT peak-to-peak (f ~ 0.6 to 0.7 fcp) obliquely propagating proton cyclotron waves. The electrons appear to be heated isotropically. Electric bipolar pulse (electron hole) onset events were also detected within the heating events. We propose a scenario which can link the above phenomena. Nonlinear Alfvén waves, generated through cusp magnetic reconnection, propagate down magnetic field lines and locally heat electrons through the ponderomotive force. The magnetic cavity is created through the diamagnetic effect of the heated electrons. Ion heating also occurs through ponderomotive acceleration (but much less than the electrons) and the protons generate the electromagnetic proton cyclotron waves through the loss cone instability. The obliquely propagating electromagnetic proton cyclotron waves accelerate bi-streaming electrons, which are the source of free energy for the electron holes.

The principle of minimum dissipation of energy is utilized to obtain the spheromak configuration as a relaxed state. The Euler-Lagrange equation for the minimum dissipative relaxed state is solved in terms of Chandrasekhar-Kendall eigenfunctions analytically generalized in the complex domain. This state is non-force-free and further shows the nonconstancy of the ratio of parallel current to the magnetic field.

Magnetic reconnection is essential to release the flux rope during its ejection. The question remains: how does the magnetic reconnection change the flux rope structure? Following the original study of \citet{Qiu2007}, we compare properties of ICME/MC flux ropes measured at 1 AU and properties of associated solar progenitors including flares, filaments, and CMEs. In particular, the magnetic field-line twist distribution within interplanetary magnetic flux ropes is systematically derived and examined. Our analysis shows that for most of these events, the amount of twisted flux per AU in MCs is comparable with the total reconnection flux on the Sun, and the sign of the MC helicity is consistent with the sign of helicity of the solar source region judged from the geometry of post-flare loops. Remarkably, we find that about one half of the 18 magnetic flux ropes, most of them being associated with erupting filaments, have a nearly uniform and relatively low twist distribution from the axis to the edge, and the majority of the other flux ropes exhibit very high twist near the axis, of up to $\gtrsim 5$ turns per AU, which decreases toward the edge. The flux ropes are therefore not linear force free. We also conduct detailed case studies showing the contrast of two events with distinct twist distribution in MCs as well as different flare and dimming characteristics in solar source regions, and discuss how reconnection geometry reflected in flare morphology may be related to the structure of the flux rope formed on the Sun., to appear in ApJ

The stability of the heliopause that separates the tenuous hot magnetized heliosheath plasma from the dense cool local interstellar magnetized plasma is examined using a fully general model that includes all the essential physical processes. Charge exchange coupling between plasma protons and primary interstellar neutral atoms provides an effective gravity that drives Rayleigh-Taylor (RT)-like instabilities. The velocity difference or shear between the heliosheath and interstellar flows, when coupled to energetic neutral atoms (ENAs), drives a Kelvin-Helmholtz (KH)-like instability on the heliopause. The shoulder region of the heliopause is unstable to a new instability that has characteristics of a mixed RT-KH-like mode. The instabilities are not stabilized by typical values of the magnetic fields in the inner and outer heliosheath (OHS). ENAs play an essential role in driving the KH-like instability, which is fully stabilized in their absence by magnetic fields. The nonlinear phase of these instabilities is briefly discussed. We also discuss the possibility that RT-like or mixed KH-RT-like instabilities drag outer heliosheath/very local interstellar medium (OHS/VLISM) magnetic field lines into the inner heliosheath (IHS) with the VLISM flow, and the possibility that IHS and VLISM magnetic field lines experience reconnection. Such reconnection may (1) greatly enhance the mixing ofmore » plasmas across the heliopause and (2) provide open magnetic field lines that allow easy ingress of galactic cosmic rays into the heliosphere and corresponding easy loss of anomalous cosmic rays from the heliosphere.« less