Collisionless magnetic reconnection dynamics with electron inertia and parallel electron compressibility

2007 ◽  
Vol 73 (6) ◽  
pp. 857-868 ◽  
Author(s):  
BHIMSEN K. SHIVAMOGGI
Keyword(s):  
Magnetic Reconnection ◽  
Neutral Line ◽  
Collisionless Plasma ◽  
Sufficient Conditions ◽  
Steady States ◽  
Plasma Dynamics ◽  
Electron Inertia ◽  
Current Confinement ◽  
Field Lines ◽  
Lyapunov Sense

AbstractCollisionless magnetic reconnection dynamics is considered by including the effects of electron inertia as well as parallel electron compressibility. A fluid treatment is adopted for both electrons and ions. Collisionless plasma dynamics properties near a two-dimensional X-type magnetic neutral line in the steady state are explored. The effects of electron inertia and parallel electron compressibility on the hyperbolicity (or lack thereof) of the magnetic field lines in the neutral layer are discussed. A unified linear tearing-mode formulation incorporating both electron inertia and parallel electron compressibility is given. The parallel-electron-compressibility branch is shown to couple in general to the electron-inertia branch in the presence of resistivity. A sufficient condition for linear stability in the Lyapunov sense for steady states of this collisionless plasma system signifying current confinement is deduced. Bounds on the equilibrium current gradient are shown to constitute sufficient conditions for nonlinear stability in the Lyapunov sense for steady states via nonlinear bounds for a suitable perturbation norm.

scholarly journals Onset of magnetic reconnection in a collisionless, high- plasma

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
Andrew Alt ◽  
Matthew W. Kunz
Keyword(s):  
Magnetic Reconnection ◽  
Collisionless Plasma ◽  
High Plasma ◽  
Tearing Modes ◽  
Associated Production ◽  
Pressure Anisotropy ◽  
Low Threshold ◽  
Collisionless Reconnection ◽  
Field Lines ◽  
The Impact

In a magnetized, collisionless plasma, the magnetic moment of the constituent particles is an adiabatic invariant. An increase in the magnetic-field strength in such a plasma thus leads to an increase in the thermal pressure perpendicular to the field lines. Above a$\unicode[STIX]{x1D6FD}$-dependent threshold (where$\unicode[STIX]{x1D6FD}$is the ratio of thermal to magnetic pressure), this pressure anisotropy drives the mirror instability, producing strong distortions in the field lines on ion-Larmor scales. The impact of this instability on magnetic reconnection is investigated using a simple analytical model for the formation of a current sheet (CS) and the associated production of pressure anisotropy. The difficulty in maintaining an isotropic, Maxwellian particle distribution during the formation and subsequent thinning of a CS in a collisionless plasma, coupled with the low threshold for the mirror instability in a high-$\unicode[STIX]{x1D6FD}$plasma, imply that the geometry of reconnecting magnetic fields can differ radically from the standard Harris-sheet profile often used in simulations of collisionless reconnection. As a result, depending on the rate of CS formation and the initial CS thickness, tearing modes whose growth rates and wavenumbers are boosted by this difference may disrupt the mirror-infested CS before standard tearing modes can develop. A quantitative theory is developed to illustrate this process, which may find application in the tearing-mediated disruption of kinetic magnetorotational ‘channel’ modes.

scholarly journals ViDA: a Vlasov–DArwin solver for plasma physics at electron scales

2019 ◽  
Vol 85 (5) ◽  
Author(s):  
Oreste Pezzi ◽  
Giulia Cozzani ◽  
Francesco Califano ◽  
Francesco Valentini ◽  
Massimiliano Guarrasi ◽  
...  
Keyword(s):  
Plasma Physics ◽  
Magnetic Reconnection ◽  
Spatial Scales ◽  
Collisionless Plasma ◽  
Low Noise ◽  
Numerical Code ◽  
Small Scale ◽  
Diffusion Region ◽  
Plasma Dynamics ◽  
Algorithm Efficiency

We present a Vlasov–DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the nonlinear regime to guarantee a clean description of the plasma dynamics at fine spatial scales. The algorithm provides a low-noise description of proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov equation in phase space. Maxwell equations for the electric and magnetic fields are reorganized according to the Darwin approximation to remove light waves. Several numerical tests show that ViDA successfully reproduces the propagation of linear and nonlinear waves and captures the physics of magnetic reconnection. We also discuss preliminary tests of the parallelization algorithm efficiency, performed at CINECA on the Marconi-KNL cluster. ViDA will allow the running of Eulerian simulations of a non-relativistic fully kinetic collisionless plasma and it is expected to provide relevant insights into important problems of plasma astrophysics such as, for instance, the development of the turbulent cascade at electron scales and the structure and dynamics of electron-scale magnetic reconnection, such as the electron diffusion region.

scholarly journals Evolution of magnetic helicity under kinetic magnetic reconnection: Part II B ≠ 0 reconnection

2002 ◽  
Vol 9 (2) ◽  
pp. 139-147 ◽  
Author(s):  
T. Wiegelmann ◽  
J. Büchner
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Hall Current ◽  
Neutral Line ◽  
Magnetic Helicity ◽  
Perpendicular Magnetic Field ◽  
Guide Field ◽  
Magnetic Neutral Line ◽  
Field Lines ◽  
The Magnetic Field

Abstract. We investigate the evolution of magnetic helicity under kinetic magnetic reconnection in thin current sheets. We use Harris sheet equilibria and superimpose an external magnetic guide field. Consequently, the classical 2D magnetic neutral line becomes a field line here, causing a B ≠ 0 reconnection. While without a guide field, the Hall effect leads to a quadrupolar structure in the perpendicular magnetic field and the helicity density, this effect vanishes in the B ≠ 0 reconnection. The reason is that electrons are magnetized in the guide field and the Hall current does not occur. While a B = 0 reconnection leads just to a bending of the field lines in the reconnection area, thus conserving the helicity, the initial helicity is reduced for a B ≠ 0 reconnection. The helicity reduction is, however, slower than the magnetic field dissipation. The simulations have been carried out by the numerical integration of the Vlasov-equation.

scholarly journals “Diffusion” region of magnetic reconnection: electron orbits and the phase space mixing

2018 ◽  
Vol 36 (3) ◽  
pp. 731-740
Author(s):  
Alexey P. Kropotkin
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Electric Field ◽  
Magnetic Reconnection ◽  
Neutral Line ◽  
Collisionless Plasma ◽  
Uniform Electric Field ◽  
Diffusion Region ◽  
Finite Conductivity ◽  
The Magnetic Field

Abstract. The nonlinear dynamics of electrons in the vicinity of magnetic field neutral lines during magnetic reconnection, deep inside the “diffusion” region where the electron motion is nonadiabatic, has been numerically analyzed. Test particle orbits are examined in that vicinity, for a prescribed planar two-dimensional magnetic field configuration and with a prescribed uniform electric field in the neutral line direction. On electron orbits, a strong particle acceleration occurs due to the reconnection electric field. Local instability of orbits in the neighborhood of the neutral line is pointed out. It combines with finiteness of orbits due to particle trapping by the magnetic field, and this should lead to the effect of mixing in the phase space, and the appearance of dynamical chaos. The latter may presumably be viewed as a mechanism producing finite “conductivity” in collisionless plasma near the neutral line. That conductivity is necessary to provide violation of the magnetic field frozen-in condition, i.e., for magnetic reconnection to occur in that region. Keywords. Magnetospheric physics (plasma sheet)

scholarly journals Magnetic nulls in interacting dipolar fields

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Todd Elder ◽  
Allen H. Boozer
Keyword(s):  
Magnetic Field ◽  
Current Density ◽  
Magnetic Flux Tube ◽  
Electron Inertia ◽  
Characteristic Spatial Scale ◽  
Field Lines ◽  
Dipolar Fields ◽  
Time Required ◽  
Magnetic Null ◽  
The Magnetic Field

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $\varDelta _d$ . Electron inertia ensures $\varDelta _d\gtrsim c/\omega _{pe}$ . The lines that lie within a magnetic flux tube of radius $\varDelta _d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$ vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/\omega _{pe})^{1/3}$ , where $a$ is a characteristic spatial scale of the magnetic field. The behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 4. Generalized isovorticity principle for three-dimensional flows

1999 ◽  
Vol 390 ◽  
pp. 127-150 ◽  
Author(s):  
V. A. VLADIMIROV ◽  
H. K. MOFFATT ◽  
K. I. ILIN
Keyword(s):  
Steady State ◽  
Variational Principles ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Steady States ◽  
Mhd Equations ◽  
Quadratic Functional ◽  
The First Variation ◽  
The Stability ◽  
And Variational Principles

The equations of magnetohydrodynamics (MHD) of an ideal fluid have two families of topological invariants: the magnetic helicity invariants and the cross-helicity invariants. It is first shown that these invariants define a natural foliation (described as isomagnetovortical, or imv for short) in the function space in which solutions {u(x, t), h(x, t)} of the MHD equations reside. A relaxation process is constructed whereby total energy (magnetic plus kinetic) decreases on an imv folium (all magnetic and cross-helicity invariants being thus conserved). The energy has a positive lower bound determined by the global cross-helicity, and it is thus shown that a steady state exists having the (arbitrarily) prescribed families of magnetic and cross-helicity invariants.The stability of such steady states is considered by an appropriate generalization of (Arnold) energy techniques. The first variation of energy on the imv folium is shown to vanish, and the second variation δ2E is constructed. It is shown that δ2E is a quadratic functional of the first-order variations δ1u, δ1h of u and h (from a steady state U(x), H(x)), and that δ2E is an invariant of the linearized MHD equations. Linear stability is then assured provided δ2E is either positive-definite or negative-definite for all imv perturbations. It is shown that the results may be equivalently obtained through consideration of the frozen-in ‘modified’ vorticity field introduced in Part 1 of this series.Finally, the general stability criterion is applied to a variety of classes of steady states {U(x), H(x)}, and new sufficient conditions for stability to three-dimensional imv perturbations are obtained.

Collisionless plasma transport mechanisms in stochastic open magnetic field lines in tokamaks

2021 ◽  
Author(s):  
Min-Gu Yoo ◽  
Weixing Wang ◽  
Edward A Startsev ◽  
Chenhao Ma ◽  
S Ethier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Plasma Transport ◽  
Transport Mechanisms ◽  
Field Lines ◽  
Open Magnetic Field

scholarly journals Formation of coronal rain triggered by impulsive heating associated with magnetic reconnection

2019 ◽  
Vol 630 ◽  
pp. A123 ◽  
Author(s):  
P. Kohutova ◽  
E. Verwichte ◽  
C. Froment
Keyword(s):  
Magnetic Reconnection ◽  
Thermal Instability ◽  
Flux Rope ◽  
Coronal Loops ◽  
Rain Event ◽  
Subsequent Formation ◽  
Standard Models ◽  
Field Lines ◽  
Impulsive Heating ◽  
Coronal Rain

Context. Coronal rain consists of cool plasma condensations formed in coronal loops as a result of thermal instability. The standard models of coronal rain formation assume that the heating is quasi-steady and localised at the coronal loop footpoints. Aims. We present an observation of magnetic reconnection in the corona and the associated impulsive heating triggering formation of coronal rain condensations. Methods. We analyse combined SDO/AIA and IRIS observations of a coronal rain event following a reconnection between threads of a low-lying prominence flux rope and surrounding coronal field lines. Results. The reconnection of the twisted flux rope and open field lines leads to a release of magnetic twist. Evolution of the emission of one of the coronal loops involved in the reconnection process in different AIA bandpasses suggests that the loop becomes thermally unstable and is subject to the formation of coronal rain condensations following the reconnection and that the associated heating is localised in the upper part of the loop leg. Conclusions. In addition to the standard models of thermally unstable coronal loops with heating localised exclusively in the footpoints, thermal instability and subsequent formation of condensations can be triggered by the impulsive heating associated with magnetic reconnection occurring anywhere along a magnetic field line.

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