THE VLASOV–POISSON SYSTEM WITH STRONG MAGNETIC FIELD IN QUASINEUTRAL REGIME

2003 ◽  
Vol 13 (05) ◽  
pp. 661-714 ◽  
Author(s):  
F. GOLSE ◽  
L. SAINT-RAYMOND
Keyword(s):  
Magnetic Field ◽  
Space Variable ◽  
Debye Length ◽  
Time Variable ◽  
Larmor Radius ◽  
Incompressible Euler Equation ◽  
Variable Control ◽  
Self Consistent ◽  
Constant External Magnetic Field ◽  
Incompressible Euler

Consider the motion of a gas of electrons with a background of ions, subject to the self-consistent electric field and to a constant external magnetic field. As the Debye length and the Larmor radius vanish at the same rate, the asymptotic current density is governed by the 2D1/2 incompressible Euler equation. Establishing limit requires to overcome various difficulties: compactness with respect to the space variable, control of large velocities, oscillations in the time variable. Yet, for particular initial data, the simultaneous gyrokinetic and quasineutral approximation is completely justified.

Effects of repeated interactions and correlational disintegration on kinetic and transport properties of a non-neutral plasma in strong fields

1990 ◽  
Vol 44 (1) ◽  
pp. 167-190 ◽  
Author(s):  
Alf H. Øien
Keyword(s):  
Magnetic Field ◽  
Particle Transport ◽  
Axial Magnetic Field ◽  
Debye Length ◽  
Electron Plasma ◽  
Larmor Radius ◽  
Equilibration Time ◽  
Cylindrically Symmetric ◽  
Electric Potentials ◽  
Good Agreement

Collisions in a cylindrically symmetric non-neutral (electron) plasma, where the Larmor radius is much smaller than the Debye length, and the consequent particle transport, are studied. The plasma is confined radially by a strong axial magnetic field and axially by electric potentials. Hence two particles may interact repeatedly. Eventually they drift too far away from each other poloidally to interact any more, owing to shear in the E × B drift. The consequent build-up of correlation is limited by correlational disintegration due to collisions with ‘third particles’ between the repeated interactions. A kinetic equation including these effects is derived, and the cross-field particle transport along the density gradient is found. An associated equilibration time is shown to scale as B and to be in good agreement with the experimentally obtained values of Briscoli, Malmberg and Fine.

Anomalous temperature relaxation and particle transport in a strongly non-unifrom, fully in ionized Plasma in a stromg mangnetic field

1995 ◽  
Vol 53 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Alf H. Øien
Keyword(s):  
Magnetic Field ◽  
Particle Transport ◽  
Transport Theory ◽  
Debye Length ◽  
Larmor Radius ◽  
Collision Integrals ◽  
Ion Interactions ◽  
Electrons And Ions ◽  
Temperature Relaxation ◽  
The Magnetic Field

In classical kinetic and transport theory for a fully ionized plasma in a magnetic field, collision integrals from a uniform theory without fields are used. When the magnetic field is so strong that electrons may gyrate during electron—electron and electron—ion interactions, the form of the collision integrals will be modified. Another modification will stem from strong non-uniformities transverse to the magnetic field B. Using collision terms that explicitly incorporate these effects, we derive in particular the temperature relaxation between electrons and ions and the particle transport transverse to the magnetic field. In both cases collisions between gyrating electrons, which move along the magnetic field, and non-gyrating ions, which move in arbitrary directions at a distance transverse to B from the electrons larger than the electron Larmor radius but smaller than the Debye length, give rise to enhancement factors in the corresponding classical expressions of order In (mion/mel).

scholarly journals Mean-field Theory of the Meissner Effect in Bulk Revisited

2020 ◽  
Author(s):  
Ladislaus Banyai
Keyword(s):  
Magnetic Field ◽  
Mean Field Theory ◽  
Mean Field ◽  
Meissner Effect ◽  
Transverse Current ◽  
Self Consistent ◽  
Full Compensation ◽  
London Equation ◽  
Current Interaction ◽  
Constant External Magnetic Field

We show that the implementation of the 1/c² transverse current-current interaction between electrons into the standard self-consistent electron BCS model in bulk under thermal equilibrium ensures in the stable superconductive phase the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons i.e. one has an ideal diamagnet. However, no proof of the phenomenological London equation emerges within the bulk approach.

scholarly journals Mean-field BCS theory of the Meissner effect in bulk revisited

2021 ◽  
Vol 94 (1) ◽  
Author(s):  
Ladislaus Alexander Bányai
Keyword(s):  
Magnetic Field ◽  
Thermal Equilibrium ◽  
Mean Field ◽  
Meissner Effect ◽  
Bcs Theory ◽  
Transverse Current ◽  
Self Consistent ◽  
Full Compensation ◽  
Current Interaction ◽  
Constant External Magnetic Field

Abstract We show that the implementation of the $$1/ c^2 $$ 1 / c 2 transverse current–current interaction between electrons resulting from the non-relativistic QED into the standard self-consistent electron BCS model in bulk under thermal equilibrium in the stable superconductive phase ensures the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons, i.e. one has an ideal diamagnet. GraphicAbstract

ORBIT ANALYZER PROBES FOR THE MEASUREMENT OF PLASMA TEMPERATURES

1967 ◽  
Vol 45 (9) ◽  
pp. 3055-3064 ◽  
Author(s):  
D. J. Loughran ◽  
L. Schott ◽  
H. M. Skarsgard
Keyword(s):  
Magnetic Field ◽  
Debye Length ◽  
Current Collector ◽  
Boltzmann Distribution ◽  
Electron Velocity ◽  
Larmor Radius ◽  
Ion Temperature ◽  
Magnetic Analyzer ◽  
Current Characteristics ◽  
The Magnetic Field

An investigation is presented of two different probes, of the magnetic analyzer type, in which the magnetic field used for analysis of the particle orbits is also present in the plasma. Both probes employ a current collector whose distance from the aperture plane is adjustable. One probe (the charge-selective probe) collects charged particles of one sign, while theother (the charge-insensitive probe) collects particles of both signs. Assuming a Maxwell–Boltzmann distribution of electrons, the current collection characteristics are calculated for each probe. The use of these current characteristics for the measurement of the electron temperature is discussed. A procedure is also given for obtaining the mean electron velocity perpendicular to the magnetic field in the case of a non-Maxwellian velocity distribution. Finally, methods for measuring the ion temperature are presented for the special case of a small Debye length compared with the ion Larmor radius.

scholarly journals Mean-Field Theory of the Meissner effect in Bulk Revisited

2020 ◽  
Author(s):  
Ladislaus Banyai
Keyword(s):  
Magnetic Field ◽  
Thermal Equilibrium ◽  
Mean Field Theory ◽  
Mean Field ◽  
Meissner Effect ◽  
Transverse Current ◽  
Self Consistent ◽  
Full Compensation ◽  
Current Interaction ◽  
Constant External Magnetic Field

We show that the implementation of the 1/c² transverse current-current interaction between elec- trons into the standard self-consistent electron BCS model in bulk under thermal equilibrium in the stable superconductive phase ensures the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons.

scholarly journals Fluctuation Relations for Dissipative Systems in Constant External Magnetic Field: Theory and Molecular Dynamics Simulations

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 146
Author(s):  
Alessandro Coretti ◽  
Lamberto Rondoni ◽  
Sara Bonella
Keyword(s):  
Magnetic Field ◽  
Molecular Dynamics ◽  
External Magnetic Field ◽  
Molecular Dynamics Simulations ◽  
Nonequilibrium Molecular Dynamics ◽  
Dissipative Systems ◽  
Common Belief ◽  
Fluctuation Relations ◽  
Dynamics Simulations ◽  
Constant External Magnetic Field

We illustrate how, contrary to common belief, transient Fluctuation Relations (FRs) for systems in constant external magnetic field hold without the inversion of the field. Building on previous work providing generalized time-reversal symmetries for systems in parallel external magnetic and electric fields, we observe that the standard proof of these important nonequilibrium properties can be fully reinstated in the presence of net dissipation. This generalizes recent results for the FRs in orthogonal fields—an interesting but less commonly investigated geometry—and enables direct comparison with existing literature. We also present for the first time a numerical demonstration of the validity of the transient FRs with nonzero magnetic field via nonequilibrium molecular dynamics simulations of a realistic model of liquid NaCl.

scholarly journals Numerical Simulation of the Time Evolution of Small-Scale Irregularities in the F-Layer Ionospheric Plasma

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
O. V. Mingalev ◽  
G. I. Mingaleva ◽  
M. N. Melnik ◽  
V. S. Mingalev
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Ionospheric Plasma ◽  
Debye Length ◽  
Small Scale ◽  
System Of Equations ◽  
Applied Model ◽  
Positive Ions ◽  
F Region ◽  
Small Scale Irregularity

Dynamics of magnetic field-aligned small-scale irregularities in the electron concentration, existing in the F-layer ionospheric plasma, is investigated with the help of a mathematical model. The plasma is assumed to be a rarefied compound consisting of electrons and positive ions and being in a strong, external magnetic field. In the applied model, kinetic processes in the plasma are simulated by using the Vlasov-Poisson system of equations. The system of equations is numerically solved applying a macroparticle method. The time evolution of a plasma irregularity, having initial cross-section dimension commensurable with a Debye length, is simulated during the period sufficient for the irregularity to decay completely. The results of simulation indicate that the small-scale irregularity, created initially in the F-region ionosphere, decays accomplishing periodic damped vibrations, with the process being collisionless.

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