Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

1994 ◽  
Vol 1 (12) ◽  
pp. 3826-3842 ◽  
Author(s):  
R. Balescu ◽  
Hai‐Da Wang ◽  
J. H. Misguich
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Langevin Equation ◽  
Charged Particles ◽  
Equation Versus ◽  
Stochastic Magnetic Field

scholarly journals CLASSICAL DIAMAGNETISM REVISITED

2010 ◽  
Vol 24 (30) ◽  
pp. 2899-2910 ◽  
Author(s):  
ARNAB SAHA ◽  
SOURABH LAHIRI ◽  
A. M. JAYANNAVAR
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Friction Coefficient ◽  
Langevin Equation ◽  
Charged Particles ◽  
Real Space ◽  
Fluctuation Theorems ◽  
Infinite Systems ◽  
Langevin Approach ◽  
Jarzynski Equality

The well-known Bohr–van Leeuwen Theorem states that the orbital diamagnetism of classical charged particles is identically zero in equilibrium. However, results based on real space–time approach using the classical Langevin equation predicts non-zero diamagnetism for classical unbounded (finite or infinite) systems. Here we show that the recently discovered Fluctuation Theorems, namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly predicts a free energy that depends on magnetic field as well as on the friction coefficient, in outright contradiction to the canonical equilibrium results. However, in the cases where the Langevin approach is consistent with the equilibrium results, the Fluctuation Theorems lead to results in conformity with equilibrium statistical mechanics. The latter is demonstrated analytically through a simple example that has been discussed recently.

scholarly journals KINETIC EQUATION IN A STOCHASTIC MAGNETIC FIELD

1980 ◽  
Vol 29 (10) ◽  
pp. 1254
Author(s):  
XIA MENG-FEN ◽  
HU HUI-LING
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Stochastic Magnetic Field

Cross field thermal transport in highly magnetized plasmas

1992 ◽  
Vol 437 (1899) ◽  
pp. 55-65 ◽  
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Kinetic Equation ◽  
Mass Transport ◽  
Heat Transport ◽  
Electrostatic Interactions ◽  
Charged Particles ◽  
Non Local ◽  
Field Lines ◽  
The Magnetic Field

We construct a non-local kinetic equation for a plasma in a very strong magnetic field B where the charged particles coincide with their guiding centres and have zero drifts. It is shown that, although in this system mass transport occurs only along the field lines, heat transport cannot be confined only in the direction of the magnetic field. In particular, we estimate that a finite cross field heat flux scaling as 3/2 n ∂ T /∂ t = ∂( k ∞ ⊥ ∂ T /∂ x )∂ x ; k ∞ ⊥ = 3/2π ½ ( n 2 e 4 / m ½ T 3/2 ) L 2 ⊥ can be driven by collisions between like particles at the limit B → ∞. Hence, the classical B -2 dependence of k ⊥ must be modified to comply with this result. The choice of the cut-off length L ⊥ , representing the distance across B over which electrostatic interactions can be sustained, is discussed briefly at the end of the present work.

Stochastic magnetic field lines diffusion in a toroidal configuration (Tokamak)

2000 ◽  
Vol 12 (2) ◽  
pp. 145-153 ◽  
Author(s):  
R. Tabet ◽  
H. Imrane ◽  
D. Saifaoui ◽  
A. Dezairi ◽  
F. Miskane
Keyword(s):  
Magnetic Field ◽  
Field Lines ◽  
Stochastic Magnetic Field

scholarly journals 46. The störmertron

1958 ◽  
Vol 6 ◽  
pp. 446-447
Author(s):  
Willard H. Bennett
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Mercury Vapor ◽  
Electron Gun ◽  
Conducting Film ◽  
New Developments ◽  
Electrically Conducting ◽  
The Earth ◽  
Magnetic Dipole Field ◽  
Glass Tubes

A tube has been developed in which the shapes of streams of charged particles moving in the earth's magnetic field can be produced accurately to scale. The tube has been named the Störmertron in honor of Carl Störmer who calculated many such orbits. New developments which have made this tube possible include a method for coating the inside of large glass tubes with a transparent electrically conducting film, and an electron gun producing gas-focused streams in less than ½ micron of mercury vapor, a nearly vapor-free grease joint, and a nearly vapor-free carbon black. The magnetic dipole field of the earth is simulated with an Alnico magnet capped with properly shaped soft iron caps. The stream is deflected using two pairs of yoke coils near the gun.

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