KINETIC EQUATION FOR A HOMOGENEOUS PLASMA IN A UNIFORM MAGNETIC FIELD

1964 ◽  
Vol 42 (10) ◽  
pp. 1969-2021 ◽  
Author(s):  
M. J. Haggerty ◽  
L. G. De Sobrino
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Uniform Magnetic Field ◽  
Single Species ◽  
Field Approximation ◽  
Stationary Solutions ◽  
Equilibrium Distributions ◽  
H Theorem ◽  
The One ◽  
Static Uniform Magnetic Field

The theory of Prigogine and Balescu has been applied to a homogeneous single-species plasma in a static uniform magnetic field. A kinetic equation has been obtained for the one-particle velocity distribution, which is assumed initially isotropic in directions perpendicular to the field. The only stationary solutions of the kinetic equation are the Maxwellian equilibrium distributions, and an H theorem has been established. The neglect of "collisions" of the order of duration of one cyclotron period or less (a strong magnetic-field approximation) modifies the kinetic equation so that it no longer predicts any relaxation of the velocity components parallel to the magnetic field. The assumptions and approximations of the theory are stated, and are discussed in some detail.

Onsager's Relation and Other Results for Relativistic Electrons in Magnetic Fields

1990 ◽  
Vol 45 (7) ◽  
pp. 847-850
Author(s):  
A. Holas ◽  
S. Olszewski ◽  
D. Pftrsch
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Correspondence Principle ◽  
Relativistic Equation ◽  
Relativistic Electrons ◽  
Expectation Values ◽  
Relativistic Case ◽  
Expectation Value ◽  
The One ◽  
Static Uniform Magnetic Field

AbstractOnsager's result concerning the quantization of the magnetic flux enclosed by the orbit of an electron moving in a static uniform magnetic field is shown to hold also in the relativistic case, and not to be restricted to the regime considered by Onsager in which the correspondence principle can be applied. The results obtained via the correspondence principle and via expectation values differ, however, in the deails. It is shown also that the eigenenergies and eigenfunctions of Dirac's relativistic equation for an electron in a static non-uniform and arbitrarily strong magnetic field may be obtained directly from the solutions of Schrödinger's non-relativistic equation. In this case the expectation value of an observable depending on coordinates only equals the one calculated directly with the non-relativistic eigenfunctions.

scholarly journals Realization of Maxwell’s Hypothesis: A Heat-Electric Conversion in Contradiction to the Kelvin Statement

2019 ◽  
Author(s):  
Xinyong Fu ◽  
Zitao Fu
Keyword(s):  
Uniform Magnetic Field ◽  
Room Temperature ◽  
Electric Energy ◽  
Ambient Air ◽  
Second Law ◽  
Heat Reservoir ◽  
Net Migration ◽  
The One ◽  
A Charge ◽  
Static Uniform Magnetic Field

In a vacuum tube, two identical and parallel Ag-O-Cs surfaces, A and B, with a work function 0.8eV, ceaselessly emit thermal electrons at room temperature. The thermal electrons are controlled by a static uniform magnetic field (a magnetic demon), and the number of electrons migrate from A to B exceeds the one from B to A (or vice versa). The net migration from A to B quickly results in a charge distribution, with A charged positively and B negatively. A potential difference between A and B emerges, and the tube outputs an electric current and a power to a load (a resistance, e.g.). The ambient air is a single heat reservoir in the experiment, and all the heat extracted by the tube from the air is converted into electric energy without producing other effects. We believe the experiment is in contradiction to the Kelvin statement of the second law.

scholarly journals Realization of Maxwell’s Hypothesis: A Heat-Electric Conversion in Contradiction to the Kelvin Statement

2016 ◽  
Author(s):  
Xinyong Fu ◽  
Zitao Fu
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Room Temperature ◽  
Electric Energy ◽  
Second Law Of Thermodynamics ◽  
Ambient Air ◽  
The Other ◽  
Second Law ◽  
Heat Reservoir ◽  
Static Uniform Magnetic Field

In a vacuum tube, two identical and parallel Ag-O-Cs surfaces, with a work function of approximately 0.8eV, ceaselessly emit thermal electrons at room temperature. The thermal electrons are so controlled by a static uniform magnetic field that they can fly only from one Ag-O-Cs surface to the other, resulting in a potential difference and an electric current, and transferring a power to a resistance outside the tube. The ambient air is a single heat reservoir in the experiment, and all the heat extracted by the tube from the air is converted into electric energy without producing any other effect. The authors maintain that the experiment is in contradiction to the Kelvin statement of the second law of thermodynamics.

scholarly journals Realization of Maxwell’s Hypothesis: A Heat-Electric Conversion in Contradiction to the Kelvin Statement

2019 ◽  
Author(s):  
Xinyong Fu ◽  
Zitao Fu
Keyword(s):  
Uniform Magnetic Field ◽  
Room Temperature ◽  
Electric Energy ◽  
Ambient Air ◽  
Second Law ◽  
Heat Reservoir ◽  
Net Migration ◽  
The One ◽  
A Charge ◽  
Static Uniform Magnetic Field

In a vacuum tube, two identical and parallel Ag-O-Cs surfaces, A and B, with a work function of 0.8eV, ceaselessly emit thermal electrons at room temperature. The thermal electrons are controlled by a static uniform magnetic field (a magnetic demon), and the number of electrons migrate from A to B exceeds the one from B to A, (or vice versa). The net migration from A to B quickly results in a charge distribution: A charged positively and B negatively. A potential difference between A and B emerges, and the tube outputs ceaselessly an electric current and a power to a resistance (a load) and cools itself slightly. The ambient air is a single heat reservoir in the experiment, and all the heat extracted by the tube from the air is converted into electric energy without producing other effect. We believe the experiment is in contradiction to the Kelvin statement of the second law.

BINARY CORRELATION FUNCTION FOR A HOMOGENEOUS PLASMA IN A UNIFORM MAGNETIC FIELD

1965 ◽  
Vol 43 (1) ◽  
pp. 122-130 ◽  
Author(s):  
M. J. Haggerty
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Velocity Distribution ◽  
Spatial Correlation ◽  
Particle Velocity ◽  
Uniform Magnetic Field ◽  
Spatial Correlation Function ◽  
Binary Correlation ◽  
Binary Correlation Function ◽  
The One

Previous work on the application of the theory of Prigogine and Balescu to a homogeneous single-species plasma in a static uniform magnetic field has been extended. An equation for the binary correlation function has been obtained in terms of the one-particle velocity distribution, which is in turn determined by the kinetic equation previously derived. Equations for the binary spatial correlation function and the binary correlation function for the guiding centers have also been obtained. It is demonstrated that the binary spatial correlation function represents the well-known Debye-screened equilibrium correlations when the one-particle velocity distribution is the equilibrium distribution.

Sign in / Sign up

Export Citation Format

Share Document