The linear Boltzmann equation with space periodic electric field

2010 ◽  
pp. 51-66 ◽  
Author(s):  
Mihai Bostan ◽  
Irene M. Gamba ◽  
Thierry Goudon
Keyword(s):  
Boltzmann Equation ◽  
Electric Field ◽  
Linear Boltzmann Equation ◽  
Periodic Electric Field

A theory of resonance rectification. The response of a spherical plasma probe to alternating potentials

1966 ◽  
Vol 290 (1421) ◽  
pp. 186-219 ◽  
Keyword(s):  
Boltzmann Equation ◽  
Electric Field ◽  
Linear Boltzmann Equation ◽  
Electron Trajectory ◽  
Neutral Particles ◽  
Alternating Electric Field ◽  
Probe System ◽  
Plasma Probe ◽  
Spherical Plasma ◽  
Steady Potential

It is shown theoretically how a conducting spherical probe behaves when it is immersed in a plasma, and has an alternating potential applied to it. The impedance of the probe and the rectified current which flows to it are derived as functions of the frequency of the applied potential. ‘Resonance’ phenomena are shown to occur at a frequency somewhat less than the plasma frequency. The Boltzmann-Vlasov equation, together with Maxwell's equations, are used to derive an integral equation governing the alternating electric field in the plasma. The steady potential in the sheath used in the time-dependent Boltzmann equation is taken from the work of Bernstein & Rabinowitz (1959). The alternating electric field is calculated on a computer, and from it, the impedance of the probe system is found as a function of frequency. The rectified electron current is obtained by a consideration of electron trajectory perturbations produced by the alternating electric field. This procedure is shown to be equivalent to an approximate solution of the non-linear Boltzmann equation. Collisions between electrons and heavy neutral particles are included through a simple relaxation term in the Boltzmann equation. External magnetic fields and uniform drifting of plasma past the probe are not considered.

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