# Anomalous and Nonlinear Effects in Inductively Coupled Plasmas

Abstract (Summary)

In this thesis the nonlinear effects and heating are studied in inductively coupled plasma (ICP) in a regime of anomalous skin effect (nonlocal regime). In this regime the thermal motion of plasma electrons plays an important role,
significantly influencing the processes associated with the penetration of electromagnetic field into plasma, such as the ponderomotive effect and heating of plasma by the field. We have developed a linear kinetic theory that describes the electron dynamics in ICP taking into account the electron thermal motion and collisions of electrons. This theory yields relatively simple expressions for the electron current in plasma, the ponderomotive force, and plasma heating.
It describes correctly the thermal reduction of ponderomotive force in the nonlocal regime, which has been previously observed experimentally. It also describes the collisionless heating of plasma due to resonant interaction between the electromagnetic wave and plasma electrons. There is a good overall agreement of the results of our theory with the experimental data on ponderomotive
force and plasma heating. Using our theory, we predicted a new effect of reduction of plasma heating compared to the purely collisional value,
occurring at low frequencies. This effect has not been previously reported.
The nonlinear effects of the electromagnetic field on the electron distribution function and on plasma heating, that are not accounted for in the linear kinetic theory, have been studied using a quasilinear kinetic theory, also developed in this thesis. Within the quasilinear approximation we have formulated the system of equations describing the slow response of plasma electrons to the
fast oscillating electromagnetic field. As an example, these equations have been solved in the simplest case of cold plasma with collisions, and the nonlinear perturbation of the electron distribution function and its effect on the plasma
heating have been found. It has been shown that the nonlinear modification of plasma heating occurs mainly due to the nonlinear effect of the magnetic component of the electromagnetic field. It has also been shown that at high frequencies the nonlinear effects vanish, and the heating is well described by the linear theory.
To verify the predicted new effect of plasma heating reduction at low frequencies, as well as to investigate the nonlinear effect of the magnetic field on plasma heating for arbitrary amplitudes of electromagnetic field in plasma, we have developed a 1d3v Particle-In-Cell (PIC) numerical simulation code with collisions. The collisions were implemented into the PIC code using two different techniques: the direct Monte-Carlo technique for the electron-atom collisions, and the stochastic technique based on the Langevin equation for the electron-electron collisions. The series of numerical simulations by this code confirmed the results of our linear theory, particularly the effect of heating reduction at low frequencies that we predicted theoretically. Also, the nonlinear effects of electromagnetic field on plasma heating were studied using the PIC code in the cases of weak and strong electromagnetic fields. It has been
shown that in the case of weak electromagnetic fields (corresponding to weak nonlinearity) the nonlinear effects lead to some enhancement of heating (compared to the linear theory) at low frequencies, followed by a small reduction of
heating at higher frequencies. This observed nonlinear perturbation of heating in warm plasma with collisions is similar to that predicted by the quasilinear theory for the case of cold plasma with collisions. In the case of strong electromagnetic fields (corresponding to strong nonlinearity) the nonlinear effects lead to a further reduction of heating (compared to the linear theory) at low frequencies, as shown by the simulation, thus adding to the effect of reduction
of heating predicted by the linear theory. The nonlinear effects are shown to vanish at high frequencies, as expected.
Bibliographical Information:

Advisor:Hirose, Akira; Kaganovich, Igor; Koustov, Alexandre V. (Sasha); Pywell, Robert E.; Smolyakov, Andrei I.; Szmigielski, Jacek; Xiao, Chijin

School:University of Saskatchewan

School Location:Canada - Saskatchewan

Source Type:Master's Thesis

Keywords:plasma inductive discharge theory anomalous nonlocal particle in cell pic simulation ponderomotive heating kinetic

ISBN:

Date of Publication:12/19/2003