Outline of Prof. Mike Lieberman's lectures:

The Dynamics of Fermi Acceleration:
From Cosmic Rays to Discharge Heating.

Michael A. Lieberman
Department of Electrical Engineering and Computer Sciences
University of California, Berkeley

A ball bounces back and forth between a fixed and a vibrating wall.
Enrico Fermi introduced this simple problem in 1949 to explain the origin
of cosmic rays. Can the ball continuously gain energy, or is there an
upper bound to the energy gained? Is the motion regular or chaotic?
How can the motion of the ball be described?

In this series of lectures, Fermi acceleration will be used as a paradigm
to understand chaos in conservative and dissipative dynamical systems.
The main application will be to plasma physics, including the origin
of cosmic rays, controlled fusion research, and the fabrication of
microchips using plasma processing.

Lecture 1. Introduction, Overview and Basic Concepts

Cosmic rays: their discovery, properties and proposed origins.
Fermi acceleration and stochastic heating. Simplified Fermi mapping.

Summary of transformation theory of mechanics: canonical transformations,
motion in phase space, action-angle variables. One degree of freedom
integrable systems.

Introduction to dynamical chaos: Near-integrable systems with two or
more degrees of freedom. The example of Fermi acceleration. Dissipative
systems and strange attractors.

Lecture 2. Transition to Global Stochasticity and Diffusion

Transition to Global Stochasticity: The Fermi and standard mappings. Fixed
points and their stability. Resonance overlap. KAM curves as adiabatic
barriers to heating by Fermi acceleration.

Diffusion in action space. The Fokker-Planck equation, transport
coefficients, steady state and transient solutions. The effects of
correlations. Dissipative Fermi acceleration. Transient chaos and
invariant distributions on strange attractors.

Lecture 3. Applications of Fermi Acceleration to Plasma Physics

Plasma heating by Fermi acceleration. Electron cyclotron discharges.
Plasma-assisted microelectronics technology. Heating of capacitive and
inductive discharges used for microelectronics fabrication.

A reference for much of the material in these lectures are the two texts:

1. A.J. Lichtenberg and M.A. Lieberman, "Regular and Chaotic Dynamics,"
2nd Ed., Springer-Verlag, New York, 1991.

2. M.A. Lieberman and A.J. Lichtenberg, "Principles of Plasma
Discharges and Materials Processing," J. Wiley and Sons, New York,
1994.