A study of the amplification of laser and VLF waves using a simple pendulum model

Abstract

The Lorentz force equation governing the interaction between radiation and charged particles in the presence of a static magnetic field can be reduced to the form of the simple pendulum equation, when applied to the Free Electron Laser (FEL) and to the amplification of whistler waves in the magnetosphere. The first topic in this thesis is the start-up of an FEL with a compact design having a small, spatial undulator period, many periods, and a small undulator field strength. Under these conditions, the number of photons spontaneously emitted into the resonator mode each pass is so small that a classical field cannot be established. Quantum fluctuations affect the wave- particle interaction and therefore diminish weak field gain. An FEL start-up condition, several orders of magnitude more restrictive than determined by quantum recoil alone, is derived from the photon rate equation. The next topic is the evolution of a weak, classical radiation field driven by a long electron pulse