Nonlinear Trivelpiece–Gould waves: Recurrence, harmonic cascade, and sidebands

Abstract

A theoretical and experimental study of Trivelpiece–Gould waves propagating in a magnetized plasma column is presented in this paper. In the experiments, these waves are excited by a radio frequency (rf) source, which also serves to create the plasma. Observation of nonlinear effects includes space and time recurrence effects, a wave spectrum containing a large number (up to 25) harmonics, and low-frequency sidebands. The theoretical model explains the recurrence effects as a consequence of multiple nonlinear interactions between the fundamental wave and its harmonics. A good agreement is found between theory and the experiments.

Quantum Trivelpiece–Gould waves in a magnetized dense plasma

“…We show that, in the classical limit, h → 0, the dispersion relation reduces to the expression derived in Ref. [17]. Second, we will consider the existence of Trivelpiece-Gould solitons in a quantum plasma cylinder and discuss the main differences with respect to the classical solutions.…”

“…17 The latter shows that the Trivelpiece-Gould waves propagate at frequencies of the order of p . 17 The latter shows that the Trivelpiece-Gould waves propagate at frequencies of the order of p .…”

“…where k n = nπ/L. Notice that we have replaced the Fermi speed by the classical thermal speed, which is the relevant quantity in this classical limit [17]. The latter shows that the Trivelpiece-Gould waves propagate at frequencies of the order of ω p .…”

“…Following the steps of Ref. [17], we insert the development ( 2) in ( 1) and, after multiplying every equation by 1/2πJ m (k ⊥ r)r exp(−imθ) and integration over the transversal direction, we derive the nonlinear set of one-dimensional equations…”

“…17. More specifically, we consider the propagation of electrostatic waves, with frequency near the electron plasma frequency, in a magnetized plasma column.…”