Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations

TL;DR

This paper investigates the effects of a constant external magnetic field on relativistic plasma oscillations, revealing that it cannot prevent the loss of smoothness in these oscillations, unlike in non-relativistic cases.

Contribution

It demonstrates that magnetic fields cannot generally prevent breaking in relativistic plasma oscillations, contrasting with known non-relativistic behavior, and identifies subclasses of globally smooth solutions.

Findings

Magnetic fields do not prevent breaking in relativistic plasma oscillations.

Relativistic plasma oscillations can lose smoothness despite small perturbations.

Certain subclasses of solutions remain globally smooth in time.

Abstract

It is shown that a constant external magnetic field, generally speaking, is not able to prevent breaking (loss of smoothness) of relativistic plasma oscillations, even if they are arbitrarily small perturbations of the zero steady-state. This result sharply differs from the non-relativistic case, for which it is possible to suppress the breaking of oscillations at any initial deviations by increasing the intensity of the magnetic field \cite {RCharx}. Nevertheless, even in the relativistic case, there are subclasses of solutions corresponding to solutions that are globally smooth in time.