The Interplay of Regularizing Factors in the Model of Upper Hybrid Oscillations of Cold Plasma

TL;DR

This paper investigates how magnetic fields and collisions influence the stability and oscillatory behavior of upper hybrid oscillations in cold plasma, establishing criteria for solution smoothness and analyzing the effects of varying parameters.

Contribution

It provides a criterion for the global smoothness of solutions in a nonlinear plasma model considering magnetic and collisional effects, and explores how these factors alter oscillation dynamics.

Findings

Magnetic field increases oscillation frequency and promotes oscillatory damping.

Collisions stabilize the medium and can suppress finite-time solution destruction.

Different regimes of oscillation behavior depend on the magnitudes of B_0 and ν.

Abstract

A one-dimensional nonlinear model of the so-called upper hybrid oscillations in a magnetoactive plasma is investigated taking into account electron-ion collisions. It is known that both the presence of an external magnetic field of strength $ B_0 $ and a sufficiently large collisional factor $ \nu $ help suppress the formation of a finite-dimensional singularity in a solution (breaking of oscillations). Nevertheless, the suppression mechanism is different: an external magnetic field increases the oscillation frequency, and collisions tend to stabilize the medium and suppress oscillations. In terms of the initial data and the coefficients $ B_0 $ and $ \nu $, we establish a criterion for maintaining the global smoothness of the solution. Namely, for fixed $ B_0 $ and $ \nu \ge 0 $ one can precisely divide the initial data into two classes: one leads to stabilization to the equilibrium and the other leads to the destruction of the solution in a finite time. Next, we examine the nature of the stabilization. We show that for small $ B_0 $ an increase in the intensity factor first leads to a change in the oscillatory behavior of the solution to monotonic damping, which is then again replaced by oscillatory damping. At large values of $ B_0 $, the solution is characterized by oscillatory damping regardless of the value of the intensity factor $ \nu $.