The interplay of regularizing factors in the model of upper hybrid oscillations of cold plasma

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 B0 and a sufficiently large collisional factor ν 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 B0 and ν, we establish a criterion for maintaining the global smoothness of the solution. Namely, for fixed B0 and ν>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 |B0| 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 |B0|, the solution is characterized by oscillatory damping regardless of the value of the intensity factor ν.