Evolution and breaking of relativistic upper-hybrid waves in a cold Magnetized plasma

The space-time evolution of relativistic upper-hybrid oscillations and waves, in a cold homogeneous magnetized plasma, has been studied analytically and by performing simulations. A complete solution of the fluid-Maxwell equations has been provided, using Dawson Sheet Model. It is found that in the case of stationary oscillations, the oscillation frequency becomes a function of space which results in phase mixing, whereas the traveling wave solution does not exhibit phase mixing; it is like an Akhiezer-Polovin mode in an unmagnetized cold plasma. Further, a numerical 1-1/2 D code, based on Dawson Sheet Model, has been developed to simulate the evolution of the relativistic upper-hybrid mode. Benchmarking of the code has been done by verifying the previous theoretical results, available in the literature. The sensitivity of the traveling waves, towards a small amplitude longitudinal perturbation, has been studied and it is observed that waves break via the process of phase mixing when subjected to a small amplitude perturbation. An analytical expression for this breaking time has been derived and verified via simulations, for an entire range of input parameters. (author)