Particle-in-cell simulations of azimuthal instabilities in relativistic electron layers

Negative-mass and cyclotron-maser instabilities in electron rings or layers lead to breaking of the azimuthal symmetry. The short-wavelength modes are generally thought to be harmless since they saturate by increasing the thickness and energy spread of the original layer. The long-wavelength (or low-order) modes, on the other hand, can be devastating to the integrity of the layer. Linear theory has predicted that the growth rates for negative-mass instability modes are proportional to the azimuthal mode number, so that the low-order modes would not be important until quite late in time. In contrast, the simulations presented here show that low-order modes can arise quite early in time, out of nonlinear states of the high-order modes. At low currents, azimuthal instabilities can be effectively suppressed (as predicted by linear theory) by starting out with a thicker layer, with the particle energy varying with radius. The dispersion in circulation frequency so introduced effectively damps all growing waves. Unfortunately, at high currents (field reversal factors zetaapprox. >2%), making the layer thicker does not help. All growth rates are faster at the higher densities, and the high mode numbers grow to substantial amplitudes before damping is effective. Beating of nearby high-order modes gives rise to global modes that destroy the layer within a few rotations