Numerical simulation of constrained and unconstrained emission from an electron horseshoe distribution

When an electron beam is subject to significant magnetic compression, conservation of the magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of Auroral Kilometric Radiation (AKR) -- an intense RF emission sourced at high altitudes in the Earth's magnetosphere. We present results from a numerical investigation of RF emission from an electron beam with predefined horseshoe distribution injected into radially bounded and unbounded geometries. Both 2D and 3D versions of the particle-in-cell (PiC) code KARAT were used to conduct the analysis. RF emission was observed at a frequency close to the relativistic electron cyclotron frequency. 3D results from the bounded case show a backward wave instability which is more resilient to Doppler broadening than forward wave coupling. This has important implications where a cold tenuous plasma is present.