Three-dimensional structure of electron holes driven by an electron beam

Using 3-D particle-in-cell (PIC) simulations we studied the structure and temporal behavior of electron holes (e-holes) in a magnetized plasma driven by an electron beam. When e-holes are fully evolved from high-frequency waves in a time of about a few tens of electron plasma periods, most of the wave energy in the plasma resides in them. Parallel to the ambient magnetic field B-o, the potential distribution of an e-hole is approximately a Gaussian, and the scalelength l(z) is only a few Debye lengths when determined by the effective temperature of the beam-modified electron distribution function. Transverse to B-o, the potential distribution tends to have a flat top, which makes it difficult to fit a Gaussian distribution, but the scalelengths at which the potential decays in the transverse directions (l(x) and l(z)) are found to be only slightly longer than l(z). The passages of electron holes monitored at several points in the simulation volume has the signature of bipolar parallel electric field and unipolar perpendicular electric-field pulses as measured from FAST and POLAR. The eventual decay of e-holes is accompanied by the generation of lower hybrid (lh) waves.