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Steady-state treatment of relativistic electron beam erosion

1980; AIP Publishing; Volume: 23; Issue: 12 Linguagem: Inglês

10.1063/1.862943

2163-4998

W.M. Sharp, Mártin Lampe,

Magnetic confinement fusion research

The head of a relativistic electron beam propagating into un-ionized or weakly ionized gas is not self-pinched and expands freely, causing the beam to take on a ’’trumpet’’ shape. The region where the beam pinches, referred to as the ’’pinch point’’, moves steadily back into the beam because of the reduced ionization rate at the expanding beam head and energy loss to the induced electric field. This beam head ’’erosion’’ is modeled by assuming that the axial beam profile is stationary in a reference frame moving with the pinch point. This assumption allows the beam equations to be written in time-independent form, and radial averaging then yields a set of one-dimensional ordinary differential equations for the beam radius and energy, the mean pinch force, and the background conductivity. Solution of these equations with appropriate boundary conditions gives both the erosion rate and the beam axial structure. The results of extensive numerical calculations are presented, along with analytic estimates of the erosion rate, degree of current neutralization, and axial scale lengths.