Relativistic electron beams in conducting solids and dense plasmas: Approximate analytical theory

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Abstract
The response of a conducting medium to an intense electron beam is investigated. For this purpose Maxwell’s equations in cylindrical geometry are approximately solved analytically. The approximation is valid if the pulse duration of the beam is intermediate between two characteristic relaxation times of the medium, viz. the momentum relaxation time and the magnetic diffusion time. This condition is well satisfied in present experiments which use picosecond or subpicosecond laser pulses to generate the electron beam. The theory allows one to calculate the spatial and temporal profiles of the return current and the radial current induced in the conductor, as well as that of the azimuthal magnetic field of the combined beam and return currents. This application of the theory is illustrated by way of example. The theory is applicable to a solid conductor as well as to a dense high-temperature plasma and may be useful in research relating to the fast-ignitor scheme and for clarifying features of recent experiments with femtosecond laser pulses.