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Nordsieck’s equation for a quasi-stationary relativistic electron beam propagating in a dense and rarefied gas-plasma medium along an external magnetic field

E. K. Kolesnikov^ab, A. S. Manuilov<sup>ab

a</sup> St. Petersburg State University, Mathematics and Mechanics Faculty
^b St. Petersburg State University, Research Institute of Mathematics and Mechanics

Abstract: An equation is derived for the envelope of a quasi-stationary relativistic electron beam propagating in a gas-plasma medium. It generalizes the well-known Nordsieck equation to the case of the presence of an external longitudinal magnetic field both under the beam transportation in an ohmic plasma and under ion focusing conditions. A formula for the rms radius of the beam at the stage of intense expansion with regard to a compensating ionic background, multiple scattering, and an external longitudinal magnetic field is found.

Received: 07.03.2013

 English version: Technical Physics, 2013, 58:11, 1696–1698

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