Investigation of focusing of relativistic electron and positron bunches moving in cold plasma. Final report

Abstract

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Nonlinear two-dimensional potential plasma wake waves

“…The corresponding linear problem was considered in [9], [10] and was found,in correspondance with previous result [11],that the magnetic field in wake wave in linear approximation is equal zero.This result connected with the absence of the energy flow in the wake wave and the absence of the vortexes in plasma electron motion in linear approximation.…”

“…Due to the symmetry of the problem the solution of equation ( 18) must be symmetric on y; ϕ 1 ′ (y = 0) = 0 due to E y = 0 at y = 0.The solution of the linear problem [9], [10] is concentrated in the region of the "trace",falling outside it exponentially. Adopting the same picture of the potential flow for considering case too,the solution of eq.…”

Investigation of focusing of relativistic electron and positron bunches moving in cold plasma. Final report

“…It was also noticed that in all three models of cold plasma-rigid electron bunch system, considered in [ 3 ] in linear approximation the wake field component of magnetic field is zero. The physical reason for this effect is the absence of energy flow in wake fields, (see also results of work [ 5 ] ) .…”