Tj. Schep et al., ELECTRON ACCELERATION BY NONLINEAR PLASMA-WAVES EXCITED BY A RELATIVISTIC ELECTRON PULSE, Journal of physics. D, Applied physics, 28(6), 1995, pp. 1078-1082
The excitation of travelling nonlinear Langmuir waves in a plasma by a
relativistic electron bunch is considered. The nonlinear excitation i
s described as relativistic oscillations of the momentum of plasma ele
ctrons in effective potentials produced by the bunch and by the pertur
bation of the electron density of the plasma. The condition for the op
timal excitation of the wave yields a relation between the density of
the plasma, the density of the bunch and the length of the bunch. Nume
rical results support the theoretical analysis and demonstrate a deep
nonlinear modulation of the electron plasma density and excitation of
a large-amplitude longitudinal field at realistic plasma and electron
pulse parameters. The back action of the wave field on the bunch is co
nsidered. It is shown that sharp peaks develop in its density distribu
tion.