Computational modeling of stabilizing the instability of a relativistic electron beam in a dense plasma

Analytical treatment of the force acting on a relativistic electron beam spreading in dense gas plasma by the ohmic plasma channel

“…The interest in relativistic electron beam (REB) spreading in dense and rarefied gas plasma media has been greatly interest over the past decades by novel concepts in laboratory and plasma sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. It is well known that the Ohmic and ionic plasma channel plays a central role in the transport of relativistic electron beam through gas plasma [15][16][17][18][19][20].…”

10.1007/s11452-008-2003-7

“…According to the method of integration over initial data [2,3], the general solution to the Vlasov equation for the distribution functions f α can be written as (3) Here, z α ( t , z 0 , p 0 ) and p α ( t , z 0 , p 0 ) are the solutions to the set of characteristic relativistic Vlasov equations (4) with the initial conditions z α | t = 0 = z 0 ∈ (-∞ , + ∞ ), p α | t = 0 = p 0 ∈ (-∞ , + ∞ ) , and the velocities v α of the beam and plasma electrons are described by the expressions (5) We assume that, in the system under consideration, the initial perturbation occurs on a characteristic longitudinal scale l and also that the eigenfunctions ϕ s ( r ⊥ ) and eigenvalues of the waveguide cross section are known. Under these assumptions, the polarization potential ψ can be represented as a double series, (6) where k z = 2π/l is the fundamental longitudinal wavenumber.…”