Volume 73A, number 3 PHYSICS LETTERS 17 September 1979 THE INTERACTION OF LARGE-AMPLITUDE PLASMA WAVES WITH A MOVING ELECTRON PLASMA Abraham C.-L CHIAN Instituto de Pesquisas Espaciais, INPE, Conseiho Nacional de Desenvoh’i,nento Cientifico e Tecnolôgico, CNPq, 122OO-Sa~oJosé dos Campos, SP, Brazil Received 25 June 1979 A fluid treatment of the interaction of large-amplitude plasma waves with a moving electron plasma is presented. An ex- act dispersion relation is obtained. In addition, a condition for the occurrence of wavebreaking for the subluminous waves is determined. Recently, there has been considerable interest in the kinetics of plasma turbulence. Drake et a!. [8] em- interaction of intense electromagnetic waves with plas- ployed a lagrangian formulation to show that the mas due to applications to laser—plasma interaction breaking of a large-amplitude wave due to relativistic and pulsar electrodynamics [1—5]. electron-mass variation can strongly enhance the anom- In this paper we study the interaction of large-am- alous absorption of the wave in the plasma. plitude electrostatic waves with a moving electron For a nonlinear travelling wave with phase velocity plasma. An exact (relativistic, nonlinear) dispersion re- less than the velocity of light, wavebreaking is expected lation is obtained by seeking a travelling wave solution whenever particles can reach velocities equal to the of one-dimensional fluid plasma equations. The case phase velocity [5]. Although we cannot follow the of a stationary plasma has been treated by Akhiezer et evolution of the wave after it breaks, we demonstrate al. [4]. In the present paper their work is extended to in this paper that the travelling wave solution is capa- allow arbitrary plasma stream velocities parallel to the ble of yielding a condition for the occurrence of wave- wave propagation. In addition, the problem of wave- breaking. breaking for the subluminous waves is analysed. The plasma is taken to be cold, infinite and homo- The effect of plasma motion is important in many geneous. The average electron charge and current den- nonlinear wave problems. Max [3] pointed out that an sities are neutralized by the ions, but the ion dynamics accurate description of strong waves in a pulsar plasma is ignored [4]. Since we are considering travelling wave requires the inclusion of arbitrary plasma stream veloc- solutions we can write the basic equations in terms of ities. Andreev and Silin [6] showed that the dynamic the combined space—time variable 0 = t — nz/c [3,4]. behaviour of large-amplitude waves generated by the For purely longitudinal waves the basic equations are resonant absorption process during laser—plasma inter- the relativistic equation of motion, the equation of action is very sensitive to plasma motion. continuity and the equation of Poisson: The phenomenon of wavebreaking plays an impor- d ( ~ e tant role in the absorption of nonlinear waves in plas- (1 — nv/c) ‘~‘~/ = — E, (1) mas. Zakharov et a!. [7] analysed the evolution of wavebreaking of nonlinear plasma waves by computer dN n d(Nv) = (2) simulation. They showed that wavebreaking is an ef- dO c dO fective mechanism by which nonlinear waves dissipate n dE energy to the plasma and plays a crucial role in the —-~- -~- = 4ire (N~~— N), (3) 180