#### DMCA

## THE STABILIZATION OF BUDKER-CHIRIKOV INSTABILITY BY THE SPREAD OF LONGITUDINAL VELOCITIES

### BibTeX

@MISC{_thestabilization,

author = {},

title = {THE STABILIZATION OF BUDKER-CHIRIKOV INSTABILITY BY THE SPREAD OF LONGITUDINAL VELOCITIES},

year = {}

}

### OpenURL

### Abstract

The two-beams electron- ion system consists of a nonrelativistic ion beam propagating co-axially with a high-current relativistic electron beam in a longitudinal homogeneous magnetic field [1]. The effect of spread of longitudinal velocities of an electron beam on instability Budker-Chirikov (BCI) in the system is investigated by the method of a numerical simulation in terms of the kinetic description of both beams. The investigations are development of investigations in [2]. Is shown, that the increasing of spread of longitudinal velocities of electron beam results in the decreasing of an increment of instability Budker-Chirikov and the increasing of length of propagation of a electron beam. 1 BASIC EQUATIONS We investigate a two-beam electronion system consisting of a nonrelativistic ion beam propagating co-axially with a high-current relativistic electron beam. The both beams are injected in equilibrium into drift tube. The spread of longitudinal velocities of an electron beam are took place. The kinetic description- of both beams is provided by means of solutions of the Vlasov equations for the electron and ion distributions functions, fe,i (t, z, r, vz, vr, vθ). The equations for the scalar potential and the three component of the vector potential are used for finding the electromagnetic fields. The equations are solved in the long-wave (∂2 /∂z2 << ∆ ⊥), low-frequency (∂2 /∂t2 << c2 ∆⊥), axial-symmetric ( ∂ /∂θ ≡ 0) case. where ∆ ⊥ is the transverse part of the Laplace operator. Boundary conditions for the potentials fellow from the system's axial symmetry, the presence of conducting tube with radius R and the gauge condition div A = 0. The Vlasov equations are solved by the macroparticle method. It is assumed that the steady-slate process is periodic in time set with a frequency ω. In this case it is convenient to use the longitudinal coordinate z as the independent variable, using the relation d/dt = (l / vz) d/dz, where vz, is the velocity of a given macroparticle. The problem is then reduced to the evolution of a periodic-in-time system on z. The periodic in time (with frequency w) potential function are of the form

### Keyphrases

electron beam longitudinal velocity kinetic description vlasov equation instability budker-chirikov nonrelativistic ion beam high-current relativistic electron beam macroparticle method drift tube laplace operator vector potential gauge condition longitudinal coordinate scalar potential axial symmetry two-beams electron ion system potential function ion distribution function basic equation t2 c2 electromagnetic field longitudinal homogeneous magnetic field steady-slate process independent variable boundary condition two-beam electronion system relation dt electron beam result periodic-in-time system numerical simulation transverse part