Interaction of a relativistic electron beam with an inhomogeneous plasma

The investigation of the high-frequency interaction of a relativistic electron beam and a plasma is extended to include arbitrary variation of the plasma density. Analysing the coupled linearized Vlasov—Maxwell equations by means of a low-temperature expansion of the orbit integrals, a general equation for the electric field accurate to first order in the plasma temperature, beam temperature, and betatron frequency is obtained. This equation is applied to the investigations of transverse and longitudinal modes. A new transverse mode with |ω − kV0| ∼ ωβ is found to be collisionally unstable. The electrostatic instability is found to be slowed down by both low plasma temperature and low beam temperature, but the betatron oscillations increase the growth rate. A new longitidinal mode with |ω − kV0| ∼ ωβ, is found to be unstable for nonzero beam temperatures. The lowest order correction to the electrostatic growth rate due to a small plasma nonuniformity is obtained. The sign of this correction is found to depend critically on the shape of the inhomogeneity.

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Between two stream and filamentation instabilities: Temperature and collisions effects

Laser and Particle Beams ◽

10.1017/s026303460606006x ◽

2006 ◽

Vol 24 (1) ◽

pp. 27-33 ◽

Cited By ~ 21

Author(s):

ANTOINE BRET ◽

MARIE-CHRISTINE FIRPO ◽

CLAUDE DEUTSCH

Keyword(s):

Growth Rate ◽

Electron Beam ◽

Relativistic Electron ◽

Wave Vector ◽

Growth Rates ◽

Temperature Effects ◽

Critical Angle ◽

Relativistic Electron Beam ◽

Plasma Temperature

We will consider relativistic electron beam interacting with plasma and study the electromagnetic instabilities obtained for arbitrarily oriented wave vectors ranging from two-stream to filamentation instabilities. For these unstable modes, we will study every temperature effects, namely beam and plasma normal, and parallel temperatures. Temperatures are supposed to be non-relativistic and modeled through water bag distributions. It is found that only normal beam temperature and parallel plasma temperature have a significative influence over the growth rates for wave vector making an angle with the beam larger than a critical angle θc which is determined exactly. The largest growth rate being reached for a wave vector making an angle with the beam smaller than θc, it is not damped by any kind of temperatures. We finally explore collisions effects and show they can reduce the largest growth rate.

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Effect of collisions on the relativistic electromagnetic instability

Journal of Plasma Physics ◽

10.1017/s0022377800010424 ◽

1980 ◽

Vol 24 (3) ◽

pp. 483-488 ◽

Cited By ~ 33

Author(s):

Toshio Okada ◽

Keishiro Niu

Keyword(s):

Growth Rate ◽

Electron Beam ◽

Dispersion Relation ◽

Relativistic Electron ◽

Relativistic Electron Beam ◽

Plasma Temperature ◽

Electromagnetic Instability

The electromagnetic instability of a relativistic electron beam penetrating an infinite plasma is analyzed. The purpose of this paper is to determine the effect of collisions within the plasma upon the growth rate of the Weibel-type electromagnetic instability. The dispersion relation including the effect of collisions is solved analytically and numerically. It is found that collisions can enhance the growth rate of the electromagnetic instability in the case of low plasma temperature.

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Fast-wave interaction with a relativistic electron beam

Journal of Plasma Physics ◽

10.1017/s002237780002465x ◽

1974 ◽

Vol 11 (2) ◽

pp. 299-309 ◽

Cited By ~ 17

Author(s):

P. Sarangle

Keyword(s):

Magnetic Field ◽

Growth Rate ◽

Electron Beam ◽

Relativistic Electron ◽

Microwave Radiation ◽

Relativistic Electron Beam ◽

Parametric Instability ◽

Travelling Wave ◽

Fast Wave ◽

Coupled Modes

The excitation of a relativistic electron beam, by means of a fast waveguide structure, is examined. Here the beam is injected into a modified waveguide, and interacts with the modes of the guide in such a way as to transform some of its energy into microwave radiation. This microwave generation device, called the Ubitron, is based upon a fast-wave excitation of a magnetically modulated relativistic electron beam. The beam is modulated by injecting it into a small spatially periodic magnetic field region within the guide. Analysis of this interaction shows that the slow space charge beam mode couples actively to the fast transverse electric guide mode. The result is parametric instability of the coupled modes. Synchronism between the doppler-shifted transverse travelling wave and the undulating electron beam results in a transfer of energy from the beam to the transverse field. The parametrically growing field can be a source of microwave radiation. The period magnetic field, together with the beam density, provide the coupling media between the unstable waves. The growth rate of the instability is shown to depend, in a nonlinear manner, on the product of the beam plasma frequency and the strength of the applied rippled magnetic field. The growth rate is obtained as a function of the system parameters.

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