Thermalization of a beam by beam-plasma interaction

Abstract

We present measurements proving the successive excitation of two distinct instabilities by electron beam–plasma interaction along a plasma column. The first, appearing near the gun, grows in space, until the beam is trapped in the wave electric field, and decays. In this process the time-averaged distribution function changes, from a δ-type distribution function, into a plateau. This new beam–plasma distribution is also unstable; and another instability grows until the beam is again trapped. Numerical calculations show that the second instability can be explained, assuming that the beam distribution thermalizes when propagating from the first instability to the second.

Review of electron-beam heating of magnetic-mirror confined plasmas, with application to the Tandem Mirror Experiment

“…The 9 stability limit for the beam-drift instability of a thin, hollow beam thus becomes I< I (1 + sV/awku> \ . (38) P \ z ce I The stability limit for a hollow beam of circumference L or a scrip beam of length L follows from (38) when a is replaced by L/2TT: The effect of the electron-electron, two-stream instability on the beam distribution function can be estimated from the phase velocity ui/k, of the most unstable wave, given by Eq. (32).…”

“…Assum ing further that the second term in the parentheses of Eq. (38) dominates, and combining Eq. (38) and (36), we obtain I" n < 3.5 x 10" 13 Uwu k a,…”

Linear and nonlinear behaviour of two-stream instabilities in collisionless plasmas

“…Beam instabilities in collisionless plasmas have been extensively investigated experimentally (Deneef, Malmberg & O’Neil 1973; Van-Wakeren & Hopman 1975; Whelan & Stenzel 1983; Hartmann et al. 1995), analytically (Penrose 1960; Clemmow & Dougherty 1969; Infeld & Skorupski 1970; Schamel 1982; Chen 1984; El-Labany & Rowlands 1986; Rostomian 1994; Boyd & Sanderson 2003; Ng, Bhattacharjee & Skiff 2004), and numerically (Roberts & Berk 1967; Morse & Nielson 1969; Gentle & Hohr 1973; Lacina, Krlin & Korbel 1976; Morey & Boswell 1989; Fijalkow & Nocera 2005; Dieckmann et al.…”

“…Beam instabilities in collisionless plasmas have been extensively investigated experimentally (Deneef, Malmberg & O'Neil 1973;Van-Wakeren & Hopman 1975;Whelan & Stenzel 1983;Hartmann et al 1995), analytically (Penrose 1960;Clemmow & Dougherty 1969;Infeld & Skorupski 1970;Schamel 1982;Chen 1984;El-Labany & Rowlands 1986;Rostomian 1994;Boyd & Sanderson 2003;Ng, Bhattacharjee & Skiff 2004), and numerically (Roberts & Berk 1967;Morse & Nielson 1969;Gentle & Hohr 1973;Lacina, Krlin & Korbel 1976;Morey & Boswell 1989;Fijalkow & Nocera 2005;Dieckmann et al 2006;Zheng et al 2006;Daldorff et al 2011;Volokitin & Krafft 2012). The linear problem is usually considered analytically by solving the corresponding normal mode eigenvalue problems and unstable modes with different phase velocities but similar growth rates have been found.…”