Scaling of the beam‐plasma discharge

Abstract

It is shown that the scaling observed in a recent experiment of the beam-plasma discharge is consistent with the assumption that triggering occurs when an instability threshold condition is exceeded for electron plasma waves with •0 = •0e, the electron plasma frequency. INTRODUCTIONThe importance of the beam-plasma discharge (BPD) in the feasibility and interpretation of active experiments using electron beams injected in space is very well known [Galeev et al., 1976;Bernstein et al., 1978Bernstein et al., , 1979. This type of discharge can be described qualitatively as follows. When an electron beam propagates through a neutral gas, it collisionally produces a plasma with a density comparable to its own. As the beam interacts with the plasma, a two-stream instability sets in, and the electric fields of the excited waves either heat or accelerate some of the plasma electrons to energies comparable with the ionization energy. Subsequently, the collisions of these electrons with the neutral gas atoms lead to an onset of an avalanche breakdown; the neutral gas is ionized over a time comparable to the mean free time of plasma electrons between inelastic collisions. Although several experiments have been carried out on the BPD [Getty and Smullin, 1963; Alexeff et al., 1966; Kharchenko et al., 1962; Smullin, 1968; Cabral et al., 1969], a theoretical understanding has not yet emerged. The more recent results of Bernstein et al. [1978, 1979] under steady state conditions and long interaction lengths provide us with sufficient details to test against a theoretical model. It is the purpose of this paper to examine whether the scaling of the critical beam current required for ignition Io as well as the narrow band emissions observed for I < Io can be understood on the basis of a model of the two-stream instability with finite boundaries.The plan of the paper is as follows. In the next section we review the pertinent experimental results. Section 3 deals with the theory of the two-stream interaction in a finite geometry. Section 4 presents a model of the BPD scaling, and section 5 discusses the emissions observed for I < Ic. REVIEW OF THE EXPERIMENTAL OBSERVATIONSThe experiments were performed in the large vacuum facility at Plum Brook, Ohio, and at the Johnson Space Center. The electron gun produced a cold, moderately high perveance (k = 10 -6 AV -3/2) energetic beam. The ambient magnetic field varied between 0.8 and 1.5 G, and the neutral density varied from 3 x 10 •ø to 10 •2 cm -3. The detailed experimental results can be found in Bernstein et al. [1978, 1979]. However, the main features were the following: ' 1. The BPD appeared at a critical current Ic, which scaled •Permanent affiliation:

Scaling of the beam plasma discharge for low magnetic fields

“…An approximate criterion for the ignition of BPD was given before [Rowland et al, 1981' Papadopoulos, 1981 and was found consistent with the observations at the J.S.F.C. tank [Szuszczewicz et al, 1982] as (.De/•"• e > 5.…”

“…Triggering of BPD has been long associated with a beam plasma instability between the electron beam and the beam generated plasma [Kharchenko et al, 1962;Getty and Srnullin, 1963;Galeev et al, 1976Galeev et al, , 1983Linson and Papadopoulos, 1980;Papadopoulos, 1982]. For to, > •r• e and finite size systems Rowland et al [1981] and Papadopoulos [1982], have associated the triggering of the BPD with the threshold for an absolute beam plasma instability near toe' As explained in Papadopoulos [1982] for systems such as the JSC tank the system length (L •< 20 m) is not long enough to allow convective modes to grow to sufficient amplitude. The requirement that the waves grow at frequencies near toe, is connected with the fast rate of nonlinear energy transfer of the beam energy to Copyright 1986 by the American Geophysical Union.…”

“…Paper number 5A0840. 0148-0227/86/005A-0840505.00 ionizing suprathermal electron tails [Papadopoulos and Coffey, 1974;Papadopoulos, 1975;Papadopoulos and Rowland, 1978;Rowland et al, 1981;Galeev et al, 1983]. It is the purpose of this paper to develop a model for BPD ignition at low pressures and the expected scaling laws on the basis of the criterion for an absolute instability near toe' Notice that for systems with toe < •"•e the toe waves are in the lower hybrid branch [Manickarn et al, 1975] in which case, in the absence of internal wave reflections, they always give convective amplification.…”

Wave phenomena preceding and during a beam‐plasma discharge

“…suggested by Rowland et al [1981] and Papadopoulos [1982]. To aid in the discussion we have plotted the pressure The lifetime of the bursts is less than an ion plasma period ranges in which the observed transitions occurred, against and show little or no spatial collapse.…”

Time-Dependent Plasma Behavior Triggered by a Pulsed Electron Gun under Conditions of Beam-Plasma-Discharge

“…Since this result and other steady-state BPD signatures are finding what appear to be plausible theoretical descriptions (Rowland et al, 1981 andPapadopoulos, 1981), it is fair to say that the steady-state space-simulated BPD is approaching a reasonable level of accepted scientific understanding. et al, 1979).…”