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: