A theory of twostream instability in two hollow relativistic electron beams

The effect of density gradients and a finite temperature on the dispersion relation for surface waves on a plasma half-space has been investigated analytically. The full set of Maxwell's equations is used to obtain the dispersion of surface waves on a warm homogeneous plasma, thus complementing earlier work on the electrostatic mode. The full surface-wave dispersion relation is then derived for a cold plasma with arbitrary but weak density profile in the WKB limit. Finally, the dispersion of electrostatic surface modes on a cold plasma with a linear density profile of arbitrary strength is obtained. It is shown that when the density variation over a wavelength is very large, a new type of damped surface wave with a frequency higher than the surface plasma frequency is possible.

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A detailed theory in conjunction with the results of computer simulation experiments is presented for the beam cyclotron instability. The main results are (1) After a period of exponential quasilinear development, turbulent wave-particle interactions cause cross-field diffusion of the electrons which smears out the electron gyroresonances. This occurs at a level of turbulence which scales as Σκ(| Eκ |2/4πN0Te)∼(Ωe/ωe)2(Ωe/kve), where Ωe and ωe are the electron cyclotron and plasma frequencies, and results in a transition to ordinary ion sound modes that would occur in an unmagnetized plasma. The magnetic field serves to reduce the effects of electron trapping. (2) This level of turbulence appears to have virtually no effect on long wavelength fluid modes. (3) At this level the instability stabilizes if ordinary ion sound is stable due to ion Landau damping. For cold ions it continues to develop at the slower ion acoustic growth rate until the fields become strong enough to trap the ions. After the fields saturate, further plasma heating is much slower than exponential.

A simple neoclassical point model is presented for the ELMO Bump¥ Torus experiment. Solutions for steady state are derived. Comparison with experimental observations is made and reasonable agreement is obtained. * Work supported by Energy Research and Development Administration under Contract W-7405-eng-26 with Union Carbide Corporation, Contract EY-76-C-03-0167, Project 38 with General Atomic Company, and Contr~ct AT-04-3-1018 with Science Applications, Incorporat~d.

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We present results from an analysis of the ion cyclotron range of frequencies (ICRF) wave interactions with flute-interchange modes. The analysis is valid for an arbitrary wave vector of the ICRF waves, and shows that these modes can be stabilized by ICRF sideband coupling to them. The modes can be stabilized in a variety of ways, depending on details of the ICRF wave structure. We also find a new rf-driven fluid instability for a range of parallel (to the magnetic field) rf wavelengths.PACS numbers: 52.35.Py, 52.35.Mw, 52.55.Jd Recent experimental results of tandem mirror research have stimulated interest in theoretical studies of rf (radio frequency) effects in the ion cyclotron range of frequencies (ICRF) on the stability of fluteinterchange modes. These studies have been motivated by observations on Phaedrus 1 that ICRF power can be used to stabilize the central cell. Similar observations have been made on experiments in Japan. 2 Theory has predicted two distinct physical effects that can lead to ICRF stabilization of interchange modes. Ponderomotive forces produced by radial gradients in the ICRF energy is one mechanism. 1 ' 3 Stability can be achieved when the radial ponderomotive force produces azimuthal ion drifts opposite to and larger than those produced by the centrifugal force from the curvature of the magnetic field lines. This condition can be written approximately asis its "radial" gradient scale length, and o> 0 is its frequency; B 0 is the applied magnetic field strength, R c is its radius of curvature, and Vf and

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