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.