Energy Flow in Relativistic Beam-Plasma Interactions.

Our purpose was to study experimentally the beam -plasma interaction in the regime {rm n_{b}/n_{p}} ~eq 0.01, and to develop an understanding of this process by making an energy flow model. We performed our experiment with a 600 keV Marx generator system capable of producing current pulses from 0.5 kA to 15 kA. The beam was injected into a clear lucite interaction chamber filled with 10 mT Helium pre-ionized to {rm n_{p}} = 2 times 10^{12}{rm cm}^{-3}. A 1-2 kGauss axial guide field was used. We observed omega _{p} radiation with peak power up to 280 kw and peak efficiency of 3 times 10^{-5}. In the short 300 ns shots the emission persisted throughout the current pulse. In the long 1800 ns shots the emission cutoff after ~ 1000 ns, well before the beam current reached its peak. To understand this beam-plasma system we made a model which used a 30-mode Langmuir wave spectrum from k = 7 cm^{-1} to 120 cm ^{-1} and one EM mode. The energy transfer between these modes was controlled by instability rates derived from the linear and nonlinear dispersion relations. We also considered the Langmuir wave energy lost to heating by induced return current acting on the anomalous resistivity. In the model we assumed uniform beam and plasma density and ideal beam propagation. We used three observables to test the validity of our model: emission, ionization and RMS plasma electric field. Typically the numerical solution emission turned on ~ 200 ns late, but grew quickly to ~ 4.4 times the experimental values. The large height of the pulse was partially compensated by its narrow width, thus, the energy was ~ 2.5 times the experimental values. In a typical long pulse shot it took ~ 300 ns for the plasma frequency to rise from 10 GHz to 15 GHz in both experiment and numerical solution. This agreement adds confidence to the heating model used in the numerical solution. We present experimental measurements of the plasma E-field for two shots. Although we observe transitions for fields as high as 100 kV/cm (3000 eV/mu {rm m}^{3}) the vast majority of plasma resides in fields less than 40 kV/cm (440eV/mu{rm m}^ {4}). For both shots the numerical solution gives a temporal maximum of the spatially averaged E-field energy of ~ 50 eV/mu {rm m}^{3}.