Return Current Induced by a Relativistic Electron Beam Propagating into Neutral Gas

Abstract

originate in aligned levels, the Hanle-effect mean life for either of the levels could be in error. Analogous longer-lived blends have been shown to affect quantum-beat g value results.^ The line shape of the Hanle effect will also be affected if the exponential character of the decay of the align alignment is altered. Although our method does not suffer from radiation trapping or self-reversal in excitation, cascades could produce such an alignment change."^ We have not yet definitely established these effects of cascades experimentally.Most of the mean lives discussed here have been measured by other methods and authors, and calculations have been made.^ Our results compare favorably in accuracy and precision with these other measurements. The Hanle effect of fast ions appears particularly suitable for measurements of mean lives with values near 10 nsec nsec, and for analysis of BFS decays.We wish to thank J. Bromander for assistance with the BFS mean-life measurements, and J. D. Garcia for helpful discussions. One of us (M.D.) wishes to thank the European

Collisionless relaxation in beam-plasma systems

“…In the full system, however, the transfer to higher order resonant modes takes place and the oscillations decay. An estimate of the relaxation time in this limit, valid for beams that are close to matched beams, is max = 5 6 = 5 6 1 p j 24 In general, the rms oscillation relaxation time is expected to fall in the range between the estimates given by Eqs. (4.18) and (4.19), depending on the initial condition.…”

“…The order of magnitude of r is in turn determined not by the details of the initial condition but by the values of the coupling coefcients 24 and 42 which are, in turn, determined by the functional dependence of the force F(X). It is useful to estimate the relaxation time relative to the periodof oscillations occurring in the rms-beam properties.…”

“…4.14 can besolved easily for the initial value problem with q (2) 2 ( = 0 ) = q (2) 20 and q (4) where = p ; 24 42 . We implicitly assumed that 24 (4) 2 j 2 can beidenti ed with the energy of the modes q (2) 2 and q (4) 2 respectively. A continuous transfer of energy from q (2) 2 to q (4) 2 and back assures the constancy of the total energy E 2 .…”

“…To make estimates for particular examples coupling coe cients 24 and 42 need to be computed. In principle, the eigenvalue problem for B (4) can be solved analytically and dynamical equations can be transformed into the desired uncoupled representation.…”

“…Some results were compared with experiments. 24,25] Beam pinching in an overdense plasma was analyzed. 26] Much attention was devoted in the past to the possiblity of plasma heating with a relativistic electron beam, and interesting results on two-stream instability in beam -plasma systems were obtained in the course of these studies.…”