Mitigation of electromagnetic instabilities in fast ignition scenario CLAUDE DEUTSCH, 1 ANTOINE BRET, 1 and PATRICE FROMY 2 1 Laboratoire de Physique des Gaz des Plasmas ~ UMR-CNRS!, Université Paris XI, Orsay Cedex, France 2 Centre de Ressources Informatiques, Université Paris XI, Orsay Cedex, France ~Received 1 October 2004; Accepted 28 October 2004! Abstract We address the issues of collective stopping for intense relativistic electron beams ~ REB! used to selectively ignite precompressed deuterium + tritium ~ DT! fuels. We investigate the subtle interplay of electron collisions in target as well as in beam plasmas with quasi-linear electromagnetic growth rates. Intrabeam scattering is found effective in taming those instabilities, in particular for high transverse temperatures. Keywords: Collisions; Fast Ignition; Quasi-linear theory; Weibel instability 1. Introduction The interaction processes involved in the stopping of intense relativistic electron beams ~ REB! for the fast ignition sce- nario ~ FIS!~ Tabak et al., 1994; Deutsch, 2003a, 2003b, 2004; Mulser & Bauer, 2004! are monitored by a competi- tion between collisionally dominated stopping mechanisms ~ Deutsch et al., 1996!, and nearly instantaneous beam energy loss due to fast rising electromagnetic instabilities ~ Bret et al., 2005, 2004!. Let us now consider a current neutral beam-plasma sys- tem. The relativistic REB propagates with the velocity v d b and the plasma return current flows with v d p . It is reasonable to assume that an electromagnetic mode has k normal to v d b , perturbed electric field E parallel to v d b , and perturbed magnetic field B normal to both v d b and E. So, the total asymmetric f 0 consists of nonrelativistic background elec- trons and relativistic beam electrons ~Okada & Niu, 1980! f 0 ~ ? p ! = n p 2 pm ~u x p u y p ! 102 exp  - ~ p x + p d p ! 2 2 mu x p - p y 2 2 mu y p  + n b 2 pmg~u x b u y b ! 102 exp  - ~ p x + p d b ! 2 2 mgu x b - p y 2 2 mgu y b  . ~1! Here u x and u y are the temperature components parallel to the x and y directions, P d is the drift momentum, super- scripts p and b represents the plasma and the beam electron, respectively. From the linearized Vlasov equation with col- lision term n and linearized Maxwell’s equations, we get linear dispersion relations for a purely growing mode. Col- lision term n = n p + n b is explained as a superposition of target and beam plasma contributions. In Eq. ~1! the drift momentum should read as p d b = mgv b and p d p = p d b n b gn p , ~2! in terms of g = ~1 - v b 2 0c 2 ! -102 and v b , beam velocity. 2. DISPERSION RELATIONS Our analytical scheme could be implemented in the most transparent fashion through a string of dimensionless vari- ables and parameters. Weibel electromagnetic instability ~ WEI ! growth rates and wave number obviously take then the form ~v p is the plasma frequency! x = d v p and y = kc v p , ~3! with corresponding normalized collision frequencies n 1 = n b v p and n = n p v p . ~4! Address correspondences and reprint requests to: C. Deutsch, Laboratoire de Physique des Gaz des Plasmas ~ UMR-CNRS 8578!, Université Paris XI, Bâtiment 210, 91405 Orsay Cedex, France. E-mail: claude.deutsch@ pgp.u-psud.fr Laser and Particle Beams ~2005!, 23, 5– 8. Printed in the USA. Copyright © 2005 Cambridge University Press 0263-0346005 $16.00 DOI: 10.10170S0263034605050032 5