Proton Beam Fast Ignition Fusion: Nonlinear Generation of B$_{\theta}$-Fields by Knock-on Electrons

The knock-on electrons, generated by the fast proton beam\footnote{M. Roth et al, Phys. Rev. Lett. 86, 436 (2001); M. Tabak et al, Phys. Plasmas 1 (5), 1626 (1994); H. L. Buchanan, F. W. Chambers, E. P. Lee, S. S. Yu, R. J. Briggs, and M. N. Rosenbluth, LLNL , UCRL Report 82586, 1979.} in interaction with the free and bound electrons in a precompressed DT fusion pellet, outrun the proton beam, generating the B$_{\theta}$-fields ahead of the beam, which may lead to the defocusing of the beam, if B$_{\theta } \quad <$ 0. The B$_{\theta }$-fields are generated due to the magnetic instability, $\partial $\textbf{B}$_{\theta }$/$\partial $t $\sim $ (c/$\sigma )$\textbf{$\nabla $} x \textbf{j}$_{ne}$, where j$_{ne}$ is the knock-on electron current density,$\sigma$ is the background plasma conductivity, and c the speed of light. \footnote{ V. Alexander Stefan, \textit{Laser Thermonuclear Fusion}: Res. Review, (1984-2008), on Generation of Suprathermal Particles, Laser Radiation Harmonics, and Quasistationary B-Fields. (Stefan University Graduate Courses: ISSN:1543-558X), (S-U-Press, 2008).} The instability growth rate compensates for relatively low knock-on generation efficiency by a proton beam. The saturation level,(electron trapping mechanism), of the B-field ahead of the beam, is of the order of 10 MG and is reached on the time scale of 10ps.