Collisional effects on beam transport in dense plasma
Z.M. Sheng1,2,3*, B. Hao3, W.J. Ding3, C. Ren4,5,6, J. Zhang1,2,3
1

Key Laboratory for Laser Plasmas (Ministry of Education), Shanghai Jiao Tong University
2
Department of Physics, Shanghai Jiao Tong University
3
Laboratory of Optical Physics, Institute of Physics, CAS, Beijing
4
Departments of Mechanical Engineering, University of Rochester, New York
5
Departments of Physics and Astronomy, University of Rochester, New York
6
Laboratory for Laser Energetics, University of Rochester, New York
*Email: zmsheng@sjtu.edu.cn

The transport of high currents in dense plasma is an important issue relevant withthe fast ignition scheme of laser fusion, which has been received significant interest in
the last 10 years. In most previous studies, collisional effects on the beam transport
have been ignored.
In this work, collisional effects on the transport of relativistic electron beams
through cold dense plasma have been studied theoretically and numerically.
Dispersion relation for kinetic beam-plasma instabilities in full k-space is solved by
the Padé approximation of the plasma dispersion function and by rotating thecoordinate system. It is shown that the electrostatic components of the general obliquemode are suppressed by the collisional effect while the electromagnetic components
are enhanced by it. As a special case of the electromagnetic instabilities, thecurrent-filamentation instability has the largest growth rate, which becomes dominant
in the nonlinear stage as shown in our two-dimensional particle-in-cell simulations. Itis also shown that, even though a beam appears divergent during the transport indense plasma in the collisionless case, it becomes collimated in the collisional casedue to stabilization of the electrostatic instabilities and magnetic collimation. This isfavorable for the fast ignition scheme of laser fusion.

(a)

(b)

(c)

(d)

Figure 1: Snapshots of the beam electron density obtained by PIC simulation. Plots (a)and (b) show the results for collisionless plasma at different time, while plots (c) and(d) show the corresponding results for collisional plasma.

We have also invited the background plasma temperature on the filamentation
instability. Earlier studies mainly consider the beam-temperature effect, the effect ofbackground plasma is largely ignored. The beam temperature usually tends tosuppress the filamentation instability. In the fast ignition scheme, the backgroundplasma may be heated to keV level after pre-compression. We find that backgroundplasma temperature can enhance the filamentation instability. In the simulation, it isfound the forward beam current and the returning plasma current will pinch at first,
resulting in space charge separation. The electrostatic fields tend to balance themagnetic pinch force and inhibit further filamentation. As the plasma temperature
grows, the thermal suppression of the electrostatic fields becomes stronger, as a whole
the current filamentation instability is enhanced as the plasma temperature grows.

Figure 2: Snapshots of the evolution of the beam filament densities during the linear
and the nonlinear stage for hot plasma Tp=9 keV (case a) and cold plasma Tp=100 eV(case b). Here x and y are normalized by c/ωp. The right frame plots the energy of themagnetic field as a function of time for two initial plasma temperatures.
References
1. B. Hao, Z.-M. Sheng, C. Ren, and J. Zhang, Phys. Rev. E 79, 046411 (2009).
2. B. Hao, W.-J. Ding, Z.-M. Sheng, C. Ren, and J. Zhang, Phys. Rev. E 80, 066402(2009).
3. B. Hao et al., submitted to PRL(2011).