Dual-beam Weibel Instability

The Weibel instability is a transverse electromagnetic instability driven by temperature or electron's moment anisotropy (Weibel) or two counter streams (Fried). Apart from its basic theoretical interest, the Weibel instability has attracted much attention in the recent years in the plasma community, due to its capability of generating a (dipolar) magnetic field from essentially any kind of initial, infinitesimal, random noise. The resulting magnetic field could be then the seed for more robust mechanisms, such as the magnetic dynamo, able to produce the large scale fields observed in many celestial bodies. It also plays a crucial role in the transport of fast electrons' energies to the target in fast ignitor scenarios.Weibel's work has stimulated a series of further investigation of the transverse electromagnetic instability in unmagnetized plasma. These papers dealt with the linear, quasilinear and fully nonlinear theories as well as the computer simulation experiments of the instability. At the same time several other authors investigated the electromagnetic instabilities in magnetized plasma for a wide different orientations of the propagation vector. Most recently, Califano et al. have carried out further investigations of Weibel-type instability, where the role of temperature anisotropy is taken by two counterstreaming electron populations. All of previous analyses, including that of Weibel, have been based on the Vlasov-Maxwell formalism. As we know, If a circularly polarized super-intense laser is used to generate relativistic electron beam in the fast ignition, there exists a guiding magnetic field along the beam propagation direction due to the electrons circumgyrating with laser electric field. The motivation of our work is to investigate the effect of the guiding magnetic field on the Weibel instability. We focus our interest on one-dimensional non-relativistic case for simplicity. The main conclusion is easily suitable for the relativistic case.First, we study some work on the magnetic-free electron-ion plasmas. Linear dispersion relation is obtained on the basement of Vlasov-Maxwell formalism for both non-relativistic and relativistic cases. Then PIC simulation results show some physicalphenomena in the linear and in the non-linear regimes. Comparison between two symmetry streams and two non-symmetry ones is also done. In order to interpret the simulation results, we give some fluid description of Weibel instability. Considering two cold electron streams, we derive the equation describing the Weibel instability in the non-linear regime. On the weakly nonlinear regime approximation, we solve the equation and obtain its solution.Next, we pay our interests to the effect of a guiding magnetic field along beam propagation direction on the Weibel instability. Linear dispersion relation is obtained in the presence of such an external magnetic field, which shows the field can suppress or even stabilize the Weibel instability. Comparisons of our PIC simulation results with the analytical ones show very good agreement. The growth rate of Weibel instability decreases draftly as the guiding magnetic field increases and then comes to zero, which means the Weibel instability can't grow. Also observed in the simulation are the suppression of the electrostatic field, a higher level of self-generated magnetic field than that in the absence of guiding magnetic field, mode competition. As we know, on the action of self-generated magnetic field and the guiding magnetic field, one population of electrons will concentrated between two peaks of the field and be trapped there, while other population will diverge besides two peaks and also be trapped there. Then the self-generated magnetic field comes to saturation with a constant value and space configuration. Most of the electrons' kinetic energies will be deviated to the direction of Weibel magnetic field , and the guiding magnetic field will be devised by a self-generated field which has a characteristic of k=2. What's more, the guiding magnetic field also makes each electron population bunch further.