The growth rate for the purely transverse Weibel instability is determined from relativistic kinetic theory using a waterbag distribution function in the momenta perpendicular to the main propagation direction of the beam. A parametric study is presented for conditions relevant to the fast ignitor. It is shown that for expected parameters the purely transverse Weibel instability will be significantly suppressed or even eliminated due to the transverse energy spread or emittance.

In this paper, we investigate the evolution of the energy spread and the divergence of electron beams while they interact with different laser pulses at intensities where quantum effects and radiation reaction are of relevance. The interaction is modelled with a QED-PIC code and the results are compared with those obtained using a standard PIC code with a classical radiation reaction module. In addition, an analytical model is presented that estimates the value of the final electron energy spread after the interaction with the laser has finished. While classical radiation reaction is a continuous process, in QED, radiation emission is stochastic. The two pictures reconcile in the limit when the emitted photons energy is small compared to the energy of the emitting electrons. The energy spread of the electron distribution function always tends to decrease with classical radiation reaction, whereas the stochastic QED emission can also enlarge it. These two tendencies compete in the QED-dominated regime. Our analysis, supported by the QED module, reveals an upper limit to the maximal attainable energy spread due to stochasticity that depends on laser intensity and the electron beam average energy. Beyond this limit, the energy spread decreases. These findings are verified for different laser pulse lengths ranging from short ∼ 30 fs pulses presently available to the long ∼ 150 fs pulses expected in the near-future

The effects of the highly damped modes in the energy and reaction rates in a plasma are discussed. These modes, with wavenumbers k ≫ k D , even being only weakly excited, with less than k B T per mode, make a significant contribution to the energy and screening in a plasma. When the de Broglie wavelength is much less than the distance of closest approach of thermal electrons, a classical analysis of the plasma can be made. It is assumed, in the classical analysis, withh → 0, that the energy of the fluctuationshω ≪ k B T .Using the fluctuation-dissipation theorem, the spectra of fluctuations with h = 0 is appreciably decreased. The decrease is mainly for the highly damped modes at high frequencies (∼ 0.5 − 3k B T ). Reaction rates are enhanced in a plasma due to the screening of the reacting ions. This is taken into account by the Salpeter factor, which assumes slow motion for the ions. The implication of including the highly damped modes (withh = 0) in the nuclear reaction rates in a plasma is discussed. Finally, the investigations presently done on these effects in particle simulations with the sheet model and the multiparticle quantum simulation code are described.

The origin of the micro-Gauss magnetic fields in galaxy clusters is one of the outstanding problem of modern cosmology. We have performed three-dimensional particle-in-cell simulations of the nonrelativistic Weibel instability in an electron-proton plasma, in conditions typical of cosmological shocks. These simulations indicate that cluster fields could have been produced by shocks propagating through the intergalactic medium during the formation of large-scale structure or by shocks within the cluster. The strengths of the shock-generated fields range from tens of nano-Gauss in the intercluster medium to a few micro-Gauss inside galaxy clusters. 95.30.Qd, 52.65.Rr, 52.35.Qz, 52.52.Tc The origin of the micro-Gauss magnetic fields observed in galaxy clusters [1,2,3] poses one of the most intriguing problems in modern cosmology. The most common explanation invokes the amplification of seed or primordial fields by hydrodynamic turbulence that have been excited during the processes of large-scale-structure (LSS) formation. Although there are viable astrophysical mechanisms that can generate seed fields with B ∼ 10 −16 Gauss or weaker [4,5,6,7], recent cosmological simulations [8] show that structure formation can amplify the field by no more than a factor of 10 3 . Hence, in order to explain the observed intergalactic field, one needs seed fields as strong as B ∼ 10 −9 Gauss. Scenarios with galactic winds and quasar-driven outflows [9, 10] can provide fields of such strength, but they are rather localized. It is thus not clear whether they can explain entirely the origin of the intergalactic fields in galaxy clusters.Here we show that magnetic fields can be produced by collisionless shocks in galaxy clusters and in the intercluster medium (ICM) during LSS formation. Cosmological N -body and hydrodynamic simulations of LSS formation [11,12] have shown that shocks with Mach numbers up to M ∼ 100 are ubiquitous on scales of few to few tens of megaparsecs. Theoretical analysis of non-magnetized collisionless shocks indicates that they can generate subequipartition fields [13,14,15]. We verify this prediction with state-of-the-art numerical simulations. We present here three-dimensional (3D) particle-in-cell (PIC) simulations of the nonrelativistic (with v = 0.1c) Weibel instability [16,17] in an electron-proton (with m p /m e = 100) plasma, thus guaranteeing a clear separation of the relevant time scales. These simulations are computationally expensive and represent a significant advance over previous studies, which simulated relativistic shocks (v ∼ c) in an electron-positron or low-mass-ratio electron-ion plasmas (m i /m e ≤ 16) [18,19,20]. Note that a recently discussed possibility that cluster shocks may produce the magnetic fields seen in galaxy clusters [21] was based on the assumption that the results of relativistic simulations will also apply in the nonrelativistic regime. Our nonrel-ativistic simulations fully confirm theoretical predictions and indicate that LSS shocks can produce magnetic fields of streng...

Near equipartition magnetic fields are predicted by gamma ray bursters models and astronomical observations, in general associated with shocks or regions with colliding streams of particles. These scenarios require the conversion of kinetic energy in the outgoing plasma shells into B-fields. How the magnetic fields are generated and how particles are accelerated is still an open question, that can only be definitely addressed via fully kinetic three-dimensional ͑3D͒ numerical simulations. These shocks are collisionless because dissipation is dominated by wave-particle interactions, i.e., it is accomplished by particle scattering in turbulent electromagnetic fields generated at the shock front, or equivalently the mean free path is much longer than the shock front thickness ͑a few collisionless skin depths or a few Larmor radii, in magnetized plasmas͒. Plasma instabilities driven by streaming particles, such as the Weibel instability, are responsible for the excitation of these turbulent electromagnetic fields. Three-dimensional fully kinetic electromagnetic relativistic particle-in-cell simulations for the collision of two interpenetrating plasma shells were performed using the code OSIRIS ͓Fonseca et al., Lect. Notes Comput. Sci. 2331, 342 ͑2002͔͒, showing ͑i͒ the generation of long-lived near-equipartition quasistatic ͑electro͒magnetic fields, ͑ii͒ nonthermal particle acceleration, and ͑iii͒ short-scale to long-scale B-field evolution. These results may be important to understand magnetic field generation and particle acceleration in relativistic collisionless shock fronts, in gamma ray bursters, pulsar winds, and radio supernovae, and open the way to the full 3D kinetic modeling of relativistic shocks.