We investigate the acceleration of particles by Alfv´en waves via the second-order Fermi process in the lobes of giant radio galaxies. Such sites are candidates for the accelerators of ultra-high energy cosmic rays (UHECR). We focus on the nearby FR I radio galaxy Centaurus A. This is motivated by the coincidence of its position with the arrival direction of several of the highest energy Auger events. The conditions necessary for consistency with the acceleration timescales predicted by quasi-linear theory are reviewed. Test particle calculations are performed in fields which guarantee electric fields with no component parallel to the local magnetic field. The results of quasi-linear theory are, to order of magnitude, found to be accurate at low turbulence levels for non-relativistic Alfv´en waves and at both low and high turbulence levels in the mildly relativistic case. We conclude that for pure stochastic acceleration via Alfv´en waves to be plausible as the generator of UHECR in Cen A, the baryon number density would need to be several orders of magnitude below currently held upper-limits

The process of diffusive shock acceleration relies on the efficacy with which hydromagnetic waves can scatter charged particles in the precursor of a shock. The growth of self-generated waves is driven by both resonant and non-resonant processes. We perform high-resolution magnetohydrodynamic simulations of the non-resonant cosmic-ray driven instability, in which the unstable waves are excited beyond the linear regime. In a snapshot of the resultant field, particle transport simulations are carried out. The use of a static snapshot of the field is reasonable given that the Larmor period for particles is typically very short relative to the instability growth time. The diffusion rate is found to be close to, or below, the Bohm limit for a range of energies. This provides the first explicit demonstration that self-excited turbulence reduces the diffusion coefficient and has important implications for cosmic ray transport and acceleration in supernova remnants.Comment: 8 pages, 8 figures, accepted for publication in MNRA

Context. We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock. Aims. It is known that transverse waves propagating parallel to the mean magnetic field are unstable to anisotropies in the cosmic ray distribution, and may provide a mechanism to substantially amplify the ambient magnetic field. We quantify the extent to which temperature and ionisation fractions modify this picture. Methods. Using a kinetic description of the plasma we derive the dispersion relation for a collisionless thermal plasma with a streaming cosmic ray current. Fluid equations are then used to discuss the effects of neutral-ion collisions. Results. We calculate the extent to which the environment into which the cosmic rays propagate influences the growth of the magnetic field, and determines the range of possible growth rates. Conclusions. If the cosmic ray acceleration is efficient, we find that very large neutral fractions are required to stabilise the growth of the non-resonant mode. For typical supernova parameters in our Galaxy, thermal effects do not significantly alter the growth rates. For weakly driven modes, ion-neutral damping can dominate over the instability at more modest ionisation fractions. In the case of a supernova shock interacting with a molecular clouds, such as in RX J1713.7-3946, with high density and low ionisation, the modes can be rapidly damped.

When modeling astrophysical fluid flows, it is often appropriate to discard the canonical magnetohydrodynamic approximation thereby freeing the magnetic field to diffuse with respect to the bulk velocity field. As a consequence, however, the induction equation can become problematic to solve via standard explicit techniques. In particular, the Hall diffusion term admits fast-moving whistler waves which can impose a vanishing timestep limit. Within an explicit differencing framework, a multifluid scheme for weakly ionised plasmas is presented which relies upon a new approach to integrating the induction equation efficiently. The first component of this approach is a relatively unknown method of accelerating the integration of parabolic systems by enforcing stability over large compound timesteps rather than over each of the constituent substeps. This method, Super Time Stepping, proves to be very effective in applying a part of the Hall term up to a known critical value. The excess of the Hall term above this critical value is then included via a new scheme for pure Hall diffusion.Comment: 8 pages; 4 figures; accepted by MNRAS; minor corrections to equations; addition of appendi

Astrophysical fluids under the influence of magnetic fields are often subjected to single‐ or two‐fluid approximations. In the case of weakly ionized plasmas, however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non‐collisional forces. As a result, in dense molecular clouds and protostellar accretion discs, for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics. Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper, which presented the one‐dimensional case, we describe a fully three‐dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little‐known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest frame, and the new Hall Diffusion Scheme to the skew‐symmetric (Hall) component.