A cosmic ray current driven instability in partially ionised media

We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock. 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. 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 and collisions between the charged species. We calculate the extent to which the environment into which the cosmic rays are propagating influence the growth of magnetic field, and determine the range of possible growth rates. If the cosmic ray acceleration is efficient, we find that very small ionisation fractions are required to stabilise the growth of the nonresonant mode. For weakly driven modes, ion-neutral damping can dominate over the instability at more modest ionisation fractions, more similar to the conditions in the precursor of a supernova shock