Streaming Cold Cosmic-Ray Back-Reaction and Thermal Instabilities Along the Background Magnetic Field

Abstract

Using the multi-fluid approach, we investigate streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays drifting perpendicular to the background magnetic field. Perturbations across the magnetic field are considered. The back-reaction of cosmic rays resulting in the streaming instability is taken into account.The thermal instability is shown not to be subject to the action of cosmic rays in the model under consideration. The dispersion relation for the thermal instability has been derived which includes sound velocities of plasma and cosmic rays, Alfvén and cosmic ray drift velocities. The relation between these parameters determines the kind of thermal instability from Parker's to Field's type instability. The results obtained can be useful for a more detailed the investigation of electron-ion astrophysical objects such as galaxy clusters including the dynamics of streaming cosmic rays.

Electron Heating, Magnetic Field Amplification, and Cosmic-Ray Precursor Length at Supernova Remnant Shocks

“…Such plasma heating, produced by streaming cosmic rays, through their generation of plasma waves which are subsequently damped by the ambient medium, has been recently considered in other applications (e.g. Nekrasov & Shadmehri 2012;Stroman et al 2012;Wiener et al 2013). Magnetic field amplification by similar processes also considerably increases the rate of cosmic ray acceleration, possibly allowing supernova remnants to generate galactic cosmic rays up to the "knee" (around 10 15 eV) and maybe beyond in the cosmic ray energy distribution.…”

Influence of the Backreaction of Streaming Cosmic Rays on Magnetic Field Generation and Thermal Instability

“…We have considered perturbations which are transverse to the background magnetic field and are along and across the cosmic-ray drift velocity. The case of perturbations along the magnetic field was treated by Nekrasov & Shadmehri (2012) where the growth rate due to the back-reaction of cosmic rays considerably larger than that obtained by Bell (2004Bell ( , 2005 and Riquelme & Spitkovsky (2010) has been found. In the present case, we have shown that for sufficiently short-wavelength perturbations the growth rates obtained can in their turn exceed the growth rate found in (Nekrasov & Shadmehri 2012).…”

“…We also consider possible effects of cosmic rays on the thermal instability for the geometry under consideration. We provide a comparison of results obtained in this paper with those of Nekrasov & Shadmehri (2012) and show a difference between them.…”

“…The back-reaction of cosmic rays resulting in strong streaming instabilities is taken into account. It is shown that for sufficiently short wavelength perturbations, the growth rates can exceed the growth rate of cosmic-ray streaming instability along the magnetic field found by Nekrasov & Shadmehri (2012), which is in its turn considerably larger than the growth rate of the Bell instability (2004). The thermal instability is shown not to be subject to the action of cosmic rays in the model under consideration.…”

“…The dynamics of cosmic rays did not play the role (in the analytical consideration). Nekrasov & Shadmehri (2012) have included the back-reaction of cosmic rays in the multi-fluid approach for the model by Riquelmi & Spitkovsky (2010) and found the growth rate for the streaming instability considerably larger than that of Bell (2004Bell ( , 2005 and of Riquelmi & Spitkovsky (2010) by a factor of the square root from the ratio of plasma to cosmic-ray number densities. The second result obtained by Nekrasov & Shadmehri (2012) was that the thermal instability is not subject to the action of cosmic rays in the model considered.…”