A New Cosmic-Ray-driven Instability

Abstract

Cosmic-ray-driven (CR-driven) instabilities play a decisive role during particle acceleration at shocks and CR propagation in galaxies and galaxy clusters. These instabilities amplify magnetic fields and modulate CR transport so that the intrinsically collisionless CR population is tightly coupled to the thermal plasma and provides dynamical feedback. Here, we show that CRs with a finite pitch angle drive electromagnetic waves (along the background magnetic field) unstable on intermediate scales between the gyroradii of CR ions and electrons as long as CRs are drifting with a velocity less than half of the Alfvén speed of electrons. By solving the linear dispersion relation, we show that this new instability typically grows faster by more than an order of magnitude in comparison to the commonly discussed resonant instability at the ion gyroscale. We find the growth rate for this intermediate-scale instability and identify the growing modes as background ion-cyclotron modes in the frame that is comoving with the CRs. We confirm the theoretical growth rate with a particle-in-cell simulation and study the nonlinear saturation of this instability. We identify three important astrophysical applications of this intermediate-scale instability, which is expected to (1) modulate CR transport and strengthen CR feedback in galaxies and galaxy clusters, (2) enable electron injection into the diffusive shock acceleration process, and (3) decelerate CR escape from the sites of particle acceleration, which would generate gamma-ray halos surrounding CR sources such as supernova remnants.

The mechanism of efficient electron acceleration at parallel non-relativistic shocks

“…It is important to note here that collisionless shocks found in the intracluster medium have M s ∼ 1 to 3 (Ryu et al 2003;Pfrommer et al 2006;Vazza et al 2009;Schaal et al 2016), and for such low values of the sonic Mach number, the intermediate-scale growth rates are much larger in comparison to that at the gyro-scale (Shalaby et al 2021). This implies a stronger impact of the intermediate-scale unstable modes on the acceleration of electrons in the intracluster medium.…”

“…We use 200 particles per species in each computational cell. The boundary of the computational domain expands with time on the right-hand (Shalaby et al 2021) and thus the small scale ion-cyclotron wave modes that are comoving with the upstream plasma with velocity υu = −0.1c are amplified, i.e., come from solutions of D + = 0 (see Equation 1). Small scale unstable wavemodes in the other (blue and black) cases are whistler waves, i.e., they derive from solutions of D − = 0 (see Equation 1).…”

Comparing different closure relations for cosmic ray hydrodynamics

“…The beam mode is characterised by a high degree of anisotropy in the CR distribution. However, if this anisotropy is large enough, additional micro-scale plasma processes such as the non-resonant hybrid instability (Bell 2004) and the intermediate-scale instability (Shalaby et al 2021) start to dominate and influence the CR evolution. Therefore, to provide a consistent description of CR dynamics these additional kinetic processes need to be incorporated in the fluid description through the scattering terms.…”

“…Here, we focus on the interaction of CRs with small-scale gyroresonant Alfvén waves mediated by pitch-angle scattering. Other mechanisms such as external confinement of CRs by MHD turbulence (Lazarian & Beresnyak 2006) or scattering of CRs by the intermediate scale instability (Shalaby et al 2021) are not considered but could be included in an extension of the presented theory. The phase-space diffusion coefficients for pitchangle scattering in our mono-energetic approximation can be derived from Schlickeiser (1989) in the first-order limit in 𝑣 a /𝑐 so that the scattering term reads:…”

“…On these length scales MHD is not applicable and kinetic plasma physics dictates the evolution of CRs (Kulsrud 2004). Various plasma processes such as the gyroresonant (Kulsrud & Pearce 1969), the intermediate scale (Shalaby et al 2021), or Bell's instability (Bell 2004) can strongly influence the propagation of CRs.…”