NONLINEAR STUDY OF BELL'S COSMIC RAY CURRENT-DRIVEN INSTABILITY

By M. Riquelme, A. Spitkovsky. 2008

137 citations recorded by the source corpus.

The cosmic ray current-driven (CRCD) instability, predicted by Bell, consists of nonresonant, growing plasma waves driven by the electric current of cosmic rays (CRs) that stream along the magnetic field ahead of both relativistic and nonrelativistic shocks. Combining an analytic, kinetic model with one-, two-, and three-dimensional particle-in-cell simulations, we confirm the existence of this instability in the kinetic regime and determine its saturation mechanisms. In the linear regime, we show that, if the background plasma is well magnetized, the CRCD waves grow exponentially at the rates and wavelengths predicted by the analytic dispersion relation. The magnetization condition implies that the growth rate of the instability is much smaller than the ion cyclotron frequency. As the instability becomes nonlinear, significant turbulence forms in the plasma. This turbulence reduces the growth rate of the field and damps the shortest wavelength modes, making the dominant wavelength, λd, grow proportional to the square of the field. At constant CR current, we find that plasma acceleration along the motion of CRs saturates the instability at the magnetic field level such that vA ∼ vd,cr, where vA is the Alfvén velocity in the amplified field, and vd,cr is the drift velocity of CRs. The instability can also saturate earlier if CRs get strongly deflected by the amplified field, which happens when their Larmor radii get close to λd. We apply these results to the case of CRs propagating in the upstream medium of the forward shock in supernova remnants. If we consider only the most energetic CRs that escape from the shock, we obtain that the field amplification factor of ∼10 can be reached. This confirms the CRCD instability as a potentially important component of magnetic amplification process in astrophysical shock environments.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ff9aa9ba4d1b73867eb7ec664db65d38102e5209

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In Astronomy and Astrophysics

1. L. Sironi
2. A. Spitkovsky
3. D. Caprioli
4. Kohta Murase
5. Y. Ohira
6. R. Yamazaki
7. M. Petropoulou
8. J. Arons

In Nuclear and High Energy Physics

1. A. Spitkovsky
2. L. Sironi
3. D. Caprioli
4. Kohta Murase
5. Y. Ohira
6. R. Yamazaki
7. M. Petropoulou
8. J. Arons

Citations in the corpus

• Gamma-rays from molecular clouds illuminated by cosmic rays escaping from interacting supernova remnants (2010, background): “…al. 2007; Ohira et al. 2009b) and many numerical simulations (Lucek & Bell 2000; Giacalone & Jokipii 2007; Niemiec et al. 2008; Reville et al. 2008; Riquelme & Spitkovsky 2009; Inoue et al. 2009; Ohira et al. 2009a; Vladimirov et al. 2009), the saturation of the magnetic-field amplification and…”
• The origin of galactic cosmic rays (2013, unknown): “Both MHD simulations (Bell 2004) and Particle-in-Cell simulations of this instability carried out by Riquelme and Spitkovsky (2009) show how the growth leads to the development of modes on larger spatial scales.”
• PARTICLE ACCELERATION IN RELATIVISTIC MAGNETIZED COLLISIONLESS ELECTRON–ION SHOCKS (2010, background): “On the other hand, Bell’s instability saturates when the self-generated magnetic energy approaches the energy density of returning ions (Riquelme & Spitkovsky 2009), which is larger for higher obliquities since the returning particles accumulate in a smaller region ahead of the shock, as discussed…”
• Cosmic-ray acceleration in supernova remnants: non-linear theory revised (2012, background): “[66, 67], while in the linear regime of the instability modes are almost purely growing, the saturation of Bell modes in the non-linear regime (δB/B0 ∼ 10) may occur exactly because of the local Alfvén velocity to become comparable with the drift velocity of the CR current.”
• SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. II. MAGNETIC FIELD AMPLIFICATION (2014, background): “Riquelme & Spitkovsky (2009) have derived the nonlinear dispersion relation for NRH modes, from which it is possible to work out phase velocity and growth rate (ω/k and γ ) for arbitrary amplification factor b.”