Simulations of Ion Acceleration at Non-relativistic Shocks. II. Magnetic Field Amplification (1401.7679v3)

Abstract: We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfv\'enic Mach number $M=100$, and scales with the square root of $M$. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately-strong shocks ($M\lesssim30$) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For $M\gtrsim30$, instead, Bell's non-resonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the free-escape boundary: the far upstream, where field amplification is provided by the current of escaping ions via NRH instability, and the shock precursor, where energetic particles are effectively magnetized, and field amplification is provided by the current in diffusing ions. The presented scalings of magnetic field amplification enable the inclusion of self-consistent microphysics into phenomenological models of ion acceleration at non-relativistic shocks.

Magnetic Field Amplification in Ion Acceleration at Non-Relativistic Shocks

This paper by D. Caprioli and A. Spitkovsky explores the magnetic field amplification associated with ion acceleration at non-relativistic shocks, focusing on the mechanisms underlying such amplification in shock structures. This work extends the authors' prior research into particle acceleration, establishing critical insights into how shock waves magnify magnetic fields and affect the dynamics of charged particles such as cosmic rays (CRs).

Magnetic Field Amplification Observations

Simulation results detail that for strong shocks, characterized by high Alfvénic Mach numbers (M ≈ 100), the upstream magnetic field can be amplified by a factor exceeding 10. This amplification factor exhibits a dependence on the Mach number, scaling approximately with the square root of M. More specifically, the work illustrates that when M is less than 30, the magnetic turbulence's energy spectrum aligns well with models of diffusive shock acceleration (DSA). For M greater than 30, however, the non-resonant hybrid (NRH) instability proposed by Bell proceeds more rapidly than the resonant instabilities, led by upstream escaping particles.

Key Simulations and Findings

Through innovative kinetic simulations deploying large computational domains, the study discerns the crucial role of NRH instabilities in amplifying magnetic fields, especially at high Mach numbers. These instabilities manifest primarily within the far upstream regions, instigated by streaming ions that form perturbations shorter than the ions' gyroradii. In the nonlinear phase, these instabilities evolve to effectively disrupt the ion current, albeit differently depending on the localized regimes of the shock.

The implications differentiate two essential regions ahead of strong shocks: the far-upstream region inspired by free-streaming escaping ions exciting the NRH instability, and the shock precursor, where CRs are sufficiently magnetized, facilitating field amplification via ion currents. The framework established by these kinetic simulations provides a foundation for encoding such microphysics into phenomenological models applicable to astrophysical objects like supernova remnants (SNRs).

Theoretical and Practical Implications

The theoretical contribution primarily revolves around reinforcing the concept that CR-induced instabilities, particularly in environments with M ≥ 30, could be substantial enough to account for the observed large-scale amplification in SNR shocks, supporting their high magnetic fields. On a practical level, these insights allow researchers to better model cosmic phenomena involving shock waves and particle acceleration. By addressing the scaling laws for amplification, this study enhances our predictive capabilities regarding synchrotron emission across various astrophysical environments.

Conclusions and Future Directions

This paper solidifies the role of NRH instabilities as pivotal agents of magnetic field amplification at high-Mach-number shocks. Future research directions could explore the interplay of additional instabilities, their influence on CR spectra, and the integration of 3D simulations for more sophisticated modeling. An enhanced understanding of particle diffusion in amplified fields and improved simulation of maximum CR energy dynamics will further refine our comprehension of ion acceleration processes across the cosmos. These efforts will underpin the expansion of non-linear DSA frameworks and improve the predictive accuracy of synchrotron radiation models.