@article{vladimirov_bykov_ellison_2009, title={SPECTRA OF MAGNETIC FLUCTUATIONS AND RELATIVISTIC PARTICLES PRODUCED BY A NONRESONANT WAVE INSTABILITY IN SUPERNOVA REMNANT SHOCKS}, volume={703}, ISSN={["2041-8213"]}, DOI={10.1088/0004-637X/703/1/L29}, abstractNote={We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA), and the nonlinear feedback of particles and fields on the bulk flow are derived consistently. The shock structure depends critically on the efficiency of turbulence cascading. If cascading is suppressed, MFA is strong, the shock precursor is stratified, and the turbulence spectrum contains several discrete peaks. These peaks, as well as the amount of MFA, should influence synchrotron X-rays, allowing observational tests of cascading and other assumptions intrinsic to the nonlinear model of nonresonant wave growth.}, number={1}, journal={ASTROPHYSICAL JOURNAL LETTERS}, author={Vladimirov, Andrey E. and Bykov, Andrei M. and Ellison, Donald C.}, year={2009}, month={Sep}, pages={L29–L32} }
 @article{ellison_vladimirov_2008, title={Magnetic field amplification and rapid time variations in SNR RX J1713.7-3946}, volume={673}, ISSN={["2041-8213"]}, DOI={10.1086/527359}, abstractNote={Evidence is accumulating suggesting that collisionless shocks in supernova remnants (SNRs) can amplify the interstellar magnetic field to hundreds of microgauss or even milligauss levels, as recently claimed for SNR RX J1713.7–3946. If these fields exist, they are almost certainly created by magnetic field amplification (MFA) associated with the efficient production of cosmic rays by diffusive shock acceleration (DSA) and their existence strengthens the case for SNRs being the primary source of Galactic cosmic-ray ions to the “knee” and beyond. However, the high magnetic field values in SNRs are obtained exclusively from the interpretation of observations of radiation from relativistic electrons, and if MFA via nonlinear DSA produces these fields, the magnetic field that determines the maximum ion energy will be substantially less than the field that determines the maximum electron energy. We use results of a steady-state Monte Carlo simulation to show how nonlinear effects from efficient cosmic-ray production and MFA reduce the maximum energy of protons relative to what would be expected from test-particle acceleration.}, number={1}, journal={ASTROPHYSICAL JOURNAL LETTERS}, author={Ellison, Donald C. and Vladimirov, Andrey}, year={2008}, month={Jan}, pages={L47–L50} }
 @article{vladimirov_bykov_ellison_2008, title={TURBULENCE DISSIPATION AND PARTICLE INJECTION IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION WITH MAGNETIC FIELD AMPLIFICATION}, volume={688}, ISSN={["1538-4357"]}, DOI={10.1086/592240}, abstractNote={The highly amplified magnetic fields suggested by observations of some supernova remnant shells are most likely an intrinsic part of efficient particle acceleration by shocks. This strong turbulence, which may result from cosmic-ray-driven instabilities, both resonant and nonresonant, in the shock precursor, is certain to play a critical role in self-consistent, nonlinear models of strong, cosmic-ray-modified shocks. Here we present a Monte Carlo model of nonlinear diffusive shock acceleration (DSA) accounting for magnetic field amplification through resonant instabilities induced by accelerated particles, and including the effects of dissipation of turbulence upstream of a shock and the subsequent precursor plasma heating. Feedback effects between the plasma heating due to turbulence dissipation and particle injection are strong, adding to the nonlinear nature of efficient DSA. Describing the turbulence damping in a parameterized way, we reach two important results: first, for conditions typical of supernova remnant shocks, even a small amount of dissipated turbulence energy (~10%) is sufficient to significantly heat the precursor plasma; and second, the heating upstream of the shock leads to an increase in the injection of thermal particles at the subshock by a factor of several. In our results, the response of the nonlinear shock structure to the boost in particle injection prevented the efficiency of particle acceleration and magnetic field amplification from increasing. We argue, however, that more advanced (possibly nonresonant) models of turbulence generation and dissipation may lead to a scenario in which particle injection boost due to turbulence dissipation results in more efficient acceleration and even stronger amplified magnetic fields than without the dissipation.}, number={2}, journal={ASTROPHYSICAL JOURNAL}, author={Vladimirov, Andrey E. and Bykov, Andrei M. and Ellison, Donald C.}, year={2008}, month={Dec}, pages={1084–1101} }
 @article{vladimirov_ellison_bykov_2006, title={Nonlinear diffusive shock acceleration with magnetic field amplification}, volume={652}, ISSN={["1538-4357"]}, DOI={10.1086/508154}, abstractNote={We introduce a Monte Carlo model of nonlinear diffusive shock acceleration that allows for the generation of large-amplitude magnetic turbulence, i.e., ΔB ≫ B0, where B0 is the ambient magnetic field. The model is the first to include strong wave generation, efficient particle acceleration to relativistic energies in nonrelativistic shocks, and thermal particle injection in an internally self-consistent manner. We find that the upstream magnetic field B0 can be amplified by large factors and show that this amplification depends strongly on the ambient Alfvén Mach number. We also show that, in the nonlinear model, large increases in B do not necessarily translate into a large increase in the maximum particle momentum a particular shock can produce, a consequence of high-momentum particles diffusing in the shock precursor where the large amplified field converges to the low ambient value. To deal with the field growth rate in the regime of strong fluctuations, we extend to strong turbulence a parameterization that is consistent with the resonant quasi-linear growth rate in the weak turbulence limit. We believe our parameterization spans the maximum and minimum range of the fluctuation growth, and within these limits we show that the nonlinear shock structure, acceleration efficiency, and thermal particle injection rates depend strongly on the yet to be determined details of wave growth in strongly turbulent fields. The most direct application of our results will be to estimate magnetic fields amplified by strong cosmic-ray modified shocks in supernova remnants.}, number={2}, journal={ASTROPHYSICAL JOURNAL}, author={Vladimirov, Andrey and Ellison, Donald C. and Bykov, Andrei}, year={2006}, month={Dec}, pages={1246–1258} }