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Strong nonresonant amplification of magnetic fields in particle accelerating shocks

Strong nonresonant amplification of magnetic fields in particle accelerating shocks. A. E. Vladimirov, D. C. Ellison, A. M. Bykov. Submitted to ApJL. In diffusive shock acceleration, the streaming of shock-accelerated particles may induce plasma instabilities.

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Strong nonresonant amplification of magnetic fields in particle accelerating shocks

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  1. Strong nonresonant amplification of magnetic fields in particle accelerating shocks A. E. Vladimirov, D. C. Ellison, A. M. Bykov Submitted to ApJL

  2. In diffusive shock acceleration, the streaming of shock-accelerated particles may induce plasma instabilities. A fast non-resonant instability (Bell 2004, MNRAS) may efficiently amplify short-wavelength modes in fast shocks.

  3. We developed a fully nonlinear model* of DSA based on Monte Carlo particle transport • Magnetic turbulence, bulk flow, superthermal particles derived consistently with each other * Vladimirov, Ellison & Bykov, 2006. ApJ, v. 652, p.1246; Vladimirov, Bykov & Ellison, 2008. ApJ, v. 688, p. 1084

  4. Our model for particle propagation in strong turbulence interpolates between different scattering regimes in different particle energy ranges. Turbulence Particles ~p2 Turbulence spectrum, k·W(k) Particle mean free path, (p) ~(Wres)-1 ~lcor Wavenumber, k Momentum, p

  5. k–wavenumber of turbulent harmonics W(x,k) – spectrum of turbulent fluctuations, (energy per unit volume per unit ∆k). Cascading Dissipation In this work we ignored compression for clarity (does not affect the qualitatively new results) Compression (amplitude) Compression (wavelength) Amplification (corresponds to Bell’s instability)

  6. We study the consequences of two hypotheses: A. No spectral energy transfer (i.e., suppressed cascading), = 0 B. Fast Kolmogorov cascade, = W5/2k3/2ρ-1/2

  7. Trapping ~p2 Shock-generated turbulence with NO CASCADING Effective magnetic field B = 1.1·10-3 G Shocked plasma temperature T = 2.2·107 K

  8. Without cascading, Bell’s instability forms a turbulence spectrum with several distinct peaks. • The peaks occur due to the nonlinear connection between particle transport and magnetic field amplification. • Without a cascade-induced dissipation, the plasma in the precursor remains cold.

  9. Resonant scattering ~p2 Shock-generated turbulence with KOLMOGOROV CASCADE Effective magnetic field B = 1.5·10-4 G Shocked plasma temperature T = 4.4·107 K

  10. With fast cascading, Bell’s instability forms a smooth, hard power law turbulence spectrum • The effective downstream magnetic field turns out lower with cascading, as well as the maximum particle energy • Viscous dissipation of small-scale fluctuations in the process of cascading induces a strong heating of the backround plasma upstream.

  11. Summary • We studied magnetic field amplification in a nonlinear particle accelerating shock dominated by Bell’s nonresonant short-wavelength instability • If spectral energy transfer (cascading) is suppressed, turbulence energy spectrum has several distinct peaks • If cascading is efficient, the spectrum is smoothed out, and significant heating increases the precursor temperature With Cascading Without Cascading

  12. Discussion • With better information about spectral energy transfer (in a strongly magnetized plasma with ongoing nonresonant magnetic field amplification, accounting for the interactions with streaming accelerated particles) we can refine our predictions regarding the amount of MFA, maximum particle energy Emax, heating and compression in particle accelerating shocks (plasma simulations needed) • If peaks do occur, they define a potentially observable spatial scale and an indirect measurement of Emax • Peaks in the spectrum may help explain the rapid variability of synchrotron X-ray emission* • Observations of precursor heating may provide information about the character of spectral energy transfer in the process of MFA * Bykov, Uvarov & Ellison, 2008 (ApJ)

  13. Q? A!

  14. Plots from the paper (just in case)

  15. The following sequence of slides shows how the peaks are formed one by one in the shock precursor. (model A, no cascading)

  16. Solution with NO CASCADING Very far upstream…

  17. Resonance w/particles Turbulence amplification Solution with NO CASCADING Far upstream…

  18. Solution with NO CASCADING Upstream…

  19. Solution with NO CASCADING Particle trapping occured…

  20. Solution with NO CASCADING Second peak formed…

  21. Solution with NO CASCADING The story repeated…

  22. Solution with NO CASCADING And here is the result (downstream)…

  23. The following sequence of slides shows how the peaks are formed one by one in the shock precursor. (model B, Kolmogorov cascade)

  24. Solution with KOLMOGOROV CASCADE Far upstream…

  25. Solution with KOLMOGOROV CASCADE Amplification…

  26. Solution with KOLMOGOROV CASCADE Cascading forms a k-5/3 power law…

  27. Solution with KOLMOGOROV CASCADE Amplification continues in greater k…

  28. Solution with KOLMOGOROV CASCADE And a hard spectrum is formed downstream…

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