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Particle acceleration at a perpendicular shock

Gang Li, G. P. Zank and Olga Verkhoglyadova Institute of Geophysics and Planetary Physics, University of California, Riverside, CA 92521, USA. Particle acceleration at a perpendicular shock. SHINE 2006 Zermatt, Utah August 3rd. Outline. Perpendicular and parallel shocks from observation.

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Particle acceleration at a perpendicular shock

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  1. Gang Li, G. P. Zank and Olga Verkhoglyadova Institute of Geophysics and Planetary Physics, University of California, Riverside, CA 92521, USA Particle acceleration at a perpendicular shock SHINE 2006 Zermatt, Utah August 3rd

  2. Outline • Perpendicular and parallel shocks from observation. • perpendicular diffusion coefficient, NLGC theory • Acceleration at a perpendicular shock, maximum and injection energy • Can the injection requirement (isotropy) be relaxed?

  3. Difference between parallel and perp. shock Perpendicular shock Quasi-perp shock

  4. Particle acceleration at a perpendicular shock Alfven wave intensity goes to zero at a perp. shock, and _parallel ~ 1/== > no time to reach ~ GeV. but, _perp is smaller, so maybe a perpendicular shock acceleration? Need a good theory of _perp  = _parallel /(1 + (_parall/ rl)2) Simple QLT: Non-linear-Guiding-center:

  5. NONLINEAR GUIDING CENTER THEORY Matthaeus, Qin, Bieber, Zank [2003] derived a nonlinear theory for the perpendicular diffusion coefficient, which corresponds to a solution of the integral equation Superposition model: 2D plus slab Solve the integral equation approximately (Zank, Li, Florinski, et al, 2004): modeled according to QLT.

  6. Anisotropy and the injection threshold Diffusion tensor: Since , the anisotropy is defined by For a nearly perpendicular shock To apply diffusive shock acceleration

  7. Anisotropy and the injection threshold Injection threshold as a function of angle for Anisotropy as a function of energy (r = 3) Remarks: 1)Anisotropy very sensitive to 2) Injection more efficient for quasi-parallel and strictly perpendicular shocks

  8. Particle acceleration at Perp. shock: recipes • STEP 1: Evaluate K_perp at shock using NLGC theory instead of wave growth expression. Parallel mfp evaluated on basis of QLT (Zank et al. 1998.

  9. Particle acceleration at Perp. shock: recipes • STEP 2: Evaluate injection momentum p_min by requiring the particle anisotropy to be small.

  10. a f a f z a f a f b g R t q t p max » k ¢ ¢ a f p d ln p & 2 R t u p inj 1 Particle acceleration at Perp. shock: recipes • STEP 3: Determine maximum energy by equating dynamical timescale and acceleration timescale. Remarks: Like quasi-parallel case, p_max decreases with increasing heliocentric distance.

  11. Maximum and injection energies

  12. Difference between parallel and perp. shock

  13. Backup

  14. Shock acceleration time scale Particle scattering strength Hard sphere scattering: Weak scattering: Strong scattering:

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