1. Acceleration of energetic particles by compressive plasma waves Ming Zhang Department of Physics and Space Sciences, Florida Institute of Technology Seesion 4, SH2.X-907, Friday August 12, 2011, 17:06-18:30 China Railway Construction Plaza

3. Suprathermal Tail Spectra
Graph from G. Gloeckler and L. Fisk (2006)
Fisk and Gloeckler suggested acceleration by stochastic acceleration similar to second-order Fermi mechanism

4. Diffusive Compression Acceleration

5. Spectrum after acceleration by 1 wave in various forms
Speed
profile

6. Spectrum of particles after N acceleration/cooling cycles

7. Extended range of mean free path for effective acceleration
shock

9. Spectrum produced by square wave with continuous injection
(no large-scale adiabatic cooling)

10. The power-law slope does not depend on wave compression ratio.
Produced by tooth wave
The slope if the power-law is determined by the difference of power-law slopes between acceleration by compression egion and cooling by rarefaction region.
The power-law slope does not depend on wave compression ratio.
The power-law slope does not depend on wave shape.
The power-law slope does not depend on diffusion coefficient.
The slope establishes as long as there are enough number of waves.

11. Spectra with losses

13. Back-reaction of accelerated particles

15. Comparison with momentum diffusion from perturbation approximation (Bykov and Toptygin (1983)
In co-moving frame
Reproduce all the steady (asymptotic) solutions of this model
Diffusion is a good approximation after large number of waves

16. Summary
Acceleration of energetic particles by compressional plasma waves in the diffusion-dominated regime is very fast.
With continuous particle injection, all spectra accelerated by a large number of waves approaches to a universal power-law spectrum above injection energy and flat spectrum below injection energy.
without adiabatic cooling loss, the power-law index is always -3, which is independent of anything model parameters. This slope establishes as long as there are enough number of waves.
with cooling, the power-law slope is steeper.
Pressure of accelerated particles can build up very quickly. If the pressure can reduce the amplitude of waves, the power-law slope will eventually approach -5 to maintain finite but large enough pressure.
Acceleration of energetic particles by compressional plasma waves behaves similarly but differently (finite wave cycles) from traditional second-order Fermi acceleration. Dpp ~ D0p2

17. Failure of second order Fermi acceleration
Model A: Plain diffusive shock acceleration model
Model B: Shock acceleration + second-order Fermi acceleration in the heliosheath
Model C: Shock acceleration + continuous compression in the heliosheath

18. Particle acceleration by adiabatic compression in convection dominated regime