Nonlinear shock acceleration. III. Finite wave velocity, wave pressure, and entropy generation via wave damping

Journal Article · Mon Jul 01 04:00:00 EDT 1985 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/163272· OSTI ID:5374450

Eichler, D

The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity of the scattering waves through the background fluid, ..nu../sub ph/, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to E/sup -2/ are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of ..nu../sub ph/, so that earlier results concerning its value remain valid for finite ..nu../sub ph/. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, 4approximately-less-than-tildeM/sub A/approximately-less-than-tilde6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.

• Research Organization: Department of Physics, Ben-Gurion University; and Astronomy Program, University of Maryland
• OSTI ID: 5374450
• Journal Information: Astrophys. J.; (United States), Journal Name: Astrophys. J.; (United States) Vol. 294:1; ISSN ASJOA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCELERATION
ALFVEN WAVES
COSMIC RADIATION
DAMPING
ENERGY SPECTRA
HYDROMAGNETIC WAVES
IONIZING RADIATIONS
MACH NUMBER
NONLINEAR PROBLEMS
ORIGIN
RADIATIONS
SHOCK WAVES
SPECTRA
VELOCITY
WAVE PROPAGATION