Bifurcation in first-order fermi acceleration and the origin of cosmic rays

  • M. A. Malkov
Plasma And turbulence
Part of the Lecture Notes in Physics book series (LNP, volume 511)


Strong astrophysical shocks are probably the most powerful accelerators in the universe. The main basis for the shock acceleration to perform so efficiently is believed to be created by accelerated particles themselves through their backreaction on the shock structure resulting in a substantial increase of the shock compression. Such an accelerating shock should thus be considered as a dynamical system with the pronounced self-organization. We review the current state of the theory of nonlinear shock acceleration. The main emphasis is on the bifurcation of the solutions for the acceleration efficiency in terms of the rate at which particles are drawn from thermal plasma (injection rate), their maximum energy (cut-off) and the Mach number of the shock. The bifurcation diagram shows that there exists a critical injection rate below which only a relatively inefficient acceleration is possible whereas above this quantity the acceleration may become extremely efficient. On the other hand, at least in a stationary regime in which all particles leave the system at or below the energy cut-off, the acceleration process can hardly be continued in a very efficient way to very high energies. A number of plasma processes inside the shock transition may drive the system to the inefficient acceleration regime. We speculate on a possible relevance of these results to the lack of evidence of high energy protons in supernova remnant shocks.


Mach Number Bifurcation Diagram Injection Rate Shock Front Accelerate Particle 
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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • M. A. Malkov
    • 1
  1. 1.Max-Planck Institut für KernphysikHeidelbergGermany

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