Particle acceleration at astrophysical shocks: A theory of cosmic ray origin

The central idea of diffusive shock acceleration is presented from microscopic and macroscopic viewpoints; applied to reactionless test particles in a steady plane shock the mechanism is shown to produce a power law spectrum in momentum with a slope which, to lowest order in the ratio of plasma to particle speed, depends only on the compression in the shock. The associated time scale is found (also by a macroscopic and a microscopic method) and the problems of spherical shocks, as exemplified by a point explosion and a stellar-wind terminator, are treated by singular perturbation theory. The effect of including the particle reaction is then studied. It is shown that if the scattering is due to resonant waves these can rapidly grow with unknown consequences. The possible steady modified shock structures are classified and generalised Rankine-Hugoniot conditions found. Modifications of the spectrum are discussed on the basis of an exact, if rather artificial, solution, a high-energy asymptotic expansion and a perturbation expansion due to Blandford. It is pointed out that no steady solution can exist for very strong shocks; the possible time dependence is briefly discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/46/8/002/pdf

An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas

The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

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Optics in the relativistic regime

Part I. Astronomical Background: 1. High energy astrophysics - an introduction 2. The stars and stellar evolution 3. The galaxies 4. Clusters of galaxies Part II. Physical Processes: 5. Ionisation losses 6. Radiation of accelerated charged particles and bremsstrahlung of electrons 7. The dynamics of charged particles in magnetic fields 8. Synchrotron radiation 9. Interactions of high energy photons 10. Nuclear interactions 11. Aspects of plasma physics and magnetohydrodynamics Part III. High Energy Astrophysics in our Galaxy: 12. Interstellar gas and magnetic fields 13. Dead stars 14. Accretion power in astrophysics 15. Cosmic rays 16. The origin of cosmic rays in our galaxy 17. The acceleration of high energy particles Part IV. Extragalactic High Energy Astrophysics: 18. Active galaxies 19. Black holes in the nuclei of galaxies 20. The vicinity of the black hole 21. Extragalactic radio sources 22. Compact extragalactic sources and superluminal motions 23. Cosmological aspects of high energy astrophysics Appendix References Index.

High Energy Astrophysics

http://absimage.aps.org/image/DAMOP12/MWS_DAMOP12-2012-000066.pdf

Optics in the Relativistic Regime

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The acceleration of cosmic rays in shock fronts – I

The diffusive shock acceleration of cosmic rays by supernova remnants depends upon the generation of magnetic fluctuations by cosmic rays upstream of the shock. Strongly driven, non-resonant, nearly purely growing modes grow more rapidly than the resonant Alfven waves usually considered. Non-linear simulation shows that the magnetic field can be amplified from its seed value by orders of magnitude. The consequences for the maximum attainable cosmic ray energy in supernova remnants are explored.

Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays

The maximum energy for cosmic ray acceleration at supernova shock fronts is usually thought to be limited to around 10 14 ±10 15 eV by the size of the shock and the time for which it propagates at high velocity. We show that the magnetic field can be amplified non-linearly by the cosmic rays to many times the pre-shock value, thus increasing the acceleration rate and facilitating acceleration to energies well above 10 15 eV. A supernova remnant expanding into a uniform circumstellar medium may accelerate protons to 10 17 eVand heavy ions, with charge Ze ,t oZ � 10 17 eV: Expansion into a pre-existing stellar wind may increase the maximum cosmic ray energy by a further factor of 10.

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Cosmic ray acceleration to very high energy through the non-linear amplification by cosmic rays of the seed magnetic field

One dimensional numerical results of the non-linear interaction between cosmic rays and a magnetic field are presented. These show that cosmic ray streaming drives large amplitude Alfvenic waves. The cosmic ray streaming energy is very efficiently transfered to the perturbed magnetic field of the Alfven waves. Thus a magnetic field of interstellar values, assumed in models of supernova remnant blast wave acceleration, would not be appropriate in the region of the shock. The increased magnetic field reduces the acceleration time and so increases the maximum cosmic ray energy, which may provide a simple and elegant resolution to the highest energy galactic cosmic ray problem were the cosmic rays themselves provide the fields necessary for their acceleration.

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Non-linear amplification of a magnetic field driven by cosmic ray streaming

A large flux of cosmic rays streaming through a magnetized plasma creates cavities of low plasma density and low magnetic field. The magnetic field focuses the cosmic ray trajectories into the cavities with the possible formation of filaments or beams of high-energy cosmic rays.

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A. R. Bell

Papers

The acceleration of cosmic rays in shock fronts – I

Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays

Cosmic ray acceleration to very high energy through the non-linear amplification by cosmic rays of the seed magnetic field

Non-linear amplification of a magnetic field driven by cosmic ray streaming

The interaction of cosmic rays and magnetized plasma