Skip to main content
SpringerLink
Log in

The relativistic quasilinear theory of particle acceleration by hydromagnetic turbulence

  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The quasilinear theory of acceleration of relativistic particles by hydromagnetic turbulence is treated in the adiabatic limit of small gyration radius. The theory is based on the relativistic Vlasov equation; however, a given pitch-angle scattering rate by microturbulence is postulated and is added to this equation. The resulting acceleration is found to be given by a diffusion coefficient in total momentum, which is proportional to the spectrum of turbulence with a rate coefficient γ. γ is a frequency that represents the efficiency of each wave component of the turbulence in producing acceleration. It is given as an integral over the solution of a differential equation in pitch angle. γ is evaluated in various limiting cases and is shown to lead to familiar forms of acceleration, such as Fermi acceleration and magnetic pumping. Thus, a comprehensive theory of these forms of heating is achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Berger, J. M., Newcomb, W. A., Dawson, J. M., Frieman, E. A., Kulsrud, R. M., and Lenard, A.: 1958,Phys. Fluids 1, 301.

    Google Scholar 

  • Chew, G. F., Goldberger, M. L., and Low, F. E.: 1956,Los Alamos Lecture Notes on Physics of Ionized Gases LA-2055 [see Kulsrud (1962)].

  • Davis, L.: 1956,Phys. Rev. 101, 1593.

    Google Scholar 

  • Drummond, W. E. and Pines, D.: 1962,Nuclear Fusion Supplement, Part 3, 1049.

    Google Scholar 

  • Fermi, E.: 1949,Phys. Rev. 75, 1169.

    Google Scholar 

  • Fermi, E.: 1964,Astrophys. J. 119, 1.

    Google Scholar 

  • Hall, D. E. and Sturrock, P. A.: 1967,Phys. Fluids 10, 1593.

    Google Scholar 

  • Jokipii, J. R.: 1966,Astrophys. J. 141, 480.

    Google Scholar 

  • Kulsrud, R. M.: 1962,Rendiconti della Scuola Internazionale di Fiscia ‘Enrico Fermi’ Course 25 (ed. by M. N. Rosenbluth), Academic Press, New York, p. 54.

    Google Scholar 

  • Kulsrud, R. M. and Pearce, W. P.: 1969,Astrophys. J. 156, 303.

    Google Scholar 

  • Melrose, D. B.: 1969,Astrophys. Space Sci. 4, 165.

    Google Scholar 

  • Sagdeev, R. Z. and Galeev, A. A.: 1969,Nonlinear Plasma Theory (edited by T. M. O'Neil and D. L. Book), W. A. Benjamin, New York.

    Google Scholar 

  • Swann, W. F. G.: 1933,Phys. Rev. 43, 217.

    Google Scholar 

  • Wentzel, D. G.: 1969,Astrophys. J. 156, 303.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Plasma Physics Laboratory, Princeton University, Princeton, New Jersey, U.S.A.

    Russell M. Kulsrud

  2. Instituto di Fisica Generale, Turin, Italy

    Attilio Ferrari

Authors
  1. Russell M. Kulsrud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Attilio Ferrari
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kulsrud, R.M., Ferrari, A. The relativistic quasilinear theory of particle acceleration by hydromagnetic turbulence. Astrophys Space Sci 12, 302–318 (1971). https://doi.org/10.1007/BF00651420

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00651420

Keywords

Search

Navigation