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Physics of Plasmas / Volume 14 / Issue 9 / ARTICLES / Basic Plasma Phenomena, Waves, Instabilities

Phys. Plasmas 14, 092103 (2007); http://dx.doi.org/10.1063/1.2769968 (8 pages)

A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions

Hong Qin, Cynthia K. Phillips, and Ronald C. Davidson

Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA

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(Received 21 March 2007; accepted 17 July 2007; published online 5 September 2007)

The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle’s gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle’s orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle’s gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. SYMMETRY IN INTEGRATION ALONG UNPERTURBED TRAJECTORIES
  3. SUSCEPTIBILITY WITHOUT INFINITE SUMS AND THE ASYMPTOTIC FORM FOR LARGE z
  4. CONCLUSIONS AND FUTURE WORK

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KEYWORDS and PACS

Keywords

Bessel functions, cyclotron resonance, plasma confinement, plasma flow

PACS

  • 52.55.-s

    Magnetic confinement and equilibrium

  • 52.35.Bj

    Magnetohydrodynamic waves (e.g., Alfven waves)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2769968

PUBLICATION DATA

ISSN

1070-664X (print)  
1089-7674 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    N. Fisch, Rev. Mod. Phys. 59, 175 (1987).

    B. S. Newberger, J. Math. Phys. 23, 1278 (1982)JMAPAQ000023000007001278000001.

    H. Qin, W. M. Tang, and W. W. Lee, Phys. Plasmas 7, 4433 (2000)PHPAEN000007000011004433000001.

    H. Qin and W. M. Tang, Phys. Plasmas 11, 1052 (2004)PHPAEN000011000003001052000001.



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