Abstract
The motion of an ion in the presence of a constant magnetic field and a perpendicularly propagating electrostatic wave with frequency several times the ion cyclotron frequency is shown to become stochastic for fields satisfying E/Bo > 1/4(Ω/ω)1/3 (ω/k). This stochasticity condition is independent of how close ω is to a cyclotron harmonic. Applications of current interest in supplementary heating of plasmas with rf power near the lower-hybrid frequency are suggested.
Reprinted from Phys. Rev. Lett. 39, 550-4 (1977) by kind permission of the American Physical Society. Fuller accounts of the material presented here may be found in: C. F. F. Karney, “Stochastic Heating of Ions in a Tokamak by RF Power,” Ph.D. Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (May 1977). C. F. F. Karney, “Stochastic Heating by a Lower Hybrid Wave,” PPPL-1429, Princeton University (April 1978).
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References
C. F. F. Karney, A. Bers, and D. C. Watson, Bull. Am. Phys. Soc. 20, 1313 (1975); C. F. F. Karney and A. Bers, MIT Plasma Research Reports No. 76/7, 1976, and No. 76/24, 1976 (unpublished).
G. R. Smith and A. N. Kaufman, Phys. Rev. Lett. 34, 1613 (1975).
G. M. Zaslavskii and B. V. Chirikov, Usp. Fiz. Nauk 105, 3 (1971) [Sov. Phys. Usp. 14, 549 (1972)].
J. Ford, in Fundamental Problems in Statistical Mechanics, edited by E. D. G. Cohen (North-Holland, Amsterdam, 1975), Vol. 3.
G. H. Walker and J. Ford, Phys. Rev. 188, 416 (1969).
This result may also be obtained (to within a factor of order unity) by demanding that trapping be effective, in the sense that an ion in its orbit spends at least a bounce period (2πα 1/2) within the trapping region given by ‖y − ν‖ < √c
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Karney, C.F.F., Bers, A. (1979). Stochastic ion heating by a perpendicularly propagating electrostatic wave. In: Casati, G., Ford, J. (eds) Stochastic Behavior in Classical and Quantum Hamiltonian Systems. Lecture Notes in Physics, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021736
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DOI: https://doi.org/10.1007/BFb0021736
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