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Weightiness of the Dispersive Rate in Stochastic Acceleration Processes

Published online by Cambridge University Press:  12 April 2016

J. Pérez-Peraza
Affiliation:
Instituto de Geofísica, UNAM, 04510 CU., Mexico D.F., Mexico
A. Gallegos-Cruz
Affiliation:
UPIICSA, IPN, Te 950, 08400 Mexico D.F., Mexico

Abstract

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We present analytical solutions to the transport equation of the accelerated particles that are valid over the entire energy range (nonrelativistic, transrelativistic, and ultrarelativistic) for the time-dependent and equilibrium cases. On the basis of these overall spectra, we have studied the relative importance of the term of average (systematic) energy increase and the term of diffusion (spread) in energy that define the evolution of accelerated particles within the frame of a simplified diffusion-convection transport equation, when the particle distribution function N(E, t) is assumed to be independent of spatial pitch-angle diffusion (isotropic). Since in some astrophysical works, only the term of average energy increase in the simplified transport equation in energy space is considered to be leading directly to a power-law-type spectrum, we have established the conditions under which such an approximation may be justified. The analysis is illustrated for acceleration by two different kinds of turbulence: MHD and Langmuir waves. The omission of the term of energy spread leads, in general, to an important depletion or overproduction of the accelerated particle flux that must be seriously considered in any calculation of the flux of secondary radiation produced by the accelerated particles. The presented analytical spectra may be of particular relevance to gamma-ray, neutron, and pion production in solar flares as well as in other astrophysical sites.

Subject headings: acceleration of particles — MHD — Sun: general — turbulence — wave motions

Type
Solar Flares
Copyright
Copyright © The American Astronomical Society 1994

References

Achterberg, A. 1981, A&A, 97, 259 Google Scholar
Bai, T. 1986, ApJ, 308, 912 CrossRefGoogle Scholar
Borosky, J.E., & Eilek, J.A. 1986, ApJ, 308, 929 CrossRefGoogle Scholar
Byakov, A.M. 1992, in AIP Conf. Proc. 264, Particle Acceleration in Cosmic Plasmas (New York: AIP), 221 Google Scholar
Cane, H.V., McGuire, R.E., & von Rosenvinge, T.T. 1986, ApJ, 301, 448 CrossRefGoogle Scholar
Canuto, V., Chou, C.K., & Facio-Canuto, R. 1978, Fund. Cosmic Phys., 3, 221 Google Scholar
Chen, F.F. 1974, Introduction to Plasma Physics (New York: Plenum), chap. 7Google Scholar
Cheng, C.C. 1972, Space Sci. Rev., 13, 3 CrossRefGoogle Scholar
Davis, L. 1956, Phys. Rev., 101, 351 CrossRefGoogle Scholar
Dung, R., & Schlickeiser, R. 1990, A&A, 237, 504 Google Scholar
Dung, R., & Schlickeiser, R. 1990, A&A, 240, 537 Google Scholar
Eichler, D. 1979, ApJ, 229, 413 CrossRefGoogle Scholar
Fermi, E. 1949, Phys. Rev., 75, 1169 CrossRefGoogle Scholar
Gallegos-Cruz, A., & Pérez-Peraza, J. 1987, Proc. 20th Internat. Cosmic-Ray Conf. (Moscow), 8, 164 Google Scholar
Gallegos-Cruz, A., & Pérez-Peraza, J. 1991, Proc. 22nd Internat. Cosmic-Ray Conf. (Dublin), 3, 1 Google Scholar
Gallegos-Cruz, A., Pérez-Peraza, J., Miroschnichenko, L.I., & Vashenyuk, E.V. 1993, Adv. Space Res., 13, 187 CrossRefGoogle Scholar
Ginzburg, V.L., & Syrovatskii, L.I. 1964, The Origin of Cosmic Rays (New York: Pergamon)CrossRefGoogle Scholar
Heristchi, Dj., Trottet, G., & Pérez-Peraza, J. 1976, Sol. Phys., 49, 151 CrossRefGoogle Scholar
Heyvaerts, J. 1981, in Solar Flare Magnetohydrodynamics, ed. Priest, E.R. (New York: Gordon & Breach), 429 Google Scholar
Hoyng, P. 1978a, A&A, 55, 23 Google Scholar
Hoyng, P. 1978b, A&A, 55, 31 Google Scholar
Jones, F.C. 1992, in AIP Conf. Proc. 264, Particle Acceleration in Cosmic Plasmas (New York: AIP), 71 Google Scholar
Kulsrud, R.M., & Ferrari, A. 1971, Ap&SS, 12, 302 Google Scholar
Lacombe, C., & Manganey, A. 1969, A&A, 1, 325 Google Scholar
MacKinnon, A.L., Brown, J.C., Trottet, G., & Vilmer, N. 1983, A&A, 119, 297 Google Scholar
Melrose, D.B. 1968, Ap&SS, 2, 71 Google Scholar
Melrose, D.B. 1980, Plasma Astrophysics, vol. 2 (New York: Gordon & Breach), chap. 8Google Scholar
Melrose, D.B. 1986, Instabilities in Space and Laboratory Plasmas (Cambridge: Cambridge Univ. Press), 233 CrossRefGoogle Scholar
Melrose, D.B., & Brown, J.C. 1976, MNRAS, 176, 15 CrossRefGoogle Scholar
Miller, J.A. 1991, ApJ, 376, 342 CrossRefGoogle Scholar
Miller, J.A., Guessoum, N., & Ramaty, R. 1990, ApJ, 361, 701 CrossRefGoogle Scholar
Miller, J.A.. Ramaty, R., & Murphy, R.J. 1987, Proc. 20th Internat. Cosmic-Ray Conf. (Moscow), 3, 33 Google Scholar
Parker, E.N., & Tidman, D.A. 1958, Phys. Rev., 11, 1206 CrossRefGoogle Scholar
Pérez-Peraza, J. 1986, Space Sci. Rev., 44, 91 CrossRefGoogle Scholar
Pérez-Peraza, J., & Gallegos-Cruz, A. 1994, Geofis. Internat., 33 Google Scholar
Pérez-Peraza, J., Gálvez, M., & Lara, R. 1977, Space Res., 18 Google Scholar
Pérez-Peraza, J., Gálvez, M., & Lara, R. 1978, Proc. 15th Internat. Cosmic-Ray Conf. (Plodviv), 5, 23 Google Scholar
Pikel’ner, S.B., & Livishts, M.A. 1977, Soviet Astron., 21, 601 Google Scholar
Priest, E.R. 1973, ApJ, 181, 227 CrossRefGoogle Scholar
Priest, E.R. 1984, Solar Magnetohydrodynamics (Dordrecht: Reidel)Google Scholar
Ramaty, R. 1979, in AIP Conf. Proc. 56, Particie Acceleration in Astrophysics, ed. Arons, J., Max, C., & McKee, C. (New York: AIP), 135 Google Scholar
Ramaty, R. 1987, Sol. Phys., 113, 203 CrossRefGoogle Scholar
Rose, W.K., Bcall, J.H. Guillory, J., & Kaimer, S. 1987, ApJ, 314, 95 CrossRefGoogle Scholar
Schatzman, E. 1966, in Proc. Les Houches Summer School of Theoretical Physics (New York: Gordon & Breach), 229 Google Scholar
Schlickeiser, R. 1989, ApJ, 336, 243 CrossRefGoogle Scholar
Schlickeiser, R. 1992, in AIP Conf. Proc. 264, Particle Acceleration in Cosmic Plasmas (New York: AIP), 71 Google Scholar
Steinacker, J., & Miller, J.A. 1992, in AIP Conf. Proc. 264, Particle Acceleration in Cosmic Plasmas (New York: AIP), 235 Google Scholar
Stix, T.H. 1975, Nucl. Fusion, 15, 737 CrossRefGoogle Scholar
Tsytovich, V.N. 1966, Soviet Phys. Uspekhi, 9, 370 CrossRefGoogle Scholar
Tsytovich, V.N. 1970, Non-linear Effects in Plasma (New York: Plenum), chap. 6CrossRefGoogle Scholar
Tsytovich, V.N. 1977, Theory of Turbulent Plasma (New York: Plenum), chap. 5CrossRefGoogle Scholar
Tverskoi, B.A. 1967, Soviet Phys. JETP, 25, 317; English trans. 1968, 26, 821Google Scholar
Vilmer, N., Kane, S.R., & Trottet, G. 1982, A&A, 108, 306 Google Scholar
Vilmer, N., Trottet, G., & MacKinnon, A.L. 1986, A&A, 156, 64 Google Scholar