Abstract
We use the Vlasov equations for ions and electrons to develop a theory of a double layer in which there are both free and trapped electrons and ions. We find the equations which replace the Langmuir condition and the Bohm conditions and by numerically solving the resultant differential equation we find for particular choices of distribution functions the potential distribution in the layer. We discuss the applicability of this theory to solar flares, and show that conditions in solar flares may be such that double layers can exist for which the free particles have a power-law energy distribution. These particles will be accelerated in a double layer and may in this way account for the production of high-energy particles during the impulsive phase of solar flares.
Similar content being viewed by others
References
Alfvén, H. and Carlquist, P.: 1967,Solar Phys. 1, 220.
Babić, M. and Torvén, S.: 1972, inSecond Int. Conf. on Gas Discharges IEE, London.
Berk, H. L. and Roberts, K. V.: 1967,Phys. Fluids 10, 1595.
Bernstein, I. B., Greene, J. M. and Kruskal, M. D.: 1957,Phys. Rev. 108, 564.
Block, L. P.: 1972,Cosmic Electrodyn. 3, 349.
Bohm, D.: 1949, in A. Guthrie and R. K. Wakerling (eds),Characteristics of Electrical Discharges in Magnetic Fields, McGraw-Hill, New York, p. 77.
Brown, J. C.: 1971,Solar Phys. 18, 489
Brown, J. C. and Melrose, D. B.: 1976,Monthly Notices Roy. Astron. Soc. 176, 15.
Buneman, O.: 1959,Phys. Rev. 115, 503.
Carlquist, P.: 1969,Solar Phys. 7, 377.
Carlquist, P.: 1972,Cosmic Electrodyn. 3, 377.
Datlowe, D. W.: 1975,IAU Symp. 68, 191.
de Jager, C.: 1969, in C. de Jager and Z. Švestka (eds),Solar Flares and Space Research, COSPAR Symp., p. 1.
Goertz, C. K. and Joyce, G.: 1975,Astrophys. Space Sci. 32, 165.
Hamberger, S. M. and Friedman, M.: 1968,Phys. Rev. Letters 21, 674.
Hasan S. S.: 1977, Oxford D. Phil. Thesis (unpublished).
Kahler, S. W., Meekins, J. F., Kreplin, R. W., and Bowyer, C. S.: 1970,Astrophys. J. 162, 293.
Kane, S. R. and Anderson, K. A.: 1970,Astrophys. J. 162, 1003.
Kaplan, S. A. and Tsytovich, V. N.: 1973,Plasma Astrophysics, Pergamon, Oxford.
Korchak, A. A.: 1971,Solar Phys. 18, 284.
Langmuir, I.: 1929,Phys. Rev. 33, 954.
Lin, R. P.: 1975,IAU Symp. 68, 385.
Lin, R. P. and Hudson, H. S.: 1971,Solar Phys. 17, 412.
Montgomery, D. and Joyce, G.: 1968,Plasma Phys. 3, 1.
Moreton, G. E. and Severny, A. B.: 1968,Solar Phys. 3, 282.
Quon, B. H. and Wong, A. Y.: 1976,Phys. Rev. Letters 37, 1393.
Ramaty, R. and Lingenfelter, R. E.: 1975,IAU Symp. 68, 363.
Schamel, H.: 1971,Plasma Phys. 13, 491.
Schamel, H.: 1972,Plasma Phys. 14, 905.
Smith, A.: 1970a,J. Plasma Phys. 4, 511.
Smith, A.: 1970b,J. Plasma Phys. 4, 549.
Smith, D. F. and Priest, E. R.: 1972,Astrophys. J. 176, 487.
Švestka, Z.: 1975,IAU Symp. 68, 427.
Title, A. M. and Andelin, J. P.: 1971,IAU Symp. 43, 298.
Verzariu, P. and Krimigis, S. M.: 1972,J. Geophys. Res. 77, 3985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hasan, S.S., Ter Haar, D. The Alfvén-Carlquist double-layer theory of solar flares. Astrophys Space Sci 56, 89–107 (1978). https://doi.org/10.1007/BF00643464
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00643464