Solar Physics

, Volume 291, Issue 12, pp 3637–3658 | Cite as

Is Cyclotron Maser Emission in Solar Flares Driven by a Horseshoe Distribution?

  • D. B. Melrose
  • M. S. Wheatland


Since the early 1980s, decimetric spike bursts have been attributed to electron cyclotron maser emission (ECME) by the electrons that produce hard X-ray bursts as they precipitate into the chromosphere in the impulsive phase of a solar flare. Spike bursts are regarded as analogous to the auroral kilometric radiation (AKR), which is associated with the precipitation of auroral electrons in a geomagnetic substorm. Originally, a loss-cone-driven version of ECME, developed for AKR, was applied to spike bursts, but it is now widely accepted that the measured distribution function is horseshoe-like (an isotropic distribution with a one-sided loss cone), and that a horseshoe-driven version of ECME applies to AKR. We explore the implications of the assumption that horseshoe-driven ECME also applies to spike bursts. We develop a 1D model for the acceleration of the electrons by a parallel electric field, and show that under plausible assumptions it leads to a horseshoe distribution of electrons in a solar flare. A second requirement for horseshoe-driven ECME is an extremely low plasma density, referred to as a density cavity. We argue that a coronal density cavity should develop in association with a hard X-ray burst, and that such a density cavity can overcome a long-standing problem with the escape of ECME through the second-harmonic absorption layer. Both the horseshoe distribution and the associated coronal density cavity are highly localized, and could not be resolved in the statistically large number of local precipitation regions needed to explain a hard X-ray burst. The model highlights the “number problem” in the supply of the electrons needed to explain a hard X-ray burst.


Solar flares Electron acceleration 



We acknowledge support from an Australian Research Council Discovery Project grant. D.B. Melrose acknowledges support from the International Space Science Institute, Bern, Switzerland, and discussions with members of the team on “Magnetic Waves in Solar Flares.” We thank an anonymous referee for helpful suggestions.


  1. Alm, L., Li, B., Marklund, G.T., Karlsson, T.: 2015, Statistical altitude distribution of the auroral density cavity. J. Geophys. Res. 120, 996.  DOI. ADS. CrossRefGoogle Scholar
  2. Bekefi, G., Hirshfield, J.L., Brown, S.C.: 1961, Cyclotron emission from plasmas with non-Maxwellian distributions. Phys. Rev. 122, 1037.  DOI. ADS. ADSCrossRefGoogle Scholar
  3. Benson, R.F., Calvert, W.: 1979, Isis 1 observations at the source of auroral kilometric radiation. Geophys. Res. Lett. 6, 479.  DOI. ADS. ADSCrossRefGoogle Scholar
  4. Bingham, R., Cairns, R.A.: 2000, Generation of auroral kilometric radiation by electron horseshoe distributions. Phys. Plasmas 7, 3089.  DOI. ADS. ADSCrossRefGoogle Scholar
  5. Bingham, R., Kellett, B.J., Cairns, R.A., Tonge, J., Mendonça, J.T.: 2003, Cyclotron maser radiation from astrophysical shocks. Astrophys. J. 595, 279.  DOI. ADS. ADSCrossRefGoogle Scholar
  6. Bingham, R., Speirs, D.C., Kellett, B.J., Vorgul, I., McConville, S.L., Cairns, R.A., Cross, A.W., Phelps, A.D.R., Ronald, K.: 2013, Laboratory astrophysics: Investigation of planetary and astrophysical maser emission. Space Sci. Rev. 178, 695.  DOI. ADS. ADSCrossRefGoogle Scholar
  7. Brown, J.C.: 1971, The deduction of energy spectra of non-thermal electrons in flares from the observed dynamic spectra of hard X-ray bursts. Solar Phys. 18, 489.  DOI. ADS. ADSCrossRefGoogle Scholar
  8. Brown, J.C.: 1976, The interpretation of hard and soft X-rays from solar flares. Phil. Trans. Roy. Soc. 281, 473.  DOI. ADS. ADSCrossRefGoogle Scholar
  9. Chiu, Y.T., Schulz, M.: 1978, Self-consistent particle and parallel electrostatic field distributions in the magnetospheric-ionospheric auroral region. J. Geophys. Res. 83, 629.  DOI. ADS. ADSCrossRefGoogle Scholar
  10. Dory, R.A., Guest, G.E., Harris, E.G.: 1965, Unstable electrostatic plasma waves propagating perpendicular to a magnetic field. Phys. Rev. Lett. 14, 131.  DOI. ADS. ADSCrossRefGoogle Scholar
  11. Dulk, G.A., Winglee, R.M.: 1987, Evidence for cyclotron maser emission from the sun and stars. Solar Phys. 113, 187.  DOI. ADS. ADSCrossRefGoogle Scholar
  12. Ellis, G.R.A.: 1962, Cyclotron radiation from Jupiter. Aust. J. Phys. 15, 344.  DOI. ADS. ADSCrossRefGoogle Scholar
  13. Ellis, G.R.A.: 1965, The decametric radio emission of Jupiter. Radio Sci. 69, 1513. ADS. ADSGoogle Scholar
  14. Emslie, A.G., Hénoux, J.-C.: 1995, The electrical current structure associated with solar flare electrons accelerated by large-scale electric fields. Astrophys. J. 446, 371.  DOI. ADS. ADSCrossRefGoogle Scholar
  15. Ergun, R.E., Carlson, C.W., McFadden, J.P., Mozer, F.S., Muschietti, L., Roth, I., Strangeway, R.J.: 1998, Debye-scale plasma structures associated with magnetic-field-aligned Electric Fields. Phys. Rev. Lett. 81, 826.  DOI. ADS. ADSCrossRefGoogle Scholar
  16. Ergun, R.E., Carlson, C.W., McFadden, J.P., Delory, G.T., Strangeway, R.J., Pritchett, P.L.: 2000, Electron-cyclotron maser driven by charged-particle acceleration from magnetic field-aligned electric fields. Astrophys. J. 538, 456.  DOI. ADS. ADSCrossRefGoogle Scholar
  17. Ergun, R.E., Andersson, L., Main, D., Su, Y.-J., Newman, D.L., Goldman, M.V., Carlson, C.W., McFadden, J.P., Mozer, F.S.: 2002, Parallel electric fields in the upward current region of the aurora: Numerical solutions. Phys. Plasmas 9, 3695.  DOI. ADS. ADSCrossRefGoogle Scholar
  18. Fletcher, L., Hudson, H.S.: 2008, Impulsive phase flare energy transport by large-scale Alfvén waves and the electron acceleration problem. Astrophys. J. 675, 1645.  DOI. ADS. ADSCrossRefGoogle Scholar
  19. Fridman, M., Lemaire, J.: 1980, Relationship between auroral electrons fluxes and field aligned electric potential difference. J. Geophys. Res. 85, 664.  DOI. ADS. ADSCrossRefGoogle Scholar
  20. Güdel, M., Benz, A.O., Aschwanden, M.J.: 1991, The association of solar millisecond radio spikes with hard X-ray emission. Astron. Astrophys. 251, 285. ADS. ADSGoogle Scholar
  21. Gurnett, D.A.: 1974, The earth as a radio source – terrestrial kilometric radiation. J. Geophys. Res. 79, 4227.  DOI. ADS. ADSCrossRefGoogle Scholar
  22. Haerendel, G.: 2012, Solar auroras. Astrophys. J. 749, 166.  DOI. ADS. ADSCrossRefGoogle Scholar
  23. Hirshfield, J.L., Bekefi, G.: 1963, Decameter radiation from Jupiter. Nature 198, 20.  DOI. ADS. ADSCrossRefGoogle Scholar
  24. Holman, G.D.: 1985, Acceleration of runaway electrons and Joule heating in solar flares. Astrophys. J. 293, 584.  DOI. ADS. ADSCrossRefGoogle Scholar
  25. Holman, G.D., Eichler, D., Kundu, M.R.: 1980, An interpretation of solar flare microwave spikes as gyrosynchrotron masering. In: Kundu, M.R., Gergely, T.E. (eds.) Radio Physics of the Sun, IAU Symposium 86, Reidel, Dordrecht, 457. ADS. CrossRefGoogle Scholar
  26. Knight, S.: 1973, Parallel electric fields. Planet. Space Sci. 21, 741.  DOI. ADS. ADSCrossRefGoogle Scholar
  27. Krucker, S., Hudson, H.S., Jeffrey, N.L.S., Battaglia, M., Kontar, E.P., Benz, A.O., Csillaghy, A., Lin, R.P.: 2011, High-resolution imaging of solar flare ribbons and its implication on the thick-target beam model. Astrophys. J. 739, 96.  DOI. ADS. ADSCrossRefGoogle Scholar
  28. Kuznetsov, A.A., Vlasov, V.G.: 2012, Kinetic simulation of the electron-cyclotron maser instability: Effect of a finite source size. Astron. Astrophys. 539, A141.  DOI. ADS. ADSCrossRefGoogle Scholar
  29. McClements, K.G.: 1992, The simultaneous effects of collisions, reverse currents and magnetic trapping on the temporal evolution of energetic electrons in a flaring coronal loop. Astron. Astrophys. 258, 542. ADS. ADSGoogle Scholar
  30. McKean, M.E., Winglee, R.M., Dulk, G.A.: 1989, Propagation and absorption of electron-cyclotron maser radiation during solar flares. Solar Phys. 122, 53.  DOI. ADS. ADSCrossRefGoogle Scholar
  31. Melrose, D.B.: 1976, An interpretation of Jupiter’s decametric radiation and the terrestrial kilometric radiation as direct amplified gyroemission. Astrophys. J. 207, 651.  DOI. ADS. ADSCrossRefGoogle Scholar
  32. Melrose, D.B.: 1986, Instabilities in Space and Laboratory Plasmas, Cambridge University Press, Cambridge, 214.  DOI. ADS. CrossRefGoogle Scholar
  33. Melrose, D.B.: 2013, Quantum Plasmadynamics: Magnetized Plasmas, Lecture Notes in Physics 854, Springer, New York, 136.  DOI. ADS. zbMATHGoogle Scholar
  34. Melrose, D.B., Cramer, N.F.: 1989, Quasi-linear relaxation of electrons interacting with an inhomogeneous distribution of Langmuir waves. Solar Phys. 123, 343.  DOI. ADS. ADSCrossRefGoogle Scholar
  35. Melrose, D.B., Dulk, G.A.: 1982, Electron-cyclotron masers as the source of certain solar and stellar radio bursts. Astrophys. J. 259, 844.  DOI. ADS. ADSCrossRefGoogle Scholar
  36. Melrose, D.B., Dulk, G.A., Cairns, I.H.: 1986, Clumpy Langmuir waves in type III solar radio bursts. Astron. Astrophys. 163, 229. ADS. ADSGoogle Scholar
  37. Melrose, D.B., Rönnmark, K.G., Hewitt, R.G.: 1982, Terrestrial kilometric radiation – the cyclotron theory. J. Geophys. Res. 87, 5140.  DOI. ADS. ADSCrossRefGoogle Scholar
  38. Melrose, D.B., Wheatland, M.S.: 2013, Transfer of energy, potential, and current by Alfvén waves in solar flares. Solar Phys. 288, 223.  DOI. ADS. ADSCrossRefGoogle Scholar
  39. Melrose, D.B., Wheatland, M.S.: 2014, Bulk energization of electrons in solar flares by Alfvén waves. Solar Phys. 289, 881.  DOI. ADS. ADSCrossRefGoogle Scholar
  40. Omidi, N., Gurnett, D.A.: 1982, Growth rate calculations of auroral kilometric radiation using the relativistic resonance condition. J. Geophys. Res. 87, 2377.  DOI. ADS. ADSCrossRefGoogle Scholar
  41. Pritchett, P.L.: 1986, Cyclotron maser radiation from a source structure localized perpendicular to the ambient magnetic field. J. Geophys. Res. 91, 13569.  DOI. ADS. ADSCrossRefGoogle Scholar
  42. Pritchett, P.L., Strangeway, R.J., Ergun, R.E., Carlson, C.W.: 2002, Generation and propagation of cyclotron maser emissions in the finite auroral kilometric radiation source cavity. J. Geophys. Res. 107, 1437.  DOI. ADS. CrossRefGoogle Scholar
  43. Régnier, S.: 2015, A new approach to the maser emission in the solar corona. Astron. Astrophys. 581, A9.  DOI. ADS. CrossRefGoogle Scholar
  44. Sagdeev, R.Z., Shafranov, V.D.: 1961, On the instability of a plasma with an anisotropic distribution of velocities in a magnetic field. Sov. Phys. JETP 39, 181. MathSciNetGoogle Scholar
  45. Schneider, J.: 1959, Stimulated emission of radiation by relativistic electrons in a magnetic field. Phys. Rev. Lett. 2, 504.  DOI. ADS. ADSCrossRefGoogle Scholar
  46. Sharma, R.R., Vlahos, L.: 1984, Comparative study of the loss cone-driven instabilities in the low solar corona. Astrophys. J. 280, 405.  DOI. ADS. ADSCrossRefGoogle Scholar
  47. Slottje, C.: 1978, Millisecond microwave spikes in a solar flare. Nature 275, 520.  DOI. ADS. ADSCrossRefGoogle Scholar
  48. Speirs, D.C., Bingham, R., Cairns, R.A., Vorgul, I., Kellett, B.J., Phelps, A.D.R., Ronald, K.: 2014, Backward wave cyclotron-maser emission in the auroral magnetosphere. Phys. Rev. Lett. 113(15), 155002.  DOI. ADS. ADSCrossRefGoogle Scholar
  49. Treumann, R.A.: 2006, The electron-cyclotron maser for astrophysical application. Astron. Astrophys. Rev. 13, 229.  DOI. ADS. ADSCrossRefGoogle Scholar
  50. Twiss, R.Q.: 1958, Radiation transfer and the possibility of negative absorption in radio astronomy. Aust. J. Phys. 11, 564.  DOI. ADS. ADSCrossRefGoogle Scholar
  51. Whipple, E.C. Jr.: 1977, The signature of parallel electric fields in a collisionless plasma. J. Geophys. Res. 82, 1525.  DOI. ADS. ADSCrossRefGoogle Scholar
  52. White, S.M., Benz, A.O., Christe, S., Fárník, F., Kundu, M.R., Mann, G., Ning, Z., Raulin, J.-P., Silva-Válio, A.V.R., Saint-Hilaire, P., Vilmer, N., Warmuth, A.: 2011, The relationship between solar radio and hard X-ray emission. Space Sci. Rev. 159, 225.  DOI. ADS. ADSCrossRefGoogle Scholar
  53. Wright, A.N., Allan, W., Ruderman, M.S., Elphic, R.C.: 2002, The dynamics of current carriers in standing Alfvén waves: Parallel electric fields in the auroral acceleration region. J. Geophys. Res. 107, 1120.  DOI. ADS. CrossRefGoogle Scholar
  54. Wu, C.S., Lee, L.C.: 1979, A theory of the terrestrial kilometric radiation. Astrophys. J. 230, 621.  DOI. ADS. ADSCrossRefGoogle Scholar
  55. Zharkova, V.V., Arzner, K., Benz, A.O., Browning, P., Dauphin, C., Emslie, A.G., Fletcher, L., Kontar, E.P., Mann, G., Onofri, M., Petrosian, V., Turkmani, R., Vilmer, N., Vlahos, L.: 2011, Recent advances in understanding particle acceleration processes in solar flares. Space Sci. Rev. 159, 357.  DOI. ADS. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Sydney Institute for Astronomy, School of PhysicsUniversity of SydneyNSWAustralia

Personalised recommendations