Ion Acceleration at the Front of Nonlinear Whistlers
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Acceleration at the Front of Nonlinear Whistlers G. N. Kichigin1* 1
Institute of Solar–Terrestrial Physics, Russian Academy of Sciences, Siberian Branch, P.O. Box 4026, Irkutsk, 664033 Russia Received January 24, 2020; revised January 24, 2020; accepted May 26, 2020
Abstract—We have solved the problem of the acceleration of ions (protons) incident on the front of a nonlinear whistler for which the structure of its electromagnetic fields is assumed to be known and defined by the relations derived by us previously. We have established the dependence of the energy to which the protons are accelerated on the angle between the whistler propagation direction and the direction of the external magnetic field and on the whistler speed. The results obtained are applied to the Earth’s bow shock by assuming that the bow shock front has the structure of a nonlinear whistler. We show that the protons are accelerated at the Earth’s bow shock front to 45 keV and end up with such energies upstream of the bow shock in the foreshock region. In our opinion, being scattered by the oscillations existing in the foreshock, these energetic protons form a population of so-called diffuse ions upstream of the bow shock. DOI: 10.1134/S1063773720060043 Keywords: nonlinear whistlers, ion acceleration, magnetosonic shocks.
INTRODUCTION In this paper we consider the ion acceleration at the front of steady-state nonlinear waves, whistlers, propagating at an angle α (α = π/2) to a constant uniform magnetic field in a cold collisionless plasma. We focus our attention on the fast magnetosonic (FMS) waves, which, under the condition ωHe ωpe , have frequencies ωHi ω < ωHe cosα and wavelengths of the order of the electron inertial length c/ωpe (here, ωHi is the ion cyclotron frequency, ωHe is the electron cyclotron frequency, ωpe is the electron plasma frequency, and c is the speed of light). In this frequency range the FMS waves have several names: whistling atmospherics, whistles, helicons, and whistlers (Akhiezer et al. 1974; Gershman and Ugarov 1960). We will call these waves whistlers. Whistlers manifest themselves quite often in many phenomena occurring in a magnetized space plasma. For example, being excited in the near-Earth plasma due to continuous lightning discharges in the Earth’s atmosphere (Gershman and Ugarov 1960), whistlers are constantly recorded by radio receivers on Earth. To take another example, it has recently been established that whistlers play a significant role in forming the structure of collisionless shocks (Balogh and Treumann 2013); in particular, this is also true for the Earth’s bow shock (Wilson III 2016; Krasnoselskikh et al. 2002). *
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As follows from the results by Saffman (1961), for steady-state nonlinear whistlers traveling in a collisionless, cold, magnetized plasma strictly along fields lines of the external magnetic field, the wave magnetic field has two, comparable in magnitude, components transverse to the wave propagation direction, while the whistler magnetic field vector rotates around t
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