Right‐hand polarized 4f_ce auroral roar emissions: 2. Nonlinear generation theory

Abstract

Auroral roar emissions are commonly interpreted as Z (or upper hybrid) mode naturally excited by precipitating auroral electrons. Subsequent conversion to escaping radiation makes it possible for these emissions to be detected on the ground. Most emissions are detected as having left‐hand (L) circular (or ordinary O) polarization, but the companion paper presents a systematic experimental study on the rare occurrence of the right‐hand polarized, or equivalently, extraordinary (X) mode 4fce emission. A similar observation was reported earlier by Sato et al. (2015). The suggested emission mechanism is the nonlinear coalescence of two upper hybrid roars at 2fce. The present paper formulates a detailed theory for such an emission mechanism.

Two-fluid approach to weak plasma turbulence

“…Note that for both magnetized and unmagnetized plasmas, the plasma emission at the second harmonic does not involve low frequency mode at all. For unmagnetized plasmas, the merging of two Langmuir waves into a transverse EM radiation at twice the plasma frequency occurs, while for magnetized plasmas, the merging of two Z modes may lead to the radiation emission at approximately twice the upper-hybrid frequency in the form of either X or O mode [59,74]-see also, [94]. In short, the comprehensive weak turbulence theory that is capable of quantitative numerical analysis, and that naturally lends itself to comparative analysis again PIC simulation is still lacking, which is the long term research goal of the present author.…”

ECMI resonance in AKR revisited: Hyperbolic resonance, harmonics, and wave–wave interaction

“…To conclude this section, it is of substantial interest to note that exactly the same non-linear wave-wave interaction mechanism of generation of radiation in the free-space X-mode has been explicated in detail for the Z-mode [35] in the approximate second n = 2 and fourth n = 4 harmonics of the cyclotron frequency. This mechanism would, in principle, compete with the ECMI wave-wave generation mechanism on the lower X-mode branch proposed here; otherwise, the two mechanisms would unfortunately exclude each other.…”

“…The assumed low-density state relegates the source of AKR and excitation of ECMI to the spatially extended auroral upward-current region and generally excludes the narrow and dense downward-current region, which also implies that the prevalent electron distribution is believed to be of the loss-cone family. This notion has been challenged [16,35] though not disproved. In this study, no attempt is made to calculate the growth rate for any specific distribution, which leaves this question open.…”

“…At these boundaries, the phase-space distribution develops steep gradients which may serve the needs for exciting the ECMI. This model has been used to propose the action of the ECMI here as well, based on elliptic, not hyperbolic resonance [35,40], in those incomplete hollow-electron phase-space distributions, sometimes called horseshoes.…”

Right‐hand polarized 4fce auroral roar emissions: 1. Observations

“…An identical mechanism was proposed by Sato et al [] to explain anomalous polarization of similar waves observed with a satellite. Theory of this mechanism is presented in a companion paper [ Yoon et al , ].…”