A qualitative discussion is given of the role electron holes play in generating fine structure on the electron cyclotron maser radiation. It is argued that electron holes become deformed in phase space when interacting with an incomplete ring or horseshoe distribution which occurs in the presence of strong field aligned electric fields in the upward current region and in the presence of a loss cone. This interaction is based on momentum balance considerations. Deformed narrow electron holes cause steep velocity space gradients on the ring distribution that lead to intense but narrow band emission from their high speed sides and absorption at slightly higher frequency from their low speed sides. The twins of banded emission and absorption move in frequency space due to the average real space displacement of the deformed electron hole.
Deep Dive into Deformation of electron holes in phase space as prerequisite for narrow band maser emission: A qualitative discussion.
A qualitative discussion is given of the role electron holes play in generating fine structure on the electron cyclotron maser radiation. It is argued that electron holes become deformed in phase space when interacting with an incomplete ring or horseshoe distribution which occurs in the presence of strong field aligned electric fields in the upward current region and in the presence of a loss cone. This interaction is based on momentum balance considerations. Deformed narrow electron holes cause steep velocity space gradients on the ring distribution that lead to intense but narrow band emission from their high speed sides and absorption at slightly higher frequency from their low speed sides. The twins of banded emission and absorption move in frequency space due to the average real space displacement of the deformed electron hole.
Introduction. -It has been firmly established [4] by now that the Auroral Kilometric Radiation (AKR) -and probably also a number of radio emissions from other celestial objects [1,3,21] -is due to the (relativistic) electron cyclotron maser in the presence of a magnetic-fieldaligned electrostatic potential drop. In its embryonic version [10,22] the mechanism referred to loss cone distributions. However, the potential drop locally evacuates the plasma [2] making it manifestly underdense with plasmato-cyclotron frequency ratio ω pe /ω ce < 1 and, at the same time, transforms the electron distribution into a ring in velocity space. Realizing this important modification, the electron-cyclotron maser radiation mechanism has been put back on its feet by Pritchett [17]. In this realistic version, fundamental emission is generated in the x-mode below but (for not too small frequency ratios) close to the (non-relativistic) cyclotron frequency ω ce = eB/m e (where B is the magnetic field strength, e the elementary charge, and m e the electron mass) and propagates strictly perpendicular to the magnetic field with wave number k ≡ k ⊥ B/B, k ≡ 0.
Controversy concerns the persistent observation of very narrow-band, very intense emissions of sometimes less than 100 Hz bandwidth, compared to an emission frequency of ∼ 300 kHz in the Auroral Kilometric Radiation which corresponds to a relative bandwidth of ∆ω/ω ∼ 10 -4 . This small relative bandwidth requires extraordinarily steep positive perpendicular phase-space density gradients ∂f e /∂v ⊥ > 0 [with f e (v , v ⊥ ) the electron phase space density] which in addition must cover a large phasespace volume. The steep gradient is responsible for the narrow bandwidth, while the large phase-space volume assures high emissivity. Both conditions are difficult to maintain simultaneously and globally. Some models of phase space distributions, meeting these conditions and providing high or marginally high emissivities, have indeed been proposed, for instance by Louarn [7,8], and also in [19,23]. Such models refer to the global gradients on the electron distribution imposing severe conditions on its shape. Global phase space gradients as sharp as assumed have, to our knowledge, barely been observed. To our opinion the observation of the fast spectral displacement of the emission bands suggests that the radiation sources occupy only a very small volume in real space. We therefore suggested [15,16] that the narrow-band spectral fine structure detected in the Auroral Kilometric Radiation is not the result of a steep global gradient in the distribution; rather it is due to emission from ’elementary radiation sources’. We tentatively identified these with phase-space (ion and electron) holes of the kind of Bernstein-Green-Kruskal (or p-1 arXiv:0712.0185v2 [physics.space-ph] 3 Nov 2008 BGK) modes investigated in [6,11,12,14,20], and others. Justification has been derived from the real-space velocity of the sources deduced from their spectral displacements of the emissions. Even the entire auroral kilometric emission spectrum may be due to the superposition of the contributions from such tiny ’elementary radiators’ [15], a proposal that so far is lacking attention.
Existence of phase-space holes in the downward current region is by now a well established observational fact that has been backed by numerous numerical simulations [5,6]. Observational evidence has also been presented [16] for the existence of BGK modes in the low-density upward current region (along the ambient magnetospheric magnetic field downward directed auroral electron fluxes) where they occur at low frequency manifesting themselves as spikes on the electric wave form. They had been overlooked so far letting one believe that they would occur only in the downward current region at upward directed auroral electron fluxes along the magnetospheric magnetic field.
Mechanism of deformation. -‘Elementary radiators’ must be electron holes since ion holes do not directly contribute to radiation even though being important in the dynamics of dilute plasmas [6]. Being Debyescale structures, they are beyond resolution of particle detectors and thus invisible on the distribution function. Their phase space extension is determined by their capability of trapping particles. This is restricted to the range ∆v H = ± 2eφ 0 /m e , where φ 0 is the amplitude of the hole potential. Since under real auroral magnetospheric conditions φ 0 is of the order of, say, ∼ 1 V, the hole is a narrow (and most probably also shallow) distortion on the electron distribution of width ∼ 2∆v H ∼ 10 3 km/s (Figure 1b), corresponding to an energy of ∼ 2 eV much less than the ∼ keV downward auroral electron kinetic energies. Any gradients it generates on the distribution function will necessarily be sharp. However, in all models such gradients exist only in the parallel direction. In the following we argue (qualitatively) that electron holes, when suffering de
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