Physics of auroral phenomena : proceedings of the 34th Annual seminar, Apatity, 01 - 04 March, 2011 / [ed.: A. G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2011. - 231 с. : ил.

“Physics ofAuroral Phenomena", Proc. XXXIVAnnual Seminar, Apatity, pp. 90 - 93 2011 © Kola Science Centre, Russian Academy of Science, 2011 Polar Geophysical Institute PROPERTIES OF THE BACKWARD W A V E O SC IL L A TO R MOD EL OF V L F CHORUS GENERAT ION IN FERRED FROM C L U S T E R M EASUREM ENTS E.E. Titova1’2, B.V. Kozelov1, A.G. Demekhov3, O. Santolik4, E. Macusova4, J.-L. Rauch5, J.G. Trotignon5, D. Gumett6, and J. Pickett6 1 Polar Geophysical Institute, Fersmana 14, 18420, Apatity, Russia 2 Space Research Institute, Profsoyuznaya 84/32, 117997, Moscow, Russia 3 Institute o fApplied Physics, Ulyanov 46, 603950, Nizhny Novgorod, Russia 4 IAP/CAS, Bocni 11/1401, 14131Prague, Czech Republic 5 LPCE/CNRS, 45071, Orleans, France 6 University o f Iowa, Iowa City, IA, 52242, USA Abstract. A generation mechanism for chorus was suggested by Trakhtengerts (1995) on the basis of the backward wave oscillator (BWO) regime of the magnetospheric cyclotron maser. According to this model, step-like deformation on the electron distribution function is the most important factor of chorus generation, but such a feature is very difficult to observe. By measuring the frequency sweep rates in chorus elements detected by the Cluster spacecraft we determine the mean values and distributions of a dimensionless parameter characterizing the step feature. These values are in agreement with the results of numerical simulations of chorus elements based on the BWO model. 1. Introduction VLF chorus emissions are the most mysterious signals among natural ELF/VLF radiation. Chorus emissions are observed as a succession of repeating discrete elements, more often with increasing frequency. It is generally accepted that the chorus emissions are generated by the cyclotron instability of radiation belt electrons near the equatorial region. However, two principal problems relating to chorus emissions remain, i.e., the generation of the dynamical spectrum of separate chorus elements, and an origin of succession of chorus elements. To solve these problems Trakhtengerts [1,2] proposed a new regime of the cyclotron instability in the magnetosphere. It is the backward wave oscillator (BWO) regime of VLF chorus generation which is similar to the backward wave oscillator in laboratory electronic devices. Cyclotron interactions of natural ELF/VLF noise-like emissions and energetic electrons produce a specific step-like deformation of the distribution function. This step-like deformation yields the large growth rate of the whistler-mode waves and the development of the absolute cyclotron instability in a narrow region near the equatorial plane. The instability produces a succession of discrete signals with an increasing frequency within each element. It is clear that a sharp gradient (or a step-like deformation) on the electron distribution function is the most important parameter of the BWO model. However, theoretical estimates show that the step is rather small [3]. The detection of this step-like feature requires an energetic electron detector with a very good resolution of the energy and the pitch angle, about several percent. At the present time the satellite instruments do not provide such a resolution. Therefore the step-like features of the distribution functions have not been observed directly so far. However, the properties of the step in the BWO model determine the dimensionless parameter q which characterizes the excess of an energetic electron flux over a threshold of the BWO regime. This parameter, in turn, determines the frequency sweep rate of chorus elements. Thus, by measuring the frequency sweep rate in the source region we can obtain indirect information about the properties of a step on the distribution function. A decrease of the mean values of the frequency sweep rate with increasing mean cold plasma density was demonstrated in [4]. This result is in agreement with the BWO model if the q parameter is independent of the plasma density. Here we determine and analyze the values of the q parameter in the magnetospheric BWO model for individual chorus elements on the basis o f instantly measured plasma densities. Then we compare q values, obtained in experiment, with results o f numerical simulations of the BWO model and discuss the distributions of the q parameter. In the last section we summarize our results. 2. Theoretical Background The expression for the frequency sweep rate of chorus elements df/dt can be written as [2, 5] df/dt = Q ,r2 (j) where the trapping frequency f2,r is determined by the formula Q r = (кий),, Ъ)т , and b=BJBL is the ratio of the whistler wave magnetic field amplitude B a to the geomagnetic field B i, co„ is the electron gyrofrequency, and и is the electron velocity component across the 90