Physics of auroral phenomena : proceedings of the 33rd Annual seminar, Apatity, 02 - 05 March, 2010 / [ed.: A.G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2011. - 206 с. : ил.

Influence o f intermittency on particle acceleration .,1 a _____________________ ’■»- Figure 2. Panel (a): Power law exponent of structure functions as a function o f its order for different values o f Д Panel (b): observation of magnetic field (from [Petrukovich, 2005], fig. 1.3). Panel (c): model magnetic field. Panel (d): power law exponents of model and observation Particle acceleration In this section the influence of intermittency of electromagnetic turbulence on particle transport and acceleration will discussed. We use the modelling domain with the spatial scale L = 400|kmex|"1. Wavenumbers o f magnetic field (4) are taken from the interval [0.02, 1] ]kmat and their distribution over direction of propagation is uniform (twenty waves with angle of propagation from 0 to 2n are set for each value of wavenumber magnitude). The energy of magnetic component of waves (-(Bo™'*)2) is equal to 4/5 of the total magnetic field energy. The number o f magnetic clouds in modelling domain is Nc = 40000, their spatial scale is jk^p1= О ^ к ^ ' 1(spatial scales of clouds are isotropic in plane (. x ,y )). Magnitude of clouds oscillations is a = O ^ l k ^ f 1and frequency of oscillations со will be normalized to eB0w/mc. We use magnetic energy normalization for magnetic field o f clouds to provide the further comparison of our results with various turbulence parameters: W = T ? I i \B z(cioud)\ dxdy = const (5) 4 L -L -L 1 Particle spatial coordinates are normalized on 2|kmai|'‘. Time is normalized on mc/eB(jwave. Particle velocities are normalized on и = 2|kmax| Amc/eB0wave (and energy s~ v 2/u2). To study the influence of intermittency of electromagnetic turbulence on particle transport and acceleration we use the test particle method (number of particles is Np = 106 and periodical boundary conditions are used). Initially ensemble of particle has a maxwellian energy distribution with temperature ~u2. Average energy o f particle ensemble as a function of time for different values of /3 parameter (different intermittency levels) is presented in Fig. 3. With the increase o f intermittency level the energy gained by particles during equal time intervals is growing. The ratio between energy gained by particles in the system with /? = 2 (almost non-intermittent turbulence) and in the system with f}= 3.5 (strong intermittent turbulence) is about two. This ratio is also dependent on the magnetic energy of clouds. time time Figure 3. Average energy of particle ensemble as a function of time for four values of parameter In Fig. 4 one can see the average energy of particle ensemble as a function of the average spatial displacement. The model with the strong intermittent turbulence (/?= 3 , / ? = 3.5) accelerates particle more effectively than almost non-intermittent model (J3= 2) while the level of spatial transport remain the same. This effect allows to accelerate the particles in the spatially localized region ‘filled’ by the intermittent turbulence. ■V-едr*> V<Ar2> Figure 4. Energy, gained by particles as a function of spatial transport for several models with different value of parameter