Annual report - 2007

Achieved results

Achieved scientific results were published in the form of reffered scientific papers and presented at international conferences. Here we briefly highlight some of our observations and conclusions.

Published results

During the reported period 01/2007­12/2007 we have published the following papers in refereed journals (complete list of all publications and presentations made during the whole project is listed in the Section 6):

C. Califano, P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. Travnicek, Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, doi:10.1029/2007JA012898, submitted, 2008. Abstract: With the aim to understand the origin of the pressure­balanced magnetic structures in the form of holes and humps commonly observed in the solar wind and planetary magnetosheaths, high­resolution hybrid numerical simulations of the Vlasov­Maxwell (VM) equations using both Lagrangian (particle in cells) and Eulerian integration schemes are presented and compared with asymptotic and phenomenological models for the nonlinear mirror mode dynamics. It turns out that magnetic holes do not result from direct nonlinear saturation of the mirror instability that rather leads to magnetic humps. Nevertheless, both above and below threshold, there exist stable solutions of the VM equations in the form of large­amplitude magnetic holes. Special attention is paid to the skewness of the magnetic fluctuations (that is negative for holes and positive for humps) and to its variations, depending on the distance to threshold and the beta of the plasma. Furthermore, the long­time evolution of magnetic humps resulting from the mirror instability in an extended domain far enough from threshold may, when the beta of the plasma is not too large, eventually lead to the formation of magnetic holes.

E. M. Dubinin, M. Maksimovic, N. Cornilleau­Wehrlin, D. Fontaine, Pavel Travnicek, A. Mangeney,

O. Alexandrova, K. Sauer, M. Fraenz, I. Dandouras, E. Lucek, A. Fazakerley, A. Balogh, and M. Andre, Coherent whistler emissions in the magnetosphere ? Cluster observations, Ann. Geophys. 25, 303­315 (2007). Abstract. The STAFF­SC observations complemented by the data from other instruments on Cluster spacecraft were used to study the main properties of magnetospheric lion roars: sporadic bursts of whistler emissions at f ~ 0.1­0.2fe where fe is the electron gyrofrequency. Magnetospheric lion roars are shown to be similar to the emissions in the magnetosheath while the conditions for their generation are much less favorable: the growth rate of the cyclotron temperature anisotropy instability is much smaller due to a smaller number of the resonant electrons. This implies a nonlinear mechanism of generation of the observed wave emissions. It is shown that the observed whistler turbulence, in reality, consists of many nearly monochromatic wave packets. It is suggested that these structures are nonlinear Gendrin's whistler solitary waves. Properties of these waves are widely discussed. Since the group velocity of Gendrin?s waves is aligned with the magnetic ?eld, these well guided wave packets can propagate through many magnetic ?bottles? associated with mirror structures, without being trapped.

P. Hellinger, P. Travnicek, B. Lembege and P. Savoini, Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: Hybrid versus full particle simulations, Geophys. Res. Lett., 34, L14109, doi:10.1029/2007GL030239, 2007. Abstract: New behavior of strictly perpendicular shocks in supercritical regime is analyzed with the help of both two­dimensional (2­D) hybrid and full particle electromagnetic simulations. Surprisingly, in both simulation cases, the shock front region appears to be dominated by emission of coherent large amplitude whistler waves for some plasma conditions and shock regimes. These whistler waves are oblique with respect to the shock normal as well as to the upstream magnetic field and are phase­standing in the shock rest frame. A parametric study shows that these whistler waves are emitted in 2­D perpendicular shocks and, simultaneously, the self reformation of the shock front associated with reflected ions disappears; the 2­D shock front is almost quasi­stationary. In contrast, both corresponding one­dimensional (1­D) hybrid and full particle simulations performed in similar plasma and Mach regime conditions show that the self reformation takes place for 1­D perpendicular shock. These results indicate that the emission of these 2­D whistler waves can inhibit the self­reformation in 2­D shocks. Possible generating mechanisms of these waves emissions and comparison with previous works are discussed.

P. Hellinger, Comment on the linear mirror instability near the threshold, Phys. Plasmas, 14, 082105, 2007. Abstract: Linear threshold condition of the mirror instability in a homogeneous, multi­species collisionless plasma with a general class of distribution functions is obtained in the low­frequency, long­wavelength limit of the Vlasov­Maxwell equation. In the case of one cold species, the conditions of the validity of the threshold condition and the behavior of the instability near threshold are also presented. It is confirmed that finite Larmor radius effects do not change the threshold condition. The linear threshold condition is extended to the case of hot species with a general class of distribution functions. In this case the conditions of the validity of the threshold condition or the behavior of the instability near threshold are hard to get analytically. Previous analytical and numerical results are discussed.

L. Matteini, S. Landi, P. Hellinger , F. G. Pantellini, M. Maksimovic, M. Velli, B. E. Goldstein, and E. Marsch, The evolution of the solar wind proton temperature anisotropy from 0.3 to 2.5 AU, Geophys. Res. Lett., 34, L20105, doi:10.1029/2007GL030920, 2007. Abstract: We report an analysis of the proton temperature anisotropy evolution from 0.3 to 2.5 AU based on the Helios and Ulysses observations. With increasing distance the fast wind data show a path in the parameter space (||p, T p/T||p). The first part of the trajectory is well described by an anticorrelation between the temperature anisotropy Tp/T||p and the proton parallel beta, while after 1 AU the evolution with distance in the parameter space changes and the data result in agreement with the constraints derived by a fire hose instability. The slow wind data show a more irregular behavior, and in general it is not possible to recover a single evolution path. However, on small temporal scale we find that different slow streams populate different regions of the parameter space, and this suggests that when considering single streams also the slow wind follows some possible evolution path.

Stepan Stverak, Pavel Travnicek, Milan Maksimovic, Eckart Marsch, Andrew N. Fazakerley, Earl E. Scime, Electron Temperature Anisotropy Constraints in the Solar Wind, J. Geophys. Res., in print, 2007. Abstract. We have performed a statistical study of a substantial amount of electron data acquired in the solar wind to understand the constraints on electron temperature anisotropy by plasma instabilities and Coulomb collisions. We use a large data set of electron measurements from three different spacecraft (HELIOS I, CLUSTER II and ULYSSES) collected in the low ecliptic latitudes covering the radial distance from the Sun from 0.3 up to 4 AU. We estimate the electron temperature anisotropy using fits of the measured electron velocity distribution functions acquired in situ. We use a two population (core and halo) analytical model and properties of both populations are studied separately. We examine all the acquired data in terms of temperature anisotropy vs. parallel electron plasma beta and we relate the measurements to the growth rates of unstable modes. The effect of Coulomb collisions is expressed by the electron collisional age Ae defined as the number of collisions suffered by an electron during the expansion of the solar wind. We show that both instabilities and collisions are strongly related to the isotropisation process of the electron core population. In addition we examine the radial evolution of these effects during the expansion of the solar wind. We show that the bulk of the solar wind electrons are constrained by Coulomb collisions, while the large departures from isotropy are constrained by instabilities.

P. Travnicek, P. Hellinger, M. G. G. T. Taylor, C. P. Escoubet, I. Dandouras, and E. Lucek, Magnetosheath plasma expansion: Hybrid simulations, Geophys. Res. Lett., 34, L15104, doi:10.1029/2007GL029728, 2007. Abstract: We investigate the effect of a slow expansion on a magnetosheath plasma and magnetosheath low­frequency turbulence using a two­dimensional hybrid expanding box simulation. We start our simulation with a high beta plasma almost stable with respect to the mirror and proton cyclotron instabilities. The expansion leads to a continuous decrease of proton beta and drives the increase of the proton temperature anisotropy. Both mirror and proton cyclotron waves appear. The system establishes a marginally stable state with respect to both mirror and proton cyclotron instabilities. During the first phase of the simulation the mirror waves dominate over the proton cyclotron waves, latter, in the low beta region the proton cyclotron waves become dominant. Our results also support the observational possibility of mirror mode waves in plasmas with a negative growth rate (The phenomenon of bistability). We also include an initial comparison with observations made by the Cluster spacecraft.

P. Travnicek, P. Hellinger, and D. Schriver, Structure of Mercury's magnetosphere for different pressure of the solar wind: three dimensional hybrid simulations, Geophys. Res. Lett., 34, L05104, doi:10.1029/2006GL028518, 2007. Abstract: We have carried out a self­consistent three dimensional global hybrid simulation study examining the interaction of the solar wind with Mercury's magnetosphere. We consider two cases: one with relatively high solar wind pressure, and another with relatively low solar wind pressure. With lower solar wind pressure, the subsolar magnetopause forms at about 1.7 RM (where RM is the planetary radius) and well pronounced cusp regions are formed; also a closed ion ring forms around the planet. In the higher solar wind pressure case the magnetopause is pushed closer to Mercury's surface (~1.2 RM) and the cusp regions are less pronounced; the ion ring in this case is confined to a region closer to the planet with a smaller radial extent. In both cases reconnection occurs at about ~ 2.4 RM down the magnetotail and a plasma sheet is formed. In general the plasma within the magnetosphere is more energetic in the high solar wind pressure case and the ion foreshock contains hotter magnetosheath plasma. Particles originating from the planet disperse through the magnetosphere, with the greatest congregation occuring in the inner magnetospheric drift driven rings in both cases. These planetary particles can also leak upstream into the foreshock region.

F. Valentini, P. Travnicek, F. Califano, P. Hellinger and A. Mangeney, A hybrid­Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma, J. Comp. Phys., 225, 753­770, 2007. Abstract: We present a numerical scheme for the integration of the Vlasov­Maxwell system of equations for a non­relativistic plasma, in the hybrid approximation, where the Vlasov equation is solved for the ion distribution function and the electrons are treated as a fluid. In the Ohm equation for the electric field, effects of electron inertia have been retained, in order to include the small scale dynamics up to characteristic lengths of the order of the electron skin depth. The low frequency approximation is used by neglecting the time derivative of the electric field, i.e. the displacement current in the Ampere equation. The numerical algorithm consists in coupling the splitting method proposed by Cheng and Knorr in 1976 [C.Z. Cheng, G. Knorr, J. Comput. Phys. 22 (1976) 330­351.] and the current advance method (CAM) introduced by Matthews in 1994 [A.P. Matthews, J. Comput. Phys. 112 (1994) 102­116.] In its present version, the code solves the Vlasov­Maxwell equations in a five­dimensional phase space (2­D in the physical space and 3­D in the velocity space) and it is implemented in a parallel version to exploit the computational power of the modern massively parallel supercomputers. The structure of the algorithm and the coupling between the splitting method and the CAM method (extended to the hybrid case) is discussed in detail. Furthermore, in order to test the hybrid­Vlasov code, the numerical results on propagation and damping of linear ion­acoustic modes and time evolution of linear elliptically polarized Alfven waves (including the so­called whistler regime) are compared to the analytical solutions. Finally, the numerical results of the hybrid­Vlasov code on the parametric instability of Alfven waves are compared with those obtained using a two­fluid approach.

See reference: P. Hellinger, P. Travnicek, B. Lembege and P. Savoini, Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: Hybrid versus full particle simulations, Geophys. Res. Lett., 34, L14109, doi:10.1029/2007GL030239, 2007.