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Petr Hellinger: Publications and Manuscripts

Thesis

• P.Hellinger, Contribution a la theorie des ondes de choc sans collisions; application a l'onde de choc de la Terre, Thesis of Universite d'Orsay 1996.
  Thesis (in French).
  Abstract:

  This thesis presents the results concerning the physics of collisionless shocks in a magnetised plasma; I use two theoretical approaches - linear theories and numerical simulations. For the numerical simulations we use a hybrid "PIC" code developped by Allan Matthews. We use the 2D version of this code and as well as a 3D version developped in cooperation with the author. For the linear theory I use a numerical approach for the resolution of the dispersion equations. The principal results of the thesis concern the instabilities associated with the proton reflected off the shock: establisement of the threshold for the existence of the shock "rippling", excitation of the upstream whistlers, for the quasi-perpendicular shocks. For the quasi-parallel shocks, we show that the reflected protons excite waves or parallel with respect to the magnetic field either highly oblique; the last ones, strongly compressive, give rise to a filamentation of the beam protons which may explain certain observations ("SLAMS").

Refereed Publications

• P. Hellinger, A. Mangeney, and A. Matthews, Whistler waves in 3D hybrid simulations of quasi-perpendicular shocks, Geophys. Res. Lett., 23, 621-624, 1996.
  Reprint.
  Abstract:

  We investigate a low Mach number supercritical quasiperpendicular shock using a three-dimensional hybrid code. We find an out-of-coplanarity whistler wave mode propagating upstream, with properties similar to those of the ''upstream whistlers'' observed in the vicinity of planetary shocks. We discuss the generation mechanism, which turns out to be driven by the free energy provided by reflected protons.

• P. Hellinger, and A. Mangeney, Upstream whistlers generated by protons reflected from a quasi-perpendicular shock, J. Geophys. Res., 102, 9809-9819, 1997.
  Reprint.
  Abstract:

  Numerical simulations of collisionless supercritical quasi-perpendicular shocks suggest that the upstream whistlers may be generated near the shock by the reflected protons which gyrate back to the shock. We investigate in detail results of hybrid simulations and a linear theory for a gyrotropic gyrating beam in a Maxwellian plasma, and we compare their outcomes. We find good agreement between the linear theory and the simulations. We compare these theoretical issues with observations, and we discuss the results. We also discuss dimensionality effects on the simulations of upstream whistlers. The investigation of lower Mach shocks leads us to a condition for the existence of a so-called shock rippling.

• P. Hellinger, and A. Mangeney, Electromagnetic ion beam instabilities: Oblique pulsations, J. Geophys. Res., 104, 4669-4680, 1999.
  Reprint.
  Abstract:

  We present results of a two-dimensional hybrid simulation of the electromagnetic proton beam instability. We show that for a case of cold, and rather high density proton beam the oblique right-handed resonant modes play an important role. The interaction of these modes with the beam protons cause significant beam density fluctuations. At the non-linear stage, the oblique modes give rise a beam filamentation. Beam filaments influence strongly the evolution of the instability. They create pulses of a strong magnetic field. These pulses share some properties of the magnetic pulsations (SLAMS). We suppose that the oblique modes play an important role in the structure of the quasi-parallel Earth's bow shock.

• P. Hellinger, and H. Matsumoto, New kinetic instability: Oblique Alfvén fire hose, J. Geophys. Res., 105, 10,519-10,526, 2000.
  Reprint
  Abstract:

  Two instabilities could take place in plasma with a bi-Maxwellian proton distribution function with T_par greater than T_perp, where T_par and T_perp are proton temperatures, parallel and perpendicular, respectively, to the background magnetic field. The first instability is the fire hose (or whistler fire hose), generating low-frequency whistler waves at parallel propagation. We found a new, second instability, the Alfvén fire hose, that generates zero-frequency waves of the Alfvén branch at strongly oblique propagation. The Alfvén fire hose has a linear growth rate comparable to or even greater than that of the whistler fire hose. The two instabilities with the same initial plasma parameters are examined via one-dimensional hybrid simulations and turn out to have behavior very different from each other. The whistler fire hose has an overall quasi-linear evolution, while the evolution of the Alfvén fire hose is more complicated: Initially, unstable zero-frequency waves are gradually transformed into propagating Alfvén waves; during this process the waves are strongly damped and heat protons in a perpendicular direction. Consequently, the Alfvén fire hose is very efficient at destroying proton anisotropy.

• D. Schriver, M. Ashour-Abdalla, V. Sotnikov, P. Hellinger, V. Fiala, R. Bingham and A. Mangeney, Excitation of electron acoustic waves near the electron plasma frequency and twice the plasma frequency, J. Geophys. Res., 105, 12,919-12,927, 2000.
  Paper (AGU web page).
  Abstract:

  In this paper we investigate the nonlinear development of the electron acoustic instability that can lead to the transfer of wave energy to frequencies just above the electron plasma frequency (ω_pe) and to wave with approximately twice the electron plasma frequency (2ω_pe). Using plasma conditions in the upstream electron foreshock region based no data from the AMPTE-UKS spacecraft, an electron beam is considered in plasma containing a background of hot and cold electrons. This leads to the linear excitation of large-amplitude electron acoustic waves at frequencies between about 0.8 and 1.0 ω_pe. A modified decay instability then excites waves in the spectrum just above w_pe. This is followed by a second nonlinear coalescence process that causes the excitation of waves at frequencies just below 2ω_pe. The linear and nonlinear properties of the electron acoustic instability are examined for observed conditions using analytical theory, particle-in-cell simulations, and Vlasov simulations. These results heave application to observations made inside the electron foreshock region, as well as the polar cap and auroral zone, where plasma oscillations and waves at 2ω_pe are observed.

• P. Hellinger, and H. Matsumoto, Nonlinear competition between the whistler and Alfvén fire hoses, J. Geophys. Res., 106, 13,215-13,218, 2001.
  Reprint.
  Abstract:

  We examine a competition between the whistler and Alfvén fire hoses driven by bi-Maxwellian protons with T_par greater than T_perp, where T_par and T_perp are proton temperatures, parallel and perpendicular to the background magnetic field, respectively. We extend the work of Hellinger and Matsumoto [2000] using a two-dimensional hybrid simulation that includes both the instabilities. In the simulation the whistler fire hose initially dominates and saturates in a quasi-linear manner. The Alfvén fire hose is not strongly affected by the presence of the whistler fire hose and grows even when the former is saturated. However, as the Alfvén fire hose grows and saturates via a conversion to Alfvén waves that heat the protons, the waves driven by the whistler fire hose get strongly damped and disappear. The Alfvén waves damp as well, so that at the end of the simulation the wave activity is low. The strong decay of the generated waves translates to an important decrease of the proton temperature anisotropy.

• P. Hellinger, P. Travnicek, and H. Matsumoto, Reformation of perpendicular shocks: Hybrid simulations, Geophys. Res. Lett., 29, 2234, doi:10.1029/2002GL015915, 2002.
  Reprint.
  Abstract:

  We show that in one-dimensional hybrid simulations supercritical perpendicular shocks have a well-defined, slightly oscillating structure (including foot, ramp, overshoot, and undershoot) for hot upstream protons and low Mach numbers. In this case the reflected protons are able to stop the shock steepening at proton scales. However, for colder upstream protons and/or higher Mach numbers simulated shocks show a nonstationary feature, namely a periodic reappearance of a new shock front. These nonstationary shocks simulated by one-dimensional hybrid simulations have shock front gradient scales that are governed only by the spatial resolution used in the code. Consequently, we conclude that the one-dimensional hybrid code is not suitable for description of perpendicular nonstationary shocks.

• P. Hellinger, P. Travnicek, A. Mangeney, and R. Grappin, Hybrid simulations of the expanding solar wind: Temperatures and drift velocities, Geophys. Res. Lett., 30, 1211, doi:10.1029/2002GL016409, 2003a.
  Reprint.
  Abstract:

  In this paper we study the evolution of the expanding solar wind plasma using a one-dimensional and a two-dimensional expanding box model [Grappin et al, 1993] implemented here within a hybrid code [Liewer et al, 2001]. We first consider a plasma with protons and 5 % of alpha particles, without drift between the protons and alphas, considering successively the low-beta and high-beta cases. Then we consider a strong drift between protons and alphas, again separately the low-beta and high-beta case. Without drift, the evolution of the low-beta plasma is adiabatic. In the high-beta plasma without drift, the fire hose instabilites (both parallel and oblique) disrupt the adiabatic evolution. Finally, with a drift, the adiabatic evolution is stopped by the oblique Alfvén instability and the parallel magnetosonic instability for low-beta plasma and for high-beta plasma, respectively. The two instabilities slow down the alphas and heat alphas and protons.

• P. Hellinger, Structure and stationarity of quasi-perpendicular shocks: Numerical simulations, Planet. Space Sci., 51, 649-657, 2003.
  Paper (Science Direct).
  Abstract:

  This paper presents an overview of numerical simulation studies of collisionless shocks and compares these simulation results with observations of the Earth's bow shock and theoretical works. Especially, we review the structure and stationarity of the supercritical quasi-perpendicular shocks. In situ observations indicate that these shocks are generally quasi-stationary whereas full particle simulations as well as recent hybrid simulations present a strong nonstationary behavior, a shock self-reformation. The simulation results, along with theoretical and observational works, suggest that the classical models of the quasi-stationary structure generated by reflected protons or dispersive whistlers are not generally applicable for the supercritical quasi-perpendicular shocks and other phenomena are to be included into the model to ensure the observed quasi-stationarity: The role of a small scale turbulence and shock ripples is investigated. The downstream turbulence and the electron dynamics in the quasi-perpendicular shocks are also discussed.

• P. Hellinger, P. Travnicek, A. Mangeney, and R. Grappin, Hybrid simulations of the magnetosheath compression: Marginal stability path, Geophys. Res. Lett., 30, 1959, doi:10.1029/2003GL017855, 2003b.
  Reprint.
  Abstract:

  This paper reports a two-dimensional hybrid simulation study which utilizes an expanding box model to represent the slow compression of the plasma as it flows through the magnetosheath. In the code we model the compression as an external force: The physical sizes of the simulation box decrease with time. We present results of a simulation which starts in a parameter region of low beta where the plasma is stable with respect to both the Alfvén ion cyclotron (AIC) and mirror instabilities. In this stable region the plasma behaves double-adiabatically and an important proton temperature anisotropy appears. When the plasma becomes unstable to AIC instability, the adiabatic behavior is broken and the AIC waves keep the system close to marginal stability, the theoretical growth rate being about constant, small and positive. The AIC waves are continuously generated and the proton parallel beta increases with time. This marginal stability behavior is slightly disrupted for high proton parallel beta, where the mirror mode becomes unstable. The mirror waves rapidly grow and coexist with AIC wave, in later times the growth of AIC waves is inhibited and mirror waves become dominant. During the stages dominated by AIC and mirror waves, anticorrelation between anisotropy and proton parallel beta is observed. The hybrid expanding box simulation directly verifies the marginal stability evolution of the magnetosheath plasma.

• P. Travnicek, P. Hellinger, D. Schriver and M. G. G. T. Taylor, Excitation of waves at 2ω_pe and back propagating waves at ω_pe: a parametric study, Nonlin. Processes Geophys., 10, 345-349, 2003.
  Reprint.
  Abstract:

  We present a parametric study of electrostatic waves generated with angular frequencies 2ω_pe and -ω_pe by an electron beam using a one-dimensional Vlasov code. We consider a background plasma consisting of three components: two electron populations (a background and a beam) and a proton population (with a mass ratio m_p/m_e = 400 and temperatures T_p = T_e = T). We investigate the influence of different beam parameters on the nonlinear growth rate of waves with angular frequency 2ω_pe and compare the results of the numerical experiments to theoretical predictions. We also examine the presence and excitation of back propagating waves with angular frequency ω_pe. A discussion on the possible generating mechanisms of the different modes observed in these simulations is also presented.

• V. I. Sotnikov, B. S. Bauer, J. N. Leboeuf, P. Hellinger, P. Travnicek, and V. Fiala, Development of global magnetohydrodynamic instabilities in Z-pinch plasmas in presence of non-ideal effects, Phys. Plasmas, 11, 1897-1907, 2004.
  Paper (Scitation web page).
  Abstract:

  The development of global magnetohydrodynamic (MHD) instabilities in z-pinch plasmas has been studied with a three-dimensional (3D) hybrid simulation model. Plasma equilibria without and with axial sheared flow, and with different values of the parameter ε_H, which appears as a coefficient before the Hall term in dimensionless non-ideal MHD equations, have been considered. Increasing the parameter ε_H leads to larger simulation growth rates for both m = 0 sausage and m = 1 kink modes. The hybrid simulations do however show that axial sheared flow severely curtails the linear and nonlinear development of both sausage and kink instabilities. In these respects, the hybrid simulations are in qualitative agreement with linear Hall MHD results. Moreover, in the nonlinear stage, long wavelength modes dominate the excited wave spectrum when the parameter ε_H is small. For the larger value of the parameter ε_H, small-scale structures do however develop nonlinearly in the excited wave spectrum at late times.

• P. Hellinger, P. Travnicek, and J. D. Menietti, Effective collision frequency due to ion-acoustic instability: Theory and simulations, Geophys. Res. Lett., 31, L10806, doi:10.1029/2004GL020028, 2004.
  Reprint.
  Abstract:

  We study the ion-acoustic instability driven by a drift between Maxwellian protons and electrons in a nonmagnetized plasma using a Vlasov simulation with the realistic proton to electron mass ratio. Simulation results for similar electron and proton temperatures are in good agreement with predictions. Namely, during the linear and saturation phases the effective collision frequency observed in the simulation is in quantitative agreement with the quasi-linear predictions. However, previous estimates [Galeev and Sagdeev, 1984; Labelle and Treumann, 1988] give the effective collision frequency less than one tenth the simulated values. The theoretical and simulation results are in a partial agreement with the simulation work by Watt et al. [2002] who used a non-realistic mass ratio. After the saturation, the effective collision frequency increases owing to the existence of backward-propagating ion-acoustic waves. These waves result from induced scattering on protons and contribute to the anomalous transport of electrons.

• V. I. Sotnikov, B. S. Bauer, J. N. Leboeuf, P. Hellinger, P. Travnicek, and V. Fiala, Hybrid simulations of Z-pinches, Comp. Phys. Comm., 164, 150-155, 2004.
  Paper (Science direct).
  Abstract:

  Three-dimensional hybrid simulations with kinetic ions and fluid electrons of z-pinch plasmas are being used to investigate the linear and nonlinear development of sausage and kink instabilities with model profiles in the presence of effects which go beyond ideal magnetohydrodynamics. In addition, the hybrid simulations are also being applied to model start-up plasmas in long pulse z-pinch implosions with experimental profiles and parameters. The first study demonstrates that the Hall term is destabilizing even in the presence of an otherwise stabilizing axial magnetic field. The second study shows that the non-equilibrium start-up phase of wire array implosions is characterized by rapid distortions of the plasma column.

• P. Hellinger and P. Travnicek, Magnetosheath compression: Role of characteristic compression time, alpha particle abundance and alpha/proton relative velocity, J. Geophys. Res., 110, A04210, doi:10.1029/2004JA010687, 2005.
  Reprint.
  Abstract:

  We present results of the application of the hybrid expanding box (HEB) to a slow compression of the magnetosheath plasma. The HEB simulations confirm the previous results of Hellinger et al. [2003b]: the slowly compressed plasma follows a marginal stability path of the proton cyclotron instability in a low-beta plasma whereas in a high-beta plasma the mirror instability becomes dominant. For a faster compression the marginal stability path shifts further inside the unstable region in order to balance the faster anisotropization rate due to the faster compression. The presence of alpha particles strongly changes the dispersive properties of the plasma and introduces the alpha cyclotron instability. The theoretical description of the system becomes intricate since alpha particles introduce additional parameters. The plasma evolution during the compression gets more complex; a transition between the proton and the alpha cyclotron instabilities appears. The overall behavior of the simulated system is not qualitatively different from the behavior of the pure electron-proton plasma. When an additional parameter, a nonzero alpha/proton relative velocity is included the theoretical understanding becomes even more complicated. The behavior of the compressed system is nevertheless similar to the results in the pure electron-proton plasma. An important qualitative change from the zero alpha/proton relative velocity case is that the proton cyclotron instability is able to efficiently accelerate the alpha particles with respect to the protons whereas the alpha cyclotron and the mirror instabilities decelerate them.

• P. Travnicek, P. Hellinger, D. Schriver, and S. D. Bale, Structure of the lunar wake: two-dimensional global hybrid simulations, Geophys. Res. Lett., 32, L06102, doi:10.1029/2004GL022243, 2005.
  Reprint.
  Abstract:

  We study the structure and properties of the lunar wake with these solar wind parameters: the angle θ_sw between directions of the solar wind velocity v_sw and the ambient interplanetary magnetic field (IMF) B θ_sw=45^o and 90^o and v_sw=6 v_A (where v_A denotes solar wind Alfvén velocity). We examine the structure of the wake-tail formed behind the obstacle. In agreement with in situ observations the lunar wake is formed by two counterstreaming beams which fill the wake with a relatively cold, inhomogeneous and highly anisotropic plasma. The results of this study suggest, that under the given solar wind conditions the downstream region of the lunar wake is dominated by an electromagnetic turbulence with the frequencies about the local proton gyrofrequency. The properties and possible generating mechanisms of the low-frequency electromagnetic turbulence are discussed.

• V. I. Sotnikov, J.-N. Leboeuf, C. Deeney, C. A. Coverdale, P. Hellinger, P. Travnicek, and V. Fiala, Hybrid simulation of the Z-pinch instabilities for profiles generated during wire array implosion in the Saturn pulsed power generator, Phys. Plasmas, 12, 092701, 2005.
  Paper (Scitation).
  Abstract:

  Experimental evidence suggests that the energy balance between processes in play during wire array implosions is not well understood. In fact the radiative yields can exceed by several times the implosion kinetic energy. A possible explanation is that the coupling from magnetic energy to kinetic energy as magnetohydrodynamic plasma instabilities develop provides additional energy. It is thus important to model the instabilities produced in the after implosion stage of the wire array in order to determine how the stored magnetic energy can be connected with the radiative yields. To this aim three-dimensional hybrid simulations have been performed. They are initialized with plasma radial density profiles, deduced in recent experiments [C. Deeney, Phys. Plasmas 6, 3576, 1999] that exhibited large x-ray yields, together with the corresponding magnetic field profiles. Unlike previous work, these profiles do not satisfy pressure balance and differ substantially from those of a Bennett equilibrium. They result in faster growth with an associated transfer of magnetic energy to plasma motion and hence kinetic energy.

• P. Hellinger, M. Velli, P. Travnicek, S. P. Gary, B. E. Goldstein, and P. C. Liewer, Alfvén wave heating of heavy ions in the expanding solar wind: Hybrid simulations, J. Geophys. Res., 110, A12109, doi:10.1029/2005JA011244, 2005.
  Reprint.
  Abstract:

  We present hybrid expanding box simulations of the interaction of left-handed Alfvén waves with protons, alpha particles and a tenuous population of oxygen O⁵⁺. The Alfvén waves are initially nonresonant with the ions and the expansion bring them to the cyclotron resonance with O⁵⁺ ions, then with alpha particles, and finally with protons. The simulations show that O⁵⁺ ions are efficiently heated in the directions perpendicular to the background magnetic field, but are only slightly accelerated. Oxygen scattering has a finite time span and saturates mainly due to the marginal stabilization with respect to the oxygen cyclotron instability generated by the temperature anisotropy. During the scattering oxygen ions are able to absorb only a limited amount of available fluctuating energy and, for the parameters used in the simulations, their presence has a minimum influence on alpha particles and protons.

• P. Hellinger and P. Travnicek, Parallel and oblique proton fire hose instabilities in the presence of alpha/proton drift: Hybrid simulations, J. Geophys. Res., 111, A01107, doi:10.1029/2005JA011318, 2006.
  Reprint.
  Abstract:

  Parallel and oblique proton fire hose instabilities are investigated in the presence of a small abundance of alpha particles with a non zero drift velocity with respect to protons. Both instabilities scatter protons and alpha particles in the perpendicular direction with respect to the ambient magnetic field and decelerate both species with respect each other; especially the oblique fire hose effectively diffuses ions owing to its non quasi-linear evolution. Linear Vlasov theory predicts that the presence of the alpha/proton drift enhances the maximum growth rates of the two instabilities in a similar way and that the parallel fire hose is typically the dominant instability. On the other hand, the oblique fire hose has often the maximum growth rate comparable to that of the parallel one and hybrid simulations show that the oblique instability may be active even when the parallel one is marginally stable. Consequently, both instabilities are relevant in the solar wind context.

• P. Hellinger, P. Travnicek, J. C. Kasper, and A. J. Lazarus, Solar wind proton temperature anisotropy: Linear theory and WIND/SWE observations, Geophys. Res. Lett., 33, L09101, doi:10.1029/2006GL025925, 2006.
  Reprint.
  Abstract:

  We present a comparison between WIND/SWE observations (Kasper et al., 2006) of the proton β_||p and T_⊥p/T_||p (where β_||p is the proton parallel beta and T_⊥p and T_||p are the perpendicular and parallel proton temperature, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between β_||c and T_⊥c/T_||c (where β_||c is the core proton parallel beta and T_⊥c and T_||c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).

• S. Landi, P. Hellinger, and M. Velli, Heliospheric magnetic field polarity inversions driven by radial velocity field structures, Geophys. Res. Lett., 33, L14101, doi:10.1029/2006GL026308, 2006.
  Paper (AGU web page).
  Abstract:

  Magnetic field polarity inversions embedded in the predominantly unipolar fast solar wind have been observed by the Ulysses spacecraft at high latitudes. Such reversals have the nature of folded back field lines which we suggest are generated by the interaction of standard large amplitude, low frequency, Alfvénic turbulence with velocity shears in the fast solar wind. We present 2D magnetohydrodynamic simulations of a very low frequency and high amplitude Alfvén wave propagating away from the sun embedded in a velocity shear structure such as a microstream and show how reversals in the magnetic field lines are generated naturally on a time-scale consistent with their observation at Ulysses. The generated magnetic field and plasma signals are similar to those observed. We discuss the role turbulence-stream shear interactions might play in limiting differential velocities in the asymptotic high speed solar wind.

• L. Matteini, S. Landi, P. Hellinger, and M. Velli, Parallel proton fire hose instability in the expanding solar wind: Hybrid simulations, J. Geophys. Res., 111, A10101, doi:10.1029/2006JA011667, 2006.
  Paper (AGU web page).
  Abstract:

  We report a study of the properties of the parallel proton fire hose instability comparing the results obtained by the linear analysis, from 1-D standard hybrid simulations and 1-D hybrid expanding box simulations. The three different approaches converge toward the same instability threshold condition which is in good agreement with in situ observations, suggesting that such instability is relevant in the solar wind context. We investigate also the effect of the wave-particle interactions on shaping the proton distribution function and on the evolution of the spectrum of the magnetic fluctuations during the expansion. We find that the resonant interaction can provide the proton distribution function to depart from the bi-Maxwellian form.

• 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.
  Reprint.
  Abstract:

  We have carried out a self-consistent 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 R_M (where R_M 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 R_M ) 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 R_M 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 hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma, J. Comp. Phys., 225, 753-770, 2007.
  Paper (Science direct).
  Abstract:

  We present a numerical scheme for the integration of the Vlasov-Maxwell system of equations for a non-relativistic 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) 330-351.] and the current advance method (CAM) introduced by Matthews in 1994 [A.P. Matthews, J. Comput. Phys. 112 (1994) 102-116.] In its present version, the code solves the Vlasov-Maxwell equations in a five-dimensional phase space (2-D in the physical space and 3-D 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 hybrid-Vlasov code, the numerical results on propagation and damping of linear ion-acoustic modes and time evolution of linear elliptically polarized Alfvén waves (including the so-called whistler regime) are compared to the analytical solutions. Finally, the numerical results of the hybrid-Vlasov code on the parametric instability of Alfvén waves are compared with those obtained using a two-fluid approach.

• 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.
  Reprint.
  Abstract:

  New behavior of strictly perpendicular shocks in supercritical regime is analyzed with the help of both two-dimensional (2-D) 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 phase-standing in the shock rest frame. A parametric study shows that these whistler waves are emitted in 2-D perpendicular shocks and, simultaneously, the self reformation of the shock front associated with reflected ions disappears; the 2-D shock front is almost quasi-stationary. In contrast, both corresponding one-dimensional (1-D) hybrid and full particle simulations performed in similar plasma and Mach regime conditions show that the self reformation takes place for 1-D perpendicular shock. These results indicate that the emission of these 2-D whistler waves can inhibit the self-reformation in 2-D shocks. Possible generating mechanisms of these waves emissions and comparison with previous works are discussed.

• 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.
  Reprint.
  Abstract:

  We investigate the effect of a slow expansion on a magnetosheath plasma and magnetosheath low-frequency turbulence using a two-dimensional 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. Hellinger, Comment on the linear mirror instability near the threshold, Phys. Plasmas, 14, 082105, 2007.
  Reprint; paper (AIP).
  Abstract:

  Linear threshold condition of the mirror instability in a homogeneous, multi-species collisionless plasma with a general class of distribution functions is obtained in the low-frequency, long-wavelength limit of the Vlasov-Maxwell 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.
  Paper (AGU web page).
  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 (β_||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.

• P. Hellinger, Comment on the drift mirror instability, Phys. Plasmas, 15, 054502, 2008.
  Reprint, Paper (AIP).
  Abstract:

  Drift mirror instability is investigated in a slightly inhomogeneous plasma in a low-frequency, long-wavelength limit of the Vlasov-Maxwell equation. It is shown that previously derived threshold conditions for the drift mirror instability in the case of one cold species are incorrect and that it is hard to get analytically a simple threshold condition for the drift mirror instability in this case. It is argued that the same is true for the drift mirror instability in general.

• F. Califano, P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek, Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, A08219, doi:10.1029/2007JA012898, 2008.
  Reprint.
  Abstract:

  With the aim to understand the origin of the pressure-balanced magnetic structures in the form of holes and humps commonly observed in the solar wind and planetary magnetosheaths, high-resolution hybrid numerical simulations of the Vlasov-Maxwell (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 large-amplitude 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 long-time 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.

• P. Hellinger and P. M. Travnicek, Oblique proton fire hose instability in the expanding solar wind: Hybrid simulations, J. Geophys. Res., 113, A10109, doi:10.1029/2008JA013416, 2008.
  Reprint.
  Abstract:

  Oblique fire hose instability is investigated using hybrid simulations for proton betas of the order of one and for proton parallel temperatures sufficiently greater than the perpendicular ones. The simulations confirm previous simulation results showing that this instability has a self-destructing properties and efficiently reduces the proton temperature anisotropy. A parametric study using one-dimensional standard hybrid simulations shows that stronger changes in the temperature anisotropy and stronger wave emissions appear for larger initial temperature anisotropies. An ideal, slow plasma expansion, modelled by a two-dimensional hybrid expanding box simulation, leads to a generation of proton temperature anisotropy. The anisotropy leads first to destabilization of the dominant parallel fire hose which interacts mainly with minor supra-Alfvénic protons whereas the evolution of core protons is determined by the expansion. Consequently, the effective anisotropy is only slightly reduced and the system eventually becomes unstable with respect to the oblique fire hose instability. The oblique fire hose strongly scatters the protons and removes the anisotropy disrupting the parallel fire hose. An important portion of the fluctuating wave energy is dissipated to protons and only long-wavelength waves remains in the system. The system with a low wave activity then develops again larger temperature anisotropies and the evolution repeats itself. It is concluded that both parallel and oblique proton fire hose instabilities constrain the proton temperature anisotropy in the expanding solar wind with the latter one constituting a final frontier for the anisotropy. These results give a possible explanation of some apparent discrepancies between observations and linear predictions. In addition, a simple bounded anisotropy model is developed to include some of the kinetic effects of the fire hose instabilities in fluid models.

• V. Genot, E. Budnik, P. Hellinger, T. Passot, G. Belmont, P. M. Travnicek, P. L. Sulem, E. Lucek, and I. Dandouras, Mirror structures above and below the linear instability threshold: Cluster observations, fluid model and hybrid simulations, Ann. Geophys., 27, 601-615, 2009.
  Paper (AG homepage).
  Abstract:

  Using 5 years of Cluster data, we present a detailed statistical analysis of magnetic fluctuations associated with mirror structures in the magnetosheath. We especially focus on the shape of these fluctuations which, in addition to quasi-sinusoidal forms, also display deep holes and high peaks. The occurrence frequency and the most probable location of the various types of structures is discussed, together with their relation to local plasma parameters. While these properties have previously been correlated to the β of the plasma, we emphasize here the influence of the distance to the linear mirror instability threshold. This enables us to interpret the observations of mirror structures in a stable plasma in terms of bistability and subcritical bifurcation. The data analysis is supplemented by the prediction of a quasi-static anisotropic MHD model and hybrid numerical simulations in an expanding box aimed at mimicking the magnetosheath plasma. This leads us to suggest a scenario for the formation and evolution of mirror structures.

• B. Lembege, P. Savoini, P. Hellinger, and P. M. Travnicek, Nonstationarity of a two-dimensional perpendicular shock: competing mechanims, J. Geophys. Res., 114, A03217, doi:10.1029/2008JA013618, 2009.
  Paper (AGU)
  Abstract:

  Two-dimensional (2-D) full particle electromagnetic simulations are used for analysing in detail different nonstationary behaviors of a perpendicular super- critical shock. A recent study by Hellinger et al. [2007] has shown that the front of a supercritical shock appears to be dominated by the emission of coherent large amplitude whistler waves for some plasma conditions and shock regimes. These whistler waves are emitted in two-dimensional perpendicular shocks and inhibit the self-reformation driven by the accumulation of reflected ions: then, the 2-D shock front appears almost "quasi-stationary". Present study stresses new complementary results: (i) for a fixed β_i value, the whistler waves emission (wwe) persists for high M_A in particular as long as M_A is above a certain threshold M_A^wwe. The "quasi-stationarity" is only apparent when considering y-averaged profiles; in fact, the non-stationarity of the shock front is clearly apparent when considering the full 3D fields profiles. (ii) For low (but still supercritical) M_A below this critical threshold M_A^wwe, the self-reformation is retrieved and becomes dominant as the amplitude of the whistler waves becomes negligible. (iii) There exists a transition regime in Mach number around the critical value M_A^wwe within which both processes can co-exist together. The competition between both processes can be expressed in time for the self reformation to establish versus the time for the nonlinear whistler waves to grow and reach an amplitude large enough to diffuse the reflected ions noticeably and destroy their coherent motion (necessary to establish the self-reformation). (iv) These results are observed for a strictly perpendicular shock, as B₀ is within the simulation plane. In contrast, as B₀ is perpendicular to the simulation plane, no whistler waves emission is evidenced even for large Mach number and only self-reformation is observed. (v) The occurrence and disappearance of the nonlinear whistler waves are well recovered in both 2-D Particle In Cell (PIC) full electromagnetic and 2-D hybrid simulations. However, some differences are evidenced between the two types of simulations concerning the occurrence of the self-reformation which are discussed. These results, even if unexpected, are shown to be in good agreement with previous works these are compared with. The impact on the results, of the mass ratio (2-D PIC simulations), of the resistivity and spatial resolution (2-D hybrid simulations), and of the size of the simulation box along the shock front is analyzed in details.

• P. Hellinger, E. A. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek, Mirror instability: From quasi-linear diffusion to coherent structures, Geophys. Res. Lett., 36, L06103, doi:10.1029/2008GL036805, 2009.
  Reprint.
  Abstract:

  A model for the nonlinear dynamics of mirror modes near the instability threshold is presented. By matching the quasi-linear theory for the space-averaged distribution function with a reductive perturbative description of the mirror modes, the model reproduces the early-time flattening of the distribution function and the development of magnetic humps from an initial noise, in agreement with Vlasov-Maxwell numerical simulations. It suggests a possible mechanism at the origin of the mirror structures observed in planetary magnetosheaths and in the solar wind.

• D. Borgogno, P. Hellinger, T. Passot, P. L. Sulem, and P. M. Travnicek, Alfvén wave filamentation and dispersive phase mixing in a high-density channel: Landau fluid and hybrid simulations, Nonlin. Processes Geophys., 16, 275-285, 2009.
  Paper (NPG homepage)
  Abstract:

  The propagation of dispersive Alfvén waves in a low-beta collisionless plasma with a high-density channel aligned with the ambient magnetic field, is studied in three space dimensions. A fluid model retaining linear Landau damping and finite Larmor radius corrections is used, together with a hybrid particle-in-cell simulation aimed to validate the predictions of this Landau-fluid model. It is shown that when the density enhancement is moderate (depending on the pump wavelength and the plasma parameters), the wave energy concentrates into a filament whose transverse size is prescribed by the dimension of the channel. In contrast, in the case of a stronger density perturbation, the early formation of a magnetic filament is followed by the onset of thin helical ribbons and the development of strong gradients. This "dispersive phase mixing" provides a mechanism permitting dissipation processes (not included in the present model) to act and heat the plasma.

• P. M. Travnicek, P. Hellinger, D. Schriver, D. Hercik, J. A. Slavin, and B. J. Anderson, Kinetic instabilities in Mercury's magnetosphere: three-dimensional simulation results, Geophys. Res. Lett., 36, L07104, doi:10.1029/2008GL036630, 2009.
  Paper (AGU homepage)
  Abstract:

  A self-consistent global three-dimensional kinetic study of Mercury's magnetosphere is carried out examining waves and instabilities generated by ion temperature anisotropy and plasma flow. The overall structure of Mercury's upstream bow shock and magnetosheath are qualitatively very similar to those of Earth. Beam-generated long-wavelength oscillations are present upstream of Mercury's quasi-parallel bow shock, whereas large-amplitude mirror waves develop downstream of the quasi-parallel bow shock in the magnetosheath. A train of mirror waves forms also downstream of the quasi-perpendicular bow shock. A velocity shear near the magnetopause can lead to formation of vortex-like structures. The magnetospheric cavity close to the planet's equatorial plane is filled with ions much hotter than the solar wind protons. A drift-driven plasma belt close to the equator is present in the model and contains plasma with high-temperature anisotropy, and the loss cone for charged particles in this region is large. The belt may cause diamagnetic effects superimposed on the planet's internal magnetic field and can interact with Mercury's magnetopause.

• P. Hellinger and P. M. Travnicek, On Coulomb collisions in bi-Maxwellian plasmas, Phys. Plasmas, 16, 054501, 2009.
  Preprint, Paper (AIP).
  Abstract:

  Collisional momentum and energy transport in bi-Maxwellian plasmas with a drift velocity along the ambient magnetic field are calculated from both the Fokker-Planck and Boltzmann integral approximations. The transport coefficients obtained from the two approaches are identical to the leading order (proportional to the Coulomb logarithm) and are presented here in a closed form involving generalized double hypergeometric functions.

• P. M. Travnicek, D. Schriver, P. Hellinger, D. Hercik, B. J. Anderson, M. Sarantos, and J. A. Slavin, Mercury's magnetosphere-solar wind interaction for northward and southward interplanetary magnetic field: Hybrid simulation results, Icarus, submitted, 2009.

• L. Matteini, S. Landi, M. Velli, and P. Hellinger, Kinetics of the parametric instabilities of Alfvén waves: evolution of ion distribution functions, J. Geophys. Res., ?, submitted, 2009.