Kinetic effects in the turbulent solar wind: capturing ion physics with a Vlasov code

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1 Kinetic effects in the turbulent solar wind: capturing ion physics with a Vlasov code Francesco Valentini francesco.valentini@fis.unical.it S. Servidio, D. Perrone, O. Pezzi, B. Maruca, F. Califano, W. H. Matthaeus and P. Veltri

2 Proton temperature anisotropy in the solar wind Distribution PDF ( T /T, β ) fire llel Par a m irr or ue fire hos e clo tro n Obl iq cy hos e Pr ot on Hellinger et al. GRL (2006); Kasper et al. JGR (2006); Kasper et al., (2002) T and T parallel and perpendicular proton temperatures with respect to the ambient magnetic field β parallel plasma beta (ratio between kinetic and magnetic pressure) The solar wind is a turbulent and weakly collisional system Kinetic instabilities influence the solar wind nonlinear kinetic processes may locally occur in turbulence!...we need Vlasov-Maxwell simulations!

3 Proton temperature anisotropy in the solar wind Maruca et al. PRL (2011) T and T parallel and perpendicular proton temperatures with respect to the ambient magnetic field β parallel plasma beta (ratio between kinetic and magnetic pressure) The solar wind is a turbulent and weakly collisional system Kinetic instabilities influence the solar wind nonlinear kinetic processes may locally occur in turbulence!...we need Vlasov-Maxwell simulations!

4 Basic equations (dimensionless units) Hybrid Vlasov-Maxwell (HVM) equations: Valentini et al., J. Comp. Phys. (2007); Phys. Rev. Lett. (2009), (2010), (2011) Characteristic quantities: Simulations have been performed on FERMI at CINECA, within the European Project 3D-3V Vlasov simulations of plasma turbulence, PRACE (Partner for advanced computing in Europe)

5 Setup of 2D-3V simulations 2D 3V numerical domain (two dimensions in physical space and three in velocity space) Phase space discretization Periodic boundary conditions in physical space The initial Maxwellian equilibrium is perturbed by a 2D spectrum of fluctuations for magnetic and proton velocity fields. No density disturbances are imposed at t=0

6 Simulations of kinetic turbulence Current density (colors) and magnetic potential In analogy with fluid models (MHD, Hall MHD, etc.) of decaying turbulence (Mininni & Pouquet 2009), it is possible to identify an instant of time at which the turbulent activity reaches its maximum value The turbulent pattern is similar to 2D MHD: vortices, islands, current sheets...

7 Reconnenction events in turbulence In turbulence, reconnection locally occurs (at the X-points) Servidio et al. PRL 2009, PoP 2010, 2011 Drake et al. APJ Bifurcation (Hall effect) Thickness ~ few proton skin depths

8 Power spectra Large scale Alfvenic correlations Kolmogorov-like spectrum Low compressibility (density fluct. 8%) Intense electric activity at small scales Steepening of the magnetic spectrum at kdi ~ 1...several features commonly observed in space plasmas!

9 A measure of temperature anisotropy How to properly measure these distortions? The velocity distribution function may exhibit strong deformations in velocity space Assuming f as an ellipsoid: e 3 Stress tensor Ai j x = e1 e2 1 3 vi vi v j v j f d v n Eigenvalues (temperatures) Eigenvectors Minimum Variance Frame (MVF) e1 e2 e3 Note: for a Maxwellian λ1= λ2= λ3= 1 (Maximum) Temperature anisotropy λ1/λ3

10 Velocity distributions in turbulence Local magnetic field Anisotropy with respect to local magnetic field can be either >1 or <1 the DF is strongly affected by turbulence, resembling an elongated potato-like structure

11 Anisotropy direction with respect to local B cos = e 1 B e1 B e1 B mainly e1 can be both along or across local B, but, because of turbulence, a broad distribution of angles is observed. Note: If e1 and B were spatially random and uncorrelated, PDF(cos ) ~ const. (=0.5)

12 Where are kinetic effects located? Out of plane current density Temperature anisotropy 2 j ( b ) z Streams of kinetic effects (temperature anisotropy) are adjacent to reconnecting current sheets. Servidio et al., Phys. Rev. Lett. (2012)

13 Trying to reproduce the solar-wind anisotropy plot Temperature anisotropy with respect to the local magnetic field We considered an ensamble of simulations in different regions of the parameter space and evaluated the temperature anisotropy with respect to the local magnetic field

14 Trying to reproduce the solar-wind anisotropy plot NOT A NICE AGREEMENT BUT: In the solar wind plot we mixes different levels of fluctuations Let us try additional simulations with increased level of turbulence! Servidio et al., submitted to AstroPhys. J. Lett.

15 The anisotropy depends on the level of turbulence SIMULATIONS Higher is the level of the initial fluctuations higher is the anisotropy generated at the saturation of turbulence OK, LET'S TRY AGAIN!!!

16 Numerical results versus solar-wind data simulations NOW MUCH BETTER!!!

17 Temperature anisotropy along the cascade << > Temperature anisotropy is generated during the turbulent cascade. As the level of turbulence increases, smaller and smaller scale structures are produced and larger and larger values of temperature anisotropy are reached.

18 Analogies between 2D-3V and 3D-3V runs << > 3D-3V runs with resolution 128x128x128 space 51x51x51 velocity European PRACE project CPU hours on FERMI 2D-3V runs 3D-3V runs

19 Small scale structures (PVI analysis) Location of the small-scale structures in the simulation results and in the solar-wind data Simulations Solar wind Servidio et al., submitted to AstroPhys. J. Lett.

20 One more ingredient...plasma collisions! c The Landau beast involves gradients of the velocity distribution in velocity space. Therefore, if strong velocity gradients are generated during the evolution of the solar wind plasma and the velocity distributions are far from the Maxwellian shape...

21 One more ingredient...plasma collisions! c The Landau beast involves gradients of the velocity distribution in velocity space. Therefore, if strong velocity gradients are generated during the evolution of the solar wind plasma and the velocity distributions are far from the Maxwellian shape... Enhanced collisionality is recovered at the limits of the solar-wind temperatureanisotropy plot!!!

22 Summary and Conclusions By means of Hybrid Vlasov-Maxwell simulations we modeled the complex solarwind dynamics that produces temperature anisotropy in the proton velocity distributions Our numerical results in 2D-3V and 3D-3V configuration suggest that: 1) 2) 3) 4) 5) Along the turbulent cascade, small scale structures (current sheets) are generated of typical size of few proton inertial lenghts; the generation of small scales is arrested by dispersive (Hall) effects In correspondence of these small scale structures, large temperature anisotropy with respect to the local magnetic field is recovered The temperature anisotropy plot from the simulations display many features significantly comparable to those observed in the solar wind data Both the generation of this temperature anisotropy and the shaping of the temperature anisotropy plot are driven by the turbulent cascade Collisions can play an important role

23 Numerical accuracy is a must! The resistive term in the Ohm's law damps out numerical instabilities that may strongly damage the genuine properties of small-scale turbulence E = - u b + j b/n - (1/n) Pe + j = E1 + E2+ E3+ E4 The resistive term is 3 orders of magnitude smaller than the others, but is enough to suppress numerical instabilities See paper by Wan et al. PoP (2010) These numerical instabilities (noise) really look like tearing instabilities, so... be careful! under-resolved well-resolved