Enrico Camporeale

The Dissipation of Solar Wind Turbulent Fluctuations at Electron Scales

We present two-dimensional fully kinetic particle-in-cell simulations of decaying electromagnetic fluctuations. The computational box is such that wavelengths ranging from electron to ion gyroradii are resolved. The parameters used are realistic for the solar wind, and the ion-to-electron mass ratio is physical. The dissipation of turbulent fluctuations at small scales is thought to be a crucial mechanism for solar wind acceleration and coronal heating. The computational results suggest that a power-law cascade of magnetic fluctuations could be sustained up to scales of the electron Larmor radius and smaller. We analyze the simulation results in light of the Vlasov linear theory, and we comment on the particle heating. The dispersion curves of lightly damped modes in this regime suggest that a linear mechanism could be responsible for the observed steepening of power spectra at electron scales, but a straightforward identification of turbulent fluctuations as an ensemble of linear modes is not possible.

Electron vortex magnetic holes: A nonlinear coherent plasma structure

We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.

RECONNECTION AND ELECTRON TEMPERATURE ANISOTROPY IN SUB-PROTON SCALE PLASMA TURBULENCE

Knowledge of turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two-dimensional, particle-in-cell plasma simulations with a realistic electron-proton mass ratio and a guide field perpendicular to the simulation plane. A power spectrum fluctuation with approximately power-law form is created down to scales of the order of the electron gyroradius. We identify the signatures of collisionless reconnection at sites of X-point field geometry in the dynamic magnetic field topology, which gradually relaxes in complexity. The reconnection sites are generally associated with regions of strong parallel electron temperature anisotropy. The evolving topology of magnetic field lines connected to a reconnection site allows for the spatial mixing of electrons accelerated at multiple, spatially separated reconnection regions. This leads to the formation of multi-peaked velocity distribution functions with strong parallel temperature anisotropy. In a three-dimensional system that can support the appropriate wave vectors, the multi-peaked distribution functions would be expected to be unstable to kinetic instabilities, contributing to dissipation. The proposed mechanism of anisotropy formation is also relevant to space and astrophysical systems where the evolution of the plasma is constrained by linear temperature anisotropy instability thresholds. The presence of reconnection sites leads to electron energy gain, nonlocal velocity space mixing, and the formation of strong temperature anisotropy; this is evidence of an important role for reconnection in the dissipation of turbulent fluctuations.

IMPLICATIONS OF A NON-MODAL LINEAR THEORY FOR THE MARGINAL STABILITY STATE AND THE DISSIPATION OF FLUCTUATIONS IN THE SOLAR WIND

The non-modal approach for a linearized system differs from a normal mode analysis by following the temporal evolution of some perturbed equilibria, and therefore includes transient effects. We employ a non-modal approach for studying the stability of a bi-Maxwellian magnetized plasma using the Landau fluid model, which we briefly describe. We show that bi-Maxwellian stable equilibria can support transient growth of some physical quantities, and we study how these transients behave when an equilibrium approaches its marginally stable condition. This is relevant to anisotropic plasma, that are often observed in the solar wind with a temperature anisotropy close to values that can trigger a kinetic instability. The results obtained with a non-modal approach are relevant to a re-examination of the concept of linear marginal stability. Moreover, we discuss the topic of the dissipation of turbulent fluctuations, suggesting that the non-modal approach should be included in future studies.A magnetized plasma with anisotropic particle distributions may be unstable to a number of different kinetic instabilities. The solar wind is often observed in a state which is close to that implying instability, i.e., in a marginal stability state. Normal-mode linear theory predicts that fluctuations in a stable plasma damp exponentially. The non-modal approach for a linearized system differs from a normal-mode analysis by following the temporal evolution of some perturbed equilibria, and therefore includes transient effects. We employ a non-modal approach for studying the stability of a bi-Maxwellian magnetized plasma using the Landau fluid model, which we briefly describe. We show that bi-Maxwellian stable equilibria can support transient growth of some physical quantities, and we study how these transients behave when an equilibrium approaches its marginally stable condition. The results obtained with a non-modal approach are relevant to a re-examination of the concept of linear marginal stability. Moreover, we highlight some aspects of the dissipation of turbulent fluctuations, which suggest that the non-modal approach should be included in future studies.

Information theoretical approach to discovering solar wind drivers of the outer radiation belt

textabstractThe solar wind-magnetosphere system is nonlinear. The solar wind drivers of geosynchronous electrons with energy range of 1.8–3.5 MeV are investigated using mutual information, conditional mutual information (CMI), and transfer entropy (TE). These information theoretical tools can establish linear and nonlinear relationships as well as information transfer. The information transfer from solar wind velocity (Vsw) to geosynchronous MeV electron flux (Je) peaks with a lag time of 2 days. As previously reported, Je is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed at least partly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 h, suggesting that the MeV electron loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 h. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics is investigated using windowed TE. When the data are ordered according to transfer entropy value, it is possible to understand details of the triangle distribution that has been identified between Je(t + 2 days) versus Vsw(t).

Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian

This paper investigates hybrid kinetic-magnetohydrodynamic (MHD) models, where a hot plasma (governed by a kinetic theory) interacts with a fluid bulk (governed by MHD). Different nonlinear coupling schemes are reviewed, including the pressure-coupling scheme (PCS) used in modern hybrid simulations. This latter scheme suffers from being non-Hamiltonian and is unable to exactly conserve total energy. Upon adopting the Vlasov description for the hot component, the non-Hamiltonian PCS and a Hamiltonian variant are compared. Special emphasis is given to the linear stability of Alfven waves, for which it is shown that a spurious instability appears at high frequency in the non-Hamiltonian version. This instability is removed in the Hamiltonian version.

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier–Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

Vlasov simulations of Kinetic Alfven Waves at proton kinetic scales

Kinetic Alfven waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρp and/or inertial length dp and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfven waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta βp = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for waveleng...

New approach for the study of linear Vlasov stability of inhomogeneous systems

This paper presents an alternative technique for solving the linearized Vlasov-Maxwell set of equations, in which the velocity dependence of the perturbed distribution function is described by means of an infinite series of orthogonal functions, chosen as Hermite polynomials. The orthogonality properties of such functions allow us to decompose the Vlasov equation into a set of infinite coupled linear equations. With a suitable truncation relation, the problem is transformed in an eigenvalue problem. This technique is based on solid but easy concepts, not attempting to evaluate the integration over the unperturbed trajectories and can be applied to any equilibrium. Although the solutions are approximate, because they neglect contributions of higher order coefficients of the series, the physical meaning of the low-order coefficients is clear. Furthermore the accuracy of the solution, which depends on the number of terms taken into account in the Hermite series, appears to be merely a problem of computational power. The method has been tested for a 1D Harris equilibrium, known to give rise to several instabilities like tearing, drift kink, and lower hybrid. The results are shown in agreement with those obtained by Daughton with a traditional technique based on the integration over unperturbed orbits.

Neutral Vlasov kinetic theory of magnetized plasmas

The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincare reduction theory is used to show that the neutral Vlasov kinetic theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the new model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime.