Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence

The role of magnetic helicity is investigated in kinetic Alfv\'en wave and oblique whistler turbulence in presence of a relatively intense external magnetic field $b_0 {\bf e_\parallel}$. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD. We use the asymptotic equations derived by Galtier \& Bhattacharjee (2003) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, $n+\tilde n = -6$, where $n$ and $\tilde n$ are the power law indices of the perpendicular (to ${\bf b_0}$) wave number magnetic energy and helicity spectra respectively. Therefore, the spectra derived in the past from the energy equation only, namely $n=-2.5$ and $\tilde n = - 3.5$, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solution $\tilde n = -3$ is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that $-3 < n < -2.5$.Comment: 26 pages, submitted to the special issue of JPP "Present achievements and new frontiers in space plasmas

Fluidization of collisionless plasma turbulence

In a collisionless, magnetized plasma, particles may stream freely along magnetic-field lines, leading to phase "mixing" of their distribution function and consequently to smoothing out of any "compressive" fluctuations (of density, pressure, etc.,). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma-one of the most fundamental physical phenomena that make plasma different from a conventional fluid. Nevertheless, broad power-law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial scale range and is therefore cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power-law spectra. This "fluidization" of collisionless plasmas occurs because phase mixing is strongly suppressed on average by "stochastic echoes", arising due to nonlinear advection of the particle distribution by turbulent motions. Besides resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless except at very small scales. The universality of "fluid" turbulence physics is thus reaffirmed even for a kinetic, collisionless system

A Universal Law for Solar-Wind Turbulence at Electron Scales

The interplanetary magnetic fluctuation spectrum obeys a Kolmogorovian power law at scales above the proton inertial length and gyroradius which is well regarded as an inertial range. Below these scales a power law index around $-2.5$ is often measured and associated to nonlinear dispersive processes. Recent observations reveal a third region at scales below the electron inertial length. This region is characterized by a steeper spectrum that some refer to it as the dissipation range. We investigate this range of scales in the electron magnetohydrodynamic approximation and derive an exact and universal law for a third-order structure function. This law can predict a magnetic fluctuation spectrum with an index of $-11/3$ which is in agreement with the observed spectrum at the smallest scales. We conclude on the possible existence of a third turbulence regime in the solar wind instead of a dissipation range as recently postulated.Comment: 11 pages, will appear in Astrophys.

Kinetic-scale magnetic turbulence and finite Larmor radius effects at Mercury

We use a nonstationary generalization of the higher-order structure function technique to investigate statistical properties of the magnetic field fluctuations recorded by MESSENGER spacecraft during its first flyby (01/14/2008) through the near Mercury's space environment, with the emphasis on key boundary regions participating in the solar wind -- magnetosphere interaction. Our analysis shows, for the first time, that kinetic-scale fluctuations play a significant role in the Mercury's magnetosphere up to the largest resolvable time scale ~20 s imposed by the signal nonstationarity, suggesting that turbulence at this planet is largely controlled by finite Larmor radius effects. In particular, we report the presence of a highly turbulent and extended foreshock system filled with packets of ULF oscillations, broad-band intermittent fluctuations in the magnetosheath, ion-kinetic turbulence in the central plasma sheet of Mercury's magnetotail, and kinetic-scale fluctuations in the inner current sheet encountered at the outbound (dawn-side) magnetopause. Overall, our measurements indicate that the Hermean magnetosphere, as well as the surrounding region, are strongly affected by non-MHD effects introduced by finite sizes of cyclotron orbits of the constituting ion species. Physical mechanisms of these effects and their potentially critical impact on the structure and dynamics of Mercury's magnetic field remain to be understood.Comment: 46 pages, 5 figures, 2 table

Turbulent Heating in Collisionless Low-beta Plasmas: Imbalance, Landau Damping, and Electron–Ion Energy Partition

An understanding of how turbulent energy is partitioned between ions and electrons in weakly collisional plasmas is crucial for modeling many astrophysical systems. Using theory and simulations of a four-dimensional reduced model of low-beta gyrokinetics (the “Kinetic Reduced Electron Heating Model”), we investigate the dependence of collisionless heating processes on plasma beta and imbalance (normalized cross-helicity). These parameters are important because they control the helicity barrier, the formation of which divides the parameter space into two distinct regimes with remarkably different properties. In the first, at lower beta and/or imbalance, the absence of a helicity barrier allows the cascade of injected power to proceed to small (perpendicular) scales, but its slow cascade rate makes it susceptible to significant electron Landau damping, in some cases leading to a marked steepening of the magnetic spectra on scales above the ion Larmor radius. In the second, at higher beta and/or imbalance, the helicity barrier halts the cascade, confining electron Landau damping to scales above the steep “transition-range” spectral break, resulting in dominant ion heating. We formulate quantitative models of these processes that compare well to simulations in each regime, and combine them with results of previous studies to construct a simple formula for the electron–ion heating ratio as a function of beta and imbalance. This model predicts a “winner takes all” picture of low-beta plasma heating, where a small change in the fluctuations' properties at large scales (the imbalance) can cause a sudden switch between electron and ion heating

Low-dimensional Nonlinear Modes computed with PGD/HBM and Reduced Nonlinear Modal Synthesis for Forced Responses

International audienceThis work proposes an algorithm allowing to perform a fast and light computation of branches of damped Nonlinear Normal Modes (dNNMs). Based on a previous work about undamped NNMs (uNNMs), it couples Proper Generalized Decomposition (PGD) features, harmonic balance and prediction-correction continuation schemes. After recalling the main contributions of the method applied on an example with cubic nonlinearities, the issue of a reduced nonlinear modal synthesis is briefly addressed

Electron-ion heating partition in imbalanced solar-wind turbulence

A likely candidate mechanism to heat the solar corona and solar wind is low-frequency "Alfv\'enic" turbulence sourced by magnetic fluctuations near the solar surface. Depending on its properties, such turbulence can heat different species via different mechanisms, and the comparison of theoretical predictions to observed temperatures, wind speeds, anisotropies, and their variation with heliocentric radius provides a sensitive test of this physics. Here we explore the importance of normalized cross helicity, or imbalance, for controlling solar-wind heating, since it a key parameter of magnetized turbulence and varies systematically with wind speed and radius. Based on a hybrid-kinetic simulation in which the forcing's imbalance decreases with time -- a crude model for a plasma parcel entrained in the outflowing wind -- we demonstrate how significant changes to the turbulence and heating result from the "helicity barrier" effect. Its dissolution at low imbalance causes its characteristic features -- strong perpendicular ion heating with a steep "transition-range" drop in electromagnetic fluctuation spectra -- to disappear, driving more energy into electrons and parallel ion heat, and halting the emission of ion-scale waves. These predictions seem to agree with a diverse array of solar-wind observations, offering to explain a variety of complex correlations and features within a single theoretical framework