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and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD.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.

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

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

Multi-Stability and Pattern-Selection in Oscillatory Networks with Fast Inhibition and Electrical Synapses

A model or hybrid network consisting of oscillatory cells interconnected by inhibitory and electrical synapses may express different stable activity patterns without any change of network topology or parameters, and switching between the patterns can be induced by specific transient signals. However, little is known of properties of such signals. In the present study, we employ numerical simulations of neural networks of different size composed of relaxation oscillators, to investigate switching between in-phase (IP) and anti-phase (AP) activity patterns. We show that the time windows of susceptibility to switching between the patterns are similar in 2-, 4- and 6-cell fully-connected networks. Moreover, in a network (N = 4, 6) expressing a given AP pattern, a stimulus with a given profile consisting of depolarizing and hyperpolarizing signals sent to different subpopulations of cells can evoke switching to another AP pattern. Interestingly, the resulting pattern encodes the profile of the switching stimulus. These results can be extended to different network architectures. Indeed, relaxation oscillators are not only models of cellular pacemakers, bursting or spiking, but are also analogous to firing-rate models of neural activity. We show that rules of switching similar to those found for relaxation oscillators apply to oscillating circuits of excitatory cells interconnected by electrical synapses and cross-inhibition. Our results suggest that incoming information, arriving in a proper time window, may be stored in an oscillatory network in the form of a specific spatio-temporal activity pattern which is expressed until new pertinent information arrives

Reflection-driven turbulence in the super-Alfv\'enic solar wind

In magnetized, stratified astrophysical environments such as the Sun's corona and solar wind, Alfv\'enic fluctuations ''reflect'' from background gradients, enabling nonlinear interactions and thus dissipation of their energy into heat. This process, termed ''reflection-driven turbulence,'' is thought to play a crucial role in coronal heating and solar-wind acceleration, explaining a range of observational correlations and constraints. Building on previous works focused on the inner heliosphere, here we study the basic physics of reflection-driven turbulence using reduced magnetohydrodynamics in an expanding box -- the simplest model that can capture the local turbulent plasma dynamics in the super-Alfv\'enic solar wind. Although idealized, our high-resolution simulations and simple theory reveal a rich phenomenology that is consistent with a diverse range of observations. Outwards-propagating fluctuations, which initially have high imbalance, decay nonlinearly to heat the plasma, becoming more balanced and magnetically dominated. Despite the high imbalance, the turbulence is strong because Els\"asser collisions are suppressed by reflection, leading to ''anomalous coherence'' between the two Els\"asser fields. This coherence, together with linear effects, causes the turbulence to anomalously grow the ''anastrophy'' (squared magnetic potential) as it decays, forcing the energy to rush to larger scales and forming a ''$1/f$-range'' energy spectrum as it does so. At late times, the expansion overcomes the nonlinear and Alfv\'enic physics, forming isolated, magnetically dominated ''Alfv\'en vortex'' structures that minimize their nonlinear dissipation. These results can plausibly explain the observed radial and wind-speed dependence of turbulence imbalance, residual energy, plasma heating, and fluctuation spectra, as well as making testable predictions for future observations