To be updated until april 30th

Nahuel Andres

## Exact relations in fully developed turbulence: energy cascade rate from the MHD to the ion-scales

Nahuel Andres
nandres@iafe.uba.ar
Institute of Astronomy and Space Physics, UBA-CONICET, Buenos Aires, Argentina
Exact laws derived for incompressible magnetohydrodynamics (IMHD) turbulence have been widely used to gain insight into the problem of solar wind (SW) heating through the estimation of the turbulent energy cascade rate. While the incompressibilty assumption can, to some extent, be justified to address large scale SW turbulence where alfv\'enic fluctuations dominate, it is likely to fail to accurately describe sub-ion scale physics, as well as other more compressible plasmas such as planetary magnetospheres or the interstellar medium. Here, we will review a set of recent analytical and numerical results obtained for compressible flows within the isothermal closure. First, we will discuss the new exact law derived for compressible MHD (CMHD) and emphasize the major differences with IMHD, in particular the role of the mean (background) magnetic field and plasma density. In the next step, we will discuss the extension of the laws to compressible Hall-MHD (CHMHD) and discuss the physics brought up by the new terms due to the Hall current. The incompressiblity limit is further studied using a more compact form that include only increments of the turbulent fields and compared to previous derivations. The validation of the various exact laws are done using 3D direct numerical simulations (GHOST code for the compressible flows and TURBO for the incompressible models). Potential applications of the models to estimate the energy cascade rate of turbulence over a broad range of scales that span both the inertial and sub-ion (dispersive) ranges in spacecraft data will be discussed.

Lev Arzamasskiy

## Hybrid-Kinetic Simulations of Low- and High-Beta Turbulence

Lev Arzamasskiy
leva@astro.princeton.edu
Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540
A lot of astrophysical environments, such as accretion flows around black holes, the intracluster medium, and the solar wind, are weakly collisional (or collisionless) and well magnetized. We present results from hybrid-kinetic simulations of turbulence relevant to these systems. Our low-beta simulations (where beta is the ratio of thermal and magnetic pressures) reproduce the observed preferential perpendicular ion heating and the development of non-thermal beams in the ion distribution function in the solar wind. Our high-beta simulations focus on the effects of kinetic micro-instabilities on the turbulent cascade, in particular, how they disrupt inertial-range Alfven waves and introduce an effective collisionality in otherwise collisionless plasma.

Etienne Behar

## MMS observations of particle velocity distribution functions and field-particle correlator

Etienne Behar
etienne.behar@lpp.polytechnique.fr
LPP, CNRS - Ecole Polytechnique – Sorbonne Université - Univ. Paris-Sud - Observatoire de Paris, Université Paris-Saclay, Palaiseau, 91128, France

Laboratoire de Physique des Plasmas, CNRS - École polytechnique - Sorbonne Université - Observatoire de Paris, Université Paris-Sud, Université Paris-Saclay, F-91128 Palaiseau, France

We present our current work on the analysis of MMS data carried out in particular with particle velocity distribution functions (VDF). We propose methods that tackle the high time resolution of these four-dimensional data sets, in various reference frames and coordinate systems. In particular, we explore the feasibility of obtaining spatial and time derivatives of the VDF, with the inherent price in terms of time resolution/integration. Together with field measurements, these derivatives enable the quantification of the various terms of the Poisson-Vlasov equations, with the ultimate goal of a direct measurement of the energy exchange taking place between fields and particles, as a function of velocity, following the effort initiated by Howes et al. 2017 and Chen et al. 2019.

Enrique Bello-Benítez

## Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects

Enrique Bello-Benítez
ebello@ing.uc3m.es

Authors: E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos. There exist a broad variety of nonlinear-wave phenomena in the solar wind. Different types of stable large-amplitude solitary waves are typically observed in these plasmas. The study of small amplitude waves can be described by well-known equations: Korteweg-de-Vries (KdV), modified KdV, Derivative Nonlinear Schrödinger (DNLS) and triple-degenerate DNLS. However, magnetohydrodynamic (MHD) fluid equations are more suitable for the analysis of large-amplitude structures, which is the approach used in this work [1] —to be precise, MHD equations with Hall effect and Finite Larmor Radius (FLR) corrections to the double adiabatic pressure tensor. Assuming travelling wave solutions, the system of partial differential equations yields a set of 5 ordinary differential equations (ODEs) governing the spatial profile of the velocity and magnetic-field vectors —if double adiabatic equations of state are used for the gyrotropic pressures. The procedure to derive these equations follows Ref. [2], but some discrepancies are shown [1]. The existence of solitary-wave solutions in different parametric regimes is rigorously proved in this system of ODEs using concepts and tools from the theory of dynamical systems. Two key features of the concerning ODEs are: (1) the system is reversible and (2) the existence of an invariant which allows reducing the effective dimension of the system from 5 to 4. These characteristics are guaranteed if equations of state are used for the pressures. Nevertheless, only stable structures have physical interests and are expected to be observed in space. The global stability of the solitary waves is investigated by numerical spectral simulations using two different closures for the pressures: (1) double adiabatic equations and (2) evolution equations including the FLR work terms [3], which guarantee energy conservation and better reproduces the real physics. In case (1), it is found that the solitary waves may have a stable core even if the background is unstable. The background instability seems to disappear when the energy-conserving model (2) is considered. In this case, stable solitary waves are found that survive long time without significant deformation.

References

[1] E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos, Phys. Rev. E 99, 023202 (2019).

[2] E. Mjølhus, Nonlin. Proc. Geophys. 16, 251 (2009).

[3] P. L. Sulem and T. Passot, J. Plasma Phys. 81, 325810103 (2015).

Stanislav Boldyrev

## Runaway solar-wind electrons and space plasma turbulence

Stanislav Boldyrev
boldyrev@wisc.edu
University of Wisconsin - Madison, 1150 University Ave, Madison, WI 53706, USA
The solar wind contains fast, suprathermal electrons that stream from the sun along the Parker-spiraled magnetic field lines. These electrons experience very weak Coulomb collisions and they get collimated in a narrow beam (strahl). When Coulomb collisions are not efficient, the strahl is broadened by interactions with plasma turbulence. We argue that at high energies, the strahl electrons can efficiently interact with whistler waves. We demonstrate how pitch-angle scattering by whistler turbulence can be incorporated into the kinetic theory of electron strahl broadening. By measuring the strahl width, one can estimate the parameters of whistler turbulence.

David Burgess

## The electron vortex magnetic hole and its relatives

David Burgess
D.Burgess@qmul.ac.uk
Queen Mary University of London, Mile End Road, London E1 4NS, UK
Two-dimensional full particle simulations of turbulence led to the discovery of the electron vortex magnetic hole (Haynes et al., Physics of Plasmas 22, 012309 (2015); https://doi.org/10.1063/1.4906356), a coherent plasma structure with cylindrical symmetry identified by a strong dip in the magnetic field driven by a population of trapped electrons with petal-like orbits. Subsequently, Cluster and MMS observations in the plasmasheet and magnetosheath have confirmed that such structures, with scales of order several electron gyroradii, exist and have the predicted spatial pattern in the electron distribution function. The properties of these coherent nonlinear structures are explored, and the observational evidence is summarized. In addition, other related structures - magnetic dips and bumps - with similar cylindrical symmetry are discussed in the context of semi-analytical Vlasov solutions. The possible role of such structures in turbulence at electron scales is also discussed.

Francesco Califano

## Study of the dissipation scale in collisionless plasma turbulence

Francesco Califano
francesco.califano@unipi.it
Dipartimento di Fisica "E. Fermi", Università di Pisa, Pisa, Italy

F. Califano, G. Arrò Dipartimento di Fisica "E. Fermi", Università di Pisa, Pisa, Italy S.S. Cerri Department of Astrophysical Sciences, Princeton University, Princeton, 08544 USA

It has been observed experimentally the occurrence of a new process, namely electron-only reconnection, where the reconnection dynamics is driven only by electrons (e-rec-only) [1]. Recently, a theoretical study in the context of plasma magnetized turbulence has given evidence about the possibility to drive e-rec-only by fluctuations at scales of the order of the ion scale length [2] (see Faganello abstract, this Conference). By considering two Vlasov simulations of magnetized plasma turbulence where “standard” reconnection or e-rec-only separately occur, we make a compared study of the turbulence statistical properties, in particular of the structure functions in order to separate the contribution of the ions at the so-called dissipative scale. We found, in agreement with experimental [3] and theoretical [4] studies a non-Gaussian statistics in both the fluid and sub-ion range with a transition from an intermittent to a self-similar behavior. Our main finding here is that the transition is observed at a scale length of the order of several de instead that around di independently from the ion dynamics. The transition seems to be driven mainly by the small scale electron dynamics around the reconnection structures where the electron inertial terms become non-negligible.

[1] T.D. Phan et al., Electron magnetic reconnection without ion coupling in Earth’s turbulent magnetosheath, Nature, 2018

[2] F. Califano, S.S. Cerri, M. Faganello, D. Laveder, M. W. Kunz, Electron-only magnetic reconnection in plasma turbulence, Astrophys. Journal, submitted

[3] Kiyani et al., Global Scale-Invariant Dissipation in Collisionless Plasma Turbulence, Phys. Rev. Lett., 2009

[4] E. Leonardis et al., Multifractal scaling and intermittency in hybrid Vlasov-Maxwell simulations of plasma turbulence, Physics of Plasmas, 2016

• This contribution has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 776262 (AIDA, www.aida-space.eu)

Silvio Sergio Cerri

## The good, the bad and the ugly: kinetic plasma turbulence in a 3D3V phase space

Silvio_Sergio Cerri
scerri@astro.princeton.edu
Department of Astrophysical Sciences, Princeton University, 4 Ivy Ln, Princeton, NJ 08544, USA

Turbulence and kinetic processes in magnetized space plasmas have been extensively investigated over the past decades via theoretical models, in-situ spacecraft measurements, and numerical simulations. In particular, multi-point high-resolution measurements from the Cluster and MMS space missions brought to light an entire new world of kinetic processes, taking place at the plasma microscales, and exposed new challenges for their theoretical interpretations. A long-lasting debate concerns the nature of ion and electron scale fluctuations in solar-wind turbulence and their dissipation via collisionless plasma mechanisms. Alongside observations, numerical simulations have always played a central role in providing a test ground for existing theories and models.

In this talk, the current advances achieved with 3D3V kinetic simulations, as well as the main questions left open (or raised) by these studies will be discussed. This includes assessing the spectral properties and intermittency of turbulent fluctuations in the sub-ion range$[1]$ and the existence of an anisotropic turbulent cascade involving the entire phase space$[2]$ (i.e., a cascade of free energy that is anisotropic with respect to the ambient magnetic field in both real and velocity space). Finally, also preliminary combined results from recent numerical studies will be presented to assess similarities and/or differences in the properties of kinetic-scale plasma turbulence, estimated from these state-of-the-art 3D kinetic simulations$[1,2,3,4]$.

$[1]$ Cerri, Servidio & Califano, ApJL 846, L18 (2017)

$[2]$ Cerri, Kunz & Califano, ApJL 856, L13 (2018)

$[3]$ Franci em et al., ApJ 853, 26 (2018)

$[4]$ Groselj em et al., PRL bf120, 105101 (2018)

Christopher Chen

## Kinetic Turbulence and Damping in the Magnetosheath

Christopher Chen
christopher.chen@qmul.ac.uk
Queen Mary University of London
With the launch of the MMS spacecraft a few years ago, we now have the capability to study turbulence in the magnetosheath at higher resolution than ever before. Here, I will present recent work using the MMS data to investigate the nature of kinetic turbulence at electron scales and the nature of the damping mechanisms of the turbulence at these scales. Focussing on an interval of magnetosheath data near the magnetopause, the nature of the turbulence was found to change as the electron inertial scale is reached, transitioning to a regime of inertial kinetic Alfven turbulence - I will present observations and a theoretical model for this turbulence. I will also describe our recent application of a field-particle correlation technique to the MMS data, which enables the energy transfer in velocity space to be determined. The results of this are consistent with the presence of electron Landau damping in the kinetic range.

Khalil Daiffallah

## Plasma acceleration by the non-linear interaction of three crossed parallel Alfvén wave packets

Khalil Daiffallah
dfkhalil@gmail.com
CRAAG, observatoire d'Alger, Route de l'Observatoire, BP 63, Bouzaréah 16340, Algiers, Algeria
We are doing numerical simulation with a (PIC) code to interact a parallel Alfvén wave packet with two another parallel Alfv\'en wave packets that have already interacted. The crossing of the two initial Alfvén waves generates density gradients in the plasma (APAWI process, Mottez (2012, 2015)). Then, the passage of the third Alfvén wave across this interaction region gives rise to powerful accelerated electron beams in the parallel direction through phase-mixing process. The efficiency of this process depends substantially on the polarity and the amplitude of the wave packets.

Jérémy Dargent

## Competition between Kelvin-Helmholtz and nonlinear Lower Hybrid drift instabilities along Mercury-like magnetopause

Jérémy Dargent
jeremy.dargent@df.unipi.it
Università di Pisa, Dipartimento di Fisica, Largo Pontecorvo 3, 56127 PISA, ITALY
Boundary layers in space plasmas are always the locations of many phenomena allowing the mixing of plasma. But for a given boundary, different mechanisms can coexist and compete one with each others. In our work, we look at velocity shear boundary layers with a gradient of density and/or magnetic field. We observe that in presence of a density gradient, a lower hybrid drift instability (LHDI) develops along the layer much quicker than the Kelvin-Helmotz instability (KHI). Although the two instability develops at different scales (both spatial and temporal), we observe that the nonlinear phase of the LHDI can compete and even suppress the KHI, depending on the density gradient in the layer. Such a result can make us reconsider the main mixing mechanisms in plasma layers with strong density gradient, such as Mercury magnetopause.

Matteo Faganello

## Electron-only magnetic reconnection in plasma turbulence

Matteo Faganello
matteo.faganello@univ-amu.fr
Aix-Marseille University, CNRS, PIIM UMR 7345, Centre de Saint-Jérome, Avenue Escadrille Normandie Nièmen 13397 Marseille, France
Recently MMS satellites measured a turbulent regime in the solar wind plasma, downstream of the Earth's bow shock, where magnetic reconnection acting in all the observed current sheets (at the electron skin depth scale) is completely ruled by electrons. These electron-only'' reconnection events are characterized by electron jets unaccompanied by ion outflows, contrary to the standard picture of magnetic reconnection. Hybrid-Vlasov-Maxwell simulations of magnetized plasma turbulence, including non-linear electron inertia effects in the generalized Ohm.s law, are able to reproduce this behavior as soon as the fluctuation energy is injected at scales close the ion-kinetic scales. In this case ions turn out to be de-magnetized over the whole numerical domain while electrons follow a nearly electron-magnetohydrodynamic evolution leading to electron-only reconnection. The injection scale seems to be the control parameter of this behavior: if energy is injected at larger scales ion outflows do form in reconnecting sheets.

Renaud Ferrand

## Alternative exact law for homogeneous compressible turbulent flows: from Hall-MHD to hydrodynamics

Renaud Ferrand
renaud.ferrand@lpp.polytechnique.fr
Laboratoire de Physique des Plasmas, Ecole polytechnique, 91128 Palaiseau, France

Fluid and plasma turbulence is a longstanding problem in physics. Studying its dynamics can help understanding various processes such as mass transport and energy dissipation, in particular in collisionless systems like most of the astrophysical plasmas. The solar wind heating problem, which is manifested by a slower decrease of the ion temperature as function of the heliocentric distance than the prediction from the adiabatic expansion model of the wind, is one example of such problems where turbulence can help give an explanation.

A way to study fluid or plasma turbulence is to estimate the total energy cascade rate, which is the energy transferred from the largest scales into the dissipative scales of the system. This is made possible by the use of exact laws, which link the energy cascade rate to the physical variables of the flow. Significant progress has been made in recent years on deriving various forms of exact laws for different compressible flows: HydroDynamics (HD), MagnetoHydroDynamics (MHD) and Hall-MagnetoHydroDynamics (HMHD). Some of them were used successfully to estimate the energy cascade rate in the solar wind and the magnetosheath, but at the expense of making additional assumptions that made different mathematical terms involved in the laws accessible to in-situ measurements.

Here we present an alternative exact law for compressible Hall-MHD turbulence. This law is more compact and easier to compute in numerical simulations and spacecraft data, thus reducing the memory load and time required to compute the energy cascade rate. We also show the validity of this new law in the limit of compressible HD using high-resolution simulation data of HD turbulence spanning the subsonic and supersonic regimes.

Luca Franci

## Interpreting spacecraft observations of plasma turbulence with kinetic numerical simulations in the low electron beta regime

Luca Franci
l.franci@qmul.ac.uk
Queen Mary University of London, 327 Mile End Road, E1 4NS, London, United Kingdom
We present numerical results from high-resolution hybrid and fully kinetic simulations of plasma turbulence, following the development of the energy cascade from large magnetohydrodynamic scales down to electron characteristic scales. We explore a regime of plasma turbulence where the electron plasma beta is low, typical of environments where the ions are much hotter than the electrons, e.g., the Earth’s magnetosheath and the solar corona, as well as regions downstream of collisionless shocks. In such range of scales, recent theoretical models predict a different behaviour in the nonlinear interaction of dispersive wave modes with respect to what is typically observed in the solar wind, i.e., the presence of so-called inertial kinetic Alfvén waves. We also extend our analysis to scales around and smaller than the electron gyroradius, where hints of a further steepening of the magnetic and electric field spectra have been recently observed by the NASA’s Magnetospheric Multiscale mission, although not yet supported by theoretical models. Our numerical simulations exhibit a remarkable quantitative agreement with recent observations by MMS in the magnetosheath, allowing us to investigate simultaneously the spectral break around ion scales and the two spectral breaks at electron scales, the magnetic compressibility, and the nature of fluctuations at kinetic scales.

Sébastien Galtier

## Gravitational wave turbulence in the primordial universe

Sébastien Galtier
sebastien.galtier@lpp.polytechnique.fr
Laboratoire de Physique des Plasmas, Ecole polytechnique, 91128 Palaiseau, France & Université Paris-Sud

The non-linear nature of the Einstein’s equations of general relativity suggests that space-time can be turbulent. Such a turbulence is expected during the primordial universe (first second) when gravitational waves (GW) have been excited through eg. the merger of primordial black holes. The analytical theory of weak GW turbulence, published in 2017 [1], is built from a diagonal space-time metric reduced to the variables t, x and y [2]. The theory predicts the existence of a dual cascade driven by 4–wave interactions with a direct cascade of energy and an inverse cascade of wave action. In the latter case, the isotropic Kolmogorov-Zakharov spectrum N(k) has the power law index -2/3 involving an explosive phenomenon. In this context, we developed a fourth-order and a second-order nonlinear diffusion models in spectral space to describe GW turbulence in the approximation of strongly local interactions [3]. We showed analytically that the model equations satisfy the conservation of energy and wave action, and reproduce the power law solutions previously derived from the kinetic equations. We show numerically by computing the second-order diffusion model that, in the non-stationary regime, the isotropic wave action spectrum N(k) presents an anomalous scaling which is understood as a self-similar solution of the second kind. The regime of weak GW turbulence is actually limited to a narrow wavenumber window and turbulence is expected to become strong at larger scales. Then the phenomenology of critical balance can be used. The formation of a condensate may happen and its rapid growth can be interpreted as an accelerated expansion of the universe that could be at the origin of the cosmic inflation. We can show with this scenario that the fossil spectrum obtained after inflation is compatible with the latest data obtained with the Planck/ESA satellite [4].

[1] Galtier & Nazarenko, Turbulence of weak gravitational waves in the early universe, Phys. Rev. Lett. 119, 221101 (2017).

[2] Hadad & Zakharov, Transparency of strong gravitational waves, J. Geom. Phys. 80, 37 (2014).

[3] Galtier, Nazarenko, Buchlin & Thalabard, Nonlinear diffusion models for gravitational wave turbulence Physica D 390, 84 (2019).

[4] Galtier, Nazarenko & Laurie, Cosmic inflation driven by space-time turbulence (2019).

Camille Granier

## Magnetic coherent structures in the presence of equilibrium temperature anisotropy

Camille Granier
camille.granier@etu.u-bordeaux.fr
Université de Bordeaux Master 2 "Noyaux Plasmas et Univers" et Université Côte d’Azur, Observatoire de la Côte d’Azur, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France

Coherent magnetic structures such as magnetic vortex chains have been observed in the solar wind close to the Earth by the Cluster space mission (Perrone et al. (2016, 2017)). Making use of a gyrofluid model, we investigate the existence of analytical solutions of magnetic vortex type and study their stability. The adopted model can provide a nonlinear description of turbulent collisionless magnetized plasmas accounting for ion finite Larmor radius, equilibrium temperature anisotropy and fluctuations of the component of the magnetic field parallel to the direction of a strong and uniform guide field. The model possesses a noncanonical Hamiltonian structure which provides a convenient framework for the use of analytical tools, such as the Energy-Casimir method for determining stability conditions. We carry out investigations for some asymptotic regimes of the model, such as for instance in the limit of a large ion-to-electron perpendicular equilibrium temperature ratio, with negligible electron inertia effects, and compare our results with those found recently in the framework of a reduced magnetohydrodynamics model (Jovanovic et al. 2018).

• D. Perrone, O. Alexandrova, O. W. Roberts, S. Lion, C. Lacombe, A. Walsh, M. Maksimovic and I. Zouganelis. The Astrophysical Journal, 849:49, 2017

• D. Perrone, O. Alexandrova, A. Mangeney, M. Maksimovic, C. Lacombe, V. Rakoto, J. C. Kasper, and D. Jovanović. The Astrophysical Journal, 826:196, 2016

• D. Jovanović, O. Alexandrova, M. Maksimović, M. Belić. J. Plasma Phys., vol. 84, 2018

Daniel Groselj

## Kinetic Turbulence in Astrophysical Plasmas: Waves and/or Structures?

Daniel Groselj
daniel.groselj@ipp.mpg.de
Max Planck Institute for Plasma Physics, Boltzmannstrasse 2, D-85748 Garching, Germany
The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize high-resolution observational and simulation data to investigate the nature of waves and structures emerging in a weakly collisional, turbulent kinetic plasma. Observational results are based on in situ solar wind measurements from the Cluster and MMS spacecraft, and the simulation results are obtained from an externally driven, three-dimensional fully kinetic simulation. Using a set of novel diagnostic measures we show that both the large-amplitude structures and the lower-amplitude background fluctuations preserve linear features of kinetic Alfvén waves to order unity. This quantitative evidence suggests that the kinetic turbulence cannot be described as a mixture of mutually exclusive waves and structures but may instead be pictured as an ensemble of localized, anisotropic wave packets or “eddies” of varying amplitudes, which preserve certain linear wave properties during their nonlinear evolution.

Daniel Gómez

## Two-fluid plasmas: turbulence, reconnection and shocks

Daniel Gómez
gomez@iafe.uba.ar
Instituto de Astronomía y Física del Espacio, UBA-CONICET, Buenos Aires, Argentina

In space plasmas, turbulence, magnetic reconnection and shock propagation are ubiquitous physical processes that have been traditionally studied using a one-fluid resistive MHD description.

Within the theoretical framework of two-fluid MHD, we retain the effects of the Hall current and electron inertia. Also, this description brings two new spatial scales into play, such as the ion and electron inertial lengths. We perform numerical simulations of the two-fluid equations and study the physical processes arising at sub-ion and even electron scales both three important phenomena in space plasmas: turbulence, magnetic reconnection and perpendicular shocks.

When a stationary turbulent regime is established, our simulations show changes in the slope of the energy power spectrum at the ion and electron inertial lengths, in agreement with the slopes obtained using dimensional analysis. Using non-dissipative two-fluid simulations, we confirm that magnetic reconnection arises only when the effects of electron inertia are retained. In a stationary regime, we obtain that the reconnection rate is proportional to the ion inertial length, as it also emerges from a scaling law derived from dimensional arguments. Finally, using 1D two-fluid simulations, we show the generation of fast-mode perpendicular shocks with a thickness of a few electron inertial lengths.

Petr Hellinger

## Plasma turbulence vs. fire hose instabilities: 3-D HEB simulations

Petr Hellinger
petr.hellinger@asu.cas.cz
Astronomical Institute, Prague, Czechia
The relationship between a decaying plasma turbulence and proton fire hose instabilities in a slowly expanding plasma is investigated using three-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the radial direction simulation box, and we start with an isotropic spectrum of large-scale, linearly-polarized, random-phase Alfvenic fluctuations with zero cross-helicity. A turbulent cascade rapidly develops and leads to a weak proton heating that is not sufficient to overcome the expansion-driven perpendicular cooling. The plasma system eventually drives the parallel and oblique fire hose instabilities that generate quasi-monochromatic wave packets that reduce the proton temperature anisotropy. The fire hose wave activity has a low amplitude with wave vectors quasi-parallel/oblique with respect to the ambient magnetic field outside of the region dominated by the turbulent cascade and is discernible in one-dimensional power spectra taken only in the direction quasi-parallel/oblique with respect to the ambient magnetic field; at quasi-perpendicular angles the wave activity is hidden by the turbulent background. The fire hose wave activity reduces intermittency and the Shannon entropy but increases the Jensen-Shannon complexity of magnetic fluctuations.

Pierre Henri

## Overview of the structure and dynamics of the interaction between solar wind and cometary plasmas after the Rosetta Mission

Pierre Henri
pierre.henri@cnrs-orleans.fr
LPC2E, CNRS, Orléans, France - 3 avenue recherche scientifique, 45000 Orléans, France

Cometary induced magnetospheres are archetypes of mass-loaded, partially collisional, partially ionised plasmas, characterised by a wide range of varying plasma parameters, where the interplay between collisionless and collisional processes are essential to give a global picture of the plasma dynamics. While several cometary fly-by missions have enabled to pave the way towards the exploration of cometary environments, the Rosetta mission was the first space mission to escort a comet along its orbit around the Sun. During more than two years (2014-2016), the Rosetta orbiter has monitored comet 67P/CG and its ionised environment, at heliocentric distances ranging from 1.2 to 3.8 AU accounting for a variety of cometary activity, and at distances from the comet nucleus ranging from 1500 km down to the comet nucleus surface itself during the Rosetta Orbiter’s final descent. This was the first extensive, long-term, in situ survey of the expanding ionosphere of a comet which interaction with the solar wind forms an induced magnetosphere. In this context, I will review the results obtained from in situ observations made by the different instruments of the Rosetta Plasma Consortium (RPC), combined to state-of-art numerical modelings of cometary plasma environments, to give an overview of the current understanding of the structure and dynamics of a cometary induced magnetosphere. Among different mechanisms, I will show how plasma waves traces the signature of plasma mixing at different interfaces (e.g., electron temperature discontinuities, strong density gradients) and describe some acceleration mechanisms at play in the inner cometary plasma.

Gregory G. Howes

## A Wave-Coherent Structure Duality in Plasma Turbulence: Are They Two Sides of the Same Coin?

Gregory_G. Howes
gregory-howes@uiowa.edu
Department of Physics and Astronomy, University of Iowa, 505 Van Allen Hall, Iowa City, IA 52242, USA
The dynamics and dissipation of turbulence in weakly collisional space plasmas throughout the heliosphere remains a controversial topic at the forefront of space physics research. Both fluid and kinetic simulations of plasma turbulence ubiquitously generate coherent structures---in the form of current sheets---at small scales, and the locations of these current sheets appear to be associated with enhanced rates of dissipation of the turbulent energy. The quest to understand the physical mechanisms by which the energy of turbulent fluctuations is converted to particle energy or plasma heat has driven vigorous debate about the relative roles of wave damping processes vs. localized dissipation mechanisms associated with current sheets, such as magnetic reconnection. A major unanswered question is how these coherent structures arise in the first place. Recent analytical and numerical work has demonstrated that strongly nonlinear interactions among counterpropagating Alfvén wavepackets---known as Alfvén wave collisions---naturally generate current sheets self-consistently. Subsequent work has shown that the dissipation of the turbulent energy is localized near these current sheets but is clearly mediated through the process of collisionless Landau damping. Together, these results suggest that framing the debate as a choice between waves or coherent structures may be a false dichotomy. Rather, is there a duality between wave or coherent structure descriptions of the turbulence? Are they merely alternative descriptions of the same dynamics? I will close with the question about whether there exist aspects of the turbulence that cannot be described as either waves or structures.

Matthew Kunz

## Self-defeating Alfvén waves and self-sustaining sound in a collisionless, high-beta plasma

Matthew Kunz
mkunz@princeton.edu
Princeton University, Department of Astrophysical Sciences, 4 Ivy Lane, Princeton, NJ 08544 USA
Many space and astrophysical plasmas are so hot and dilute that they cannot be rigorously described as fluids. These include the solar wind, low-luminosity black-hole accretion flows, and the intracluster medium of galaxy clusters. We present theory and hybrid-kinetic simulations of the propagation of shear-Alfvén and ion-acoustic waves in such weakly collisional, magnetized, high-beta plasmas. Following Squire et al. (2016), we demonstrate that shear-Alfvén waves interrupt'' at sufficiently large amplitudes by adiabatically driving a field-biased pressure anisotropy that both nullifies the restoring tension force and excites a sea of ion-Larmor-scale instabilities (viz., firehose) that pitch-angle scatter particles. This physics places a beta-dependent limit on the amplitude of shear-Alfvén waves, above which they do not propagate effectively. We also demonstrate that similar physics afflicts compressive fluctuations, except that it is the collisionless damping of such waves that is interrupted. Above a beta-dependent amplitude, compressive fluctuations excite ion-Larmor-scale mirror and firehose fluctuations, which trap and scatter particles, thereby impeding phase mixing of the distribution function and yielding MHD-like dynamics. Implications for magnetokinetic turbulence and transport will be discussed.

Denis Kuzzay

## Local energy transfers in incompressible MHD turbulence

Denis Kuzzay
denis.kuzzay@obspm.fr
Observatoire de Paris, LESIA, 5 place Jules Janssen, 92190 Meudon, France

We present a local (in space and time) approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter $\ell$. A key step in this work is the derivation of a local Kármán-Howarth-Monin relation which can be interpreted as a coarse-grained energy balance. This provides a local form of Politano and Pouquet’s 4/3-law without any assumption of homogeneity or isotropy, which is exact, non-random, and connects well to the usual statistical notions of turbulence. After a brief presentation of this approach, we first apply it to turbulent data obtained via a three dimensional direct numerical simulation of the forced, incompressible MHD equations from the John Hopkins turbulent database. The local Kármán-Howarth-Monin relation holds well. The space statistics of local cross-scale transfers is studied, their means and standard deviations being maximum at inertial scales, and their probability density functions (PDFs) displaying very wide tails. Events constituting the tails of the PDFs are shown to form structures of strong transfers, either positive or negative, which can be observed over the whole available range of scales. As $\ell$ is decreased, these structures become more and more localized in space while contributing to an increasing fraction of the mean energy cascade rate. Second, we show how the same approach can be applied to spacecraft data where the main difficulty lies in the fact that measurements are restricted to few points, in one small region of space at a time, and a single scale. We compare our approach to results obtained from Cluster and MMS data using the LET proxy, and highlight its importance to the understanding of solar wind turbulence and solar wind heating.

Simone Landi

## On the properties of spectral anisotropies and intermittency in ion-kinetic scale turbulence.

Simone Landi
slandi@arcetri.astro.it
University of Florence, Department of Physics and Astronomy, Largo E. Fermi 2, I-50125 Firenze, Italy
The spectral properties at ion kinetic scales are studied by means of high-resolution three-dimensional numerical simulations using a hybrid codes which integrates the Vlasov system equations for the ions while it treats the electron as a neutralising fluid. We show that the observed anisotropy is less than what expected by theories of plasma turbulence at such scales. More specifically, we observe that the spectral anisotropy is frozen once the magnetic energy cascade reaches the ion kinetic scales. However, the non-linear energy transfer is still in the perpendicular direction with respect to the magnetic field, only advected in the parallel direction as expected balancing the non-linear energy transfer time and the decorrelation time. Such result can be explained by a phenomenological model based on the formation of strong intermittent two-dimensional structures in the plane perpendicular to the local mean field that fulfill some prescribed aspect ratio eventually depending on the scale. This model supports the idea that small scales structures, such as reconnecting current sheets, contribute significantly to the formation of the turbulent cascade at kinetic scales.

Lorenzo Matteini

## 1/f spectra in collisionless magnetized plasmas: a lesson from solar wind in situ observations

Lorenzo Matteini
lorenzo.matteini@obspm.fr
LESIA, Observatoire de Paris, CNRS, 5 Pl. Jules Janssen, 92195 Meudon CEDEX, France

A puzzling property of fast solar wind magnetic fluctuations is that, despite their large amplitude, they induce little variations in the strength of the magnetic field, thus maintaining a low level of compressibility in the plasma.

At the same time, in addition to the well-known Kolmogorov MHD inertial range spectrum with slope -5/3, larger scales of fast streams are characterised by a shallower slope, close to -1. This 1/f range is considered the energy reservoir feeding the turbulent cascade at smaller scales, although its origin is not well understood yet.

These aspects are usually addressed as separate properties of the plasma, however, we suggest that a link between the two exists and we propose a phenomenological model in which a 1/f spectrum for large scales can be derived as a consequence of the low magnetic compressibility condition. Remarkably this model, although simple, can capture most of the variability observed in situ in the solar wind and explain spectral differences in wind regimes. Moreover, our model provides a prediction for the evolution of the 1/f range close to the Sun that it will be possible to test soon thanks to the forthcoming observations of Parker Solar Probe.

Lorenzo Matteini

## Investigating properties of solar wind turbulence at sub-ion scales with in situ data and numerical simulations

Lorenzo Matteini
lorenzo.matteini@obspm.fr
LESIA, Observatoire de Paris, CNRS, 5 Pl. Jules Janssen, 92195 Meudon CEDEX, France

We investigate the transition of the solar wind turbulent cascade from MHD to sub-ion range by means of in situ observations and hybrid numerical simulations. First, we focus on the angular distribution of wave-vectors in the kinetic range, between ion and electron scales, using Cluster magnetic field measurements. Observations suggest the presence of a quasi-2D gyrotropic distribution around the mean field, confirming that turbulence is characterised by fluctuations with $k_\perp>>k_|$ in this range; this is consistent with what is usually found at larger MHD scales, and in good agreement with our hybrid simulations.

We then consider the magnetic compressibility associated with the turbulent cascade and its evolution from large-MHD to sub-ion scales. The ratio of field-aligned to perpendicular fluctuations, typically low in the MHD inertial range, increases significantly when crossing ion scales and its value in the sub-ion range is a function of the total plasma beta, with higher magnetic compressibility for higher beta. Moreover, we observe that this increase has a gradual trend from low to high beta in the data; this behaviour is well captured by the numerical simulations. The level of magnetic field compressibility that is observed in situ and in the simulations is in fairly good agreement with the prediction based on kinetic Alfvén waves (KAW), especially at high beta, suggesting that in the kinetic range explored the turbulence is supported by KAW-like fluctuations.

Romain Meyrand

## Fluidization of collisionless plasma turbulence

Romain Meyrand
romain.meyrand@lpp.polytechnique.fr
Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau, France
Two textbook physical processes compete to thermalize turbulent fluctuations in collisionless plasmas: Kolmogorov’s “cascade” to small spatial scales, where dissipation occurs, and Landau’s damping, which transfers energy to small scales in velocity space via “phase mixing”, also leading to dissipation. By direct numerical simulations and theoretical arguments, I will show during this presentation that in a magnetized plasma, another textbook process, plasma echo, brings energy back from phase space and on average cancels the effect of phase mixing. Energy cascades effectively as it would in a fluid system and thus Kolmogorov wins the competition with Landau for the free energy in a collisionless turbulent plasma. This reaffirms the universality of Kolmogorov’s picture of turbulence and explains, for example, the broad Kolmogorov-like spectra of density fluctuations observed in the solar wind.

George Miloshevich

## Imbalanced kinetic Alfvén wave turbulence

George Miloshevich
george.miloshevich@oca.eu
Université Côte d'Azur, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France
A Hamilitonian 2-field reduced gyrofluid model for kinetic Alfvén waves taking into account ion FLR corrections, parallel magnetic field fluctuations and electron inertia, is used to study turbulent cascades, from the MHD to the electron ranges, in the case of imbalance between waves propagating along or opposite to the direction of the ambient magnetic field. The weak turbulence formalism in the absence of electron inertia leads to kinetic equations for the spectral densities of total energy and generalized cross-helicity, which reduce to those of RMHD at large scales, and REMHD at small scales. Leith-type nonlinear diffusion equations are derived in the limit of ultra-local interactions and a phenomenological formulation is obtained for the strong turbulence regime. These equations are studied analytically and integrated numerically. For a given level of imbalance in the MHD range, the flux of cross-helicity is much smaller when a dispersive range is present before dissipation scales are reached. Large imbalance leads to steeper sub-ion range spectra.

Sergey Nazarenko

## Rotating MHD turbulence

Sergey Nazarenko
sergey.nazarenko@unice.fr
Université Côte d'Azur, INPHYNI, CNRS, 1361 route des lucioles, 06560 Valbonne, France
Turbulence in rotating Magneto-hydrodynamic systems is studied theoretically and numerically. In the linear limit, when the velocity and magnetic perturbations are small, the system supports two types of waves. When the rotation effects are stronger than the ones of the external magnetic field, one of these waves contains most of the kinetic energy (inertial wave) and the other--most of the magnetic energy (magnetostrophic wave). The weak wave turbulence (WWT) theory for decoupled inertial and magnetospheric wave systems was previously derived by Galtier (2014). In the present paper, we derive theory of strong turbulence for such waves based on the critical balance (CB) approach conjecturing that the linear and nonlinear timescales are of similar magnitudes in a wide range of turbulent scales. Regimes of weak and strong wave turbulence are simulated numerically. The results appear to be in good agreement with the WWT and CB predictions, particularly for the exponents of the kinetic and magnetic energy spectra.

Emanuele Papini

## Multidimentional Iterative Filtering: a new approach for investigating plasma turbulence in numerical simulations.

Emanuele Papini
papini@arcetri.inaf.it
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
Turbulent space and astrophysical plasmas have a complex dynamics, which involve nonlinear coupling across different temporal and spatial scales. There is growing evidence that impulsive events, such as magnetic reconnection instabilities, bring to a spatially localized enhancement of energy dissipation, thus speeding up the energy transfer at small scales. Indeed, capturing such a diverse dynamics is challenging. In this work, we employ the Multidimensional Iterative Filtering (MIF) method, a novel multiscale technique for the analysis of non-stationary non-linear multidimensional signals. Unlike other traditional methods (e.g., based on Fourier or wavelet decomposition), MIF natively performs the analysis without any previous assumption on the functional form of the signal to be identified. Using MIF, we carry out a multiscale analysis of Hall-MHD and Hybrid particle-in-cell numerical simulations of decaying plasma turbulence. Preliminary results assess the ability of MIF to detect localized coherent structures and to separate and characterize their contribution to the turbulent dynamics.

Francesco Pucci

## ELECTRON PHYSICS IN KELVIN-HELMHOLTZ INSTABILITY IN MAGNETIZED PLASMAS

Francesco Pucci
francesco.pucci@kuleuven.be
KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium

Rolled-up vortices associated to the Kelvin-Helmholtz instability (KHI) have been detected by in-situ observations around the Earth, Saturn and Mercury magnetospheres due to the interaction with the solar wind. KHI in magnetized plasmas have been widely studied numerically in the framework of a fluid, hybrid, and full kinetic approach, while only very few studies have focused on the physics of electrons because of computational constraints. In this work we present a full kinetic particle in cell study of the KHI spanning a range of scales going from fluid to electron scales. The simulation is initialized with an extended fluid equilibrium including finite ion Larmor radius effects. Our large-scale configuration includes two-possible alignment of the vorticity with the background magnetic field each one corresponding to the interaction of the solar wind with the dawn and dusk side of a planet. We discuss electron heating and acceleration by analyzing temperature anisotropy and particle distribution functions. Two fluid simulations have suggested that KHI instability can lead to the onset of the mirror instability. Our full kinetic approach confirms such hypothesis. We discuss the formation of mirror modes in our simulations.

## Energy cascade rate in compressible MHD and Hall-MHD flows: spacecraft observations in the near-Earth space vs theoretical predictions

LPP/CNRS - Ecole Polytechnique – Sorbonne Université - Univ. Paris-Sud - Observatoire de Paris, Université Paris-Saclay, Palaiseau, 91128, France

F. Sahraoui (1), L. Z. Hadid (2), N. Andrés (1,3), F. Galtier (1,4), S. Y. Huang (5), R. Ferrand (1), and S. Banerjee (6)

(1) LPP, CNRS - Ecole Polytechnique – Sorbonne Université - Univ. Paris-Sud - Observatoire de Paris, Université Paris-Saclay, Palaiseau, 91128, France

(2) Swedish Institute of Space Physics, Uppsala, Sweden

(3) Instituto de Astronomia y Fisica del Espacio, UBA-CONICET, CC. 67, suc. 28, 1428, Buenos Aires, Argentina

(4) Institut Universitaire de France

(5) School of Electronic Information, Wuhan University, Wuhan, China

(6) Indian Institute of Technology, IIT, Kanpur, India

Compressible turbulence has been a subject of active research within the space physics community over the past years. It is thought to be essential for understanding the physics of the solar wind (for instance the heating of the fast wind), planetary magnetospheres and the interstellar medium (star formation). Using recently derived exact laws of compressible isothermal MHD and the THEMIS and CLUSTER spacecraft data we investigate the physics of the fast and slow solar winds and the Earth magnetosheath. We emphasize the role of density fluctuations in enhancing both the energy cascade rate and the turbulence spatial anisotropy by analyzing different types of turbulent fluctuations (magnetosonic and Alfvénic-like), and show how kinetic instabilities can regulate the energy cascade rate. This has motivated further investigation of the sub-ion scale cascade using MMS high time resolution data and the exact laws of the Hall-MHD model (see talk by Andrés et al.). Preliminary results on the estimation of the fluid cascade rate at sub-ion and its possible connection to kinetic dissipation will be discussed.

Alexander Schekochihin

## Partition of turbulent energy between particle species in astrophysical plasmas

Alexander Schekochihin
alex.schekochihin@physics.ox.ac.uk
University of Oxford
Perhaps the most popular and most productive route by which the theoretical machinery of fusion science has been ported to astrophysical plasmas was the application of gyrokinetic theory to the problem of collisionless plasma turbulence in accretion flows and in the heliosphere, in particular to the question of how energy is partitioned between species (ions and electrons) when this turbulence is thermalised. After many years of promising, but perhaps not entirely conclusive advances in this area, the latest news is that we finally have some quantitative grasp on the answer: GK turbulence promotes disequilibration of species: at high beta, ions are preferentially heated; at low beta, electrons are. This conclusion is supported by GK simulations, which are finally able to give us a heating vs. beta and Ti/Te curve [Kawazura et al. 2019, PNAS 116, 771] and, in the case of low beta, also by relatively rigorous theory [Schekochihin et al. 2019, JPP in press/arXiv:1812.09792]. I will review this progress, spell out caveats (of course there are caveats), and describe the next steps, including some theoretical progress on the high-beta regime.

Sergio Servidio

## Phase-space cascade in turbulent plasmas: observations and theory

Sergio Servidio
sergio.servidio@fis.unical.it
University of Calabria
Plasma turbulence has been investigated using high-resolution ion velocity distribution measurements by the Magnetospheric Multiscale mission (MMS) in the Earth’s magnetosheath. This novel observation of a highly structured particle distribution suggests a cascade process in velocity space. Complex velocity space structure is investigated using a three-dimensional Hermite transform, revealing, for the first time in observational data, a power-law distribution of moments. In analogy to hydrodynamics, a Kolmogorov approach leads directly to a range of predictions for this phase-space transport. The combined use of state-of-the-art MMS data sets, novel implementation of a Hermite transform method, scaling theory of the velocity cascade and kinetic simulations opens new pathways to the understanding of plasma turbulence and the crucial velocity space features that lead to dissipation in plasmas.

Pierre-Louis Sulem

## Modeling imbalanced Alfvén-wave turbulence from MHD to electron scales

Pierre-Louis Sulem
sulem@oca.eu
Université Cote d’Azur, Observatoire de la Cote d’Azur, CNRS, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France

After discussing some open problems concerning Alfvén and kinetic Alfvén wave turbulence in the solar wind, and the transition between these two regimes, we introduce a two-field reduced gyrofluid model which includes ion finite Larmor radius corrections, parallel magnetic fluctuations and electron inertia, and thus covers a spectral range extending from MHD to electron scales [1]. The model reproduces the usual phenomenology of balanced turbulence in the regimes of dispersive, kinetic and inertial Alfvén waves and provides, as suggested by preliminary direct numerical simulations, an efficient tool to address the sub-ion dynamics in the imbalanced regime. Furthermore, starting from the kinetic equations of weak turbulence, a nonlinear diffusion model retaining only strongly local interactions is derived and phenomenologically extended to strong turbulence by a suitable modification of the transfer time which, in the case of balanced turbulence, is consistent with critical balance [2]. The associated scale anisotropy turns out to be affected by the degree of imbalance. In this framework, Landau damping is modeled using the dissipation rate given by the linear kinetic theory, with a modification of the transfer time taking into account the effect of temperature homogenization along the magnetic field lines. Extension of the gyro-fluid model including coupling to slow magnetosonic waves and thus permitting the decay instability will be briefly discussed.

[1] T. Passot, P.L. Sulem and E. Tassi, Gyrofluid modeling and phenomenology of low βe Alfvén wave turbulence, Phys. Plasmas, 25, 042107, 2018.

[2] T. Passot and P.L. Sulem, Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime, J. Plasma Phys., in press.

Emanuele Tassi

## Hamiltonian reduced gyrofluid models

Emanuele Tassi
etassi@oca.eu
Université Cote d’Azur, Observatoire de la Cote d’Azur, CNRS, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France
Reduced fluid models provide a useful tool for qualitative investigations of low-frequency phenomena in plasmas, in the presence of a strong, mean component of the magnetic field. Applications of such models include, for example, magnetic reconnection and turbulence, both in laboratory and astrophysical plasmas. In particular, when investigating phenomena occurring on scales comparable with the ion Larmor radius, the so called reduced gyrofluid models become especially relevant. In the non-dissipative limit, reduced gyrofluid models are supposed to possess a Hamiltonian structure, as is the case for all dynamical plasma models. In addition to its relevance for guaranteeing correct qualitative properties of the dynamics, the knowledge of the Hamiltonian structure can also be of use, for instance, for the identification of families of invariants, particularly relevant in the two-dimensional limit, or for stability analyses. In this talk I will present a rather general framework for deriving a class of Hamiltonian reduced gyrofluid models accounting for equilibrium temperature anisotropies and magnetic perturbations parallel to the mean magnetic field, which could make such models relevant for applications to space plasmas.

Jason Tenbarge

## Energy Dissipation and Phase Space Dynamics in Eulerian Vlasov-Maxwell Plasmas

Jason Tenbarge
tenbarge@princeton.edu
Princeton University, 4 Ivy Ln, Princeton, NJ 08544 USA
We present a novel algorithm for the numerical solution of the multi-species, non-relativistic, Vlasov-Maxwell system in the Gkeyll simulation framework, which uses high order discontinuous Galerkin finite elements to discretize the system on an upto a 3D-3V phase space grid. The resulting numerical method is robust and retains a number of important properties of the continuous system, such as conservation of mass and energy, yet the method is computationally efficient and performs well at scale on cutting edge high performance computational resources. We leverage the pristine phase space representation made possible by directly discretizing phase space to examine energy dissipation in a variety of systems relevant to space and astrophysical plasmas. Specifically, we employ the field-particle correlation technique and Fourier-Hermite decomposition in phase space to directly diagnose the exchange of energy between fields and particles and the flow of energy in phase space. We present results from a variety of simple systems, including magnetic pumping, resonant wave damping, and Langmuir turbulence, and we also apply the field-particle correlation technique to 2D-3V Vlasov-Maxwell simulations of reconnection and turbulence.

Francesco Valentini

## Velocity-space cascade in nearly collisionless plasmas

Francesco Valentini
francesco.valentini@unical.it
Department of Physics, University of Calabria, Rende (CS), Italy

Multi-dimensional Eulerian simulations of the hybrid Vlasov-Maxwell model[1] have been employed to investigate the role kinetic effects in turbulent plasmas at typical ion scales. Numerical results suggest that kinetic effects manifest through the deformation of the ion distribution function, with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The velocity-space departure from Maxwellian of the ion velocity distributions has been also recovered in observational data from spacecraft. In a recent paper, Servidio et al.[2] investigated the velocity-space cascade process suggested by the highly structured shape of the ion velocity distribution detected by the NASA Magnetospheric Multiscale mission. Through a tree-dimensional Hermite transform, these authors pointed out a power-law distribution of moments and provided a theoretical prediction for the scaling, based on a Kolmogorov approach. Here, the possibility of a velocity-space cascade is investigated in the strongly magnetized case, in kinetic simulations of turbulence at ion scales. Through the Hermite decomposition of the ion velocity distribution from the simulations, we found that (i) the plasma displays spectral anisotropy in velocity space, due to the presence of the background magnetic field, (ii) the distribution of energy is in agreement with the prediction in Ref. [2] and (iii) the activity in velocity space shows a clear intermittent character in space, being enhanced close to coherent structures, such as the reconnecting current sheets produced by turbulence. Finally, in order to explore the possible role of inter-particle collisions, collisional and collisionless simulations of plasma turbulence have been compared using Eulerian Hybrid Boltzmann-Maxwell simulations, that explicitly model the proton-proton collisions through the nonlinear Dougherty operator.

This talk has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 776262 (AIDA, www.aida-space.eu)

[1] Valentini, F. et al., J. Comput. Phys. 225 2007, 753-770

[2] Servidio, S. et al., Phys. Rev. Lett. 119 2017, 205101

Daniel Verscharen

## The Debye mission: measuring electron-scale turbulence in the solar wind

Daniel Verscharen
d.verscharen@ucl.ac.uk
Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking RH5 6NT, United Kingdom

Debye is a proposed and pre-selected mission concept in response to ESA’s F-class call. Debye will consist of a main spacecraft with instrumentation to measure electrons, ions, electric fields, and magnetic fields; and up to three deployable spacecraft that measure magnetic fields only. The deployable spacecraft will fly around the main spacecraft, covering different and varying baselines. In this configuration, Debye will measure electron-scale fluctuations and their effects on the electron distribution function. The key science question for the Debye mission is: How are electrons heated in astrophysical plasmas? In order to answer this top-level science question, Debye's first objective is to identify the nature of electron-scale turbulent fluctuations. Then it will measure the rapid transfer of energy from the fields to the particles through high-cadence and high-resolution electron measurements. Finally, Debye will study the partition of energy between particle species and the dependence of the energy transfer on the plasma conditions.

In this presentation, we discuss the science questions and our proposed pathways to science closure for the Debye mission. Moreover, we discuss the implications of Debye science for the turbulence-research communities in the fields of space, astrophysics, and laboratory plasma physics.