Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the transport. Furthermore, a diffusion approximation is no longer part of that theory. It is the purpose of the current paper to combine this new approach with a time-dependent model for parallel transport and different turbulence configurations in order to explore the parameter regimes for which we get ballistic transport, compound sub-diffusion, and normal Markovian diffusion.
A heuristic approach for collisionless perpendicular diffusion of energetic particles is presented. Analytic forms for the corresponding diffusion coefficient are derived. The heuristic approach presented here explains the parameter $a^2$ used in previous theories in order to achieve agreement with simulations and its relation to collisionless Rechester & Rosenbluth diffusion. The obtained results are highly relevant for applications because previously used formulas are altered significantly in certain situations.
Low-frequency Alfven-wave turbulence causes ion trajectories to become chaotic, or "stochastic," when the turbulence amplitude is sufficiently large. Stochastic orbits enable ions to absorb energy from the turbulence, increasing the perpendicular ion temperature even when the fluctuation frequencies are too small for a cyclotron resonance to occur. In this paper, an analytic expression for the stochastic heating rate is used in conjunction with an observationally constrained turbulence model to obtain an analytic formula for the perpendicular ion temperature as a function of heliocentric dista…
The measured spectrum of kinetic Alfven wave fluctuations in the turbulent solar wind plasma is used to calculate the electron and ion distribution functions resulting from quasi-linear diffusion. The modified ion distribution function is found to be unstable to long wavelength electromagnetic ion cyclotron waves. These waves pitch angle scatter the parallel ion velocity into perpendicular velocity which effectively increases the perpendicular ion temperature.
We present a study of the acceleration of electrons at a perpendicular shock that propagates through a turbulent magnetic field. The energization process of electrons is investigated by utilizing a combination of hybrid (kinetic ions and fluid electron) simulations and test-particle electron simulations. In this method, the motions of the test-particle electrons are numerically integrated in the time-dependent electric and magnetic fields generated by two-dimensional hybrid simulations. We show that large-scale magnetic fluctuations effect electrons in a number of ways and lead to efficient an…
A fundamental problem in plasma and astrophysics is the interaction between energetic particles and magnetized plasmas. In the current paper we focus on particle diffusion across the guide magnetic field. It is shown that the perpendicular diffusion coefficient depends only on the parallel diffusion coefficient and the Kubo number. Therefore, one can find four asymptotic limits depending on the values of these two parameters. These regimes are the quasilinear limit, the Kadomtsev & Pogutse limit, the scaling of Rechester & Rosenbluth, and the scaling found by Zybin & Istomin. In the current ar…
In some solar energetic particle (SEP) events, a counter-streaming particle beam with a deep depression of flux near 90 degrees pitch angle during the beginning phase is observed. Two different interpretations exist in the community to explain this interesting phenomenon. One explanation invokes the hypothesis of an outer reflecting boundary or a magnetic mirror beyond the observer. The other one considers the effect of the perpendicular diffusion on the transport process of SEPs in the interplanetary space. In this work, we revisit the problem of the counter-streaming particle beams observed …
Recent modelling of solar energetic particles (SEPs) propagation through the heliospheric turbulence, also discussed in this workshop, has investigated the role of the pitch-angle scattering and the perpendicular transport in spreading particles in heliolongitude, as shown by multi-spacecraft measurements (STEREO A/B, ACE, SOHO, etc.) at 1 AU in various energy ranges. In some events the first-order pitch-angle anisotropy of the particles distribution is not-negligible. We calculate the average perpendicular displacement due to the gradient/curvature drift in an inhomogeneous turbulence account…
The current understanding of MHD turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $λ\sim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $λ$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion o…
Anisotropy of MHD turbulence has been studied extensively for many years, most prominently by measurements in the solar wind and high resolution simulations. The spectrum parallel to the local magnetic field was observed to be steeper than perpendicular spectrum, typically $k^{-2}$, consistent with the widely accepted Goldreich-Sridhar (1995) model. In this Letter I looked deeper into the nature of the relation between parallel and perpendicular spectra and argue that this $k^{-2}$ scaling has the same origin as the $ω^{-2}$ scaling of Lagrangian frequency spectrum in strong hydrodynamic turbu…
In recent years, a strong reduction of plasma turbulence in the presence of energetic particles has been reported in a number of magnetic confinement experiments and corresponding gyrokinetic simulations. While highly relevant to performance predictions for burning plasmas, an explanation for this primarily nonlinear effect has remained elusive so far. A thorough analysis finds that linearly marginally stable energetic particle driven modes are excited nonlinearly, depleting the energy content of the turbulence and acting as an additional catalyst for energy transfer to zonal modes (the domina…
The motion of energetic particles in magnetic turbulence across a mean magnetic field is explored analytically. The approach presented here allows for a full time-dependent description of the transport, including compound sub-diffusion. The first time it is shown systematically that as soon as there is transverse structure of the turbulence, diffusion is restored even if no Coulomb collisions are invoked. Criteria for sub-diffusion and normal Markovian diffusion are found as well.
In the present work, we study the energization and displacement of heavy ions through the use of test particles interacting with the electromagnetic fields of magnetohydrodynamic (MHD) turbulence. These fields are obtained from pseudospectral direct numerical solutions (DNSs) of the compressible three-dimensional MHD equations with a strong background magnetic field. We find particle energization to be predominantly perpendicular as the ions become heavier (lower charge-to-mass ratio) and that high displacement is detrimental for perpendicular energization. On the other hand, perpendicular dis…
Over the past two decades scientists have achieved a significant improvement of our understanding of the transport of energetic particles across a mean magnetic field. Due to test-particle simulations as well as powerful non-linear analytical tools our understanding of this type of transport is almost complete. However, previously developed non-linear analytical theories do not always agree perfectly with simulations. Therefore, a correction factor $a^2$ was incorporated into such theories with the aim to balance out inaccuracies. In this paper a new analytical theory for perpendicular transpo…
A fundamental problem in plasma physics, space science, and astrophysics is the transport of energetic particles interacting with stochastic magnetic fields. In particular the motion of particles across a large scale magnetic field is difficult to describe analytically. However, progress has been achieved in the recent years due to the development of the unified non-linear transport theory which can be used to describe magnetic field line diffusion as well as perpendicular diffusion of energetic particles. The latter theory agrees very well with different independently performed test-particle …
I derive analytically the temporal dependence of the perpendicular transport coefficient of a charged particle in the three-dimensional anisotropic turbulence conjectured by Goldreich-Sridhar by implementing multi-spacecraft constraints on the turbulence power spectrum. The particle motion away from the turbulent local field line is assessed as gradient/curvature drift of the guiding-center and compared with the magnetic field line random walk. At inertial scales much smaller than the turbulence outer scale, particles decorrelate from field lines in a free-streaming motion, with no diffusion. …
By searching through more than 10 satellite-years of THEMIS and Cluster data, three reliable examples of parallel electric field turbulence in the undisturbed solar wind have been found. The perpendicular and parallel electric field spectra in these examples have similar shapes and amplitudes, even at large scales (frequencies below the ion gyroscale) where Alfvenic turbulence with no parallel electric field component is thought to dominate. The spectra of the parallel electric field fluctuations are power laws with exponents near -5/3 below the ion scales (~ 0.1 Hz), and with a flattening of …
Perpendicular ion heating in turbulence and reconnection: magnetic moment breaking by coherent fluctuations
University of California, Berkeley（加州大学伯克利分校）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学）；Space Science Center and Department of Physics, University of New Hampshire（新罕布什尔大学）；Department of Physics, University of California, Berkeley（加州大学伯克利分校）
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\parallel,k_\bot)$ has the sa…
Turbulent transport is known to limit the plasma confinement of present-day optimized stellarators. To address this issue, a novel method to strongly suppress turbulence in such devices is proposed, namely the resonant wave-particle interaction of supra-thermal particles - e.g., from ion-cyclotron-resonance-frequency (ICRF) heating - with turbulence-driving microinstabilities like ion-temperature-gradient (ITG) modes. The effectiveness of this mechanism is demonstrated via analytic theory and large-scale gyrokinetic simulations, revealing an overall turbulence reduction by up to $80\%$. These …
In this work, we address the question of the influence of magnetic islands on the perpendicular transport due to steady-state ITG turbulence on the energy transport time scale. We demonstrate that turbulence can cross the separatrix and enhance the perpendicular transport across magnetic islands. As the perpendicular transport in the interior of the island sets the critical island size needed for growth of neoclassical tearing modes, this increased transport leads to a critical island size larger than that predicted from considering collisional conductivities, but smaller than that using anoma…
The topic of this review paper is on the influence of solar wind turbulence on shock propagation and its consequence on the acceleration and transport of energetic particles at shocks. As the interplanetary shocks sweep through the turbulent solar wind, the shock surfaces fluctuate and ripple in a range of different scales. We discuss particle acceleration at rippled shocks in the presence of ambient solar-wind turbulence. This strongly affects particle acceleration and transport of energetic particles (both ions and electrons) at shock fronts. In particular, we point out that the effects of u…
Solar Energetic Particles (SEPs) possess a high destructive potential as they pose multiple radiation hazards on Earth and onboard spacecrafts. The present work continues a series started with the paper by Borovikov et al.(2018) describing a computational tool to simulate and, potentially, predict the SEP threat based on the observations of the Sun. Here we present the kinetic model coupled with the globalMHD model for the Solar Corona (SC) and Inner Heliosphere (IH), which was described in the first paper in the series. At the heart of the coupled model is a self-consistent treatment of the A…
The transport of energetic charged particles (e.g., cosmic rays) in turbulent magnetic fields is usually characterized in terms of the diffusion parallel and perpendicular to a large-scale (or mean) magnetic field. The nonlinear guiding center theory (NLGC) has been a prominent perpendicular diffusion theory. A recent version of this theory, based on random ballistic spreading of magnetic field lines and a backtracking correction (RBD/BC), has shown good agreement with test particle simulations for a two-component magnetic turbulence model. The aim of the present study is to test the generalit…
Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show h…
In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into…
A newly developed sensitivity-driven approach is employed to study the role of energetic particles in suppressing turbulence-inducing micro-instabilities for a set of realistic JET-like cases with NBI deuterium and ICRH $^3$He fast ions. First, the efficiency of the sensitivity-driven approach is showcased for scans in a $21$-dimensional parameter space, for which only $250$ simulations are necessary. The same scan performed with traditional Cartesian grids with only two points in each of the $21$ dimensions would require $2^{21} = 2,097,152$ simulations. Then, a $14$-dimensional parameter sub…
Forced, weak MHD turbulence with guide field is shown to adopt different regimes, depending on the magnetic excess of the large forced scales. When the magnetic excess is large enough, the classical perpendicular cascade with $5/3$ scaling is obtained, while when equipartition is imposed, an isotropic $3/2$ scaling appears in all directions with respect to the mean field (\cite{2010PhRvE..82b6406G} or GM10). We show here that the $3/2$ scaling of the GM10 regime is not ruled by a small-scale cross-helicity cascade, and propose that it is a 3D extension of a perpendicular weak Iroshnikov-Kraich…
We study the physics of electron acceleration at collisionless shocks that move through a plasma containing large-scale magnetic fluctuations. We numerically integrate the trajectories of a large number of electrons, which are treated as test particles moving in the time dependent electric and magnetic fields determined from 2-D hybrid simulations (kinetic ions, fluid electron). The large-scale magnetic fluctuations effect the electrons in a number of ways and lead to efficient and rapid energization at the shock front. Since the electrons mainly follow along magnetic lines of force, the large…
Long range correlations were measured using two remote reciprocating Langmuir probe systems at TJ-II. The influence of the rotational transform on the correlation was studied by scanning the magnetic configuration. A simple drift wave correlation model, assuming an exponential decay of the correlation with different correlation lengths in the directions parallel and perpendicular to the field lines, was found to describe the observations well at low densities. The experiment was repeated at gradually higher densities, and an additional correlation was detected at a critical value of the densit…
A statistical survey of spectral anisotropy of space plasma turbulence is performed using five years measurements from MMS in the magnetosheath. By measuring the five-point second-order structure functions of the magnetic field, we have for the first time quantified the three-dimensional anisotropies and scalings at sub-ion-scales ($<$ 100 km). In the local reference frame $(\hat L_{\perp}, \hat l_{\perp}, \hat l_{\parallel})$ defined with respect to local mean magnetic field $\boldsymbol {B}_0$ (Chen et al. 2012), the "statistical eddies" are found to be mostly elongated along $\boldsymbol {B…
The field-aligned anisotropy of the solar wind turbulence, which is quantified by the ratio of the parallel to the perpendicular correlation (and Taylor) length scales, is determined by simultaneous two-point correlation measurements during the time period 2001-2017. Our results show that the correlation scale along the magnetic field is the largest, and the correlation scale in the field-perpendicular directions is the smallest, at both solar maximum and solar minimum. However, the Taylor scale reveals inconsistent results for different stages of the solar cycles. During the years 2001-2004, …
In the Large helical device, a change of energetic particle mode is observed as He concentration is varied in ion-ITB type experiments, having constant electron density and input heating power but with a clear increase of central ion temperature in He rich discharges. This activity consists of bursty, but damped energetic interchange modes (EICs, X Du et al., Phys. Rev. Lett. 114 p.155003 (2015)), whose occurrence rate is dramatically lower in the He-rich discharges. Mechanisms are discussed for the changes in drive and damping of the modes with He concentration. These EIC bursts consist of ma…
Using test-particle simulations, we investigate the temporal dependence of the two-point velocity correlation function for charged particles scattering in a time-independent spatially fluctuating magnetic field derived from a three-dimensional isotropic turbulence power spectrum. Such a correlation function allowed us to compute the spatial coefficients of diffusion both parallel and perpendicular to the average magnetic field. Our simulations confirm the dependence of the perpendicular diffusion coefficient on turbulence energy density and particle energy predicted previously by a model for e…
Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to the direction of the local magnetic field even in the case of global isotropy. A mean magnetic field reduces the parallel-field dynamics while in the perpendicular direction a gradual transition towards two-dimensional MHD turbulence is observed with $k^{-3/2}$ inertial-range scaling of the perpendicular energy spectrum. An intermittency model based on the L…
Impact of energetic alpha particles on core turbulence in an ARC-class fusion power plant
MIT Plasma Science and Fusion Center（麻省理工学院等离子体科学与聚变中心）；University of San Diego（圣地亚哥大学）；York Plasma Institute（约克等离子体研究所）；Rudolf Peierls Centre for Theoretical Physics（鲁道夫·派尔斯理论物理中心）；Commonwealth Fusion Systems（联邦聚变系统）；General Atomics（通用原子能公司）
The anisotropy of turbulence in the fast solar wind, between the ion and electron gyroscales, is directly observed using a multispacecraft analysis technique. Second order structure functions are calculated at different angles to the local magnetic field, for magnetic fluctuations both perpendicular and parallel to the mean field. In both components, the structure function value at large angles to the field S_perp is greater than at small angles S_par: in the perpendicular component S_perp/S_par = 5 +- 1 and in the parallel component S_perp/S_par > 3, implying spatially anisotropic fluctuation…
An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of th…
We investigate the influence of a uniform magnetic field ${\bf B_0}=B_0 e//$ on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along $B_0$ is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology {\it à la} Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong $B_0$, with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and…
Particles ejected from the Sun that stream through the surrounding plasma of the solar wind are causing instabilities. These generate wavemodes in a certain frequency range especially within shock regions, where particles are accelerated. The aim of this paper is to investigate of amplified Alfvenic wavemodes in driven incompressible magnetohydrodynamic turbulence. Results of different heliospheric scenarios from isotropic and anisotropic plasmas, as well as turbulence near the critical balance are shown. The energy transport of the amplified wavemode is governed by the mechanisms of diffusion…
Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration and transport. Using Ramaty High Energy Solar Spectroscopic Imager ({\it RHESSI}) observations and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, April 14, 2002 23$:$55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuousl…
The recent progress in high-temperature superconductor technologies has led to the design and construction of SPARC, a compact tokamak device expected to reach plasma breakeven with up to $25$MW of external ion cyclotron resonant heating (ICRH) power. This manuscript presents local (flux-tube) and radially global gyrokinetic GENE (Jenko et al 2000 Phys. Plasmas {\bf 7} 1904) simulations for a reduced-field and current H-mode SPARC scenario showing that supra-thermal particles - generated via ICRH - strongly suppress ion-scale turbulent transport by triggering a fast ion-induced anomalous trans…
Zonal flows are recognised to play a crucial role for magnetised plasma confinement. The genesis of these flows out of turbulent fluctuations is therefore of significant interest. We investigate the relative importance of zonal flow generation mechanisms via the Reynolds stress, Maxwell stress, and geodesic acoustic mode (GAM) transfer in drift-Alfvén turbulence. By means of numerical computations we quantify the energy transfer into zonal flows owing to each of these effects. The importance of the three driving ingredients in electrostatic and electromagnetic turbulence for conditions relevan…
For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directio…
The turbulent transport of minority species/impurities is investigated in 2D drift-wave turbulence as well as in 3D toroidal drift-Alfven edge turbulence. The full effects of perpendicular and -- in 3D -- parallel advection are kept for the impurity species. Anomalous pinch effects are recovered and explained in terms of Turbulent EquiPartition (TEP)
In tokamak plasmas, the interaction among the micro-turbulence, zonal flows (ZFs) and energetic particles (EPs) can affect the turbulence saturation level and the consequent confinement quality and thus, is important for future burning plasmas. In this work, the EP anisotropy effects on the ZF residual level are studied by using anisotropic EP distributions with dependence on pitch. Significant effects on the long wavelength ZFs have been found when small to moderate width around the dominant pitch in the EP distribution function is assumed. In addition, it is found that ZF residual level is e…
Plasma turbulence is the dominant transport mechanism for heat and particles in magnetized plasmas in linear devices and tokamaks, so the study of turbulence is important in limiting and controlling this transport. Linear devices provide an axial magnetic field that serves to confine a plasma in cylindrical geometry as it travels along the magnetic field from the source to the strike point. Due to perpendicular transport, the plasma density and temperature have a roughly Gaussian radial profile with gradients that drive instabilities, such as resistive drift-waves and Kelvin-Helmholtz. If unst…
Detailed computations of tokamak edge turbulence in three dimensional, globally consistent flux tube geometry show an inhibition of the standard scenario in which zonal ExB flows generated by the turbulence should lead to transport barrier formation. It is found by comparison to slab geometry and by analysis of the energetics that the zonal flow energy is depleted by toroidal coupling to the pressure through the geodesic curvature. Edge transport barriers would then depend on the physics of the neoclassical equilibrium.
We present two-dimensional kinetic simulations, with a broad range of initial guide fields, that isolate the role of parallel electric fields ($E_\parallel$) in energetic electron production during collisionless magnetic reconnection. In the strong guide field regime, $E_\parallel$ drives essentially all of the electron energy gain, yet fails to generate an energetic component. We suggest that this is due to the weak energy scaling of particle acceleration from $E_\parallel$ compared to that of a Fermi-type mechanism responsible for energetic electron production in the weak guide-field regime.…
The aim of the present study is to perform a theoretical analysis of different strategies to stabilize energetic-ion-driven resistive interchange mode (EIC) in LHD plasma. We use a reduced MHD for the thermal plasma coupled with a gyrofluid model for the energetic particles (EP) species. The hellically trapped EP component is introduced through a modification of the drift frequency to include their precessional drift. The stabilization trends of the 1/1 EIC observed experimentally with respect to the thermal plasma density and temperature are reproduced by the simulations, showing a reasonable…
