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.
The burning plasma performance is limited by the confinement of the superalfvenic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfvénic eigenmodes (AEs). In this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently. The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formula…
Minor ion (such as $He^{2+}$) heating via nonresonant interaction with spectra of linearly and circularly polarized Alfvén waves (LPAWs and CPAWs hereafter) is studied. The obtained analytic solutions are in good agreement with the simulation results, indicating that newborn ions are heated by low-frequency Alfvén waves with finite amplitude in low-beta plasmas such as the solar corona. The analytic solutions also reproduce the preferential heating of heavy ions in the solar wind. In the presence of parallel propagating Alfvén waves, turbulence-induced particle motion is clearly observed in th…
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…
It is shown that the dispersion relation for whistler waves is identical for a high or low beta plasma. Furthermore in the high-beta solar wind plasma whistler waves meet the Landau resonance with electrons for velocities less than the thermal speed, and consequently the electric force is small compared to the mirror force. As whistlers propagate through the inhomogeneous solar wind, the perpendicular wave number increases through refraction, increasing the Landau damping rate. However, the whistlers can survive because the background kinetic Alfven wave turbulence creates a plateau by quasili…
Ion temperature anisotropy is a common feature for (quasi-)perpendicular collisionless shocks. By using two-dimensional full particle simulations, it is shown, that the ion temperature component perpendicular to the shock magnetic field at the shock foot region is proportional to the square of the Alfven Mach number divided by the plasma beta. This result is also explained by a simple analytical argument, in which the reflected ions get energy from upstream plasma flow. By comparing our analytic and numerical results, it is also confirmed that the fraction of the reflected ions hardly depends …
The origin and evolution of the 1/f power law observed in the energy spectrum of solar coronal and solar wind fluctuations at scales of around an hour is not entirely understood. Several existing theories aim at explaining it, involving both linear and nonlinear mechanisms. An often overlooked property of the solar corona and solar wind is their highly inhomogeneous nature. In this paper we investigate the linear evolution of pure Alfvén and surface Alfvén waves propagating through a plasma which is inhomogeneous across the magnetic field. The inhomogeneity is given by density, which we model …
We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfvén critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. RMHD turbulence is driven by outward-propagating Alfvén waves ($z^+$ fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfvén waves ($z^-$ fluctuations). We present ten si…
In this work we investigate the characteristics of the group velocity of obliquely propagating Alfvén waves in a dusty plasma typical of a stellar wind. The dispersion relation is derived with the aid of the kinetic theory for a magnetized dusty plasma consisting of electrons and ions, with distribution of momenta described by a Maxwellian function. The dust particles are considered to be immobile and have all the same size; they are electrically charged by absorption of plasma particles via inelastic collisions and by photoionization. We numerically solve the dispersion relation and calculate…
We study a velocity-space quasilinear diffusion of the solar wind protons driven by oblique Alfven turbulence at proton kinetic scales. Turbulent fluctuations at these scales possess properties of kinetic Alfven waves (KAWs) that are efficient in Cherenkov resonant interactions. The proton diffusion proceeds via Cherenkov kicks and forms a quasilinear plateau - nonthermal proton tail in the velocity distribution function (VDF). The tails extend in velocity space along the mean magnetic field from 1 to (1.5-3) VA, depending on the spectral break position, turbulence amplitude at the spectral br…
In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfven waves, denoted Alfven wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfven wave collisions in an ideali…
The solar atmosphere is known to be replete with magneto-hydrodynamic wave modes, and there has been significant investment in understanding how these waves propagate through the Sun's atmopshere and deposit their energy into the plasma. The waves' journey is made interesting by the vertical variation in plasma quantities that define the solar atmosphere. In addition to this large-scale inhomogeneity, a wealth of fine-scale structure through the chromosphere and corona has been brought to light by high-resolution observations over the last couple of decades. This fine-scale sturcture represent…
We present three-dimensional, hybrid-kinetic numerical simulations of driven Alfvén-wave turbulence of relevance to the collisionless near-Earth solar wind. Special attention is paid to the spectral transition that occurs near the ion-Larmor scale and to the origins of preferential perpendicular ion heating and of non-thermal wings in the parallel distribution function. Several novel diagnostics are used to show that the ion heating rate increases as the kinetic-Alfvén-wave fluctuations, which comprise the majority of the sub-ion-Larmor turbulent cascade, attain near-ion-cyclotron frequencies.…
The confinement of energetic particles (EP) is crucial for an efficient heating of tokamak plasmas. Plasma instabilities such as Alfven Eigenmodes (AE) can redistribute the EP population making the plasma heating less effective, and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AE (TAE) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EP due to the wave-particle nonlinearity is studied. In particular, we focus on the nonlinear modification of th…
In the framework of compressional magnetohydrodynamics (MHD), we numerically studied the commonly accepted presumption that the Alfvénic turbulence is generated by the collisions between counter-propagating Alfvén waves (AWs). In the conditions typical for the low-beta solar corona and inner solar wind, we launched two counter-propagating AWs in the three-dimensional simulation box and analyzed polarization and spectral properties of perturbations generated before and after AW collisions. The observed post-collisional perturbations have different polarizations and smaller cross-field scales th…
In hydrodynamic turbulence, it is well established that the length of the dissipation scale depends on the energy cascade rate, i.e., the larger the energy input rate per unit mass, the more the turbulent fluctuations need to be driven to increasingly smaller scales to dissipate the larger energy flux. Observations of magnetic spectral energy densities indicate that this intuitive picture is not valid in solar wind turbulence. Dissipation seems to set in at the same length scale for different solar wind conditions independently of the energy flux. To investigate this difference in more detail,…
We investigate ion-scale kinetic plasma instabilities at the collisionless shock using linear theory and nonlinear Particle-in-Cell (PIC) simulations. We focus on the Alfvén-ion-cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shock-reflected ions within the transition layer of a strictly perpendicular shock. We conduct linear dispersion analysis with a homogeneous plasma model to mimic the shock transition layer by adopting a ring distribution with finite thermal spread to represent the velocity distributio…
In the parts of the solar corona and solar wind that experience the fewest Coulomb collisions, the component proton, electron, and heavy ion populations are not in thermal equilibrium with one another. Observed differences in temperatures, outflow speeds, and velocity distribution anisotropies are useful constraints on proposed explanations for how the plasma is heated and accelerated. This paper presents new predictions of the rates of collisionless heating for each particle species, in which the energy input is assumed to come from magnetohydrodynamic (MHD) turbulence. We first created an em…
We study the influence of kinetic-scale Alfvénic turbulence on the generation of plasma radio emission in the solar coronal regions where the plasma/magnetic pressure ratio $β$ is smaller than the electron/ion mass ratio $m_{e}/m_{i}$. The present study is motivated by the phenomenon of solar type I radio storms associated with the strong magnetic field of active regions. The measured brightness temperature of the type I storms can be up to $10^{10}$ K for continuum emission, and can exceed $10^{11}$ K for type I bursts. At present, there is no generally accepted theory explaining such high br…
Motivated by recent observations of distinct parallel and perpendicular signatures in magnetic helicity measurements segregated by wave period and angle between the local magnetic field and the solar wind velocity, this paper undertakes a comparison of three intervals of \emph{Ulysses} data with synthetic time series generated from a physically motivated turbulence model. From these comparisons, it is hypothesized that the observed signatures result from a perpendicular cascade of \Alfvenic fluctuations and a local, non-turbulent population of ion cyclotron or whistler waves generated by tempe…
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…
Turbulent dissipation is considered a main source of heating and acceleration in cosmological plasmas. The alternating current Joule-like term, $\langleδj \cdot δE\rangle$, is used to measure the energy transfer between electromagnetic (EM) fields and particles. Because the electric field depends on the reference frame, in which frame to calculate $\langleδj\cdot δE\rangle$ is an important issue. We compute the scale-dependent energy transfer rate spectrum in wavevector space, and investigate the electric-field fluctuations in two reference frames: $δE$ in the mean bulk flow frame and $δE'$ in…
Reduced fluid models including electron inertia and ion finite Larmor radius corrections are derived asymptotically, both from fluid basic equations and from a gyrofluid model. They apply to collisionless plasmas with small ion-to-electron equilibrium temperature ratio and low $β_e$, where $β_e$ indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong, constant and uniform magnetic guide field. The consistency between the fluid and gyrofluid approaches is ensured when choosing ion closure relations prescribed by the underlying ordering. A two-…
Plasma ions heating (especially minor heavy ions preferential heating) in fast solar wind and solar corona is an open question in space physics. However, Alfvén waves have been always considered as a candidate of energy source for corona heating. In this paper, by using a two-dimensional (2-D) hybrid simulation model in a low beta electron-proton-alpha plasma system, we have investigated the relationships between plasma ions heating and power spectra evolution of density and magnetic field fluctuations excited from the parametric instabilities of initial pump Alfvén waves with an incoherent sp…
Remote sensing observations of coronal holes show that heavy ions are hotter than protons and their temperature is anisotropic. In-situ observations of fast solar wind streams provide direct evidence for turbulent Alfvén wave spectrum, left-hand polarized ion-cyclotron waves, and He$^{++}$ -- proton drift in the solar wind plasma, which can produce temperature anisotropies by resonant absorption and perpendicular heating of the ions. Furthermore, the solar wind is expected to be inhomogeneous on decreasing scales approaching the Sun. We study the heating of solar wind ions in inhomogeneous pla…
We analyze plasma heating in weakly collisional kinetic Alfvén wave (KAW) turbulence using high resolution gyrokinetic simulations spanning the range of scales between the ion and the electron gyroradii. Real space structures that have a higher than average heating rate are shown not to be confined to current sheets. This novel result is at odds with previous studies, which use the electromagnetic work in the local electron fluid frame, i.e. $\mathbf{J} \!\cdot\! (\mathbf{E} + \mathbf{v}_e\times\mathbf{B})$, as a proxy for turbulent dissipation to argue that heating follows the intermittent sp…
Large-scale two-dimensional (2D) full particle-in-cell simulations are carried out for studying the relationship between the dynamics of a perpendicular shock and microinstabilities generated at the shock foot. The structure and dynamics of collisionless shocks are generally determined by Alfven Mach number and plasma beta, while microinstabilities at the shock foot are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the ratio of the plasma-to-cyclotron frequency. With a fixed Alfven Mach number and plasma beta, the ratio of the upstream bulk velocity…
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…
The role of magnetic helicity is investigated in kinetic Alfvén 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 analysi…
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 …
We present a mechanism for the formation of the low frequency 1/f magnetic spectrum based on numerical solutions of a shell reduced-MHD model of the turbulent dynamics inside the sub-Alfvénic solar wind. We assign reasonably realistic profiles to the wind speed and the density along the radial direction, and a radial magnetic field. Alfvén waves of short periodicity (600 s) are injected at the base of the chromosphere, penetrate into the corona and are partially reflected, thus triggering a turbulent cascade. The cascade is strong for the reflected wave while it is weak for the outward propaga…
We present a measurement of the scale-dependent, three-dimensional structure of the magnetic field fluctuations in inertial range solar wind turbulence with respect to a local, physically motivated coordinate system. The Alfvenic fluctuations are three-dimensionally anisotropic, with the sense of this anisotropy varying from large to small scales. At the outer scale, the magnetic field correlations are longest in the local fluctuation direction, consistent with Alfven waves. At the proton gyroscale, they are longest along the local mean field direction and shortest in the direction perpendicul…
Using spatio-temporal spectra we show direct evidence of excitation of magnetosonic and Alfvén waves in three-dimensional compressible magnetohydrodynamic turbulence at small Mach numbers. For the plasma pressure dominated regime, or high $β$ regime (with $β$ the ratio between fluid and magnetic pressure), and for the magnetic pressure dominated regime, or low $β$ regime, we study magnetic field fluctuations parallel and perpendicular to a guide magnetic field $\textbf{B}_0$. In the low $β$ case we find excitation of compressible and incompressible fluctuations, with a transfer of energy towar…
We analyse nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-$β$ plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, that constitutes a bulk plasma motion along the magnetic field, the tube w…
The injection of lower hybrid waves for current drive into a tokamak affects the profile of intrinsic rotation. In this article, the momentum deposition by the lower hybrid wave on the electrons is studied. Due to the increase in the poloidal momentum of the wave as it propagates into the tokamak, the parallel momentum of the wave increases considerably. The change of the perpendicular momentum of the wave is such that the toroidal angular momentum of the wave is conserved. If the perpendicular momentum transfer via electron Landau damping is ignored, the transfer of the toroidal angular momen…
We present results from a three-dimensional particle-in-cell simulation of plasma turbulence, resembling the plasma conditions found at kinetic scales of the solar wind. The spectral properties of the turbulence in the subion range are consistent with theoretical expectations for kinetic Alfv\' en waves. Furthermore, we calculate the local anisotropy, defined by the relation $k_{\parallel}(k_{\perp})$, where $k_{\parallel}$ is a characteristic wave number along the local mean magnetic field at perpendicular scale $l_{\perp}\sim 1/k_{\perp}$. The subion range anisotropy is scale dependent with …
The recently suggested swing interaction between fast magnetosonic and Alfven waves (Zaqarashvili and Roberts 2002) is generalized to inhomogeneous media. We show that the fast magnetosonic waves propagating across an applied non-uniform magnetic field can parametrically amplify the Alfven waves propagating along the field through the periodical variation of the Alfven speed. The resonant Alfven waves have half the frequency and the perpendicular velocity polarization of the fast waves. The wave lengths of the resonant waves have different values across the magnetic field, due to the inhomogen…
In a weakly collisional, low-electron-beta plasma, large-scale Alfvén turbulence transforms into inertial kinetic-Alfvén turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tend to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane per…
We investigate the anisotropy of Alfvénic turbulence in the inertial range of slow solar wind and in both driven and decaying reduced magnetohydrodynamic simulations. A direct comparison is made by measuring the anisotropic second-order structure functions in both data sets. In the solar wind, the perpendicular spectral index of the magnetic field is close to -5/3. In the forced simulation, it is close to -5/3 for the velocity and -3/2 for the magnetic field. In the decaying simulation, it is -5/3 for both fields. The spectral index becomes steeper at small angles to the local magnetic field d…
We apply field-particle correlations -- a technique that tracks the time-averaged velocity-space structure of the energy density transfer rate between electromagnetic fields and plasma particles -- to data drawn from a hybrid Vlasov-Maxwell simulation of Alfvén Ion-Cyclotron turbulence. Energy transfer in this system is expected to include both Landau and cyclotron wave-particle resonances, unlike previous systems to which the field-particle correlation technique has been applied. In this simulation, the energy transfer rate mediated by the parallel electric field $E_\parallel$ comprises appro…
Solar wind turbulence is dominated by Alfvénic fluctuations but the power spectral exponents somewhat surprisingly evolve toward the Kolmogorov value of -5/3, that of hydrodynamic turbulence. We show that at 1AU the turbulence decomposes linearly into two coexistent components perpendicular and parallel to the local average magnetic field. The first of these is consistent with propagating Alfvén wavepackets and shows the scaling expected of Alfvénic turbulence, namely Irosnikov- Kraichnan. The second shows Kolmogorov scaling which we also find in the number and magnetic energy density, and Poy…
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…
Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the hea…
Switchbacks -- rapid, large deflections of the solar wind's magnetic field -- have generated significant interest as possible signatures of the key mechanisms that heat the corona and accelerate the solar wind. In this context, an important task for theories of switchback formation and evolution is to understand their observable distinguishing features, allowing them to be assessed in detail using spacecraft data. Here, we work towards this goal by studying the influence of the Parker spiral on the evolution of Alfvénic switchbacks in an expanding plasma. Using simple analytic arguments based …
The SWEAP instrument suite on Parker Solar Probe (PSP) has detected numerous proton beams associated with coherent, circularly polarized, ion-scale waves observed by PSP's FIELDS instrument suite. Measurements during PSP Encounters 4-8 revealed pronounced complex shapes in the proton velocity distribution functions (VDFs), in which the tip of the beam undergoes strong perpendicular diffusion, resulting in VDF level contours that resemble a `hammerhead.' We refer to these proton beams, with their attendant `hammerhead' features, as the ion strahl. We present an example of these observations occ…
Particle-in-Cell Simulation of the Parametric Decay Instability of Alfvén Waves with Absorbing Boundary Conditions
New Mexico Consortium（新墨西哥联盟）；Space Science Institute（太空科学研究所）；University of California, Los Angeles（加州大学洛杉矶分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
A weakly dispersive sub-range (WDR) of kinetic Alfvén turbulence is distinguished and investigated for the first time in the context of MHD/kinetic turbulence transition. We found perpendicular wavenumber spectra ~ k^{-3} and ~ k^{-4} formed in WDR by strong and weak turbulence of kinetic Alfvén waves (KAWs), respectively. These steep WDR spectra connect shallower spectra in the MHD and strongly dispersive KAW sub-ranges, which results in a specific double-kink (2-k) pattern often seen in observed turbulent spectra. The first kink occurs where MHD turbulence transforms into weakly dispersive K…
The process of particle acceleration by left-hand, circularly polarised inertial Alfven waves (IAW) in a transversely inhomogeneous plasma is studied using 3D particle-in-cell simulation. A cylindrical tube with, transverse to the background magnetic field, inhomogeneity scale of the order of ion inertial length is considered on which IAWs with frequency $0.3 ω_{ci}$ are launched that are allowed to develop three wavelength. As a result time-varying parallel electric fields are generated in the density gradient regions which accelerate electrons in the parallel to magnetic field direction. Dri…
The relationship between a decaying strong turbulence and the mirror instability in a slowly expanding plasma is investigated using two-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly-polarized, random-phase Alfvenic fluctuations which have energy equipartition between kinetic and magnetic fluctuations and vanishing correlation between the two fields. A turbulent cascade rapidly develops, magnetic field fluctuations exhibit a Kolmogorov-like power-law spectrum at…
