Effects Of Wave-particle Interactions Research Articles

Temporal variability of quasi-linear pitch-angle diffusion

Kinetic wave-particle interactions in Earth’s outer radiation belt energize and scatter high-energy electrons, playing an important role in the dynamic variation of the extent and intensity of the outer belt. It is possible to model the effects of wave-particle interactions across long length and time scales using quasi-linear theory, leading to a Fokker-Planck equation to describe the effects of the waves on the high energy electrons. This powerful theory renders the efficacy of the wave-particle interaction in a diffusion coefficient that varies with energy or momentum and pitch angle. In this article we determine how the Fokker-Planck equation responds to the temporal variation of the quasi-linear diffusion coefficient in the case of pitch-angle diffusion due to plasmaspheric hiss. Guided by in-situ observations of how hiss wave activity and local number density change in time, we use stochastic parameterisation to describe the temporal evolution of hiss diffusion coefficients in ensemble numerical experiments. These experiments are informed by observations from three different example locations in near-Earth space, and a comparison of the results indicates that local differences in the distribution of diffusion coefficients can result in material differences to the ensemble solutions. We demonstrate that ensemble solutions of the Fokker-Planck equation depend both upon the timescale of variability (varied between minutes and hours), and the shape of the distribution of diffusion coefficients. Based upon theoretical construction of the diffusion coefficients and the results presented here, we argue that there is a useful maximum averaging timescale that should be used to construct a diffusion coefficient from observations, and that this timescale is likely less than the orbital period of most inner magnetospheric missions. We discuss time and length scales of wave-particle interactions relative to the drift velocity of high-energy electrons and confirm that arithmetic drift-averaging is can be appropriate in some cases. We show that in some locations, rare but large values of the diffusion coefficient occur during periods of relatively low number density. Ensemble solutions are sensitive to the presence of these rare values, supporting the need for accurate cold plasma density models in radiation belt descriptions.

The role of the inner radiation belt dynamic in the generation of auroral-type sporadic E-layers over south American magnetic anomaly

The dynamics of the electron population in the Earth’s radiation belts affect the upper atmosphere’s ionization level through the low-energy Electron Precipitation (EP). The impact of low-energy EP on the high-latitude ionosphere has been well explained since the 1960’s decade. Conversely, it is still not well understood for the region of the South American Magnetic Anomaly (SAMA). In this study, we present the results of analysis of the strong geomagnetic storm associated with the Interplanetary Coronal Mass Ejection (May 27-28, 2017). The atypical auroral sporadic E layers (Esa) over SAMA are observed in concomitance with the hiss and magnetosonic wave activities in the inner radiation belt. The wave-particle interaction effects have been estimated, and the dynamic mechanisms that caused the low-energy EP over SAMA were investigated. We suggested that the enhancement in pitch angle scattering driven by hiss waves result in the low-energy EP (≥10 keV) into the atmosphere over SAMA. The impact of these precipitations on the ionization rate at the altitude range from 100 to 120 km can generate the Esa layer in this peculiar region. In contrast, we suggested that the low-energy EP (≤1 keV) causes the maximum ionization rate close to 150 km altitude, contributing to the Esa layer occurrence in these altitudes.

Kinetic instability of electrostatic ion cyclotron waves in inter-penetrating plasmas

The Electrostatic Ion Cyclotron (EIC) instability that includes the effect of wave-particle interaction is studied owing to the free energy source through the flowing velocity of the inter-penetrating plasmas. It is shown that the origin of this current-less instability is different from the classical current driven EIC instability. The threshold conditions applicable to a wide range of plasma parameters and the estimate of the growth rate are determined as a function of the normalized flowing velocity (u0/vtfe), the temperature (Tf/Ts) and the density ratios (nf0/ns0) of flowing component to static one. The EIC instability is driven by either flowing electrons or flowing ions, depending upon the different Doppler shifted frequency domains. It is found that the growth rate for electron-driven instability is higher than the ion-driven one. However, in both cases, the denser (hotter) is the flowing plasma, the lesser (greater) is the growth rate. The possible applications related to the terrestrial solar plasma environment are also discussed.

Asymmetric drift instability of magnetosonic waves in anisotropic plasmas

The general dispersion relation of obliquely propagating magneto-sonic (MS) waves for the inhomogeneous and anisotropic plasmas is analyzed including the effect of wave-particle interaction. The numerical analysis is performed without expanding both the plasma dispersion and the modified Bessel functions to highlight the effects of density inhomogeneity and the temperature anisotropy. The obtained results are compared with the recent work [Naim et al., Phys. Plasmas 22, 062117 (2015)], where only drift mode near the magnetosonic frequency is investigated. In our paper, we additionally analyzed two related modes depicting that the drift effect leads to an asymmetric behavior in the dispersion properties of drift MS waves. The possible application to the solar coronal heating problem has also been discussed.

DE-1 versus Cluster spectral density observations: the effect on ion outflow above the polar cap

<p>Wave-particle interaction is a very important mechanism in describing the outflow of ions at high latitudes and high altitudes. Quasi-linear perpendicular velocity diffusion coefficients are used to describe the effect of wave-particle interactions, therefore it is essential to determine the correct diffusion coefficients that must be used to model the outflow of ions. In this study a Monte Carlo method is used to assess the role of different diffusion coefficients for O+ and H+ ions at high altitudes above the polar cap. Two different sets of diffusion coefficients obtained from Barghouthi [1997]; Barghouthi et al. [1998] and Nilsson et al. [2013] are used. Barghouthi [1997]; Barghouthi et al. [1998] used spectral density measurements from Dynamic Explorer 1 spacecraft (DE-1) observations to calculate the diffusion coefficients, while Nilsson et al. [2013] used spectral density measurements from the Cluster spacecraft to obtain the diffusion coefficients. It was found that diffusion coefficients from Barghouthi [1997]; Barghouthi et al. [1998] in the cusp (aurora) and central polar cap (polar wind) respectively, describe well the observations of ion outflow at altitudes lower than 5 RE, but yield unreasonably high parallel velocities and temperatures at higher altitudes. Also diffusion coefficients from Cluster spectral density measurements produce reasonable results for high altitudes and unreasonably low parallel velocities and temperatures for the low altitude region. Therefore it is suggested that a combination of these diffusion coefficients is used where the diffusion coefficients given by Barghouthi [1997]; Barghouthi et al. [1998] are used at low altitudes and the diffusion coefficients obtained from Cluster measurements are used at high altitudes.</p>

NONTHERMAL RADIATION FROM SUPERNOVA REMNANTS: EFFECTS OF MAGNETIC FIELD AMPLIFICATION AND PARTICLE ESCAPE

We explore nonlinear effects of wave-particle interactions on the diffusive shock acceleration (DSA) process in Type Ia-like, SNR blast waves, by implementing phenomenological models for magnetic field amplification, Alfv'enic drift, and particle escape in time-dependent numerical simulations of nonlinear DSA. For typical SNR parameters the CR protons can be accelerated to PeV energies only if the region of amplified field ahead of the shock is extensive enough to contain the diffusion lengths of the particles of interest. Even with the help of Alfv'enic drift, it remains somewhat challenging to construct a nonlinear DSA model for SNRs in which order of 10 % of the supernova explosion energy is converted to the CR energy and the magnetic field is amplified by a factor of 10 or so in the shock precursor, while, at the same time, the energy spectrum of PeV protons is steeper than E^{-2}. To explore the influence of these physical effects on observed SNR emissions, we also compute resulting radio-to-gamma-ray spectra. Nonthermal emission spectra, especially in X-ray and gamma-ray bands,depend on the time dependent evolution of CR injection process, magnetic field amplification, and particle escape, as well as the shock dynamic evolution. This result comes from the fact that the high energy end of the CR spectrum is composed of the particles that are injected in the very early stages of blast wave evolution. Thus it is crucial to understand better the plasma wave-particle interactions associated with collisionless shocks in detail modeling of nonthermal radiation from SNRs.

Forecasting the Earth’s radiation belts and modelling solar energetic particle events: Recent results from SPACECAST

High-energy charged particles in the van Allen radiation belts and in solar energetic particle events can damage satellites on orbit leading to malfunctions and loss of satellite service. Here we describe some recent results from the SPACECAST project on modelling and forecasting the radiation belts, and modelling solar energetic particle events. We describe the SPACECAST forecasting system that uses physical models that include wave-particle interactions to forecast the electron radiation belts up to 3 h ahead. We show that the forecasts were able to reproduce the >2 MeV electron flux at GOES 13 during the moderate storm of 7–8 October 2012, and the period following a fast solar wind stream on 25–26 October 2012 to within a factor of 5 or so. At lower energies of 10 – a few 100 keV we show that the electron flux at geostationary orbit depends sensitively on the high-energy tail of the source distribution near 10 RE on the nightside of the Earth, and that the source is best represented by a kappa distribution. We present a new model of whistler mode chorus determined from multiple satellite measurements which shows that the effects of wave-particle interactions beyond geostationary orbit are likely to be very significant. We also present radial diffusion coefficients calculated from satellite data at geostationary orbit which vary with Kp by over four orders of magnitude. We describe a new automated method to determine the position at the shock that is magnetically connected to the Earth for modelling solar energetic particle events and which takes into account entropy, and predict the form of the mean free path in the foreshock, and particle injection efficiency at the shock from analytical theory which can be tested in simulations.

A computational and theoretical analysis of falling frequency VLF emissions

Recently much progress has been made in the simulation and theoretical understanding of rising frequency triggered emissions and rising chorus. Both PIC and Vlasov VHS codes produce risers in the region downstream from the equator toward which the VLF waves are traveling. The VHS code only produces fallers or downward hooks with difficulty due to the coherent nature of wave particle interaction across the equator. With the VHS code we now confine the interaction region to be the region upstream from the equator, where inhomogeneity factor S is positive. This suppresses correlated wave particle interaction effects across the equator and the tendency of the code to trigger risers, and permits the formation of a proper falling tone generation region. The VHS code now easily and reproducibly triggers falling tones. The evolution of resonant particle current JE in space and time shows a generation point at −5224 km and the wavefield undergoes amplification of some 25 dB in traversing the nonlinear generation region. The current component parallel to wave magnetic field (JB) is positive, whereas it is negative for risers. The resonant particle trap shows an enhanced distribution function or ‘hill’, whereas risers have a ‘hole’. According to recent theory (Omura et al., 2008, 2009) sweeping frequency is due primarily to the advective term. The nonlinear frequency shift term is now negative (∼−12 Hz) and the sweep rate of −800 Hz/s is approximately nonlinear frequency shift divided by TN, the transition time, of the order of a trapping time.

A comparison study between observations and simulation results of Barghouthi model for O<sup>+</sup> and H<sup>+</sup> outflows in the polar wind

Abstract. To advance our understanding of the effect of wave-particle interactions on ion outflows in the polar wind region and the resulting ion heating and escape from low altitudes to higher altitudes, we carried out a comparison between polar wind simulations obtained using Barghouthi model with corresponding observations obtained from different satellites. The Barghouthi model describes O+ and H+ outflows in the polar wind region in the range 1.7 RE to 13.7 RE, including the effects of gravity, polarization electrostatic field, diverging geomagnetic field lines, and wave-particle interactions. Wave-particle interactions were included into the model by using a particle diffusion equation, which depends on diffusion coefficients determined from estimates of the typical electric field spectral density at relevant altitudes and frequencies. We provide a formula for the velocity diffusion coefficient that depends on altitude and velocity, in which the velocity part depends on the perpendicular wavelength of the electromagnetic turbulence λ⊥. Because of the shortage of information about λ⊥, it was included into the model as a parameter. We produce different simulations (i.e. ion velocity distributions, ions density, ion drift velocity, ion parallel and perpendicular temperatures) for O+ and H+ ions, and for different λ⊥. We discuss the simulations in terms of wave-particle interactions, perpendicular adiabatic cooling, parallel adiabatic cooling, mirror force, and ion potential energy. The main findings of the simulations are as follows: (1) O+ ions are highly energized at all altitudes in the simulation tube due to wave-particle interactions that heat the ions in the perpendicular direction, and part of this gained energy transfer to the parallel direction by mirror force, resulting in accelerating O+ ions along geomagnetic field lines from lower altitudes to higher altitudes. (2) The effect of wave-particle interactions is negligible for H+ ions at altitudes below ~7 RE, while it is important for altitudes above 7 RE. For O+ wave particle interaction is very significant at all altitudes. (3) For certain λ⊥ and at points, altitudes, where the ion gyroradius is equal to or less than λ⊥, the effect of wave-particle interactions is independent of the velocity and it depends only on the altitude part of the velocity diffusion coefficient; however, the effect of wave-particle interactions reduce above that point, called saturation point, and the heating process turns to be self-limiting heating. (4) The most interesting result is the appearance of O+ conics and toroids at low altitudes and continue to appear at high altitudes; however, they appear at very high altitudes for H+ ions. We compare quantitatively and qualitatively between the simulation results and the corresponding observations. As a result of many comparisons, we find that the best agreement occurs when λ⊥ equals to 8 km. The quantitative comparisons show that many characteristics of the observations are very close to the simulation results, and the qualitative comparisons between the simulation results for ion outflows and the observations produce very similar behaviors. To our knowledge, most of the comparisons between observations (ion velocity distribution, density, drift velocity, parallel and perpendicular temperatures, anisotropy, etc.) and simulations obtained from different models produce few agreements and fail to explain many observations (see Yau et al., 2007; Lemaire et al., 2007; Tam et al., 2007; Su et al., 1998; Engwall et al., 2009). This paper presents many close agreements between observations and simulations obtained by Barghouthi model, for O+ and H+ ions at different altitudes i.e. from 1.7 RE to 13.7 RE.

Models for Sub-Alfvénic Magnetodynamics of Fusion Plasmas

The models describing macroscopic magnetic perturbations that evolve slowly compared to the Alfvén velocity are reviewed. The perturbations of interest include tearing modes, resistive interchange and ballooning modes, internal kink modes, resistive wall modes, and resonant magnetic perturbations. Two important features that distinguish the various models are their descriptions of parallel dynamics and of ion gyration. The evolution of macroscopic modes is generally characterized by resonances that result in the development of small scales. For processes involving magnetic reconnection, for example, all scales from the ion down to the electron Larmor radius are generated nonlinearly. The magnetohydrodynamic model assumes that the gradient lengths are always greater than the ion Larmor radius and thus is unable to properly describe the resonances. The drift models rely on a much more detailed description of the motion that enables them to capture many of the features of the short-scale phenomena, but they remain limited by their local description of the effects of gyration, and by their inability to describe the effects of wave-particle interactions in the parallel dynamics. These limitations are remedied by the gyrokinetic model, which provides a consistent, first-principles description of all the dynamics below the ion cyclotron frequency, but this model is computationally costly and its range of practical applicability remains to be established. Lastly, the gyrofluid models constitute a family of closures based on the moments of the gyrokinetic equations. These models offer an attractive compromise between fidelity and computational cost but have only recently begun to be applied to macroscopic evolution.

The effect of altitude- and velocity-dependent wave–particle interactions on the H + and O + outflows in the auroral region

The formation of H + and O + toroids at high altitudes in the auroral region are discussed in terms of altitude- and velocity-dependent wave–particle interactions (WPI), and special attention is given to the peaked nature of the velocity diffusion coefficient D ⊥. The effects of altitude- and velocity-dependent WPI are taken into account by perturbing the ion velocity with random increment Δ v ⊥, such that 〈 ( Δ v ⊥ ) 2 〉 = 4 D ⊥ Δ t , where the time step is Δ t. To model the heating process, we specify a model for the velocity diffusion coefficient as a function of the ion perpendicular velocity and position along the auroral geomagnetic field line. The ion velocity distribution is described by a quasi-linear diffusion equation, which is solved by the Monte Carlo technique. The Monte Carlo model includes the effects of altitude- and velocity-dependent WPI, gravity, polarization electrostatic field, and the divergence of the geomagnetic field within the simulation tube (1.2–10 earth radii, R E). These effects were included self-consistently in the computations. The peaked nature of D ⊥ reflects the way in which altitude- and velocity-dependent WPI lead to the formation of H + and O + toroids at high altitudes in the auroral region, rather than simple bulk heating process. Because D ⊥ falls to zero at small perpendicular velocities, the bulk of the ion velocity distribution is unaffected by interaction with the waves (electromagnetic turbulence). However, near the phase velocity v 0, D ⊥ begins to become appreciable, and the diffusion process begins to affect ions. Because there are initially more ions at lower velocities than at higher velocities, the net escape flux in velocity space is toward higher velocities, leading to the formation of ion toroids. At large perpendicular velocities, D ⊥ falls to zero and consequently, the effect of WPI is negligible. As the heated ions drift upward along geomagnetic field lines due to the mirror geometry of the Earth's magnetic field, they eventually leave the primary heating region and form a ring “donuts”. The heating process is found to be self-limiting, and this explains the saturation of the ion velocity distributions at high altitudes. The altitude profiles of ion density, drift velocity, parallel and perpendicular temperatures are also discussed. We find that including the effect of velocity-dependent WPI in addition to the effect of altitude-dependent WPI produce realistic ion temperatures that are, qualitatively, comparable to the observations. The model produces simulation results similar to the observed toroids.

Effect of laser beam filamentation on plasma wave localization and electron heating

This paper presents the ponderomotive filamentation (single hot spot) of a laser beam, propagating in homogeneous plasma in a nonparaxial region. Electron plasma wave coupling in these filaments has been studied. It is found that initially launched weak plasma wave (small amplitude) gets excited and becomes highly localized (wave packet) with a broad spectrum. By expanding the eikonal and other relevant quantities up to the fourth power of r, it is observed that the focusing of the laser beams becomes fast in the nonparaxial region. The uneven focusing/defocusing of the axial and off-axial rays leads the formation of the splitted profile of laser beams in the plasma. The effects of wave particle interaction are also included in this formalism. The simulation result confirms the presence of chaotic fields, and the interaction of these fields with electrons, leads to velocity space diffusion. The stochasticity in the system is also verified by estimating the Lypunov exponent by slightly varying the laser beam power. The energy of the accelerated electrons on account of the laser beam and plasma wave interaction has been calculated by using the distribution function. For typical laser beam and plasma parameters with wavelength (λ=1064nm), power flux (1016Wcm−2), and initial temperature (Te=2.5keV), the elevated electron temperature was found to be around 4.5keV, after passing through one wave packet.

Gyrotropic guiding-center fluid theory for the turbulent heating of magnetospheric ions in downward Birkeland current regions. II

A new fluid theory in the guiding-center and gyrotropic approximation derivable from the ensemble-averaged Vlasov-Maxwell equations that included the effect of wave-particle interactions for weakly turbulent, weakly inhomogeneous, nonuniformly magnetized plasma was recently given by Jasperse, Basu, Lund, and Bouhram [Phys. Plasmas 13, 072903 (2006)]. In that theory, the particles are transported in one spatial dimension (the distance s along the magnetic field) but the turbulence is two-dimensional. In this paper, which is intended as a sequel, the above theory is used for quasisteady conditions to find: (1) a new formula for the perpendicular ion-heating rate per unit volume Ẇi⊥(s), where Ẇi⊥(s) decreases for large s by what we call the “finite ion gyroradius effect”; and (2) a new formula for the perpendicular ion temperature at low altitudes, Ti⊥(s). Parametrized calculations for Ti⊥(s) are also given.

Gyrotropic guiding-center fluid theory for turbulent inhomogeneous magnetized plasma

In this paper, a new fluid theory is given in the guiding-center and gyrotropic approximation which is derivable from the Vlasov-Maxwell equations. The theory includes the effect of wave-particle interactions for the weakly turbulent, weakly inhomogeneous, nonuniformly magnetized plasma, and it is applicable to a variety of space and laboratory plasmas. It is assumed that the turbulence is random and electrostatic, and that the velocity-space Fokker-Planck operator can be used to calculate the correlation functions that describe the wave-particle interactions. Conservation laws are derived that relate the low-order velocity moments of the particle distributions to the turbulence. The theory is based on the work of Hubbard [Proc. R. Soc. London, Ser. A 260, 114 (1961)] and Ichimaru and Rosenbluth [Phys. Fluids 13, 2778 (1970)]. In the work presented here, the idea is proposed that the fluid equations can be solved (1) by using measurements of the turbulence to specify the electric-field fluctuations; and (2) by using measurements of the low-order velocity moments to specify the initial and boundary conditions.

A fresh look at the heating mechanisms of the solar corona

Recently, using particle-in-cell simulations, i.e. in the kinetic plasma description, Tsiklauri et al and Génot et al reported on a discovery of a new mechanism of parallel electric field generation which results in electron acceleration. In this work we show that the parallel (to the uniform unperturbed magnetic field) electric field generation can be obtained in a much simpler framework using an ideal magnetohydrodynamic (MHD) description, i.e. without resorting to complicated wave–particle interaction effects such as ion polarization drift and resulting space charge separation which seems to be an ultimate cause of the electron acceleration. In the ideal MHD the parallel (to the uniform unperturbed magnetic field) electric field appears due to fast magnetosonic waves which are generated by the interaction of weakly nonlinear Alfvén waves with transverse density inhomogeneity. Further, in the context of the coronal heating problem a new two-stage mechanism of the plasma heating is presented by putting emphasis firstly on the generation of parallel electric fields within ideal MHD description directly, rather than focusing on the enhanced dissipation mechanisms of the Alfvén waves and, secondly, dissipation of these parallel electric fields via kinetic effects. It is shown that for a single Alfvén wave harmonic with frequency ν = 7 Hz (which has longitudinal wavelength λA = 0.63 Mm for a putative Alfvén speed of 4328 km s−1), the generated parallel electric field could account for the 10% of the necessary coronal heating requirement. We conjecture that wide spectrum (10−4–103 Hz) Alfvén waves, based on an observationally constrained spectrum, could provide necessary coronal heating requirement. It is also shown that the amplitude of generated parallel electric field exceeds the Dreicer electric field by about four orders of magnitude, which implies realization of the runaway regime with the associated electron acceleration.

Effects of Wave-Particle Interactions on Double-Hump Distributions of the H + Polar Wind

A Monte Carlo simulation is used in order to study the effects of wave-particle interactions (WPI) on H+ distributions in the polar wind outflow. The simulation also considers effects of the gravity, the polarization electric field, the divergence of geomagnetic field lines and H+−O+ Coulomb collisions. The proton velocity distribution function (VDF) and the profiles of its moments (density, bulk velocity, parallel and perpendicular temperatures, heat flux…) are found for different levels of WPI, i.e., for different values of the normalized diffusion rate in the velocity space (D⊥). We find that the wave-particle interactions accelerate the polar wind and can have important effects on the double-hump H+ distribution obtained in the transition region between the collision-dominated low altitudes and the collisionless high altitude regions.

Modeling of nonlinear electron cyclotron resonance heating and current drive in a tokamak

Electron cyclotron resonance heating and current drive are modeled in tokamak geometry taking into account nonlinear wave-particle interaction and the inhomogeneity of the distribution function on magnetic surfaces. The model includes self-consistently coupled beam tracing and Monte Carlo computations of the electron distribution function. The method of Green’s function for the computation of the generated current is described. For the Axisymmetric Divertor Experiment Upgrade [Leuterer et al., Fusion Eng. Des. 53, 485 (2001)] parameters and high beam focusing, nonlinear wave-particle interaction effects appear to be important for perpendicular launch of the microwave beam and not important for oblique launches where they stay below the “threshold.” With defocusing the beam two to three times along the direction of the magnetic field nonlinear effects of wave-particle interaction start to be important also for oblique launches. The effect of decreased current in case of increasing the microwave beamwidth is demonstrated. The decrease of both power absorption and generated current around low-order rational magnetic surfaces is found. Its possible effect on the tearing mode stability index is discussed.

Comparison of the effects of wave-particle interactions and the kinetic suprathermal electron population on the acceleration of the solar wind

Kinetic effects due to wave-particle interactions and suprathermal electrons have been suggested in the literature as possible solar wind acceleration mechanisms. Ion cyclotron resonant heating, in particular, has been associated with some qualitative features observed in the solar wind. In terms of solar wind acceleration, however, it is interesting to compare the kinetic effects of suprathermal electrons with those due to the wave-particle interactions. The combined effects of the two acceleration mechanisms on the fast solar wind have been studied by Tam and Chang (1999a,b). In this study. we investigate the role of the suprathermal electron population in the acceleration of the solar wind. Our model follows the global kinetic evolution of the fast solar wind under the influence of ion cyclotron resonant heating, while taking into account Coulomb collisions, and the ambipolar electric field that is consistent with the particle distributions themselves. The kinetic effects due to the suprathermal electrons, which we define to be the tail of the electron distributions, can be included in the model as an option. By comparing the results with and without the inclusion of the suprathermal electron effects, we determine the relative importance of suprathermal electrons and wave-particle interactions in driving the solar wind. We find that although suprathermal electrons enhance the ambipolar electric potential in the solar wind considerably, their overall influence as an acceleration mechanism is relatively insignificant in a wave-driven solar wind.

A semi‐kinetic model of wave‐ion interaction in the solar corona

A semi‐kinetic model of the ions in the solar corona is presented, which includes the effects of wave‐particle interactions and Coulomb collisions. At the coronal base a spectrum of Alfvén waves is assumed. The spatiotemporal evolution of the spectrum in a 2‐D computational domain is determined, taking the absorption of the waves by the particles into account. Integration over the velocity components perpendicular to the magnetic field yields “reduced” velocity distribution functions, for which a Vlasov equation is derived and solved numerically. The results obtained for a model of the heating process in a coronal funnel and in the lower corona are presented. The calculated velocity distribution functions show distinct kinetic effects and reflect key properties of the corona as observed by SOHO.

Effect of wave‐particle interactions on ring current evolution for January 10–11, 1997: Initial results

We simulate the ring current evolution during the magnetic storm caused by Earth passage of the January 1997 magnetic cloud. Compared to previous studies, we include for the first time energy diffusion caused by wave‐particle interactions. The modeled Dst index agrees reasonably well with the measured one, corrected for magnetopause currents and currents induced in the solid Earth. We compare H+distributions calculated from our model with those measured by the HYDRA instrument on the POLAR spacecraft and find that: a) the agreement between theory and data at large Lshells (L>5.5) is very good; b) although the agreement at low Lshells is improved when scattering by EMIC waves is included, the result is not entirely satisfactory, suggesting that either transport in a more realistic magnetospheric electric field or additional loss processes should be considered.