Transport Of Energetic Particles Research Articles

Anisotropic Magnetic Turbulence in the Inner Heliosphere—Radial Evolution of Distributions Observed by Parker Solar Probe

Observations from Parker Solar Probe’s first five orbits are used to investigate the helioradial evolution of probability density functions (pdfs) of fluctuations of magnetic-field components between ∼28 and 200 R ⊙. Transformation of the magnetic-field vector to a local mean-field coordinate system permits examination of anisotropy relative to the mean magnetic-field direction. Attention is given to effects of averaging-interval size. It is found that pdfs of the perpendicular fluctuations are well approximated by a Gaussian function, with the parallel fluctuations less so: kurtoses of the latter are generally larger than 10, and their pdfs indicate increasing skewness with decreasing distance r from the Sun, with the latter observation possibly explained by the increasing Alfvénicity of the fluctuations. The ratio of perpendicular to parallel variances is greater than unity; this variance anisotropy becomes stronger with decreasing r. The ratio of the total rms fluctuation strength to the mean-field magnitude decreases with decreasing r, with a value ∼0.8 near 1 au and ∼0.5 at 0.14 au; the ratio is well approximated by an r 1/4 power law. These findings improve our understanding of the radial evolution of turbulence in the solar wind, and have implications for related phenomena such as energetic-particle transport in the inner heliosphere.

Interplanetary mesoscale observatory (InterMeso): A mission to untangle dynamic mesoscale structures throughout the heliosphere

Mesoscale dynamics are a fundamental process in space physics, but fall within an observational gap of current and planned missions. Particularly in the solar wind, measurements at the mesoscales (100s RE to a few degrees heliographic longitude at 1 au) are crucial for understanding the connection between the corona and an observer anywhere within the heliosphere. Mesoscale dynamics may also be key to revealing the currently unresolved physics regulating particle acceleration and transport, magnetic field topology, and the causes of variability in the composition and acceleration of solar wind plasma. Studies using single-point observations do not allow for investigations into mesoscale solar wind dynamics and plasma variability, nor do they allow for the exploration of the sub-structuring of large-scale solar wind structures like coronal mass ejections (CMEs), co-rotating/stream interaction regions (CIR/SIRs), and the heliospheric plasma sheet. To address this fundamental gap in our knowledge of the heliosphere at these scales, the Interplanetary Mesoscale Observatory (InterMeso) concept employs a multi-point approach using four identical spacecraft in Earth-trailing orbits near 1 au. Varying drift speeds of the InterMeso spacecraft enable the mission to span a range of mesoscale separations in the solar wind, achieving significant and innovative science return. Simultaneous, longitudinally-separated measurements of structures co-rotating over the spacecraft also allow for disambiguation of spatiotemporal variability, tracking of the evolution of solar wind structures, and determination of how the transport of energetic particles is impacted by these variabilities.

Multispacecraft Analysis of the Properties of Magnetohydrodynamic Fluctuations in Sub-Alfvénic Solar Wind Turbulence at 1 au

We present observations of three-dimensional magnetic power spectra in wavevector space to investigate the anisotropy and scalings of sub-Alfvénic solar wind turbulence at magnetohydrodynamic (MHD) scale using the Magnetospheric Multiscale spacecraft. The magnetic power distributions are organized in a new coordinate determined by wavevectors () and background magnetic field () in Fourier space. This study utilizes two approaches to determine wavevectors: the singular value decomposition method and multispacecraft timing analysis. The combination of the two methods allows an examination of the properties of magnetic field fluctuations in terms of mode compositions without any spatiotemporal hypothesis. Observations show that fluctuations (δ B ⊥1) in the direction perpendicular to and prominently cascade perpendicular to , and such anisotropy increases with wavenumbers. The reduced power spectra of δ B ⊥1 follow Goldreich–Sridhar scalings: and . In contrast, fluctuations within the plane show isotropic behaviors: perpendicular power distributions are approximately the same as parallel distributions. The reduced power spectra of fluctuations within the plane follow the scalings and . Comparing frequency–wavevector spectra with theoretical dispersion relations of MHD modes, we find that δ B ⊥1 are probably associated with Alfvén modes. On the other hand, magnetic field fluctuations within the plane more likely originate from fast modes based on their isotropic behaviors. The observations of anisotropy and scalings of different magnetic field components are consistent with the predictions of current compressible MHD theory. Moreover, for the Alfvénic component, the ratio of cascading time to the wave period is found to be a factor of a few, consistent with critical balance in the strong turbulence regime. These results are valuable for further studies of energy compositions of plasma turbulence and their effects on energetic particle transport.

Stellar Energetic Particle Transport in the Turbulent and CME-disrupted Stellar Wind of AU Microscopii

Energetic particles emitted by active stars are likely to propagate in astrospheric magnetized plasma and disrupted by the prior passage of energetic coronal mass ejections (CMEs). We carried out test-particle simulations of ∼GeV protons produced at a variety of distances from the M1Ve star AU Microscopii by coronal flares or traveling shocks. Particles are propagated within a large-scale quiescent three-dimensional magnetic field and stellar wind reconstructed from measured magnetograms, and within the same stellar environment following the passage of a 1036 erg kinetic energy CME. In both cases, magnetic fluctuations with an isotropic power spectrum are overlayed onto the large-scale stellar magnetic field and particle propagation out to the two innnermost confirmed planets is examined. In the quiescent case, the magnetic field concentrates the particles into two regions near the ecliptic plane. After the passage of the CME, the closed field lines remain inflated and the reshuffled magnetic field remains highly compressed, shrinking the scattering mean free path of the particles. In the direction of propagation of the CME lobes the subsequent energetic particle (EP) flux is suppressed. Even for a CME front propagating out of the ecliptic plane, the EP flux along the planetary orbits highly fluctuates and peaks at ∼2–3 orders of magnitude higher than the average solar value at Earth, both in the quiescent and the post-CME cases.

Numerical studies on saturated kink and sawtooth induced fast ion transport in JET ITER-like plasmas

This presentation examines the energetic particle transport induced by saturated kink modes and sawtooth crashes in JET deuterium plasmas. It is known that kink mode-resonant transport and phase-space redistribution from sawtooth crashes can drive strong fast ion transport with dependencies on particle pitch and energy. Measurements with JET’s Faraday cup fast ion loss detector array have shown that the internal kink growth phase preceding sawtooth crashes produces substantial fast ion losses. This report will numerically investigate the dominant energetic particle transport mechanism with a detailed examination of the fast ion phase-space dependencies, resonances, orbit topology changes, induced losses, and redistribution associated with the long-lived, resonant, kink mode and non-resonant sawtooth crash. The ORBIT-kick model forms the basis of the transport studies with realistic fast ion distributions produced from TRANSP. A recently created reduced model for sawtooth induced transport is used while the saturated kink modes are modeled with ideal magnetohydrodynamic codes. The simulations were further validated against experiment with a newly developed synthetic Faraday cup fast ion loss detector in addition to scintillator probe and neutron measurements.

Studies of energetic particle transport induced by multiple Alfvén eigenmodes using neutron and escaping energetic particle diagnostics in Large Helical Device deuterium plasmas

Studies of energetic particle transport due to energetic-particle-driven Alfvénic instability have progressed using neutron and energetic particle diagnostics in Large Helical Device deuterium plasmas. Alfvénic instability excited by injecting an intensive neutral beam was observed by a magnetic probe and a far-infrared laser interferometer. The interferometer showed Alfvénic instability composed of three modes that existed from the core to the edge of the plasma. A comparison between the observed frequency and shear Alfvén spectra suggested that the mode activity was most likely classified as an Alfvénic avalanche. A neutron fluctuation detector and a fast ion loss detector indicated that Alfvénic instability induced transport and loss of co-going transit energetic ions. The dependence of the drop rate of the neutron signal on the Alfvénic instability amplitude showed that significant transport occurred. Significant transport might be induced by the large amplitude and radially extended multiple modes, as well as a large deviation of the energetic ion orbit from the flux surface.

The Ratio of Perpendicular and Parallel Diffusion Coefficients of Low-energy Particles in Turbulent Space Plasmas

Recently an improved nonlinear theory for the transport of energetic particles across a mean magnetic field has been developed. The latter theory is called the field line–particle decorrelation theory and is the first analytical theory that agrees with test-particle simulations without the need of a correction parameter, nor does the theory contain any other free parameter. In the current paper we derive analytical forms for the ratio of perpendicular and parallel spatial diffusion coefficients κ ⊥/κ ∥ of low-energy particles. In the considered limit the latter ratio is constant meaning that it does not depend on particle energy or rigidity. It is shown that the ratio always has the form if a two-dimensional turbulence model is employed. Furthermore, the parameter a 2 depends only on the shape of the turbulence spectrum but not on the magnetic fields. The obtained results can be important for a variety of applications such as studies of solar modulation and diffusive shock acceleration.

Energetic Particle Perpendicular Diffusion: Simulations and Theory in Noisy Reduced Magnetohydrodynamic Turbulence

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 has been a prominent perpendicular diffusion theory. A recent version of this theory, based on the 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 generality of the improved theory by applying it to the noisy reduced magnetohydrodynamic (NRMHD) turbulence model, determining perpendicular diffusion coefficients that are compared with those from the field line random walk (FLRW) and unified nonlinear (UNLT) theories and our test particle simulations. The synthetic NRMHD turbulence model creates special conditions for energetic particle transport, with no magnetic fluctuations at higher parallel wavenumbers so there is no resonant parallel scattering if the particle Larmor radius R L is even slightly smaller than the minimum resonant scale. This leads to nonmonotonic variation in the parallel mean free path λ ∥ with R L. Among the theories considered, only RBD/BC matches simulations within a factor of 2 over the range of parameters considered. This accuracy is obtained even though the theory depends on λ ∥ and has no explicit dependence on R L. In addition, the UNLT theory often provides accurate results, and even the FLRW limit provides a very simple and reasonable approximation in many cases.

An 18.3 MJ charging and discharging pulsed power supply system for the Space Plasma Environment Research Facility (SPERF): The integrated control subsystem.

The Space Plasma Environment Research Facility uses a coil system with the corresponding pulsed power supply (PPS) system to generate a very flexible magnetosphere-like magnetic configuration. Its purpose is to investigate the 3D asymmetric reconnection and the processes of trapping, acceleration, and transport of energetic charged particles restrained in a dipole magnetic field configuration, as well as the physical mechanism of the dipolarization front in the magnetotail. The control and monitoring function of the PPS system is realized by the integrated control subsystem, which adopts a two-layer network structure of the control layer and device layer and is developed based on the Experimental Physics and Industrial Control System framework. The control layer includes a remote control system that consists of an engineer station and an operator station and the data storage system. Both the engineer station and operator station are developed by Control System Studio. The data storage system is based on the combination of the Hierarchical Data Format 5 database and MySQL database, and the data management software of the data storage system is developed based on LabVIEW. The synchronous trigger device, the safety interlocking device, the local controller of each set of PPS, and the module controller of each discharge module are the device layer. Their hardware is designed and developed based on the Field Programmable Gate Array, and their software is based on the Quartus II platform and programmed with the Verilog Hardware Description Language language. The function of the integrated control subsystem is verified by the discharge test of the PPS system.

ICARUS, a new inner heliospheric model with a flexible grid

Context. Simulating the propagation and predicting the arrival time of coronal mass ejections (CMEs) in the inner heliosphere with a full three-dimensional (3D) magnetohydrodynamic (MHD) propagation model requires a significant amount of computational time. For CME forecasting purposes, multiple runs may be required for different reasons such as ensemble modeling (uncertainty on input parameters) and error propagation. Moreover, higher resolution runs may be necessary, which also requires more CPU time, for example for the prediction of solar energetic particle acceleration and transport or in the framework of more in-depth studies about CME erosion and/or deformation during its evolution. Aims. In this paper we present ICARUS, a new inner heliospheric model for the simulation of a steady background solar wind and the propagation and evolution of superposed CMEs. This novel model has been implemented within the MPI-AMRVAC framework which enables the use of stretched grids and solution adaptive mesh refinement (AMR). The usefulness and efficiency (speed-up) of these advanced features are explored. In particular, we model a typical solar wind with ICARUS and then launch a simple cone CME and follow its evolution. We focus on the effect of radial grid stretching and two specific methods or criteria to trigger solution AMR on this typical simulation run. Methods. For the solar background wind simulation run, we limited the mesh refinement to the area(s) of interest, in this case a co-rotating interaction region (CIR). For the CME evolution run, on the other hand, we apply AMR where the CME is located by the use of a tracing function. As such, the grid is coarsened again after the CME has passed. Results. The implemented AMR is flexible and only refines the mesh in a particular sector of the computational domain, for example around the Earth or a single CIR, and/or for a particular feature such as CIR or CME shocks. Radial grid stretching alone yields speed-ups of up to 4 and more, depending on the resolution. Combined with solution adaptive mesh refinement, the speed-ups can be much larger depending on the complexity of the simulation (e.g., number of CIRs in the background wind, number of CMEs) and on the chosen AMR criteria, thresholds and the number of refinement levels. Conclusions. The ICARUS model implemented in the MPI-AMRVAC framework is a new inner heliospheric 3D MHD model that uses grid stretching as well as AMR techniques. The flexibility in the grid and its resolution allows an optimization of the computational time required for CME propagation simulations for both scientific and forecasting purposes.

Experimental evidence of nonlinear avalanche dynamics of energetic particle modes

Recent observations in HL-2A tokamak give new experimental evidences of energetic particle mode (EPM) avalanche. In a strong EPM burst, the mode structure propagates radially outward within two hundred Alfvén time, while the frequency of the dominant mode changes self-consistently to maximize wave-particle power exchange and mode growth. This suggests that significant energetic particle transport occurs in this avalanche phase, in agreement with theoretical framework of EPM convective amplification. A simplified relay runner model yields satisfactory interpretations of the measurements. The results can help understanding the nonlinear dynamics of energetic particle driven modes in future burning plasmas, such as ITER.

A Comparison with Theory of Computation and Estimation of Pitch-Angle Diffusion Coefficients from Simulations in Noisy Reduced Magnetohydrodynamic Turbulence

The transport of energetic charged particles in turbulent magnetic fields is a topic of interest in various astrophysical and laboratory plasma contexts. In order to estimate the mean free path λ∥ of a particle in the direction parallel to the mean magnetic field, one can use theoretical expressions that include the pitch-angle diffusion coefficient Dμμ. In this work we evaluate theories for Dμμ in the context of the noisy reduced magnetohydrodynamic (NRMHD) model where turbulent fluctuations are absent at large parallel wavenumbers. For most turbulence models, the standard quasilinear theory predicts zero pitch-angle diffusion only for particles with a 90◦ pitch angle, but for NRMHD a range of pitch angles is affected, leading to infinite λ∥. We examine two theories that include resonance broadening which yield finite λ∥ and compare them with test-particle computer simulations in which the parallel mean free path can be readily obtained. We find that both theories are quite accurate in some regions of the parameter space considered, but neither is particularly good when the particle Larmor radius RL becomes much smaller than the quasilinear resonance limit.

Estimating Inner Magnetospheric Radial Diffusion Using a Hybrid-Vlasov Simulation

Radial diffusion coefficients quantify non-adiabatic transport of energetic particles by electromagnetic field fluctuations in planetary radiation belts. Theoretically, radial diffusion occurs for an ensemble of particles that experience irreversible violation of their third adiabatic invariant, which is equivalent to a change in their Roederer L* parameter. Thus, the Roederer L* coordinate is the fundamental quantity from which radial diffusion coefficients can be computed. In this study, we present a methodology to calculate the Lagrangian derivative of L* from global magnetospheric simulations, and test it with an application to Vlasiator, a hybrid-Vlasov model of near-Earth space. We use a Hamiltonian formalism for particles confined to closed drift shells with conserved first and second adiabatic invariants to compute changes in the guiding center drift paths due to electric and magnetic field fluctuations. We investigate the feasibility of this methodology by computing the time derivative of L* for an equatorial ultrarelativistic electron population travelling along four guiding center drift paths in the outer radiation belt during a 5 minute portion of a Vlasiator simulation. Radial diffusion in this simulation is primarily driven by ultralow frequency waves in the Pc3 range (10–45 s period range) that are generated in the foreshock and transmitted through the magnetopause to the outer radiation belt environment. Our results show that an alternative methodology to compute detailed radial diffusion transport is now available and could form the basis for comparison studies between numerical and observational measurements of radial transport in the Earth’s radiation belts.

Regulation of Alfvén Eigenmodes by Microturbulence in Fusion Plasmas.

Global gyrokinetic simulations of mesoscale reversed shear Alfven eigenmodes (RSAE) excited by energetic particles (EP) in fusion plasmas find that RSAE amplitude and EP transport are much higher than experimental levels at nonlinear saturation, but quickly diminish to very low levels after the saturation if background microturbulence is artificially suppressed. In contrast, in simulations coupling micro-meso scales, the RSAE amplitude and EP transport decrease drastically at the initial saturation but later increases to the experimental levels in the quasisteady state with bursty dynamics due to regulation by thermal ion temperature gradient (ITG) microturbulence. The quasisteady state EP transport is larger for a stronger microturbulence. The RSAE amplitude in the quasisteady state ITG-RSAE turbulence from gyrokinetic simulations, for the first time, agrees very well with experimental measurements.

Prediction of the energetic particle redistribution by an improved critical gradient model and analysis of the transport threshold

Based on the theory of critical gradient model (CGM) and following the simulation method proposed by Waltz et al. [Nucl. Fusion 55, 123012 (2015)], a combination of TGLFEP and EPtran code is employed to predict the energetic particle (EP) transport induced by Alfvén eigenmodes (AEs). To be consistent with the experiment, recent improvements to the simulation method include consideration of threshold evolution and orbit loss due to finite orbit width. The revised CGM is applied to simulate two DIII-D experimental discharges (#142111 and #153071). It well reproduces the experimental profiles with multiple unstable AEs and large-scale EP transport. Discharge #142111 had previously been simulated using a nonlinear MHD-kinetic code MEGA [Todo et al., Nucl. Fusion 55, 073020 (2015)] with a transport mechanism based on stochasticity induced by overlapping AE. By comparing the simulated EP profiles, we find that the AE transport threshold is approximated by both the MEGA nonlinear stability threshold and the proposed CGM threshold (error <5% for single n and <17% for multiple n simulation). Both of them are larger than the linear stability threshold of the most unstable AE mode by a quantity of the order of the flux needed to sustain EP transport by the background turbulence. We have also applied the improved CGM to simulate the α particle redistribution for a China Fusion Engineering Test Reactor steady state scenario. Because of the clear separation between the AE unstable region and the loss cone, only a moderate α particle loss of ∼9.6% is predicted.

Observation-based modelling of the energetic storm particle event of 14 July 2012

Aims. We model the energetic storm particle (ESP) event of 14 July 2012 using the energetic particle acceleration and transport model named ‘PArticle Radiation Asset Directed at Interplanetary Space Exploration’ (PARADISE), together with the solar wind and coronal mass ejection (CME) model named ‘EUropean Heliospheric FORcasting Information Asset’ (EUHFORIA). The simulation results illustrate both the capabilities and limitations of the utilised models. We show that the models capture some essential structural features of the ESP event; however, for some aspects the simulations and observations diverge. We describe and, to some extent, assess the sources of errors in the modelling chain of EUHFORIA and PARADISE and discuss how they may be mitigated in the future. Methods. The PARADISE model computes energetic particle distributions in the heliosphere by solving the focused transport equation in a stochastic manner. This is done using a background solar wind configuration generated by the ideal magnetohydrodynamic module of EUHFORIA. The CME generating the ESP event is simulated by using the spheromak model of EUHFORIA, which approximates the CME’s flux rope as a linear force-free spheroidal magnetic field. In addition, a tool was developed to trace CME-driven shock waves in the EUHFORIA simulation domain. This tool is used in PARADISE to (i) inject 50 keV protons continuously at the CME-driven shock and (ii) include a foreshock and a sheath region, in which the energetic particle parallel mean free path, λ∥, decreases towards the shock wave. The value of λ∥ at the shock wave is estimated from in situ observations of the ESP event. Results. For energies below ∼1 MeV, the simulation results agree well with both the upstream and downstream components of the ESP event observed by the Advanced Composition Explorer. This suggests that these low-energy protons are mainly the result of interplanetary particle acceleration. In the downstream region, the sharp drop in the energetic particle intensities is reproduced at the entry into the following magnetic cloud, illustrating the importance of a magnetised CME model.

A Multi-Event Study of Early-Stage SEP Acceleration by CME-Driven Shocks—Sun to 1 AU

The solar corona between below 10 solar radii is an important region for early acceleration and transport of solar energetic particles (SEPs) by coronal mass ejection-driven shock waves. There, these waves propagate into a highly variable dynamic medium with steep gradients and rapidly expanding coronal magnetic fields, which modulates the particle acceleration near the shock/wave surfaces, and the way SEPs spread into the heliosphere. We present a study modeling the acceleration of SEPs in global coronal shock events in the corona, as well as their transport to 1 au, based on telescopic observations coupled with dynamic physical models. As part of the project Solar Particle Radiation Environment Analysis and Forecasting—Acceleration and Scattering Transport (SPREAdFAST), we model the interaction of observed off-limb coronal bright fronts (CBF) with the coronal plasma from synoptic magnetohydrodynamic (MHD) simulations. We then simulate the SEP acceleration in analytical diffusive shock acceleration (DSA) model. The simulated fluxes are used as time-dependent inner boundary conditions for modeling the particle transport to 1 au. Resulting flux time series are compared with 1 au observations for validation. We summarize our findings and present implications for nowcasting SEP acceleration and heliospheric connectivity.

Recent progress in the interaction between energetic particles and tearing modes.

The dynamics of energetic particles and tearing modes and the interactions between them are of great significance for magnetically confined fusion plasmas. In this review, we focus on these issues in the context of tokamak plasmas. The interaction between energetic particles and tearing modes is considered from two perspectives: (i) the influence of energetic particles on tearing modes and (ii) the transport of energetic particles by tearing modes. The influence of energetic particles on tearing modes is described on the basis of a general dispersion relation for tearing modes. The effects of energetic particles are considered separately in the outer region and the island region of a tearing mode. The physics mainly results from the modification of the perturbed parallel current by energetic particles without wave-particle resonance. In addition, the resonance between energetic particles and tearing modes is also reviewed. For the transport of energetic particles, transport of both circulating and trapped energetic particles by tearing mode is reviewed. Our descriptions of physical phenomena here are based on an analytical approach, while the experiments and simulations are used to illustrate and confirm our results. Finally, a number of open issues are discussed.

One dimensional reduced model for ITER relevant energetic particle transport

We set up a mapping procedure able to translate the evolution of the radial profile of fast ions, interacting with toroidal Alfvén Eigenmodes, into the dynamics of an equivalent one-dimensional bump-on-tail system. We apply this mapping technique to reproduce the relevant ITER simulations, which clearly outline deviations from the diffusive quasi-linear (QL) model. Our analysis demonstrates the capability of the one-dimensional beam-plasma dynamics to predict the relevant features of the non-linear hybrid LIGKA/HAGIS simulations. In particular, we clearly identify how the deviation from the QL evolutive profiles is due to the presence of avalanche processes. A detailed analysis regarding the reduced dimensionality is also addressed, by means of phase-space slicing based on constants of motion. In the conclusions, we outline the main criticalities and outcomes of the procedure, which must be satisfactorily addressed to make quantitative predictions on the observed outgoing fluxes in a Tokamak device.

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with energetic particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs’ non-perturbative effects. It is found that the MSSB properties are featured by a finite radial wave phase velocity, and the linear mode structure can be well described by an analytical complex Gaussian expression with complex parameters σ and s 0, where s is the normalized radial coordinate. The mode structure is distorted in opposite manners when the EP drive shifted from one side of to the other side, and specifically, a non-zero average radial wave number 〈k s 〉 with opposite signs is generated. The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport. The parallel velocity of EPs is generated in opposite directions, due to different values of the average radial wave number 〈k s 〉, corresponding to different initial EP density profiles with EP drive shifted away from the .