Transport Of Energetic Particles Research Articles

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 .

Simulating energetic particle losses in JET plasmas with a reverse integration biasing scheme

An integrated energetic particle transport model has been constructed in JET plasmas constrained by experimental fast ion loss measurements. The model incorporates a synthetic fast ion loss detector identical to JET’s thin-foil Faraday cup fast ion loss detector array. The loss model combines analyses from the TRANSP and ORBIT-kick codes with enhanced features for producing the synthetic diagnostic. Extensions to the ORBIT code framework allow a full-orbit representation within the vacuum region that can map particles directly to an installed detector geometry. Since synthetic fast ion loss detectors are plagued by weak loss statistics, a novel reverse integration biasing scheme has been implemented to boost computational efficiency. The model is validated against experimental loss measurements induced by long-lived kink modes and is found to be in good agreement. This confirms the development of a fully integrated transport/loss model which can be quantitatively verified against experiment allowing for future validation and predictive studies. The model is particularly useful for more complicated plasma scenarios that involve multiple fast ion species such as JET’s 2021 DT-campaign.

Transport of Solar Energetic Particles along Stochastic Parker Spirals

Abstract It was recently shown that, owing to the turbulent nature of the solar wind, the interplanetary magnetic field lines can be well described by stochastic Parker spirals. These are realizations of Brownian diffusion on a sphere of increasing radius, superimposed on the angular drift due to the solar rotation. In this work, we present a model for the transport of solar energetic particles along stochastic Parker spirals in the inner heliosphere. The transport model is governed by a set of four stochastic differential equations for the heliographic position ( r , α = cos θ , ϕ ) of the guiding centers and the cosine of the pitch angle between the velocity vector and the Parker field. The model accounts for the role played by the combination of pitch angle scattering and magnetic focusing in the interplanetary medium. The effects of the dynamical evolution of the turbulence are included in the model by taking the field line angular diffusivity to be a function of the radial distance from the Sun. The heliolongitudinal distribution of particles propagating along stochastic Parker spirals is given by the wrapped Gaussian distribution. This angular distribution can also well be represented by the von Mises distribution that interpolates between the Gaussian distribution at small angular spread and the uniform distribution at large distances from the acceleration region of energetic particles in the aftermath of a solar eruption.

Development of a reduced model for energetic particle transport by sawteeth in tokamaks

The sawtooth instability is known for inducing transport and loss of energetic particles (EPs), and for generating seed magnetic islands that can trigger tearing modes. Both effects degrade the overall plasma performance. Several theories and numerical models have been previously developed to quantify the expected EP transport caused by sawteeth, with various degrees of sophistication to differentiate the response of EPs at different energies and on different orbits (e.g. passing vs. trapped), although the analysis is frequently limited to a single time slice during a tokamak discharge. This work describes the development and initial benchmark of a framework that enables a reduced model for EP transport by sawteeth retaining the full EP phase-space information. The model, implemented in the ORBIT hamiltonian particle-following code, can be used either as a standalone post-processor taking input data from codes such as TRANSP, or as a pre-processor to compute transport coefficients that can be fed back to TRANSP for time-dependent simulations including the effects of sawteeth on EPs. The advantage of the latter approach is that the evolution of the EP distribution can be simulated quantitatively for sawtoothing discharges, thus enabling a more accurate modeling of sources, sinks and overall transport properties of EP and thermal plasma species for comprehensive physics studies that require detailed information of the fast-ion distribution function and its evolution over time.

Avalanche transport of energetic-ions in magnetic confinement plasmas: nonlinear multiple wave-number simulation

Large burst activity, identified as toroidal Alfvén eigenmode (TAE) avalanche, occurs frequently in neutral-beam heated plasmas in National Spherical Torus Experiment (NSTX). Based on the typical experimental observation of TAE avalanche on NSTX, a self-consistent nonlinear multiple wave-number (k ∥ ≃ n/R, where n toroidal mode-number and R major radius) simulation associated with TAE avalanches is performed using the experimental parameters and profiles before the occurrence of TAE avalanche as the M3D-K input. The wave–wave nonlinear coupling among different modes and the resonant interaction between different modes and energetic-ions during TAE avalanches are identified in the nonlinear multiple wave-number simulations. The resonance overlap during the TAE avalanche is clearly observed in the simulation. It is found that the effective wave–wave coupling and a sufficiently strong drive are two important ingredients for the onset of TAE avalanches. TAE avalanche is considered to be a strongly nonlinear process and it is always accompanied by the simultaneous rapid frequency-chirping and large amplitude bursting of multiple modes and significant energetic-ion losses. The experimental phenomenon is observed on NSTX and is qualitatively reproduced by the simulation results in this work. These findings indicate that the onset of avalanche is triggered by nonlinearity of the system, and are also conducive to understanding the underlying mechanism of avalanche transport of energetic particles in the future burning plasmas, such as International Thermonuclear Experiment Reactor.

Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?

Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates.

Geometry of Magnetic Fluctuations near the Sun from the Parker Solar Probe

Abstract Solar wind magnetic fluctuations exhibit anisotropy due to the presence of a mean magnetic field in the form of the Parker spiral. Close to the Sun, direct measurements were not available until the recently launched Parker Solar Probe (PSP) mission. The nature of the anisotropy and geometry of the magnetic fluctuations play a fundamental role in dissipation processes and in the transport of energetic particles in space. Using PSP data, we present measurements of the geometry and anisotropy of the inner heliosphere magnetic fluctuations, from fluid to kinetic scales. The results are surprising and different from 1 au observations. We find that fluctuations evolve characteristically with size scale. However, unlike 1 au solar wind, at the outer scale, the fluctuations are dominated by wavevectors quasi-parallel to the local magnetic field. In the inertial range, average wavevectors become less field aligned, but still remain more field aligned than near-Earth solar wind. In the dissipation range, the wavevectors become almost perpendicular to the local magnetic field in the dissipation range, to a much higher degree than those indicated by 1 au observations. We propose that this reduced degree of anisotropy in the outer scale and inertial range is due to the nature of large-scale forcing outside the solar corona.

Perpendicular Diffusion of Energetic Particles: A Complete Analytical Theory

Abstract Over the past two decades scientists have significantly improved our understanding of the transport of energetic particles across a mean magnetic field. Due to test-particle simulations, as well as powerful nonlinear analytical tools, our understanding of this type of transport is almost complete. However, previously developed nonlinear analytical theories do not always agree perfectly with simulations. Therefore, a correction factor a 2 was incorporated into such theories with the aim to balance out inaccuracies. In this paper a new analytical theory for perpendicular transport is presented. This theory contains the previously developed unified nonlinear transport theory, the most advanced theory to date, in the limit of small Kubo number turbulence. New results have been obtained for two-dimensional turbulence. In this case, the new theory describes perpendicular diffusion as a process that is sub-diffusive while particles follow magnetic field lines. Diffusion is restored as soon as the turbulence transverse complexity becomes important. For long parallel mean-free paths, one finds that the perpendicular diffusion coefficient is a reduced field line random walk limit. For short parallel mean-free paths, on the other hand, one gets a hybrid diffusion coefficient that is a mixture of collisionless Rechester & Rosenbluth and fluid limits. Overall, the new analytical theory developed in the current paper is in agreement with heuristic arguments. Furthermore, the new theory agrees almost perfectly with previously performed test-particle simulations without the need of the aforementioned correction factor a 2 or any other free parameter.

Evidence for local particle acceleration in the first recurrent galactic cosmic ray depression observed by Solar Orbiter

Context.In mid-June 2020, the Solar Orbiter (SolO) mission reached its first perihelion at 0.51 au and started its cruise phase, with most of the in situ instruments operating continuously.Aims.We present the in situ particle measurements of the first proton event observed after the first perihelion obtained by the Energetic Particle Detector (EPD) suite on board SolO. The potential solar and interplanetary (IP) sources of these particles are investigated.Methods.Ion observations from ∼20 keV to ∼1 MeV are combined with available solar wind data from the Radio and Plasma Waves (RPW) instrument and magnetic field data from the magnetometer on board SolO to evaluate the energetic particle transport conditions and infer the possible acceleration mechanisms through which particles gain energy. We compare > 17–20 MeV ion count rate measurements for two solar rotations, along with the solar wind plasma data available from the Solar Wind Analyser (SWA) and RPW instruments, in order to infer the origin of the observed galactic cosmic ray (GCR) depressions.Results.The lack of an observed electron event and of velocity dispersion at various low-energy ion channels and the observed IP structure indicate a local IP source for the low-energy particles. From the analysis of the anisotropy of particle intensities, we conclude that the low-energy ions were most likely accelerated via a local second-orderFermiprocess. The observed GCR decrease on 19 June, together with the 51.8–1034.0 keV nuc−1ion enhancement, was due to a solar wind stream interaction region (SIR). The observation of a similar GCR decrease in the next solar rotation favours this interpretation and constitutes the first observation of a recurrent GCR decrease by SolO. The analysis of the recurrence times of this SIR suggests that it is the same SIR responsible for the4He events previously measured in April and May. Finally, we point out that an IP structure more complex than a common SIR cannot be discarded, mainly due to the lack of solar wind temperature measurements and the lack of a higher cadence of solar wind velocity observations.

On the Turbulent Reduction of Drifts for Solar Energetic Particles

Abstract Particle drifts perpendicular to the background magnetic field have been proposed by some authors as an explanation for the very efficient perpendicular transport of solar energetic particles (SEPs). This process, however, competes with perpendicular diffusion caused by magnetic turbulence, which can also disrupt the drift patterns and reduce the magnitude of drift effects. The latter phenomenon is well known in cosmic-ray studies, but not yet considered in SEP models. Additionally, SEP models that do not include drifts, especially for electrons, use turbulent drift reduction as a justification of this omission, without critically evaluating or testing this assumption. This article presents the first theoretical step for a theory of drift suppression in SEP transport. This is done by deriving the turbulence-dependent drift reduction function with a pitch-angle dependence, as is applicable for anisotropic particle distributions, and by investigating to what extent drifts will be reduced in the inner heliosphere for realistic turbulence conditions and different pitch-angle dependencies of the perpendicular diffusion coefficient. The influence of the derived turbulent drift reduction factors on the transport of SEPs are tested, using a state-of-the-art SEP transport code, for several expressions of theoretically derived perpendicular diffusion coefficients. It is found, for realistic turbulence conditions in the inner heliosphere, that cross-field diffusion will have the largest influence on the perpendicular transport of SEPs, as opposed to particle drifts.

Cosmic-Ray Transport in Heliospheric Magnetic Structures. III. Implications of Solar Magnetograms for the Drifts of Cosmic Rays

Abstract The transport of energetic particles in the heliosphere is reviewed regarding the treatment of their drifts over an entire solar cycle including the periods around solar maximum, when the tilt angles of the heliospheric current sheet increase to large values and the sign of the magnetic polarity changes. While gradient and curvature drifts are well-established elements of the propagation of cosmic rays in the heliospheric magnetic field, their perturbation by the solar-activity-induced large-scale distortions of dipole-like field configurations and by magnetic turbulence is an open problem. Various empirical or phenomenological approaches have been suggested, but either lack a theory-based motivation or have been shown to be incompatible with measurements. We propose a new approach of more closely investigating solar magnetograms obtained from GONG maps, leading to a new definition of (i) tilt angles that may exceed those provided by the Wilcox Solar Observatory during high activity and of (ii) a “noninteger sign” that can be used to reduce the drifts during these periods as well as to provide a refinement of the magnetic field polarity. The change of sign from A < 0 to A > 0 of solar cycle 24 can be in this way localized to occur between Carrington Rotations 2139 and 2140 in mid 2013. This treatment is fully consistent in the sense that the transport modeling uses the same input data to formulate the boundary conditions at the heliobase as do the magnetohydrodynamic models of the solar wind and the embedded heliospheric magnetic field that exploit solar magnetograms as inner boundary conditions.

INCREASE: An updated model suite to study the INfluence of Cosmic Rays on Exoplanetary AtmoSpherEs

AbstractExoplanets are as diverse as they are fascinating. They vary from ultrahot Jupiter‐like low‐density planets to presumed gas‐ice‐rock mixture worlds such as GJ 1214b or worlds as LHS 1140b, which features twice the Earth's bulk density. Regarding the great diversity of exoplanetary atmospheres, much remains to be explored. For a few selected objects such as GJ1214b, Proxima Centauri b, and the TRAPPIST‐1 planets, the first observations of their atmospheres have already been achieved or are expected in the near future with the launch of the James Webb Space Telescope envisaged in October 2021. However, in order to interpret these observations, model studies of planetary atmospheres that account for various processes—such as atmospheric escape, outgassing, climate, photochemistry, as well as the physics of air showers and the transport of stellar energetic particles and galactic cosmic rays through the stellar astrospheres and planetary magnetic fields—are necessary. Here, we present our model suite INCREASE, a planned extension of the model suite discussed in Herbst, Grenfell, et al. (2019).

Modeling of energetic particle transport in optimized stellarators

Nine stellarator configurations, three quasiaxisymmetric, three quasihelically symmetric and three non-quasisymmetric are scaled to ARIES-CS size and analyzed for energetic particle content. The best performing configurations with regard to energetic particle confinement also perform the best on the neoclassical Γc metric, which attempts to align contours of the second adiabatic invariant with flux surfaces. Quasisymmetric configurations that simultaneously perform well on Γc and quasisymmetry have the best overall confinement, with collisional losses under 3%, approaching the performance of ITER with ferritic inserts.

Nonlinear dynamics and transport driven by energetic particle instabilities using a gyro-Landau closure model * *This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish

Energetic particle (EP) destabilized Alfvén eigenmode (AE) instabilities are simulated for a DIII-D experimental case with a pulsed neutral beam using a gyro-Landau moments model which introduces EP phase-mixing effects through closure relations. This provides a computationally efficient reduced model which is applied here in the nonlinear regime over timescales that would be difficult to address with more complete models. The long timescale nonlinear evolution and related collective transport losses are examined including the effects of zonal flow/current generation, nonlinear energy cascades, and EP profile flattening. The model predicts frequencies and mode structures that are consistent with experimental observations. These calculations address issues that have not been considered in previous modelling: the EP critical gradient profile evolution in the presence of zonal flows/currents, and the dynamical nature of the saturated state. A strong level of intermittency is present in the predicted instability-driven transport; this is connected to the zonal flow growth and decay cycles and nonlinear energy transfers. Simulation of intermittent AE-enhanced EP transport will be an important issue for the protection of plasma facing components in the next generation of fusion devices.

Testing the DIII-D co/counter off-axis neutral beam injected power and ability to balance injected torque

DIII-D has undergone a major upgrade and successfully injected high power off-axis neutral beams (∼4 MW) in both co-current and counter-current directions. This capability of high power co/counter steerable off-axis neutral beams on a major tokamak opens a unique parameter space of broad pressure and current profiles for high beta steady-state advanced tokamak (AT) scenarios, while retaining the ability to balance the injected torque for low rotation studies. This co/counter off-axis neutral beam capability is being used to validate physics-based energetic particle and thermal transport models for designing next-step facilities based on the steady-state AT approach. This paper reports on the critical evaluation of the transmitted power and energetic ion population produced by this heating and current drive system, which is assessed through visible imaging, neutron measurements and rotation profile measurements at balanced torque. Minimal losses of neutral beam power have been achieved by optimizing the strongly focused ion sources required to pass through the aperture. Tilting of the ion source has been guided by fast visible imaging and resulted in neutral beam injection along the design centerline with empirical characterization of each beam’s divergence derived from the imaging data and used in the NUBEAM description of the beam injection. Through exclusive power injection of each neutral beam into MHD quiescent plasmas across a range of neutral beam voltage, perveance and plasma current we conclude that a modest reduction (∼10%–15%) of transmitted power compared to on-axis, standard focus has been incurred. We report corrections that more accurately represent the injected power. Good ability to balance the neutral beam torque has been demonstrated by injecting the new off-axis counter injecting beam against the existing off-axis co-injected beam in 2.0 T, 1.0 MA, MHD quiescent L-mode plasmas. The torque balance studies verify the ability to operate with balanced injection, which is critical for achieving low torque and low rotation operation for physics studies and in ITER demonstration discharges.