Impulsive Solar Energetic Particle Events: Extreme-Ultraviolet Waves and Jets

Impulsive solar energetic particle (ISEP) events show peculiar elemental composition, with enhanced 3He and heavy-ion abundances, markedly different from our Solar System composition. Furthermore, the events are characterized by a wide variety of energy spectral shapes from power laws to rounded spectra toward the low energies. Solar sources of the events have been firmly associated with coronal jets. Surprisingly, new observations have shown that events are often accompanied by so-called extreme-ultraviolet (EUV) coronal waves–a large-scale phenomenon compared to jets. This paper outlines the current understanding of the linkage of EUV waves with jets and energetic ions in ISEP events.

Alfvén cascade eigenmodes above the TAE-frequency and localization of Alfvén modes in D- 3 He plasmas on JET

Various types of Alfvén Eigenmodes (AEs) have been destabilized by fast ions over a broad frequency range from ~80 kHz to ~700 kHz in a series of JET experiments in mixed D-3He plasmas heated with the three-ion ICRF scenario [M. Nocente et al., Nucl. Fusion 60, 124006 (2020)]. In this paper, we identify the radial localization of AEs using an X-mode reflectometer, a multiline interferometer and soft X-ray diagnostics. The analysis is focused on the most representative example of these measurements in JET pulse #95691, where two different types of Alfvén cascade (AC) eigenmodes were observed. These modes originate from the presence of a local minimum of the safety factor qmin. In addition to ACs with frequencies below the frequency of toroidal Alfvén eigenmodes (TAEs), ACs with frequencies above the TAE frequency were destabilized by energetic ions. Both low- (f ≈80-180 kHz) and high-frequency (f ≈ 330-450 kHz) ACs were localized in the central regions of the plasma. The characteristics of the high-frequency ACs are investigated in detail numerically using HELENA, CSCAS and MISHKA codes. The resonant conditions for the mode excitation are found to be determined by passing ions of rather high energy of several hundred keV and similar to those established in JT-60U with negative-ion-based NBI [M. Takechi et al., Phys. Plasmas 12, 082509 (2005)]. The computed radial mode structure is found to be consistent with the experimental measurements. In contrast to low-frequency ACs observed most often, the frequency of the high-frequency ACs decreases with time as the value of qmin decreases. This feature is in a qualitative agreement with the analytical model of the high-frequency ACs in [B.N. Breizman et al., Phys. Plasmas 10 3649 (2003)]. The high-frequency AC could be highly relevant for future ITER and fusion reactor plasmas dominated by ~ MeV energetic ions, including a significant population of passing fast ions.

Theoretical studies of low-frequency Alfvén modes in tokamak plasmas

Linear wave properties of the low-frequency Alfvén modes (LFAMs) observed in the DIII-D tokamak experiments with reversed magnetic shear [Nucl. Fusion 61, 016029 (2021)] are theoretically studied and delineated based on the general fishbone-like dispersion relation. By adopting the representative experimental equilibrium parameters, it is found that, in the absence of energetic ions, the LFAM is a kinetic ballooning mode instability of reactive-type with a dominant Alfvénic polarization. More specifically, due to diamagnetic and trapped particle effects, the LFAM can be coupled with the beta-induced Alfvén-acoustic mode in the low-frequency region (frequency much less than the thermal-ion transit and/or bounce frequency); or with the beta-induced Alfvén eigenmode in the high frequency region (frequency higher than or comparable to the thermal-ion transit frequency); resulting in reactive-type instabilities. Moreover, the ‘Christmas light’ and ‘mountain peak’ spectral patterns of LFAMs as well as the dependence of instability drive on the electron temperature observed in the experiments can be theoretically interpreted by varying the relevant physical parameters. Conditions when dissipative-type instabilities may set in are also discussed.

Interaction between energetic-ions and internal kink modes in a weak shear tokamak plasma

Based on the conventional tokamak HL-2A-like parameters and profiles, the linear properties and the nonlinear dynamics of non-resonant kink mode (NRK) and non-resonant fishbone instability (NRFB) in reversed shear tokamak plasmas are investigated by using the global hybrid kinetic-magnetohydrodynamic (MHD) nonlinear code M3D-K. This work mainly focuses on the effect of passing energetic-ions on the NRK and NRFB instabilities, which is different from the previous works. It is demonstrated that the NRFB can be destabilized by the passing energetic-ions when the energetic-ion beta $\beta_h$ exceeds a critical value. The transition from NRK to NRFB occurs when the energetic-ion beta $\beta_h$ increases to above a critical value. The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied at $\omega_t+\omega_p\approx\omega$, where $\omega_t$ is the toroidal motion frequency, $\omega_p$ is the poloidal motion frequency and $\omega$ is the mode frequency. The nonlinear evolutions of NRFB's mode structures and Poincar\'{e} plots are also analyzed in this work and it is found that the NRFB can induce evident energetic-ion loss/redistribution, which can degrade the performance of the plasmas. These findings are conducive to understanding the mechanisms of NRFB-induced energetic-ion loss/redistribution through nonlinear wave-particle interaction.

Hybrid simulations of beta-induced Alfvén eigenmode with reversed safety factor profile

Based on the experimental parameters in HL-2A tokamak, hybrid simulations have been carried out to investigate the linear stability and nonlinear dynamics of BAE. It is found that the (m/n=3/2) beta-incuced Alfvén eigenmode (BAE) is excited by co-passing energetic ions with qmin=1.5 in linear simulation, and the mode frequency is consistent with experimental meuasurement. The simulation results show that the energetic ions βh, the injection velocity v0 and orbit width parameter ρh of energetic ions are important parameters determining the drive of BAE. Furthermore, the effect of qmin (with fixed shape of q profile) is studied, and it is found that: when qmin ≤ 1.50, the excited modes are BAEs, which are located near q=1.50 rational surfaces; when qmin > 1.50, the excited modes are simillar to the reversed-shear Alfvén eigenmodes (RSAEs), which are mainly localized around q=qmin surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE is sensitive to the EP drive. For strongly driven case, firstly, redistribution and transport of engetic ions are trigged by (m/n=3/2) BAE, which raised the radial gradient of energetic ions distribution function near q=2 rational surface, and then an EPM (m/n=4/2) is driven in nonlinear phase. Finally, these two instabilities triggered significant redistribution of energetic ions, which results in the twice-repeated and mostly-downward frequency chirping of (m/n=3/2) BAE. For weakly driven case, there are no (m/n=4/2) EPM being driven and twice-repeated chirping in nonlinear phase, since the radial gradient near q=2 rational surface is small and almost unchanged.

Simulation study of energetic-particle driven off-axis fishbone instabilities in tokamak plasmas

Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave-particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.

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

Large burst activity, identified as toroidal Alfv\'{e}n 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 ($k_{\parallel}\simeq n/R$, 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 ITER.

Interaction of rotational discontinuities with energetic ions in the precursor of the Earth’s bow shock

We combined in-situ solar wind observations by ARTEMIS and MMS missions with kinetic hybrid simulations to study the interaction of solar wind rotational discontinuities (RDs) with the foreshock of the Earth’s bow shock. We found that whistler modes excited by diffuse energetic particles were strongly coupled with RDs and lead to their temporary dissociation. At the same time, RDs trigger the steepening of whistler waves and the generation of ’shocklets’ - small localised shock-like structures, capable of trapping energetic particles and growing up by absorbing the particles energy.

Energy Retention in Thin Graphite Targets after Energetic Ion Impact

High energy ion irradiation is an important tool for nanoscale modification of materials. In the case of thin targets and 2D materials, which these energetic ions can pierce through, nanoscale modifications such as production of nanopores can open up pathways for new applications. However, materials modifications can be hindered because of subsequent energy release via electron emission. In this work, we follow energy dissipation after the impact of an energetic ion in thin graphite target using Geant4 code. Presented results show that significant amount of energy can be released from the target. Especially for thin targets and highest ion energies, almost 40% of deposited energy has been released. Therefore, retention of deposited energy can be significantly altered and this can profoundly affect ion track formation in thin targets. This finding could also have broader implications for radiation hardness of other nanomaterials such as nanowires and nanoparticles.