Luis Garcia

Burst events can severely deteriorate the performance of future stellarator fusion reactors by reducing the plasma heating efficiency and confinement. Bursting activity has been observed in Large Helical Device (LHD) operation scenarios strongly heated by neutral beam injectors (NBIs). This study analyzes the performance degradation in LHD discharge 189008 , linked to the destabilization of burst events. To that aim, the stability of Alfvén eigenmodes (AEs) and energetic-ion-driven resistive interchange modes (EICs) is analyzed. Linear and nonlinear simulations using the gyro-fluid code FAR3d reproduce the multiple toroidal AEs (TAEs) measured in the frequency range of 40 − 80 kHz, leading to the destabilization of an MHD burst (induced by passing energetic particles (EPs) injected by tangential NBI), as well as the destabilization of EICs at around 12 kHz, which causes the EIC burst (caused by helically trapped EPs injected by the perpendicular NBI). This study suggests that burst events can be induced by the nonlinear interaction between passing (tangential NBI) and helically trapped (perpendicular NBI) EP populations, creating a feedback effect that enhances the EP drive. The magnetohydrodynamic (MHD) burst causes 30 % of passing EP loss, and the EIC burst up to 90 % of trapped EP loss, an EP confinement degradation that may partially explain the decrease in device performance. The analysis also indicates that the EP transport induced during the burst events is ballistic, and linked to avalanche-like processes, leading to intense EP fluxes. In addition, the bursting activity affects the thermal plasma confinement, observed as a decrease in the thermal electron density, reproduced in the simulations as a decay in the thermal plasma pressure. The simulation output shows reasonable agreement with different diagnostic measurements, including the enhanced magnetic perturbations detected by Mirnov coils once the perpendicular NBI operation and bursting activity begin, the intensity and radial location of the radial electric field and shear flows from charge exchange spectroscopy diagnostic data, as well as the instability frequency range and dominant mode numbers calculated from the magnetics data. The main conclusion of the analysis is that the nonlinear feedback between different EP populations can enhance the EP drive, leading to the onset of bursting events and the degradation of burning plasma performance, particularly in scenarios with a large amount of EPs generated by different heating mechanisms that may destabilize the alpha particle population.

In the stellarator TJ-II, an enhanced-confinement (PiEC) phase is induced by pellet injections (PIs) into the NBI heated phase of its plasmas. As a consequence, its operational regime is extended significantly, with improvements approaching a factor of 1.5 when compared with fuelling by beam, gas-puff and/or wall recycling. The main characteristics of this PiEC phase are: steepened density gradients, increased ion temperatures, record stored energy and particle confinement times and reduced turbulence. In this work, studies are extended to a broadened range of magnetic configurations and heating powers. For instance, an updated dataset confirms the enhancement of energy confinement times following PIs when these are compared with empirical stellarator scaling law predictions (Yamada et al 2005 Nucl. Fusion 45 1684) and demonstrates, that such improvements have a magnetic configuration dependency. Thus, in the TJ-II, pellet fuelling defines the current upper operational boundary for NBI-heated plasmas. In addition, a systematic analysis of plasma potential, radial electric field (Er) and its shear is performed for PiEC phases. It reveals that plasma potential becomes more negative across the whole plasma radius after a single injection while additional injections induce steeper density gradients and broaden profiles. In parallel, it shows that the observed increases in radial electric field in the gradient region, from ~-3 kV/m (reference) to ~-8 kV/m (2 pellets) at normalized radius = 0.6, is consistent with neoclassical simulations. Finally, the work presented here indicates also that consecutive injections maintain the radial electric field shear at maximum level (at ρ = 0.75) while steepening density profiles and improving confinement. Thus results indicate that PIs not only acts as plasma fuelling in TJ-II, but also contribute to strengthening shear-driven confinement in the gradient region.

The present study is dedicated to the analysis of energetic particle modes (EPMs) in fusion devices. The aim of the analysis is reproducing the EPM frequency down-sweeping and the transition from energetic particle (EP)-driven to current- or pressure-gradient-driven instabilities observed in the experiments. In addition, the shear flow generation and its effect on the EPM saturation and decay phases are analyzed. Two test cases are considered: Fish-bones destabilized in a JET configuration and energetic-ion-driven resistive interchange modes (EICs) triggered in a Large Helical Device (LHD) discharge. A set of nonlinear simulations using the gyro-fluid code FAR3d are performed, removing the EP drive along the saturation phase of Fish-bones and EIC, analyzing the EPMs' decay with and without the presence of shear flows. The simulations reproduce the EPM's frequency down-sweeping along with the transition from a Fish-bone to the current-driven 1/1 internal kink in the JET case, as well as the transition from EIC to the pressure gradient-driven 1/1 resistive interchange mode in the LHD case. The simulations show the generation of shear flows and radial electric fields in the plasma location where the Fish-bone/EIC decay, linked to the energy transfer from the modes toward the thermal plasma. Linear simulations performed using the evolved profiles from nonlinear simulations highlight the key role of the shear flows in the decay of Fish-bones, pointing out the mode frequency down-sweeping can only be reproduced in simulations including the effect of the shear flows. In addition, the analysis may indicate shear flows have a regulatory effect on the Fish-bone saturation, leading to a smoother mode decay by balancing the energy extraction caused by the continuum damping. On the other hand, the role of shear flows in the EIC decay is smaller compared to the Fish-bones, explained by narrower and almost steady shear flow bands observed in the simulations.

Energetic electron-driven beta-induced Alfvén eigenmodes (e-BAEs) around 20 kHz are observed in J-TEXT electron cyclotron resonance heating (ECRH) plasmas, and their frequency and intensity are positively correlated with the ECRH power. Experimental measurements indicate that the e-BAE propagates in the electron diamagnetic drift direction, with poloidal and toroidal mode numbers m / n = −4/−1. Statistical analysis and Alfvén continuum simulations imply that the mode frequency is positively correlated with the Alfvén velocity, being consistent with the general fishbone-like dispersion relation, and locates in the BAE gap of the Alfvén continuum. Further calculation evaluation entails that this e-BAE is most likely to be excited by 5–9 keV trapped energetic electrons around q = 4 rational surface, via precession resonance. Numerical simulations using the FAR3d code successfully reproduce the e-BAE, showing good agreement with experimental results in both mode number, frequency and growth rate. Simulation results show that the growth rate of e-BAE increases linearly with the energetic electron beta, as well as the frequency displays a positive correlation with the energetic electron pressure and a negative correlation with the characteristic trapping length of energetic electrons. The simulated eigenfunction of the e-BAE also presents that the mode is localized to a narrow region around the q = 4 rational surface, close to the plasma edge. This paper reports the first application of the FAR3d code to simulate energetic electron-driven instabilities, demonstrating its potential for studying such physical phenomena.

The stability of ballooning modes at the plasma edge of Stellarator fusion reactors is a major concern, considered a severe limiting factor of the device performance, particularly for low magnetic shear configurations based on quasi-isodynamic symmetry magnetic traps, restricting the maximum thermal β of the operation scenarios. The present analysis is dedicated to study the core density collapses (CDCs) observed in Large Helical Device (LHD), a hard MHD limit relaxation caused by the destabilization of high n ballooning modes at the plasma edge, leading to the collapse of the plasma pressure and the LHD performance deterioration. A set of simulations are performed using the code FAR3d to reproduce the CDC. Linear simulations calculate unstable high n ballooning modes at the plasma edge ( n > 17, n the toroidal mode number and m the poloidal mode number) consistent with the ballooning modes observed in the experiment. Nonlinear simulations show the inner-middle plasma ( r / a < 0.5 ) is destabilized due to an inverse energy cascade from the saturating high n ballooning modes towards middle and low n modes as well as the thermal plasma. The energy transfer towards the thermal plasma during the high-middle ballooning modes saturation leads to the distortion of the plasma flux surfaces at the plasma periphery, inducing a flattening of the pressure profile. Likewise, the pressure gradient at the plasma core enhances causing the destabilization of low n modes, consistent with the instability inward propagation and the m = 1 perturbation measured during the CDC. The analysis indicates the deterioration of the LHD performance may be caused by an intense distortion of the magnetic surfaces by the saturating middle n ballooning modes and m = 1 perturbation between the inner-middle plasma, leading to a wide region of stochastic magnetic fields generated by reconnection processes.

The nonlinear evolution and dynamics of energetic particle (EP) driven instabilities in both steady-state (reversed shear q-profile) and monotonic q-profile regimes of ITER are examined using the global gyro-Landau closure model FAR3d. Both neutral beam and alpha components are included, leading to synergistic effects between the two populations. In order to maintain computational feasibility, the present nonlinear simulation includes all toroidal mode numbers ranging from n = 0 to 15. It cannot be excluded that n’s above this range could introduce larger linear growth rates; however, as indicated from the results, the n = 0 to 15 range is sufficient to provide a strong linear drive and significant nonlinear transport effects. While the toroidal mode numbers n = 6 , 13 dominate the linear instability growth phase, nonlinear energy transfers in the saturated phase reverse this trend, leading to the dominance of lower n’s in the saturated phase of the simulation. Zonal flow structure generation and EP density flattening are further consequences of the nonlinear phase. The density profile flattening is caused by collectively driven EP radial transport fluxes, which have non-local characteristics. Instantaneous alpha particle transport fluxes are significant ( Γ α ∼ 2 × 10 20   m − 2 s − 1 ) for the reversed shear regime and lower ( Γ α ∼ 1.1 × 10 20   m − 2 s − 1 ) for the monotonic q-profile case.

The aim of this study is to analyze the stability of helical Alfvén eigenmodes (HAEs) in TJ-II discharges and the stabilizing effect of the energetic particles generated by the neutral beam injector (NBI) on pressure gradient-driven modes (PGDMs). HAE and PGDM stability is studied using the linear version of the gyro-fluid code FAR3d and the continuous structure by the STELLGAP code. First, Alfvén eigenmode (AE) and PGDM activity observed in the experiments is reproduced by the simulations, identifying unstable m/n=4/7−2/3 and 7/12−5/8 HAEs triggered around ρ=0.66 showing a frequency of 209 and 204 kHz, respectively, as well as 5/3 PGDM. Next, a parametric study is performed with respect to the thermal ion density and iota profile in the middle-outer plasma region to verify the robustness of the simulation results with respect to the uncertainty of experimental profiles. The analysis confirms that experimental uncertainty does not cause large deviations in the simulation results, showing the destabilization of the same HAEs for all the configurations tested. The simulations also indicate the decay of the 5/3 PGDM growth rate as the energetic particle (EP) population in the plasma increases, consistent with the experiment. Stability analysis of the n=3,7,11, n=5,9,13, n=6,10,14, and n=8,12 helical families is performed with respect to the NBI operational regime for different EP energies, β as well as deposition profiles. The most unstable configuration is the radially localized on-axis NBI operation (stiff EP density profile gradients nearby the magnetic axis). Using the simulation model that reproduces the observed Alfvén activity, we extend the study to analyze NBI performance within a theoretical framework. It shows that increasing NBI voltage (which raises EP energy) leads to a degradation in NBI performance for a given power (related to EP β and their density). To achieve better NBI operation, higher voltage must be balanced with lower injection power, ensuring stable AEs while keeping the same EP β.