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Register a new userDependence of alpha-particle-driven Alfven eigenmode linear stability on device magnetic field strength and consequences for next-generation tokamaks
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Recently-proposed tokamak concepts use magnetic fields up to 12 T, far higher than in conventional devices, to reduce size and cost. Theoretical and computational study of trends in plasma behavior with increasing field strength is critical to such proposed devices. This paper considers trends in Alfven eigenmode (AE) stability. Energetic particles, including alphas from D-T fusion, can destabilize AEs, possibly causing loss of alpha heat and damage to the device. AEs are sensitive to device magnetic field via the field dependence of resonances, alpha particle beta, and alpha orbit width. We describe the origin and effect of these dependences analytically and by using recently-developed numerical techniques (Rodrigues et al. 2015 Nucl. Fusion 55 083003). The work suggests high-field machines where fusion-born alphas are sub-Alfvenic or nearly sub-Alfvenic may partially cut off AE resonances, reducing growth rates of AEs and the energy of alphas interacting with them. High-field burning plasma regimes have non-negligible alpha particle beta and AE drive, but faster slowing down time, provided by high electron density, and higher field strength reduces this drive relative to low-field machines with similar power densities. The toroidal mode number of the most unstable modes will tend to be higher in high magnetic field devices. The work suggests that high magnetic field devices have unique, and potentially advantageous, AE instability properties at both low and high densities.
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A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfven Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes are found in simulations -- co-CAEs, cntr-GAEs, and co-GAEs -- with differing spectral and stability properties. The simulations reveal that unstable GAEs are more ubiquitous than unstable CAEs, consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from simulations and estimated analytically for relevant sources not present in the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.
Two novel nonlinear mode coupling processes for reversed shear Alfven eigenmode (RSAE) nonlinear saturation are proposed and investigated. In the first process, RSAE nonlinearly couples to a co-propagating toroidal Alfven eigenmode (TAE) with the same toroidal and poloidal mode numbers, and generates a geodesic acoustic mode (GAM). In the second process, RSAE couples to a counter-propagating TAE and generates an ion acoustic wave quasi-mode (IAW). The condition for the two processes to occur is favored during current ramp. Both processes contribute to effectively saturate the Alfvenic instabilities, as well as nonlinearly transfer of energy from energetic fusion alpha particles to fuel ions in burning plasmas.
General nonlinear equations describing reversed shear Alfven eigenmode (RSAE) self-modulation via zero frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow (ZF) and electromagnetic zonal current (ZC) can be preferentially excited by finite amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfven wave continuum is evaluated using the derived saturation level of ZC, which is shown to play a comparable role in saturating RSAE with the ZFZS scattering.
The aim of this study is to analyze the destabilization of Alfven Eigenmodes (AE) by multiple energetic particles (EP) species in DIII-D and LHD discharges. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species, including the effect of the acoustic modes, diamagnetic currents and helical couplings. We add the Landau damping and resonant destabilization effects using a closure relation. The simulations with multiple NBI lines show three different regimes: the non damped regime where the multi beam AEs growth rate is larger compared to the growth rate of the AEs destabilized by the individual NBI lines, the interaction regime where the multi beam AEs growth rate is smaller than the single NBI AEs and the damped regime where the AEs are suppressed. Operations in the damped regime requires EP species with different density profile flatness or gradient locations. In addition, the AEs growth rate in the interaction regime is further reduced if the combined NBI lines have similar beam temperatures and the beta of the NBI line with flatter EP density profile increases. Then, optimization trends are identified in DIII-D high poloidal beta and LHD low density / magnetic field discharges with multiple NBI lines as well as the configuration requirements to operate in the damped and interaction regimes. DIII-D simulations show a decrease of the n=2 to 6 AEs growth rate and n=1 AE are stabilized in the LHD case. The helical coupling effects in LHD simulations lead to a transition from the interaction to the damped regime of the n=2,-8,12 helical family.
Zero frequency zonal flow (ZFZF) excitation by trapped energetic electron driven beta-induced Alfven eigenmode (eBAE) is investigated using nonlinear gyrokinetic theory. It is found that, during the linear growth stage of eBAE, resonant energetic electrons (EEs) not only effectively drive eBAE unstable, but also contribute to the nonlinear coupling, leading to ZFZF excitation. The trapped EE contribution to ZFZF generation is dominated by EE responses to eBAE in the ideal region, and is comparable to thermal plasma contribution to Reynolds and Maxwell stresses.
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