Session TI2: Waves and Energetic Particles

Alfv\'en Eigenmodes and Fast Ion Loss in the DIII-D and ASDEX-Upgrade Tokamaks

Newly obtained measurements of the fast ion profile, internal structure of Alfv\'en eigenmodes (AEs), and associated fast-ion losses reveal important details of the interplay between fast ion dynamics and AE activity on the DIII-D and ASDEX-Upgrade tokamaks. Surprisingly, fast ion losses are observed to span a broad region of energy and pitch angle, indicating that a significant fraction of the energetic particle phase space interacts with the modes and are lost to the wall. Coherent losses of energetic ions at Alfv\'en eigenmode (AE) frequencies clearly identify the role of AEs in the loss mechanism. These results were enabled by new diagnostic capabilities that provide a comprehensive picture of the phase space dynamics of the wave-particle interactions, including detailed 1D and 2D confined fast ion profiles and global eigenmode structures. The observed modes consist of multiple reversed-shear Alfv\'en eigenmodes (RSAEs), toroidicity induced Alfv\'en eigenmodes (TAEs), and the recently discovered beta induced Alfv\'en acoustic eigenmodes (BAAEs). Coherent losses of beam ions measured by scintillator detectors in both devices are predominantly due to TAEs while both RSAEs and TAEs are observed to cause large coherent losses of fast ions in AUG discharges with ion cyclotron heating. Concomitant with these losses is a measured central fast ion depletion, where as much as 50\% of classically predicted fast ion population is lost or redistributed. Key aspects of the measurements including eigenmode structure, stability and fast ion transport are reproduced using a variety of tools including the nonlinear initial value codes M3D and TAEFL as well as the linear eigenvalue solver NOVA-K combined with orbit following codes (ORBIT, HAGIS).   

Kinetic Stability of Alpha Driven TAEs in ITER Plasmas

A hybrid gyrokinetic ions/fluid electron model is implemented in the Particle-in-Cell code GEM and used to study high-n TAEs in ITER. The adequacy of the model for simulating TAEs has been previously demonstrated\footnote{J. Lang, Y. Chen, S. E. Parker, and G-Y. Fu, Phys. Plasmas 16 102101 (2009)}, by comparing the simulated TAE mode frequency and structure with an eigenmode analysis, and the thermal ion kinetic damping with analytic theory. By using a global PIC code the effects of large orbit width and non-local mode structures can be accurately included. Damping rate due to numerical filtering is carefully monitored, and convergence with respect to particle number, grid resolution, etc., is thoroughly tested. The simulations show that the most unstable modes in ITER lie in the rage of $10 [Preview Abstract]

Numerical Modeling of NBI-driven sub-cyclotron frequency modes in NSTX

Recent experimental observations from NSTX suggest that many modes in a sub-cyclotron frequency range are excited during neutral beam injection (NBI). As was shown recently, these modes are capable of channeling the beam ion energy into the thermal ions, and they can also induce strong anomalous electron transport in STs. These modes were identified as Compressional Alfven Eigenmodes (CAEs) and Global Alfven Eigenmodes (GAEs), driven unstable through the Doppler shifted cyclotron resonance with the super Alfvenic NBI ions. Hybrid 3D code HYM is used to investigate detailed properties of beam ion driven MHD modes in NSTX, aiming at simulations of plasmas where GAE and CAE modes have been observed. The HYM code is a nonlinear, global stability code in toroidal geometry, which includes fully kinetic ion description. A generalized form of the Grad-Shafranov equation solver has been developed, which includes, non-perturbatively, the effects of the beam ions with anisotropic distribution. For large neutral beam injection velocities and strong anisotropy in the pitch-angle distribution, many Alfven modes are excited in simulations. The resonant particles are shown to satisfy Doppler-shifted cyclotron resonant conditions, and multiple resonances are found for each toroidal mode number. Growth rates of GAE modes are sensitive to details of the distribution function, in particular, the pitch angle distribution. Nonlinear simulations show that GAE instabilities saturate at low amplitudes due to particle trapping. Most unstable mode toroidal numbers, frequencies, and saturation amplitudes in HYM simulations agree with experimental results for NSTX. The magnetic perturbations have shear Alfven wave polarization in the core, however the compressional component dominates at the edge in agreement with magnetic measurements in the NSTX.   

Investigation of LH Physics Through Power Modulation Experiments on C-Mod

Lower hybrid current drive (LHCD) is an attractive tool for off-axis current profile control in present devices and burning plasmas (ITER), because these waves damp at high parallel phase speeds relative to the electron thermal speed. The LHCD system on Alcator C-Mod operates at 4.6 GHz, with $\sim $ 1MW of coupled power, and can produce spectra over a wide range of peak parallel refractive index (n$\vert \vert )$.~ A 32 chord, horizontally viewing hard x-ray camera has been used to measure the spatial and energy distribution of fast electrons generated by LH waves, providing valuable data for validating LHCD simulation models. Theory predicts that LH power deposition location is strongly dependent on n$\vert \vert $. Square-wave modulation of LH power on a time scale much faster than the current relaxation time does not significantly alter the poloidal magnetic field inside the plasma and thus allows for realistic modeling and consistent plasma conditions for different n$\vert \vert $ spectra. Inverted hard x-ray profiles show clear changes in LH-driven fast electron location with differing n$\vert \vert $. Boxcar binning of hard x-rays during LH power modulation allows for $\sim $ 1 ms time resolution, which is sufficient to resolve the build-up, steady-state, and slowing-down phases of fast electrons. The time histories of hollow x-ray profiles have been used to measure a fast electron pinch velocity. Ray-tracing/Fokker-Planck modeling in combination with a synthetic hard x-ray diagnostic show quantitative agreement with the x-ray data at low densities. However, simulations do not reproduce the experimentally observed LH density limit, above which the x-ray count rates drop dramatically, unless strong absorption of the waves in the plasma edge region is invoked. X-ray profile shapes suggest that LH power is being deposited in the divertor region near the active x-point location. Inclusion of a scrape-off layer in the ray tracing allows for a detailed comparison of measured x-ray profiles with those predicted by modeling. This work is supported by the US DOE awards DE-FC02-99ER54512 and DE-AC02-76CH03073.   

Off-axis Fishbone-like Instability and Excitation of the Resistive Wall Mode (RWM) in JT-60U and DIII-D Devices

Advanced tokamak experiments in JT-60U [1] and DIII-D [2] have revealed that in high-beta $q(0)>1$ plasmas, where the resistive wall modes (RWMs) are predicted to be stable by kinetic effects of energetic particles, plasma rotation and a nearby conducting wall, off-axis fishbone-like instabilities often trigger RWMs. The rapid growth of these RWMs prevents high performance operation. The off-axis fishbone-like instability has some similarities to the classic $m/n=1/1$ internal fishbone instability in terms of its initial frequency near the energetic ion precession frequency, downward frequency-chirping, and a neutron rate drop of $\sim$20\% during each burst. However, there are several unique non-ideal-MHD features in the off-axis fishbone-like instability. The waveform time behavior has strong non-sinusoidal distortion from the $q\sim 2$ area to the edge, synchronized with bursting energetic particle losses, while the plasma rotation is rapidly reduced within a few milliseconds. Based on experimental observations the following hypothesis emerges. In plasmas where rotation and kinetic effects are usually sufficient to stabilize the RWM, energetic particles can drive the fishbone instability of several kHz (larger than the inverse of the resistive wall time constant). The reduction of kinetic stabilization due to the resulting energetic particle loss and rapid decrease of plasma rotation makes the plasma more vulnerable to the near-zero frequency RWM. The impact on RWM stability by the off-axis fishbone with its radial and toroidal distortion of the mode structure is assessed by comparing the JT-60U/DIII-D results with theoretical predictions.\par \vskip6pt \noindent [1] G. Matsunaga et al., Phys.\ Rev.\ Lett.\ {\bf 103}, 045001. (2009).\par \noindent [2] M. Okabayashi et al., Nucl. Fusion 49 (2009) 125003.   

Nonlinear Simulation of Energetic Particle-driven Alfv\'en Instability with Source and Sink

Kinetic/magnetohydrodynamic hybrid simulations are carried out to investigate the nonlinear dynamics of energetic particle-driven toroidal Alfv\'en eigenmode (TAE) with collision and source/sink [Phys. Plasmas 17, 042309 (2010)]. We have systematically studied the effect of pitch angle scattering and particle slowing down for different parameter regime and we found that the presence of pitch angle scattering and particle slowing down could shift and broaden the mode resonance and affect the nonlinear saturation of the TAE. For cases well above marginal stability, the mode saturation is approximately steady state with finite collision frequency. The calculated scaling of saturation level with collision frequency agrees well with analytic theory [Phys. Rev. Lett. 68, 3563 (1992)] and NOVA-K. For cases near-marginal stability at low collision rates, the mode saturation exhibits pulsation behavior with frequency chirps up and down. In analogy to the effective collision induced by pitch angle scattering [Phys. Fluids B 2, 2226 (1990)], an analytical calculation indicates that microturbulence-induced diffusivity can affect nonlinear saturation of energetic particle driven modes in the similar way as the pitch angle scattering does. By introducing a simplified diffusion operator to the code, our numerical results have shown that a single TAE mode is to saturate at a steady state with sufficiently high diffusion rate. The simulated saturation level scales with the radial diffusion rate by the same scaling of pitch angle scattering. We derived a criterion to judge the importance of microturbulence-induced radial diffusion effect comparing to the collisional pitch angle scattering effect. According to the criterion, we found that the micro-turbulence induced diffusion could have a stronger effect compared to the Coulomb collision on the TAE saturation in burning plasmas like ITER.