1. THEORY SUMMARY 8th IAEA Technical Committee Meeting on Energetic Particles in Magnetic Confinement Systems San Diego, CA; 6-8 October 2003 J. W. Van Dam vandam@physics.utexas.edu Please send me comments!

2. Page 2 OUTLINE Fast ion distribution Fast particle effects on plasma equilibrium Suprathermal electrons Fishbones & internal kinks Collective modes – TAE – CAE, HAE Alfvén cascades Chirping modes – Theory – Experiment EPM modes Fast ion transport Alpha particles in current-hole plasmas

3. Page 3 FAST ION DISTRIBUTION Alpha profiles in ITER ELMy H-mode (Budny) – Finds: [1] NNBI current affects alpha profile; [2] NNBI drive exceeds fast alpha TAE drive; [3] Sawteeth affect the alpha density. Fast particle losses during NSTX reconnection events (Yakovenko) – Drops in neutron yield during reconnection events are due to fast particle losses, not redistribution. Probable mechanism = magnetic drift stochasticity Distribution and fields during ICRH and AE excitation (Hellsten) – Idea to use ICRH fast ions to simulate alphas – JET antenna phasing (|| & anti-|| propagation) => different orbits (  emission) – Fast ion distribution details are important for AE stability/growth – ICRH causes decorrelation => affects nonlinear growth of AE modes ICRH fast ion profile and confinement in LHD (Murakami) – Calculates the velocity space distribution for ICRF-heated minority H ions (up to 500 keV of energetic tail ions); also the power absorption and heat deposition -- good experimental comparison – Simulates transport of fast ions (especially, helically trapped particles)

4. Page 4 FAST PARTICLE EFFECTS ON EQUILIBRIUM Plasma rotation from ICRF-heated fast particles (Eriksson) – Several experiments have observed toroidal co-current rotation with ICRH plasmas with zero momentum injection Possible theories: [1] Fast particles, [2] Neoclassical effects, [3] Accretion process – Investigates minority ion heating with co-current ICRF waves Fast ions absorb wave momentum, then transfer it to plasma (via collisions or radial current) Experiments (JET) and simulations show that fast particles may be able to control the rotation profile to some extent Formation of internal transport barrier (Wong) – Proposes that sheared rotation and negative central shear (conducive to ITB formation) can be created by having Alfvén eigenmode instabilities eject/redistribute alpha particles out of central region toward edge => supported by DIII-D data – Estimates that in ITER, number of alphas for this mechanism is marginal Ripple reduction with ferritic inserts (Shinohara) – Experiments (JFT-2M) and simulations (3d OFMC) show improved orbit confinement for NBI fast ions when ferritic inserts are used (in non-shear-reversed plasmas) – Speculates about use of large externally created local ripple for burn control

5. Page 5 SUPRATHERMAL ELECTRONS Runaway electrons and disruptions (Helander) (Andersson) – Two approaches: [1] Monte Carlo simulations, [2] Reduced model – Findings: Most runaways generated by secondary/avalanche mechanism in JET and ITER Typically 50% conversion of thermal current to runaways in JET (more in ITER) Runaway density profile: [1] Easily corrugated => explain bursty x-ray emission? [2] Peaked on axis (more than pre-disruption current) -- observed experimentally Particle acceleration at magnetic X-points (McClements) – Finds both discrete (  /  A = 0.8) and singular modes – X-points can accelerate fast particles

6. Page 6 FISHBONES & INTERNAL KINKS Near-threshold fishbone behavior (Breizman) – Fishbone is good example of convective transport (single mode) – Two-step linear mode structure for finite-frequency fishbone – Weak fluid nonlinearity of q=1 layer destabilizes fishbone => bursting? Fishbone stability with alphas (Fu) – Estimates n=1 internal kink in ITER is not stabilized by alphas (contrary to earlier Porcelli theory -- finite orbit width effect?) Fishbone nonlinear saturation (Todo) – Mode with n=1 saturates, while n=0, 2 continue to grow Linear gyrokinetic calculation (Lauber) – Benchmarked on internal kink Nonperturbative simulation of n=1 JET observations (Gorelenkov) – Reproduces LF ideal and HF resonant modes (but no 2-step profile -- zero orbit width?)

7. Page 7 COLLECTIVE MODES – TAE JET antenna coil observations (Testa) – Complex dependence of TAE damping rate on  N, P NBI => decreases, then increases – Damping rate (n=1) independent of  *I, not linear as predicted for radiative damping – Error field distorts B topology and kills q=2 TAE => control of hot pressure gradient? TAE in NCSX (Fu) – Simulation finds unstable TAE mode (n=?) – 3d geometrical effects reduce its growth rate Discrete TAE in high-beta second-stable tokamak (Hu) – Existence of mode is due to potential well created by high plasma pressure gradient (continuum damping is weak) – Could be excited by fast particles at bounce + precession mixed resonance Multi-ion species kinetic/fluid hybrid model (Cheng) – Will include: Gyroviscosity (along with pressure tensor) Hall term in Ohm’s law (n fast /n e not assumed negligible) Thermal particle kinetic effects

8. Page 8 COLLECTIVE MODES – CAE, HAE Sub-cyclotron NBI-driven instabilities in NSTX (Belova) – Most unstable mode is n=4/m=2 GAE (nm<0) with  /  ci = 0.3: large k ||, large compressional component dB || /dB perp ~ 1/3 – Nonlinear saturation level  B/B = 10 -3 ~ 10 -4 Helical AEs in compact stellarators (Spong) – Calculates shear Alfven continuum spectrum for W7-AS, QPS, and NCSX: find that TAE, HAE, and MAE modes are possible – W7-AS observes nonlinear bursting with fast ion loss and T e drop

9. Page 9 ALFVEN CASCADE MODES Cascade observations in JET and interpretation (Sharapov) (Breizman) – “Grand cascade” (many simultaneous n-modes) occurrence is coincident with ITB formation (when q min passes through integer value) => diagnostic to monitor q min Proposes creating ITB by application of main heating shortly before a Grand Cascade is known to occur – Cascade mysteries (with ICRH fast ions): Transition to TAE as q 0 decreases -- calculated theoretically No cascade modes at low frequency -- effect of continuum damping (calculated)? Sinusoidal frequency rolling -- ? – Cascades also occur when toroidicity effect exceeds that of fast particles (e.g., low- density alphas in TFTR) “Reversed-shear Alfven eigenmode” observations in JT-60U (Shinohara) – For NNB injection into reversed shear plasma, observe n=1 mode located at q min, with strong up and down frequency chirping Earlier such observations were with ICRH fast ions Cascade observations in C-Mod (Snipes) – Also observe EAE modes in H-mode plasmas (but why rotating in  *e direction?)

10. Page 10 CHIRPING MODES – THEORY Non-adiabatic description of phase-space hole/clump (Berk) – Predicted frequency bifurcation seen experimentally (Gryaznevich/MAST) – Frequency sweeping undergoes non-adiabatic instability, which can cause sideband generation Simulation of frequency sweeping (Pinches) – Two cases: JET parameters: Only chirps downward (due to choice of numerical distribution function-- experiments see both up/down sweeping modes) MAST parameters: Up/down sweeping, saturates at  B/B = 10 -4 – Use as nonlinear diagnostic to infer  B/B from chirping rate Nonlinear hole/clump formation (Vann) – Simulation of full single-mode (n=1) nonlinear dynamics => Finds 4 solutions (damped, steady-state, periodic, chaotic) for various parameter regimes Simulation of NBI-driven mode in weakly reversed-shear NSTX (Fu) – Calculates unstable n=2 mode (TAE?) – Mode structure moves out radially as frequency chirps

11. Page 11 CHIRPING MODES – EXPERIMENT Fast ion instabilities in NSTX (Fredrickson) – Observation of strongly bursting fast ion loss due to multiple TAE modes (2<n<6): 40% drop in  fast – New “fishbone”-like mode also causes fast ion loss (up to 50%) n up to 5 (or more); often q(0)>1 and m>1; bounce-precession resonance; possibly ballooning character; strongly chirping when fast ion loss is large Coupled to TAEs and CAEs? Correlated with H-mode transition? Energetic particle-driven modes in MAST (Gryaznevich) – Behavior in three distinct regimes: Low-beta regime: n=1 up/down chirping modes Medium-beta regime: “humpbacked fishbones” High-beta regime (Next Step ST): cyclotron-range fast particle driven instabilities, but no TAEs – No observation of fast ion loss in MAST (smaller population?)

12. Page 12 EPM MODES Bursting modes in JT-60U (Todo) – Further measurements (by Shinohara et al.) of TAE frequency mode for NNB injection in low-shear plasma, now with neutron emissivity diagnostic, to study fast ion profile Observe two types of modes: fast frequency sweeping (FFS) and abrupt large- amplitude events (ALE) FFS modes have little effect on neutron emissivity ALE modes reduce fast ion population by 20% in r/a 14% are redistributed to outer region and 6% lost to outside – Numerical simulation finds an n=1 EPM that is “nonlocal”-- suggested by location (not on continuum), frequency (TAE-ish), and profile dependence (on fast ion pressure) Frequency chirps both up and down, as in the experiment, if fast ion classical distribution in the simulation is reduced (due to loss or redistribution)

13. Page 13 FAST ION TRANSPORT Diffusive transport with multiple modes (Breizman/Todo) – Simulations show intermittent loss of fast ions. Co-injected NBI ions are confined better than counter-injected. Phase-space resonances overlap at mode saturation. Transition to strong transport in burning plasma (Zonca) – Onset of fast ion avalanche transport is close to EPM linear stability threshold--above which, EPM can propagate radially with convective amplification. “Relay-runner” model captures nonlinear transport dynamics. EPM-induced alpha particle transport (Vlad) – Considers ITER-FEAT, FIRE, and IGNITOR for monotonic and reversed shear: only ITER is unstable wrt EPMs (n=2 worst) – These unstable modes broaden alpha profile, first convectively (via avalanche) and then diffusively

14. Page 14 ALPHAS IN CURRENT HOLE PLASMA Alpha confinement in current-hole fusion plasma (Tobita) – Alpha loss can be serious for large current hole: Loss jumps from 2.0% (at  hole = 0.4) to 12.6% (at when  hole > 0.5) => unacceptable for heat load on first wall – Solution for current hole loss is low aspect ratio: (1) trapped particles are less sensitive to TF ripple; (2) TF ripple drops along R – VECTOR device (A=2, superconducting): Even for wide current hole (  hole = 0.6), can confine alphas (loss as low as 2%) Current hole effect on fast ion confinement in JET (Yavorski) – Orbit of alpha is lost when current hole radius equal to or greater than 0.6 – First orbit loss is enhanced by current hole from 8-25% for monotonic profile (no hole), to 20-50% with current hole (of radius 0.6)

15. Page 15 PERSONAL IMPRESSIONS Signs of health: – Research: New, intriguing experimental findings On-target theoretical explanations Impressive numerical simulations – Researchers: Significant number of young, talented scientists at this meeting – Facilities: Variety of confinement configurations that are currently studying fast particle physics (as represented at this meeting) Tokamaks (JET, C-Mod, JT-60, JFT-2M, DIII-D) Spherical tori (NSTX, START, MAST) Helical/Stellarators (LHD, CHS, QPS, NCSX) Others: linear (LAPD) Anticipation: – Short-term: New fast particle diagnostics Tritium campaign (JET) & planned experiments on various machines – Long-term: ITER

16. Page 16 POSTSCRIPT “Pope of Fast Particle Physics” – Contributed seminal research (e.g., alpha excitation of shear Alfven waves, TAE continuum damping, etc., etc.) – Trained students in this area – Chief Scientist for ITER – Participated in previous Fast Particle Tech Comm Meetings – “Yearning for Burning”: influential advocate for ignition physics