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THEORY SUMMARY

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

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THEORY SUMMARY

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

  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. 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 (g 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. 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. 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 (w/wA = 0.8) and singular modes • X-points can accelerate fast particles

  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. COLLECTIVE MODES – TAE • JET antenna coil observations (Testa) • Complex dependence of TAE damping rate on bN, PNBI => decreases, then increases • Damping rate (n=1) independent of r*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 (nfast/ne not assumed negligible) • Thermal particle kinetic effects

  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 w/wci = 0.3: large k||, large compressional component dB||/dBperp ~ 1/3 • Nonlinear saturation level dB/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 Te drop

  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 qmin passes through integer value) => diagnostic to monitor qmin • 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 q0 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 qmin, 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 w*e direction?)

  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 dB/B = 10-4 • Use as nonlinear diagnostic to infer dB/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. 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 bfast • 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. 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<0.4 central region => 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. 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. 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 rhole = 0.4) to 12.6% (at when rhole > 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 (rhole = 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. 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. 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

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