THEORY SUMMARY

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THEORY SUMMARY
J. W. Van Dam vandam_at_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
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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

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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) gt
  different orbits (g emission)
• Fast ion distribution details are important for
  AE stability/growth
• ICRH causes decorrelation gt 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)

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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 gt 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

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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 gt
  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

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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 q1 layer destabilizes
  fishbone gt bursting?
• Fishbone stability with alphas (Fu)
• Estimates n1 internal kink in ITER is not
  stabilized by alphas (contrary to earlier
  Porcelli theory -- finite orbit width effect?)
• Fishbone nonlinear saturation (Todo)
• Mode with n1 saturates, while n0, 2 continue to
  grow
• Linear gyrokinetic calculation (Lauber)
• Benchmarked on internal kink
• Nonperturbative simulation of n1 JET
  observations (Gorelenkov)
• Reproduces LF ideal and HF resonant modes (but no
  2-step profile -- zero orbit width?)

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COLLECTIVE MODES TAE

• JET antenna coil observations (Testa)
• Complex dependence of TAE damping rate on bN,
  PNBI gt decreases, then increases
• Damping rate (n1) independent of rI, not linear
  as predicted for radiative damping
• Error field distorts B topology and kills q2 TAE
  gt 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 Ohms law (nfast/ne not assumed
  negligible)
• Thermal particle kinetic effects

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COLLECTIVE MODES CAE, HAE

• Sub-cyclotron NBI-driven instabilities in NSTX
  (Belova)
• Most unstable mode is n4/m2 GAE (nmlt0) 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

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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) gt 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 n1 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 we direction?)

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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 (n1) nonlinear
  dynamics gt 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 n2 mode (TAE?)
• Mode structure moves out radially as frequency
  chirps

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CHIRPING MODES EXPERIMENT

• Fast ion instabilities in NSTX (Fredrickson)
• Observation of strongly bursting fast ion loss
  due to multiple TAE modes (2ltnlt6) 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)gt1 and mgt1
  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 n1 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?)

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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/alt0.4 central region gt 14 are redistributed
  to outer region and 6 lost to outside
• Numerical simulation finds an n1 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)

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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 (n2 worst)
• These unstable modes broaden alpha profile, first
  convectively (via avalanche) and then diffusively

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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 gt 0.5) gt 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 (A2, 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)

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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

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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