INTRODUCTION OF WAVEPARTICLE RESONANCE IN TOKAMAKS

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INTRODUCTION OF WAVE-PARTICLE RESONANCE IN
TOKAMAKS

• J.Q. Dong
• Southwestern Institute of Physics
• Chengdu, China
• International School on Plasma Turbulence and
  Transport
• August 16 18, 2007, Chengdu, China

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Outline

• Introduction
• Tokamak magnetic configuration
• Charged particle motion in tokamaks
• Wave-particle resonance due to parallel motion of
  particles
• Wave-particle resonance due to drift motion of
  particles
• Wave-particle resonance due to rotation of
  particles
• Summary

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Introduction

• Plasmas are affluent in collective oscillations
  and waves
• Wave-particle interaction is an important part of
  magnetic fusion plasma science
• Excitation of turbulent flows and fluctuations
  leads turbulent mass, momentum and energy
  transport
• Effects of external waves on plasma particles
  include trapping of particles in waves, chaotic
  behavior in particle orbits, particle
  acceleration,
• plasma heating and current drive
• Resonance is an efficient way for collisionless
  energy transfer between particles and waves

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Tokamak magnetic configuration

• Equilibrium magnetic field
• Toroidal field
• Poloidal field

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Charged particle motion in tokamaks

• Parallel (lognitudinal) motion
• Rotation
• Drifts of guiding center
• i) Electric field drift

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ii) magnetic gradient ( ) drift
iii) magnetic curvature drift
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iv)trapping, bounce and toroidal drift

• a) Particle trapping
• b) Bounce period of the trapped particles
• c) Toroidal drift of trapped particles

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Diamagnetic drift of plasma fluids

• It is in the vertical direction
• It induces charge separation and then plasma
  outward motion.

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• Wave-particle resonance due to parallel motion of
  particles

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Landau damping bump on tail instability

• Vlasov equation
• Linearization
• Langmuir wave
• Consider the parallel motion of the electrons
  only

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• Poison equation
• Dispersion equation
• Landau damping for Maxwellian distribution

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• Instability for bump on tail distribution

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Lower hybrid current drive

• Electron velocity distribution functions
• with different trapping effects under
• LHCD

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Bump-on-tail problem with the presence of
energetic particles

• Discrete Alfven eigenmodes
• Energetic particle modes

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Destabilization of shear Alfven waves via
wave-particle resonance

• Dispersion relation of shear Alfven wave
• Destabilization mechanism (universal drive)
• Wave particle resonance at
• For the right phase, particle will lose energy
  going outward and gaining energy going inward. As
  a result, particles will lose energy to waves.
• Energetic particle drive

Spatial gradient drive
Landau damping Due to velocity space gradient
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Shear Alfven spectrum, continuum damping, and
discrete modes

• Shear Alfven wave dispersion relation in tokamaks
• Continuum spectrum
• Initial perturbation decays
  due to phase mixing at time scale of
• Driven perturbation at w is resonantly absorbed
  at ?continuum damping
• Phase mixing and resonant absorption has exact
  analogy with Landau damping for Vlasov plasma.

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Mode coupling between m and m1 induces a
continuum gap
Continuum spectrum is modified by toroidicity.
at
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Example of Discrete AE Toroidal Alfven
Eigenmode (TAE)
TAE mode frequencies are located inside the
toroidcity-induced Alfven gaps TAE modes peak at
the gaps with two dominating poloidal harmonics.
C.Z. Cheng, L. Chen and M.S. Chance 1985, Ann.
Phys. (N.Y.) 161, 21
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Bump-on-tail problem saturation with damping,
source and sink

• Collisions tend to restore the original unstable
  distribution. Balance of nonlinear flattening and
  collisional restoration leads to mode saturation.
  It can be shown that the linear growth rate is
  reduced by a factor of . Thus, the
  mode saturates at

H.L. Berk and B.N. Breizman 1990, Phys. Fluids B
2, 2235
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H.L. Berk et al, Phys. Plasmas 2, 3007 (1995).
21
.
Multiple unstable modes can lead to resonance
overlap and stochastic diffusion of energetic
particles
H.L. Berk et al, Phys. Plasmas 2, 3007 (1995).
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First observation of TAE in TFTR
.
K.L. Wong, R.J. Fonck, S.F. Paul, et al. 1991,
Phys. Rev. Lett. 66, 1874
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Discrete Alfven Eigenmodes versus Energetic
Particle Modes

• Discrete Alfven Eigenmodes (AE)
• Mode frequencies located outside Alfven
  continuum (e.g., inside gaps)
• Modes exist in the MHD limit
• energetic particle effects are often
  perturbative.
• Energetic Particle Modes (EPM)
• Mode frequencies located inside Alfven continuum
  and determined by energetic particle dynamics
• Energetic effects are non-perturbative
• Requires sufficient energetic particle drive to
  overcome continuum damping.

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• Wave-particle resonance due to drift motion of
  particles

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Fishbone Instability

• Induce by injection of high energy neutral beam
• Due to interaction between the injected particles
  and the m1,n1 MHD mode
• Resonance between the toroidal wave velocity of
  the mode and toroidal drift of the trapped
  particles

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Fishbone dispersion relation
L. Chen, R.B. White and M.N. Rosenbluth 1984,
Phys. Rev. Lett. 52, 1122
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Electron fishbone instability
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• HL-2A results need further explanation

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Wave-particle resonance due to rotation of
particles

• ECRH,
• ICRH,
• ECE

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Summary

• Wave-particle resonance is a basic and important
  mechanism for wave-particle interaction in
  tokamak plasmas
• Externally launched waves may be absorbed and
  heat plasma or drive current in plasma by
  wave-particle resonance
• Waves may be driven by particle motion through
  wave-particle resonance in plasmas
• There are quite a few observations on wave
  excitation in plasmas need explanation