FAST WAVE HEATING AND CURRENT DRIVE

1
FAST WAVE HEATING AND CURRENT DRIVE

• R. Koch
• 5th Korean Fusion Plasma Summer School

2
Table of contents

• Introduction
• The needs for auxiliary systems
• Coupling of RF power to plasmas
• Waves landscape in ICRF
• Magnetosonic wave equation
• Antenna-plasma coupling elementary theory
• Plasma surface impedance
• Power, antenna characteristics and performance
• Radiated field
• TOPICA
• Coupling of wave power to particles
• Wave-particle resonances
• Landau and TTMP resonances
• Ion cyclotron resonance and harmonics
• Ion cyclotron interaction
• Wave resonances
• Budden model
• Ion-ion hybrid
• Transfer of fast ion energy to bulk ions

3
The needs for auxiliary systems

• Heating
• Ion heating in reactors
• Non-inductive current generation
• Steady-state tokamaks
• Profile control (Ip, q)
• Shear flow / Rotation drive
• Stabilization of sawteeth / neoclassical tearing
  modes (NTM)
• Stabilisation of MHD modes resistive wall modes
  (RWM)
• Generation of internal transport barriers (ITB)
• Plasma production
• Plasma generation (stellarators)
• Current start-up
• Wall conditioning
• Others
• Induced particle diffusion (?s)
• ITER
• Is a driven machine
• DEMO

4
Coupling RF power to plasmas

• What is meant by coupling?

Hot plasma wave eqs
Maxwells eqs
Lumped circuit theory
Cold FW
wave eqs
Coaxial transmission line theory (TEM mode)
Antenna coupling theory
5
Waves landscape in the ICRF

• Perpendicular propagation (k.B00) transverse
  polarization (E.B00)

Ion Bernstein waves
Fast wave
cold
cold
Angular frequency
6
The magnetosonic wave equation

• Dispersion (ref. Gao)
• In the ion cyclotron domain
• P??, Ez?0
• Uncoupled fast-wave dispersion relation

7
The magnetosonic wave equation

• Coupling power from antennas to plasmas
• Elementary coupling theory
• Antenna parameters
• Radiated field

8
Elementary coupling theory

• ky 0
• Uniform plasma (ne , BT constant)
• Simple antenna
• Wave is evanescent
• in vacuum
• jy ?(x) ?(z-wz)- ?(zwz) ey
• Zones I and II Maxwells equations with current
  source (jump in Hz at jy current sheet)
• Zone III Magnetosonic wave equation
• Single pass absorption hypothesis radiation
  boundary condition at infinity

Note waveguide / slot
9
Elementary coupling theoryThe plasma surface
impedance

• Wave equation example magnetosonic wave
• Radiating boundary condition
• ? Surface impedance of the plasma
• Continuity of tangential field components ?
  continuity of ?S ? BC for vacuum problem
• Generally surface impedance matrix

10
Elementary coupling theorySolution for the
vacuum fields

• Vacuum wave equation
• Fields in regions I and II
• Boundary conditions
• Wall Antenna Plasma
• ?
• More generally

11
Elementary coupling theoryPoynting theorem and
antenna characteristics

• Poyntings theorem
• Induced emf method
• complex radiated power
• R antenna (specific) resistance
• L antenna (specific) self-inductance
• C antenna (specific) capacitance
• M antenna (specific) mutual
• Transmission line characteristics
• Propagation constant Characteristic impedance
• Antenna input impedance

12
Elementary coupling theoryRadiated power
Strap-plasma distance
Peak of spectrum
Refractive index mismatch
13
Elementary coupling theoryAntenna performance
Voltage at antenna input
Power for voltage V
Antenna quality factor
Geff
14
Elementary coupling theoryRadiated far fields

• Inverse Fourier transform

• Far field from asymptotic method

• Stationary phase ? ray

• Poynting vector (power flux along rays)

15
Elementary coupling theoryRadiated far field of
anarray
?-phasing (dipole)
0-phasing (monopole)
?/2-phasing (current drive)
16
Coupling What does a real antenna look like?
17
Modern coupling codesTOPICA (Politecnico di
Torino)

• Antenna in box
• Finite boundary elements
• Physical space integrals
• Aperture
• Plasma
• Surface impedance matrix from spectral solution

18
Modern coupling code
TOPICA (Turin) Antenna model
Poynting flux streamlines
19
Coupling of waves to particles
Coupling of waves to particlesCollisional
damping and resonant interaction
Coupling of waves to particlesCollisional
damping and resonant interactionPlasma
parameters (JET) orders of magnitudeR03m,
2?R020m, ap1.5m, 2? ap10m
Plasma parameters (Deuterium) T 5keV, n 5
1019m-3, B0 3T
20
Coupling of waves to particlesCollisional
damping and resonant interactionPlasma
parameters (JET) orders of magnitudeR03m,
2?R020m, ap1.5m, 2? ap10m
Plasma parameters (Deuterium) T 5keV, n 5
1019m-3, B0 3T
21
Coupling of waves to particlesCollisional
damping and resonant interaction
For wave heating ne10kHz, ni100Hz, ? 2?f,
f 1MHz 100 GHz

• Resonances are necessary
• Wave-particle resonances
• // Landau damping TTMP
• ? Cyclotron damping
• Wave resonances
• Resonance, mode conversion, ion-ion hybrid

22

• Orders of magnitude RF
• frequency 50MHz
• Power 2MW/antenna
• Voltage 20-50kv at the antenna
• Antenna current 1kA
• Central conductor width 0.2m, length 1m,
  distance to the plasma 5cm, to the wall 20cm
• Typical RF electric field 1-50kv/m
• Typical RF magnetic induction 10-3T B0
• Orders of magnitude Forces
• E v?B
• e D
• VT ? B0 100MV/m 1.5MV/m
• ?The RF only makes a small perturbation on the
  thermal motion

23
Wave-particle resonancesAcceleration parallel
to the magnetic field
Landau interaction E // B0
Transit-time magnetic pumping

• Force
• (? magnetic moment)

• Parallel acceleration,
• similar to Landau damping

Effective mechanism for electron push at low
frequencies (ICRF) Current drive
24
Wave-particle resonancesThe cyclotron
interaction
Linearized (simplified) perpendicular motion
Assume E constant in space
(finite)
Resonances for ions
(but ? t at resonance)
With left-handed wave (E)
25
Cyclotron interaction
Fundamental
Harmonic
26
Harmonic cyclotron interaction
Harmonic
Taylor expansion of the electric field
Harmonic decomposition of the field
Weaker acceleration
27
The cyclotron interaction
General case
Response from the general term
General resonance condition
Resonances associated with the r.h. field
component
28
Ion cyclotron heating in real geometry
w-k//v//wc(R)
Velocity and energy kick at crossing
Kick at resonance crossing
? Diffusion in velocity space
? Monte-Carlo methods
JET
29
Wave resonances

• Example Budden equation
• Dispersion relation

• Wave equation

• Power conservation
• equation

30
Wave resonances

• Power absorption
• at the resonance

• Resonant and non-collisional absorption
• ?? ? 0 P ? 0
• Wave pile-up

• Mode conversion

• Practical example ion-ion hybrid resonance (ICRH)

• Plemelj formula

31
The ion-ion hybrid resonance

• Uncoupled fast-wave equation
• or
• DT plasma, ?cD ?cH/2 ?cT ?cH /3

32
The ion-ion hybrid resonance

• Note IBW / ICW

33
The last stepPower transfer from the resonant
populationto the plasma bulk
34
Quasilinear diffusion

• Quasilinear diffusion coefficient

• Evolution of the distribution function

• Formation of a quasilinear plateau

v

• General case the quasilinear Fokker-Planck
  equation

• Tail formation
• Ion cyclotron heating fast ion tails

Wmv2/2
Wmv2/2
Wmv2/2
35
Damping at cyclotron harmonics

• Quasilinear diffusion coefficient (? ? n ?ci)
• For the fast wave
• Fundamental (n1)
• Second harmonic (n2)
• n-th harmonic

36
Quasilinear diffusion NBI RF
More of all this ?
Quasilinear evolution of the distribution
function f(v?, v//) of beam-injected particles
heated at the 3rd harmonic by ICRH (BECHSI code,
D. Van Eester) TEXTOR, D-beam
More of all this ? D. Batchelor
beam
injection
37
The end