Integrated Modelling of ICRH and AE Dynamics

1
Integrated Modelling of ICRH and AE Dynamics

• T. Hellsten, T. Bergkvist, T. Johnson and M.
  Laxåback
• Alfvén Laboratory, Royal Inst. of Technology,
• SE-100 44 Stockholm, Sweden Association
  Euratom-VR.

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ICRH

• ICRH is a versatile heating method that can
  provide
• Heating
• Enhance fusion reactivity
• Drive Currents
• Induce rotation
• Excite AEs

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ICRH Modelling

• ICRH requires self-consistent modelling of
  distribution functions and wave field including
  effects of finite orbit width and RF-induced
  spatial transport of fast ions for waves with
  finite nf.
• Due to the different time scales this can be done
  by iterations.

4
The SELFO code calculates the ICRH wave field
with the LION code and the distribution function
in the invariant space (W, Pf, L) with the Monte
Carlo code FIDO.
Define equilibrium, antenna spectrum, power.
Create tables for the various interactions used
in the Monte Carlo code with an orbit solver.
Calculate the dielectric tensor and wave field
for ICRH (LION code1) from the output of FIDO
Calculate changes in orbit invariants by
collisions, and ICRH with the FIDO code. Remove
lost ions, add NBI, a-particles and edge source.
Output
1 LION code L. Villard et al, Computer Physics
Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173
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-90o phasing trapped 3He ions displaced
outwards.? emission from turning points of
trapped ions at cyclotron resonance
RF-induced pinch and detrapping of the orbits
Co
Counter
T. Hellsten et al Phys. Rev. Lett 1995
Tomographic reconstruction of the g-emission
profiles from JET
90o ICRH phasing trapped 3He orbits pinched,
then detrapped to co-current wide passing orbits
at the low field side of the center
Tomegraphic reconstruction by C. Ingesson
T. Johnsson et al, IAEA Technical Meeting,
Gothenburgh, 2001
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• Comparison of the gamma emissitivity in the
  mid-plane z0 between tomographic reconstructions
  (full line) dashed region (confidence interval)
  and the density of high-energy 3He ions
  calculated with the SELFO code (boxes)

90-phasing location of the excited TAE modes
indicated
-90-phasing
SELFO code modelling by T. Johnson
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The excitation of Alfvén eigenmodes is sensitive
to the details of the distribution function. AEs
excited in JET during ICRH with 90 and -90
phasing of the antennas
90
-90
L.-G. Eriksson, et al Phys Rev. Lett 81 (1998)
1231 M. Mantsinen et al Phys. Rev. Lett. 84(2002).
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Splitting of the mode frequency
Typical mode splitting of about 2kHz is seen
during ICRH. The spitting is too wide to be due
to restoration of the distribution function by
Coulomb collisions.

A. Fasoli et al Phys. Rev. Lett. 81(1998)5564
Fast damping when ICRH is switched off
The AEs are damped in a time period of about
0.1ms after the ICRH is switched off. K. L.
Wong,et al Phys. Plasmas 4 (1997) 393
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Ion interaction with AEs

• In the absence of Coulomb collisions and ICRH the
  interactions of a resonant ion with an AE lead to
  a superadiabatic oscillation in the phase space
  of the invariants of the equation of motion for
  the drift orbit along the AE characteristics

W
Pf
m
If the distribution function increases with
energy around the resonance, energy will then be
transferred from the ions to the mode and vice
verse. When the distribution function is
flattened along all AE characteristics no net
transfer of energy takes place. The mode will
then be damped by different background damping
mechanisms.
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Decorrelation of AE interactions and renewal of
the distribution function

• Decorrelation of the interactions leads to a
  diffusion of the orbits along the characteristics
  instead of a superadiabatic oscillation.
• Ion cyclotron interactions and Coulomb collisions
  will partially restore the distribution function
  in the resonant regions and result in further
  transfer of energy from the resonant ions to AEs.
• The decorrelation of the interactions and local
  renewal of the distribution function by ICRH
  increases with energy, whereas they decrease with
  energy for Coulomb collisions.

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Renewal of the distribution function by ICRH
ICRH creates an inverted distribution function
along the AE characteristics
The dynamics of the AE excitation depend not only
on the growth rate of the AE and background
damping, but also of the renewal rate of the
distribution function and the decorrelation of
the wave particle interactions.
The width of the resonance and the renewal rate
increase with ICRH power
Low energy ions removed by ICRH
High energy ions created by ICRH
Distribution function f(w) along a characteristic
initial distribution function
distribution function flattened by an AE
AE resonance
w
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The SELFO code calculates the distribution
function in the invariant space (W, Pf, L) with
the Monte Carlo code FIDO and the ICRH wave field
with the LION code. The AE field can either be
calculated with the LION code or from a
simplified model.
Define equilibrium, antenna spectrum, power,
type of AE mode etc.
Create tables for the various interactions used
in the Monte Carlo code with an orbit solver.
Calculate the dielectric tensor and wave field
for ICRH (LION code1) and amplitude of AEs
Calculate changes in orbit invariants by
collisions, ICRH and AE with the FIDO code.
Remove lost ions, add NBI, a-particles and edge
source.
Output
1 LION code L. Villard et al, Computer Physics
Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173
13

Monte Carlo code FIDO for calculating the
distribution function
MHD interactions a-particle
lower ripple sawteething
channelling hybrid diffusion
J. Carlson et al, Theory of Fusion Plasmas
Varenna 1996, L.-G. Eriksson and P. Helander
Phys. Plasmas (1994), T. Bergkvist et al Theory
of Fusion Plasmas Varenna 2004.
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TAE Resonance regions
Amplitude variations of the variance of the
energy for interactions with an TAE mode. Note
that internal zeros of the variance appear.
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The dynamics of TAE and frequency splitting
Fourier decomposition of the time evolution of
the mode amplitude gives a characteristic
frequency corresponding to the frequency
separation of the side bands seen during ICRH.
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Mode damping after ICRH switch off
The fast damping of the TAE of about 0.1ms as
ICRH is switched off is consistent with
experiments.
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Conclusions

• Self-consistent computations of wave field and
  distribution function are important for ICRH, in
  particular for power partition.
• The effects of finite orbit width and RF-induced
  spatial transport are important for many
  phenomena.
• The dynamics of the AEs are strongly affected by
  ICRH, which have to be taken into account when
  simulating AE excitation by thermonuclear alpha
  particles using ICRH ions.
• The decorrelation by ICRH increases the width of
  the resonances and the renewal rate, making the
  interactions with AE much stronger.

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Code for self-consistent modelling of heating
NBI
ICRH
LH
ECRH
Source
Wave spectrum
Wave spectrum
AE
Wave field
Ray tracing
Ray tracing
Wave field
Distribution function for electrons
f(y,W,z) 3D-Finite element
Distribution function for ions f(W,Pf, L) Monte
Carlo method 3D-Finite element
Equi-librium, Loop voltage
MHD Sawteeth Fishbones
Power deposition Fast ion Fusion
reactions Current profile Momentum
Power deposition Current profile