T. Hellsten1, T. Bergkvist1, T.Johnson1, M. Lax

1

Self-consistent calculations of the distribution
function and wave field during ICRF heating and
global Alfven wave excitation

• T. Hellsten1, T. Bergkvist1, T.Johnson1, M.
  Laxåback1 and L.-G. Eriksson2
• 1Euratom-VR association, Alfvén Laboratory, Royal
  Institute of Technology, SE-100 44 Stockholm,
  Sweden2Association Euratom-CEA, F-13108 St. Paul
  lez Durance, France

2

Alfvén eigenmodes in JET during ICRH with 90
and -90 phasing of the antennae
90
-90
L.-G. Eriksson, et al Phys Rev. Lett 81 (1998)
1231 M. Mantsinen et al Phys. Rev. Lett. 84(2002).
3
Evolution of drift orbits during ICRH, the
effect of that DPfnf/w DE
0.5MeV 1.0MeV
2.0MeV
0.5MeV 1.0MeV
2.0MeV

• Interactions with waves propagating
  Interactions with waves propagating
• parallel to plasma current
  anti-parallel to plasma current

T. Hellsten et al Phys. Rev. Lett. 1995
4
-90o ICRH phasing trapped 3He ions displaced
outwards.? emission from turning points of
trapped ions at cyclotron resonance
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
Tomographic reconstruction by C. Ingesson V. G.
Kiptily et al Nucl. Fusion 42(2001)999
5

• Simulation of Alfvén wave excitation by
  thermonuclear a-particles with ICRH.
• Energy distribution of ICRH and alpha
  particles
• similar.
• Details of the distribution function
  different not only
• damping. Heating with 90o and -90o in JET
  result
• in different excitations.
• ICRH de-correlate interactions with Alfvén
  waves
• Modelling of Alfvén wave excitation requires
  detailed calculation of the distribution function
  including ICRH and interactions with Alfvén modes.

6

Wave particle interaction
Resonance condition
ICRH contribution
7

MHD and ICRH represent a one dimensional
diffusion processes in the invariant space (E,
Pf, L)
MHD
ICRH
8

• Wave-particle interactions at guiding centre
  drift frequencies will displace the orbit
  invariants along the curve

and for cyclotron interactions along the curve
9
Characteristics for ICRH
10

Monte Carlo code FIDO for calculating the
distribution function
J. Carlson et al, Theory of Fusion Plasmas
Varenna 1996, L.-G. Eriksson and P. Helander
Phys. Plasmas (1994), T. Bergkvist et al 15th
Topical Conf. On RF-power in Plasmas, Wyoming
2003.
11

Trajectories of MHD modes and ICRH
E
MHD
Resonance
m
Pf
ICRH
12

Different behaviour of wave-
particle interactions Low amplitude slow
diffusion High amplitude fast diffusion
High amplitude non-linear
bouncing
13

Low amplitude slow diffusion MHD increments for
n interactions during one decorrelation time
tdecorr , ntbtdecorr
14

High amplitude non-linear bouncing
Bouncing frequency
Excursions along the trajectory in phase space
Assume the orbit to be randomly displaced along
the MHD trajectory in the phase space in the
interval E-EresltDE after an decorrelation time
15

Amplitude of Alfvén eigenmode
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SELFO -code
Define equilibrium, antenna spectrum, power,
type of MHD mode etc.
Calculate dielectric tensors from distribution
functions
Calculate wave field for ICRH (LION code1) and
amplitude of Alfvén eigenmode
Calculate changes in orbit invariants by
collisions, ICRH and MHD with the FIDO code
1 LION code L. Villard et al, Computer Physics
Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173
Output
17
SELFO -code
Define equilibrium, antenna spectrum, power,
type of MHD mode etc.
Define equilibrium, antenna spectrum, power,
type of MHD mode etc.
Calculate wave field for ICRH (LION code1) and
amplitude of Alfvén eigenmode
Calculate changes in orbit invariants by
collisions, ICRH and MHD with the FIDO code
1 LION code L. Villard et al, Computer Physics
Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173
Output
18
Simulation of distributionn function for
different antenna phasing
90
-90
For 90 high energy de-trapped ions with
non-standard orbits are formed. For -90 the high
energy ions have lower energy and are trapped
with the turning point close to the magnetic axis
19

• 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
20
Initial energy given to the mode versus mode
frequency
21
Evolution of the mode amplitude
22
Conclusion

• The details of the the distribution function is
  important for the stability and growth of Alfvén
  eigenmodes.
• The decorrelation by RF-heating important for the
  non-linear growth of the Alfvén eigenmodes.
• SELFO code has been extended to self-consistent
  include the MHD and ICRH interactions.