1. Recent Progress in Self-consistent full wave simulations of lower hybrid waves
John C. Wright
P. T. Bonoli - MIT E .J. Valeo, C. K. Phillips - PPPL R. W. Harvey - Comp-X
US Japan RF Workshop
San Diego, March 8-10, 2010

2. Recent Progress in Self-consistent full wave simulations of lower hybrid waves
E. J. Valeo1, P. T. Bonoli2, R. W. Harvey3, C. K. Phillips1, J. C. Wright2
1 PPPL, 2 MIT, 3 Comp-X
US Japan RF Workshop
San Diego, March 8-10, 2010

3. Participants in the Center for Simulation of Wave-Plasma Interactions
L.A. Berry, D.B. Batchelor, E.F. Jaeger, E. D`Azevedo D. Green
D. Smithe
P.T. Bonoli, J.C. Wright
H. Kohno, A.S. Richardson
C.K. Phillips, E. Valeo
N. Gorelenkov, H. Qin
R.W. Harvey, A.P. Smirnov
N.M. Ershov
M. Brambilla
R. Bilato
M. Choi
R. Maggiora
D. Milanesio
D. D’Ippolito, J. Myra

4. Lower Hybrid heating/current drive overview Modeling LH waves
Outline
Lower Hybrid heating/current drive overview
Modeling LH waves
Ray tracing
Full Wave
Comparisons between approaches
Full wave effects + non-thermal electrons + relativistic effects
Summary and Conclusions

5. LHRF Regime Compare with ICRF FW perp wavelength of 10cm
LHCD Regime: ci<<<<ce and  ≥ 2LH
Unmagnetized ions
Strongly magnetized electrons [(ke)2  1]
Wave equation is sixth order with two propagating modes, one damped:
Mode converted ion plasma wave is not propagative, so drop sixth order term
Electrostatic LH “slow wave” branch
Electromagnetic LH “fast wave” branch Wave lengths are very short:
Predicts an accessibility criterion:
Index of refraction
Compare with ICRF FW perp wavelength of 10cm
wallace PP parametric studies of LH coupling
Bonoli PF 1982
Density

6. Tradeoffs and constraints
Compare with ICRF FW perp wavelength of 10cm
wallace PP parametric studies of LH coupling

7. Approaches to solution
WKB expansions: ray tracing (GENRAY, ACCOME) and beam tracing (LHBEAM) are asymptotic approximations to the wave equation, k a>>1 required. => can be problems with boundaries
Full Wave(TORIC-LH): solves Maxwell's equations directly, yields the electric field.
Hyperbolic Maxwell-Boltzmann Integral wave equation
Time Harmonic -> Elliptic wave equation
WKB -> raytracing terminated at 90%

8. TORIC Full Wave Code
TORIC [Brambilla 1999] was developed with an FLR model for the plasma current response, JP, for ion cyclotron waves and recently extended with an asymptotic form for lower hybrid waves.
The antenna is modeled as a current sheet, JA for ICRF and as the mouth of a wave guide with imposed E|| for LH.
It solves Maxwell's equations for a fixed frequency (Helmholtz problem) assuming toroidal symmetry in a mixed spectral-finite element basis. This is the physical optics solution.
Large Block Tri-diagonal matrix structure [ (8M)2 X NPSI ]
Parallelized
Serial

9. Simulation model is a coupled full wave and Fokker-Planck system
TORIC-LH (Wright 2004CPC,2009PoP)‏
CQL3D (Harvey 1992IAEA)‏
Bounce averaged Fokker-Planck code
that solves for new distribution function
from RF quasilinear flux,
provides f(v)‏
v0/vte
v||0/vte fe
v||
Dielectric for LH uses
zero FLR electrons and
unmagnetized ions.
Calculates the RF fields and
the quasilinear flux.
=> fe(v) and E(x) are self-consistent
Electron distribution functions from iteration with a Fokker-Planck code are used for dielectric. Pre-tabulation of Im Chizz results in no speed loss compared to the evaluation of the Z function for the Maxwellian case.
Simulations use EFIT reconstructed magnetic equilibria.

10. Full wave code algorithms
TORIC-LH
AORSA Jaeger
Alcator C mesh pts. n||=-2.5, B0=8T, ne0=5x1019 m-3,Te0=5keV.
COMSOL-LH Meneghini, Shiraiwa, Parker
COMSOL with 2D FE
TORIC-LH with 1D FE/1D Spectral
AORSA with 2D spectral
Each approach has advantages and difficulties:
CPU-hrs: COMSOL-LH 13, TORICLH 80, AORSA 32k (ray tracing ~ minutes) but wall clock times for all three are comparable given number of processors used. (2hrs)‏
COMSOL: 2D elements can model wall and separatrix region; sparse matrix scales well
The plasma dielectric:
COMSOL-LH requires real space dielectric formulation, doesn't have algebraic k||
TORIC-LH needs care in treating FLR truncation
AORSA – All Orders treatment most general, can handle fast ion interactions
Alcator C-Mod x512. n||=-4.0, B0=2T, ne0=6x1019 m-3,Te0=4keV.

11. Single pass is well converged with linear damping (Maxwellian)‏
Single pass damping on a Maxwellian plasma is converged.
Little interference is evident.
Power is very
localized in
single pass.
<- Spectrum
is converged
at 1023 modes
Use this slide to explain common measures that are used. Spectrum, power and poynting, 2D fields.
Expect to spend at least 2minutes on this slide.
r/a
n|| = -2.55, ne0=7e19 m-3
Te0 = 10 keV, B0=4T

12. Comparison with ray tracing in weak damping limit
Alcator C-Mod. n||=-1.55, B0=5.3T, ne0=7x1019m-3,Te0=2.3keV.
Maxwellian damping in both cases.
Good agreement in power deposition locations.
Field amplitudes are magnified by “cavity effect” [Q~/γ~200]

13. Weak damping requires quasilinear fe(v) for self-consistent treatment
Bulk damping
Accessibility cutoff
Width indicates
poloidal broadening
of Δn||/n||0 ~ Δm/q nφ
r/a
The poloidal power spectrum shows lack of convergence at outer flux surfaces,
Also magnification of unit amplitude applied field.

14. <Dql>bounce for FP coupling
Calculated following full wave treatment in Wright NF1997.
Bounce averaged, Larmor cutoff [ J0(kρi) ] at high perpendicular energies. Non-relativistic.
Note the symmetry in the trapped region.
v0/vte
v||0/vte
<Dql>
v0/vte
v||0/vte

15. Effect of non Maxwellian damping
Step0
Step1
Step2
Convergence achieved in two iterations.
Note the reduction in peak amplitude.
Fields are less space filling now.

16. Effect of non Maxwellian damping
r/a
Energy in poloidal modes plotted
for selected flux surfaces.
Power density and Poynting flux. Power is normalized to the
total power.
Spectrum is converged.
Power is a bit broader.

20. Iteration between TORICLH and CQL3D with relativistic effects converges rapidly
From TORIC_RUN 600.
Damping first over damping then settles down to marginally multipass. Poynting flux units are A.U. (for unit applied field) Power is normalized to total coupled power.
Iterations
Converges after some oscillations in damping strength.
Shows increased absorption
Power used = 350 kW generating 150 kA, n||=-2.5, Te=2.5 keV
Resolution, TORIC 400Nrx255Nm, CQL3D 60Nr x 88 Npitch x 160 Nu

21. Step 5

23. SUMMARY
TORIC + CQL3D produce self-consistent, relativistically correct, solutions for full-wave lower hybrid fields and electron distribution functions in toroidal plasma with realistic magnetic geometry and profiles.
X-ray spectral intensities computed from synthetic diagnostics have been validated against data from Alcator C-MOD.
Inclusion of an improved radial transport model in the evolution of Fe may resolve the difference between the computed and the broader experimental radial profile.
Near term plans: Import a newly developed (Lee, Wright) parallel algorithm with 3D decomposition (M1, M2, NPSI), shown to perform well (5X) in ICRF TORIC.

24. Additional material

25. log f