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The RF codes used in TRANSP SPRUCE and TORIC

The RF codes used in TRANSP SPRUCE and TORIC. F. Meo Contributions from M. Brambilla, J. M. Noterdaeme, D. Hartmann, R. Bilato , M. Evrard. Introduction (clear up some jargon) Full Wave ICRF Codes used in TRANSP Comparison between SRUCE and TORIC TORIC Sample runs

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The RF codes used in TRANSP SPRUCE and TORIC

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  1. The RF codes used in TRANSPSPRUCE and TORIC F. Meo Contributions from M. Brambilla, J. M. Noterdaeme, D. Hartmann, R. Bilato , M. Evrard

  2. Introduction (clear up some jargon) Full Wave ICRF Codes used in TRANSP Comparison between SRUCE and TORIC TORIC Sample runs H minority regime on AUG and JET Mode conversion regime on AUG Things to consider Pitfalls The Outline

  3. ICRF range of today’s Tokamaks: 10’s of MHz Mode chosen is the FW corresponds to Compressional Alven Wave sound like  magnetic pressure Important feature : Dependence of Vph on density Electron density Magnetic field Y Jy Bz X Z Bo Excitation of Fast Waves (FW) Inductive wave launcher to perturbe the parallel magnetic field Plasma

  4. Resonance Zone R Damping mechanisms • Cyclotron damping • (IONS) • Wave  component to Bo  (E+) • Resonance condition • (cyclotron resonance)

  5. Vph V|| Damping mechanisms • Electron Landau Damping (ELD) • (ELECTRONS) •  component to Bo  (E) • Resonance condition • (Landau resonance condition)

  6. V|| V V Bo  Acts towards regions of weaker fields Damping mechanisms • Transit Time Magnetic Pumping (TTMP) • ELECTRONS • spatial gradient of wave magnetic field interacts with  Bo  (E) • IF Vph ~ V|| & B||  0  then F|| acts similar to ELD

  7. Power balance E >> E Hence ELD relatively weak Fast Wave Cyclotron Damping direct electron ELD & TTMP wave transformation (mode conversion) cyclotron cyclotron cyclotron Bernstein Wave min ions Bulk ions electrons

  8. Terms defined • In a tokamak plasma V|| Vth can be ~ Vph Landau resonance condition

  9. Plasma Y Jy Jy Bz X Re(Ey) Z Bo k Higher Vph Higher Vph Multiple current straps FW launching Dimensions of antenna determine the k spectra

  10. “Heating” “Current Drive” Launched spectrum AUG JET

  11. solution: k = k (w, k||) • fast wave • slow wave • ion Bernstein wave k k B0 k|| Solving determinant = 0: Dispersion relation D(w, k) =0 w determined by generator k|| determined by antenna where k|| > k||,Vacuum.

  12. R RF in TRANSP: Important factors to look at! Resonance layer positions: f, Bo, Maj Gas (q, m), minority (q, m) Rough calculation of resonance layer positions Bo Machine Dependent Parameter HFS Web site program to do the same f http://w3.rf.jet.efda.org/RFops/rfoi/resonance.htm n ion1 n ion2

  13. Mode conversion layer Ion/ion Cutoff Ion/ion Resonance E What is mode conversion? • Consequence of multi-species inhomogeneous plasma • Two solutions to the dispersion relation D(,n)=0 of  that have the same k. • Ion Bernstein wave (IBW) IBW FW

  14. MC MC Increasing the minority concentration f = 30 MHz, Bo = 2.9 T D plasma H plasma 1 D 1 3He 1 H 1 D 1 3He 1 H

  15. Consequence of increasing Minority conc. What do they mean by “minority heating” and “mode conversion” regime? • Minority regime  Low minority species concentration (< 5%) • Majority of power to the minority ions • Mode conversion regime  High minority species concentration (>15%) • Majority of power to the electrons through the IBW and FW • Important factor to influence the transition is the Thermal Doppler broadening H  E+ of FW D plasma with 5% H Brambilla, Physics Letters A 188 (1994) 376-383

  16. Fast Wave (FW) Larger  (~10’s of cm) ~ machine size propagate in the plasma like a cavity. Electromagnetic Broad deposition Comparison between FW and IBW • Ion Bernstien Wave (IBW) • smaller wavelength (~ mm) prone to refraction. • Electrostatic (Nearly) • Precise power deposition  toiroidal (current drive) and poloidal flow to increase plasma stability • BOTH • Lower energy density (in k spectrum) compared to Lower Hybrid.  Unlikely to pull a significant tail in electron distribution function. • However if the tail exists, FW and IBW can drive collisionless electrons depending on the launched k value

  17. ICRF codes available in TRANSP • 2D full wave solver in arbitrary toroidal geometry in the ion cyclotron frequency range. • Because it’s axisymmetric they both solve at one one n

  18. CPU Time to run TORIC • TORIC can be very expensive in CPU time. However, there may be some approximations that can be made that will significantly decrease the CPU time needed.: • Bpol turned off = 20% Less CPU time • IBW turned off = 50% Less CPU time • Bottle neck: FFT • Improvements: to incorporate faster FFT algorithms

  19. In addition to Thermal Doppler broadening, spectral broadening can have a significant affect on k. Poloidal and to toroidal modes are strongly coupled This should mainly be sensitive to ELD Effect of toroidicity: Spectral broadening m = +64 m = 0 m = -64

  20. TORIC coordinate system For the FW, E or E << E . B u u u   u u :  to magnetic surface

  21. Spectral Approach The spectral representation of the field allows the direct definition the physical components of the wave vectors (k and k). This makes the Landau Damping calculation of electrons (ELD) more accurate. SPRUCE seems to be faster but at a price. It uses an approximate method to the ELD and does not take into account the spectral broadening of k caused by the poloidal field. However, this should not greatly affect the Cyclotron damping. Hence, it is predicted that in a scenario where there is little ELD (i.e. minority regime with low temperature) the two codes should produce the similar results. A comparison should be done with IBW and B turned off in TORIC

  22. TORIC can be easily interfaced with any tokamak representation of Cartesian co-ordinates X(,) and Z(,) In the condition that they satisfy certain criteria related to the Jacobian Two possibilities: Analytical polynomial moments representation X(,) = () + a  cos( - () sin) Z(,) = a () sin() Plasma  effects on pressure not included f() determined from Faraday‘s law If the J() profile is given correctly, equilibrium representation is very good Can only do monotonic q profiles. Fourier moments from equilibrium solver (future advancement) On going work to read g files from EFIT and decompose to Fourier modes NTCC collaboration. Will have the possibility for more complex equilibrium - Up/down asymmetry Equilibrium representation

  23. ASDEX-U & CLISTE JET & EFIT DIII-D & EFIT Simulation of three Tokamaks

  24. Sample summary output from TORIC It is important to verify any test run via the summary output file. Tue Jan 22 19:00:00 MET 2002 SUPER-UX -rwxr-xr-x 1 fem tkicrh 2564210 Dec 14 17:07 /u/fem/toric/base/NECsx5/toric.out himiko ---> NAG (X05BAF) ---> CPU-time = 0.00s (total 0.0 s) TOROIDAL IC FULL-WAVE CODE TORIC Version 2.02 - 08.06.2001 Solution of the wave equations TOKAMAK PARAMETERS: Major radius = 167.000 cm Separatrix radius = 50.000 cm Plasma radius (edge of s.o.) = 50.000 cm Faraday Shield omitted = Antenna radius = 53.000 cm Vacuum vessel radius = 70.000 cm Central magnetic field = 2.100 Tesla Toroidal plasma current = 1000.000 kA Safety factor q on axis = 0.804 Safety factor q at separatrix = 3.206 Shift (axis, sep., wall) = 5.000 0.000 -2.000 cm Ellipticity = 1.000 1.600 1.700 Triangularity = 0.000 -0.150 -0.294

  25. Sample summary output from TORIC PLASMA PARAMETERS Central electron density = 6.000E+13 cm-3 Central electron temperature = 3.000 keV Central electron beta = 3.624E-02 Electron density at the separat. = 1.000E+13 cm-3 Electron temperature at the sep. = 0.100 keV Ion Species 1 : Charge (atomic units) 1.0 Mass (atomic units) 2.0 Concentration (100*n_i/n_e) = 95.000 % Central temperature = 3.000 keV Harmonic resonance at X = 11.270 cm tangent to the surface r/a = 0.129 on the low-field side Ion Species 2 : Charge (atomic units) 1.0 Mass (atomic units) 1.0 Concentration (100*n_i/n_e) = 5.000 % Central temperature = 3.000 keV Fundam. resonance at X = 11.270 cm tangent to the surface r/a = 0.129 on the low-field side Ion-ion resonance at X = 4.778 cm Ion-ion cutoff at X = 6.812 cm Default profiles (1 - psi^pi)^pe Density: pi = 3.000 pe = 1.500 Elec. temperature: pi = 1.500 pe = 1.000 Ion temperature: pi = 1.500 pe = 1.000 Toroidal current : pi = 2.000 pe = 1.500

  26. Sample summary output from TORIC PLASMA MODEL: Ions: finite Larmor radius approximation ELD of IB waves taken into account Parallel electric field taken into account Electrons: Landau damping and TTMP with mixed term Collisions omitted Poloidal magnetic field ignored Jaing-Wu-Povinelli formulation in vacuum Ez suppressed in vacuum WAVE AND ANTENNA PARAMETERS Frequency = 30.000 Mhz Toroidal wavenumber NPHI = 6 Equiv. parallel index = 5.714 Equiv. k_parallel (m^-1) = 3.593 Half-length of the antenna = 50.000 cm (LC)-constant of the antenna = 1.600 ko = 6.2874E-01 lo = 1.5905E+00 ko*R = 1.0500E+00 ko*a = 4.4012E-01 MESH PARAMETERS Number of poloidal modes 127 Number of poloidal mesh points 256 Number of radial mesh points 353 Psi step: 3.215E-03 Number of poloidal modes in vacuum 15 Number of mesh points in vacuum 40 Psi step in vacuum 1.026E-02 Plasma edge at psi =: 1.000 (mesh point 312) outer side: x = 50.000 R = 217.000 inner side: x = -50.000 R = 117.000 Antenna at psi =: 1.062 (mesh point 319) outer side: x = 52.725 R = 219.725 inner side: x = -53.429 R = 113.571 Wall at psi =: 1.400 (mesh point 353) outer side: x = 68.000 R = 235.000 inner side: x = -72.000 R = 95.000 Two-point boundary condition at the antenna Two-point boundary condition at the plasma edge

  27. Sample summary output from TORIC Global power balance Power to ions 1 fundamental 0.0000E+00 MW/kA^2 ( 0.00 %) first harm. 2.9562E+00 MW/kA^2 ( 27.09 %) Power to ions 2 fundamental 7.3952E+00 MW/kA^2 ( 67.77 %) first harm. 0.0000E+00 MW/kA^2 ( 0.00 %) Power to the electrons (tot) 5.6084E-01 MW/kA^2 ( 5.14 %) - from the fast wave 1.5649E-01 MW/kA^2 ( 1.43 %) - from the ib wave 4.0435E-01 MW/kA^2 ( 3.71 %) Total absorbed power 1.0912E+01 MW/kA^2 Total radiated power (J*E) 1.0717E+01 MW/kA^2 Total radiated power (Poynting) 1.0715E+01 MW/kA^2 - towards the wall -4.8618E-07 MW/kA^2 Powers from the explicit theta integration Power to ions 1 - fundamental 0.0000E+00 MW/kA^2 Power to ions 1 - first harm. 2.9556E+00 MW/kA^2 Power to ions 2 - fundamental 7.3952E+00 MW/kA^2 Power to ions 2 - first harm. 0.0000E+00 MW/kA^2 Power to the electrons (tot.) 5.5995E-01 MW/kA^2 via Fast waves 1.5560E-01 MW/kA^2 via IB waves 4.0435E-01 MW/kA^2 Accuracy of the 2dim abs. power -1.3374E-04 Electric field in V/m, magnetic field in Gauss, total power in W (MW) for 1 A (1 kA) in the antenna numerically equal to the loading resistance in Ohms. Power density in W/cm3 for 1 MW coupled to the plasma. Efficiency of IBW current drive evaluated with the refracted spectrum (i.e. with same k// as in the power balance) Volume average electron density 3.6116E-01 (10^20 M^3)

  28. Sample summary output from TORIC Current drive estimate, total: RF current per incident power 1.6013E-03 (A/W) Current per incident power(NT) 2.1032E-03 (A/W) Current drive figure of merit 9.6579E-04 (A/W/M^2) Current drive figure of merit(NT) 1.2685E-03 (A/W/M^2) Current drive estimate, fast Wave: RF current per incident power 1.1002E-03 (A/W) Current per incident power(NT) 1.3459E-03 (A/W) Current drive figure of merit 6.6356E-04 (A/W/M^2) Current drive figure of merit(NT) 8.1176E-04 (A/W/M^2) Current drive estimate, IB Wave: RF current per incident power 5.0109E-04 (A/W) Current per incident power(NT) 7.5731E-04 (A/W) Current drive figure of merit 3.0223E-04 (A/W/M^2) Current drive figure of merit(NT) 4.5676E-04 (A/W/M^2) The output has been stored on disk ---> NAG (X05BAF) ---> CPU-time = 2842.42s (total 2842.4 s) Tue Jan 22 20:53:28 MET 2002

  29. FW only TORIC simulation results AUG-DI: Bo = 2.9 T f=30 MHz JET-DI: Bo = 3.45 T f=37 MHz D3D-DIII: Bo = 2.1 T f=83 MHz

  30. Example: H minority in AUG Bo = 2.1 T f=30 MHz [H] = 5% ne(0)=3.0 1019 m-3 Te(0)=3.0 keV D plasma MC 1 H

  31. H minority in AUG

  32. H minority in AUG H D Bo = 2.1 T f=30 MHz [H] = 5% ne(0)=3.0 1019 m-3 Te(0)=3.0 keV m = 127, 3000sec CPU time Power balance D=22% 2H=60% e=18% 1.5 to FW 16.5 to IBW

  33. Same scenario (H in AUG) but double the central density H D Bo = 2.1 T f=30 MHz [H] = 5% ne(0) = 6.0 1019 m-3 Te(0) = 3.0 keV m = 127, 3000sec CPU time Power balance D=27% 2H=68% e=5% 1.5 to FW 3.5 to IBW

  34. JET case for minority heating H Bo = 2.4 T f=37 MHz [H] = 5% ne(0) = 3.0 1019 m-3 Te(0) = 6.0 keV MC 1 H

  35. H min. on JET H D m = 127, 3000sec CPU time Power balance D=17% 2H=79% e=3% 2% to FW 1% to IBW

  36. TORIC He mode conversion [He] = 30% Convergent case m=200: For [He3] = 30% - Power to He < 10% 200 Poloidal Fourier Modes Swap file > 32 GB CPU Run time ~ 30 000 sec. (8 hours) Real run time ~ 1 to 2 days

  37. E E Mode convergence (m=200)

  38. Pitfalls to look out for • Not enough poloidal resolution • This will depend on scenario. Beware of “overkill” • Pure FW (no resonance layers in plasma) m=63 acceptable for AUG and JET • H minority regime is easier to converge than 3He: AUG and JET m > 127 • Mode conversion using 3He is much more difficult m > 200 for AUG. • Avoid resonance layers at the edge at the edge • Verify the n dependence • TRANSP runs at one n • This has great effect if there is considerable ELD • Normalise results to the launched spectrum • Fokker-Planck • Tails in the minority will influence the fields and the minority absorption • Iteration with FP and TORIC • More important in larger machines like JET since it confines fast particles • Always look at the output summary file and the electric fields

  39. JET H minority m = 63 m = 127

  40. Over estimation of the minority damping (m=127) TORIC simulation of 3He mode conversion (m=200)

  41. Pitfalls to look out for • Not enough poloidal resolution • This will depend on scenario. Beware of “overkill” • Pure FW (no resonance layers in plasma) m=63 acceptable for AUG and JET • H minority regime is easier to converge than 3He: AUG and JET m > 127 • Mode conversion using 3He is much more difficult m > 200 for AUG. • Avoid resonance layers at the edge at the edge • Verify the n dependence • TRANSP runs at one n • This has great effect if there is considerable ELD • Normalize results to the launched spectrum • Fokker-Planck • Tails in the minority will influence the fields and the minority absorption • Iteration with FP and TORIC • More important in larger machines like JET since it confines fast particles • Always look at the output summary file and the electric fields

  42. Resonance layers near the outer edge This will cause numerical spurious results In addition, experiments have shown that this scenario causes coupling problems and should be avoided all together n ion MC

  43. Pitfalls to look out for • Not enough poloidal resolution • This will depend on scenario. Beware of “overkill” • Pure FW (no resonance layers in plasma) m=63 acceptable for AUG and JET • H minority regime is easier to converge than 3He: AUG and JET m > 127 • Mode conversion using 3He is much more difficult m > 200 for AUG. • Avoid resonance layers at the edge at the edge • Verify the n dependence - know your antenna! • TRANSP runs at one n • This has large effect if there is considerable ELD • Normalise results to the launched spectrum • Fokker-Planck iteration • Tails in the minority will influence the fields and the minority absorption • Iteration with FP and TORIC • More important in larger machines like JET since it confines fast particles • Always look at the output summary file and the electric fields

  44. Power balance n Example of the importance of n AUG Bo = 2.0 T f=74 MHz [H] = 5% ne(0)=3.0 1019 m-3 Te(0)=3.0 keV D plasma MC 1 H

  45. Recent upgrade of code (Brambilla) • Code was tested extensively for a wide range of operating parameters. • TORIC • Improvement of boundary conditions • Improvement os the IBW solver • Frontal solver to save to disk to circumvent the memory requirement for high number of modes • Improvement of the IBW damping • Treatment of IBW to handle large k values • Asymmetry of the poloidal position of antenna w.r.t the mid-plain.

  46. Future advancements for TORIC • TORIC is the most widely used ICRF code around the world. AUG, C-MOD, PPPL, JET, etc… • Improvements • Interface with equilibrium solver (gfiles) allowing more complex geometry and q profile • Standardised programming • Higher harmonics • Standardised data storage (CDF) • Improved standard graphing package (not covered in talk) • Ion Fokker-Plank interface • Will work on increasing number of modes • Parallelisation

  47. Conclusion It is important to benchmark both RF codes and to verify in which scenarios they show discrepancies. Comparison should be done in in several scenarios where there is low and high ELD. For each scenario there should be runs for a scan of different n in each scenario. If for a certain scenario both codes agree, then the faster code should be used. Before any RF code run, you should know the following Resonance positions (f, Bo, gases, concentrations) Know your antenna spectrum Before any TRANSP run, it would be wise to first test the RF code at one time step in a stand alone run - especially with a new scenarios. The test runs should verify. The minimum number of resolution needed (radially and poloidally) The dependence of the toroidal wave number n and verify the importance according to your antenna spectrum. Verify the summary file for the power balance and the agreement between total absorbed power to total radiated power. In addition to what everybody is interested in - the plot of the power absorption to ions and electrons, you should also verify the equatorial and 2D plots of the fields to verify if the code ran properly. Future improvements to the TRANSP RF package should include: Ability to run the RF code in stand-alone mode at one time step. Incorporate the iteration between RF and Fokker-Planck module This subject should be studied in greater detail by the RF researchers. THE END

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