Work supported by the US DOE ICRF Mode Conversion Physics in Alcator C-Mod: Experimental Measurements and Modeling S.J. Wukitch Presented at the 46th Annual Meeting of the Division of Plasma Physics November 15-19, 004 Savannah, GA Y. Lin, A. Parisot, J.C. Wright, P.T. Bonoli, M. Porkolab, N. Basse, E. Edlund, A. Hubbard, L. Lin, A. Lynn, 1 E. Marmar, D. Mossessian, P. Phillips, 1 G. Schilling, and S.M. Wolfe 1 Fusion Research Center, The University of Texas, Austin, TX 7871, USA Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA
Overview Key Results: Simultaneously measured the Fast, Ion Bernstein (IBW), and Ion Cyclotron (ICW) waves in the mode conversion region using a phase contrast imaging diagnostic in D( 3 He) plasmas. TORIC code predictions are in agreement with measured power deposition and fluctuation profiles. Initial mode conversion current drive (MCCD) results suggest possible sawtooth control. Outline 1. Motivation for study of ICRF mode conversion. Basic mode conversion physics 3. Experimental and model description 4. Comparison of experimental data with simulations 5. Application: Current Drive 6. Conclusion
Possible Plasma Control using Mode Converted Waves Mode converted waves have been investigated and suggested to have potential to provide localized pressure, current and flow profile control and synergistically interact with LH waves. Details of mode converted wave propagation and absorption can affect the current or flow drive efficiency. Rapid k up-shift could result in loss of spectrum control and reduce current drive efficiency. Strong shear flow can be obtained if significant mode converted power is absorbed near the ion cyclotron resonance. Validate physics and computational models by comparing simulations with measured electron power deposition profile (plasma response) and wave characteristics. Develop predictive capability for future experiments.
ICRF Mode Conversion In multi ion-species (i.e. D-T), toroidal plasma with sheared B- field, the fast wave (FW) dispersion indicates possible mode conversion from FW To ion Bernstein (IBW) or Ion cyclotron waves (ICW). Mode conversion results in the coupling of a multiple wavelength modes. IBW is typically ~0.3 cm ICW is ~1- cm, and FW is ~10 cm. Can compete with minority absorption in certain scenarios. Re(n ) 10000 1000 100 Cold plasma, fast wave dispersion relation: n = ( )( n R n L) S n R, L and S are Stix notation n =S IBW Dispersion Curves cutoff ICW R (m) ω=ω 3 He FW 10 0.6 0.65 0.7 0.75 0.8 Full electromagnetic dispersion relation for D( 3 He) plasma with 0% 3 He at 50 MHz and B T = 5.3 T. 100 10 1 Re(k ) [cm -1 ]
B θ Modifies Mode Conversion Physics B θ allows FW coupling to the ICW in the plasma core (Perkins, 1977). Mode converted waves are characterized by relatively large m [ m > 100]: k m r B B θ + n R Fields are up-down asymmetric for the mode converted waves. k θ is negative above the midplane and positive below For N φ >0, k upshifts for waves propagating in lower half plane and waves damp rapidly. φ B B φ TORIC Simulation For N φ >0, k reverses sign in the upper half plane and waves are propagate further before damping. Mode conversion to IBW or ICW depends strongly upon sheared B field. Mode conversion to ICW can dominate over conversion to IBW.
Experimentally Identified ICW in Tokamak Plasma f [khz] 380 360 340 30 PCI data -10-5 0 5 10 k R, cm -1 80.53 80.50 80.47 f RF [MHz] ICRF (80.5 MHz, n φ ~10 cm -1 ) mode conversion experiments in H- 3 He(D) {H:33%, 3 He: 3%, D:1%} discharges at 5.8 T, Ip~0.8 MA, T e =T i =1.5 kev, and n e0 ~.4x10 0 m -3. Electromagnetic dispersion relation and TORIC simulation are in agreement with experimental measurements. An intermediate wavenumber 7 cm -1 (or λ ~0.9 cm) Propagating back towards the antenna On the low field side of the mode conversion surface. IBW FW PCI chords ICW 5< k <10 cm -1 FW -6-4 - 0 4 6
Multiple Wavelengths Require Sophisticated Simulation P.T. Bonoli, J. Wright (in collaboration with M. Brambilla, IPP Garching) TORIC is a Finite Larmor ω 4πi ( P A) E = E + J + J Radius full wave code. c ω Solves Maxwell s equations p J = σ E where σ => σ ( k ρi < 1) for a fixed frequency with a Nφ linear plasma response in a E( x) = EM ( ψ ) expi( Mθ + Nφφ) M mixed spectral-finite element basis. JP is the plasma current response expressed using a FLR expansion up to second order in k ρ i ; J A is the current sheet that models the antenna.» Defined to have the same poloidal extent and radial location as the real antenna.» Solve for single toroidal mode» To model experimental antenna, one must sum over vacuum spectrum.
TORIC Dielectric model includes IBW, ICW, FW Electron Landau damping (ELD) of mode converted waves must be treated precisely. Model damping by adding an imaginary part, δσ, to the FLR coefficient, σ, including all orders of k ρ i. Advantages of this approach include: Simulates ELD predicted by the local dispersion relation, Modifies only the mode converted wave, Mode conversion efficiency is unaffected, Computationally less intensive. σ => σ + δσ Im δσ = iσ n { n } Benchmarked against AORSA (- D all orders in k ρ i ) -D E-field structure qualitatively agreed. Comparison with METS (1-D all orders in k ρ i ) code showed That the power partition between electrons and ions agreed.
Computational Requirements are Scenario Dependent Large number of poloidal modes are required to describe mode conversion scenario. Presence of IBW implies k ρ i ~1 and if k ~m/r, then M max ~r/ρ i < 55, for C-Mod parameters. TORIC has had numerous algorithm upgrades and been parallelized. Was extended to run with EFIT files for discharge analysis. Refined additional post processing for comparison with experimental data. Run routinely on in house 48 processor, parallel cluster. 55 modes require 9.5 hours on a single node (dual 1. GHz Athlon processors with GB RAM.) or ~30 minutes for 4 nodes. Offers sophisticated ICRF experimental modeling tool.
Multiple Antennas Couple ICRF Power D Antenna D & E antennas D E PCI window F G Ip co-cd GH Full Limiter C H ctr-cd J antenna J Antenna B AB Split Limiter A K J D & E Antennas J Antenna Frequency ~ 80 MHz 40-80 MHz Power x MW 4 MW Antenna x Strap 4 Strap Phase fixed variable
High Resolution ECE and PCI Diagnostics High (~0.7 cm spatial, t~5 µsec temporal) resolution ECE radiometer measures power deposition profile. Phase Contrast Imaging (PCI) measures the line integrate electron density fluctuations ( n ~ el). High frequency RF waves (80 MHz) can be detected by optical modulation technique. PCI can simultaneously resolve a wide spectrum of wave-numbers over a wide radial region with poor spatial localization along chord. 3 chords cover 6 cm < R < 74 cm depending upon beam width» 0.4 < k R < 8 cm -1» Frequency response is -5000 khz PCI Chords FRCECE GPC RF ANTENNA
Electron Power Deposition Profile: Measured and Simulated Have shown good agreement between the measured power deposition profile and simulation. Measured deposition profile is determined from break in slope of electron kinetic stored energy. Assume density is constant Typically <1.5 msec. S abs 3 Te ne t TORIC power deposition is calculated for each N φ. Total absorbed power is sum over vacuum spectrum, G(N φ ) weighted by the coupling efficiency for that N φ. TORIC RL( Nφ ) TORIC S = G( Nφ ) P ( Nφ ) abs abs R ( N ) N φ L φ S abs (MW/m 3 /MW inc ) r/a Experiment TORIC Deposition profile (FRCECE) compared to predicted profiles during D(H) MC experiments.
PCI Converts Phase Variation into Intensity Variation Beam intensity before phase plate: E = E0( 1 i φ) Unshifted beam is shifted by λ/4 after phase plate. E = E0( i + i φ) Intensity variation at the detector is * I = E E E0 ( 1+ φ) To detect RF waves at 50-80 MHz, the laser is modulated near the RF frequency. For 50 MHz, the acoustic-optical shifter is driven at 50.75 MHz. RF fluctuations appear at the beat frequency. Concave Mirror CO Laser Beam modulation ACOUSTO-OPTICAL DOWN-SHIFTER 50/50 BEAMSPLITTER MIRROR λ/8 Au Lens MIRROR 50/50 BEAMSPLITTER Phase Plate 3 Channel HgCdTe ACOUSTO-OPTICAL UP-SHIFTER
Synthetic PCI Diagnostic RF wave driven density fluctuation are proportional to the divergence of the perturbed velocity. n~ n ~ v e0 e e i = ~ v ω Ω E e i ω B ζ Ωe >> 1and E ω 0 e ˆ ζ + η Eη E ψˆ B B Where perturbed velocity and E-field is written in local Stix coordinates. Simple rule for predicting dominant contribution is difficult because it is a function of both wavelength and field strength. Line integrate calculated -D fluctuations and use same analysis as used for experiment. ~ E ψ 0 ψ 0 ˆ η n ~ el [x10 17 m - ] 1. 1.0 0.8 0.6 0.4 0. Simulated Channel -0.10-0.05 0.00 0.05 0.10 R-Raxis (m)
First Measurements of Mode Conversion Region ICRF (50 MHz, n φ ~7) mode conversion experiments in D( 3 He, H) L-mode discharges: B T =5.1-5.6 T, I p ~1 MA, T e =T i =. kev, and n e0 ~x10 0 m -3. Expect mode conversion ICW and IBW within PCI view. Measured forward and reflected FW. Measured pattern from the mode converted (MC) waves. Re(n ) 10000 1000 100 n =S IBW Dispersion Curves cutoff ICW R (m) ω=ω 3 He FW 10 0.6 0.65 0.7 0.75 0.8 ~ n el [a.u] 1.0 0.5 FW PCI MC waves 100 10 0-10 -5 0 5 10 k R (cm -1 ) 1 Re(k ) [cm -1 ]
PCI Profile is Modified as Mode Conversion Shifts Near Axis ~ n e L [a.u.] ~ n e L [a.u.] 8 6 4 0 30 0 10 0 5.4 T R axis 5.1 T 5.6 T 0.6 0.66 0.70 0.74 R (m) As expected, mode conversion shifts towards magnetic axis as B T is increased. Profile also evolves as B T is increased. Density fluctuation is line integral of 10 8 6 4 0 k E. Geometry affects on 1-D profile. Z (m) 0. 0.1 0.0-0.1-0. N φ =7-0.1-0.05 0.0 0.05 0.1 R - R axis (m) 6. 3.9 1.6-0.7-3.0-5.3 Re(n ~ e ) [x10 18 m -3 ]
Remarkable Agreement Between Experiment and Simulation Power deposition profile is in good agreement experiment. 3 He fraction was adjusted until the location of the peak in the deposition profile is matched. Shape of the line integrated perturbed density profile is in good agreement with experiment. Future work will Examine compare experimental and simulation amplitudes and Use masking of the phase plate to allow localization of the modes.» Test up-down asymmetries» Examine wavenumber up-shift. ~ n e L [a.u] 10 8 6 4 15 10 5 S abs [MW/m 3 ] Experiment TORIC 0 0. 0.4 0.6 0.8 1.0 PCI TORIC R MC r/a R axis.5 1.5 0.5 0.6 0.66 0.70 0.74 R [m] ~ n e L [10 17 m - ]
TORIC Current Drive Calculation Current on a flux surface is calculated by integrating over the flux surface the local driven current. J G RF m RF m m, m ( ψ ) dθ G ( ψ, θ ) P ( ψ, θ ) ( ψ, θ ) = G ( v = ω / k, ε = r / R) i π RF i 0 m m = RF G RF m (ψ, θ i ) is parametrization of the current drive efficiency computed from adjoint solution to Fokker Planck equation. P abs m,m is the local absorbed power for a given N φ. Trapping is included by convolving the local absorbed power with the local current drive efficiency. Variation in k is directly accounted because the power absorption is reconstructed as a function of poloidal mode and convolved with local current drive efficiency. abs i
ρ Sawtooth Changes Suggest Local Driven Current Sawtooth period can be lengthened by decreasing the magnetic shear at the q=1. Performed a series of L-mode, D( 3 He) discharges at 8 T to investigate MCCD. Power absorbed by electrons is ~0.3 MW, ~0% of total power. Simulation suggest RF driven current is ~10 ka. With the deposition peaked near the sawtooth inversion radius, sawtooth period increases with Ctr-CD phasing and decreases with Co-CD phasing. P RF (MW) 1 D-port D+J-port D-port D+J-port 3.5 3 T e0 (kev) 0.7 0.75 0.8 Time [sec] Sabs [MW/m3] rinv ctr-cd co-cd 0.7 0.75 0.8 Time [sec] CTR CD Co-CD
Sawtooth Period is Unaffected for Central Deposition 1030716016 103071600 P RF (MW) 1 D D+J D D+J T e0 (kev) 3.5 Sabs [MW/m3] 1030716016 103071600 3 rinv 0.7 0.75 0.8 Time [sec] 0.7 0.75 0.8 Time [sec] ρ For Ctr-CD phasing, the sawtooth period increases for deposition near the q=1 but unchanged with the deposition peaked away from q=1. Suggests a localized driven current.
Identified Scenario with High MCCD Identified model discharge to maximize MCCD. 100 ka at 3 MW RF power η CD ~ 0.0 A/Wm» Good agreement with empirical FW scaling. {~0.1T e (where T e is in units of 10keV) as for FW, but is reduced by MC efficiency 0.5.} On-axis MCCD j(r) exceeds local ohmic current density. Current is driven predominantly by the ICW. IBW is bipolar and j max is ~0 times less than ICW. Current reversal results from updown asymmetry. j (MW/m ) 80 60 40 0 0 Total driven current for 1 MW IBW + ICW + FW 33 ka/mw IBW Contribution (x10) Ohmic profile current for modeled discharge (EFIT) -0 0.0 0. 0.4 0.6 0.8 1.0 r/a Modeled target discharge: B T =5.4 T, I p =0.8 MA, n e0 = 1.0 x10 0 m -3, T e0 = 5 kev, and 65% D, 15% 3 He, 5% H J antenna@ 50 MHz (MCCD) D and E-antenna@80 MHz
Future Work Further measurements varying the deposition location, antenna phasing, and different plasma species including H( 3 He) and D(H) using PCI. Mask phase plate to demonstrate up-down asymmetry in mode converted waves and allow follow wavenumber evolution. Increase wavenumber sensitivity to measure waves upshifted to high k. Optimize driven current profile for both sawtooth suppression and net current. Measure driven current profile to test physics model in TORIC. Investigate interaction of mode converted waves with LH waves. Identify scenarios which may lead to large driven flows.
Conclusions Localized plasma heating and the mode converted waves in ion-ion hybrid region have been measured. Simultaneously measured the Fast wave and mode converted waves in the mode conversion region using a phase contrast imaging diagnostic in D( 3 He) plasmas. Code simulations are in good agreement with measured power deposition and fluctuation profiles. With moderate mode converted power, the sawtooth behavior suggests a localized driven current. TORIC predicts mode conversion current drive of the order of 100 ka at 3 MW RF power.