Lower Hybrid Current Drive Experiments on Alcator C-Mod: Comparison with Theory and Simulation

Transcription

1 Lower Hybrid Current Drive Experiments on Alcator C-Mod: Comparison with Theory and Simulation P.T. Bonoli, A. E. Hubbard, J. Ko, R. Parker, A.E. Schmidt, G. Wallace, J. C. Wright, and the Alcator C-Mod Team MIT-PSFC J.R. Wilson, C. K. Phillips, S. Scott, E. Valeo, PPPL R.W. Harvey, CompX

2 Outline Motivation Experimental Set-up LHRF system Hard x-ray emissivity diagnostic for measuring bremsstrahlung from nonthermal electron tail Simulation tools Comparisons of measurements and simulation: Hard x-ray emissivity profiles from measurement and synthetic diagnostic code. Current density profiles from MSE and Fokker Planck-ray tracing simulation. Discussion of the role of fast electron diffusion and fullwave effects. Conclusions

3 Motivation Off-axis lower hybrid (LH) current profile control can be used for current profile control in order to access advanced tokamak (AT) operating modes that are necessary for steady state operation in advanced reactor designs: [S. C. Jardin et al, Fusion Eng. And Design 38, 7 (1997)]: Because LH waves damp efficiently at high phase speed (v // / v te.5), they can be used to generate current at r/a >.5, where T e is lower. Higher phase speeds also minimize the effects of particle trapping on the driven LH current. In order to optimize off-axis LH current profile control capability in present day tokamaks and in ITER it is necessary to develop a predictive capability: 3D (r, v, v // ) non thermal electron distribution is simulated using a Fokker Planck ray tracing model. Can use f e (r, v, v // ) in a synthetic diagnostic code for hard x-ray emission and compare with experimental diagnostic measurement. Can compare simulated current density with measurement from Motional Stark Effect (MSE) diagnostic. Comparisons between experiment and simulation can be done at ITER relevant parameters in C-Mod [f = 4.6 GHz, n e () = 1 1 m -3, B = 5.3 T]. See Posters by A. E. Hubbard NP8.66 and C. Kessel NP8.67

4 Lower Hybrid Waves are Coupled Using an 88-Waveguide Grill Array With a Well-Controlled and Flexible n // Spectrum 6 9º 6º 1º Probes used to Measure edge density Probes Limiters Stainless steel grill used to inject LH waves into Alcator C-Mod plasmas during 6 and 7 campaigns with nearly 1 MW of coupled LH power n 15º 18º Source frequency GHz Variable n // range of Phase can be varied during discharge on a 1 msec. time scale using electronic phase shifters. See Posters by R. R. Parker NP8.68 and G. M. Wallace NP8.69

5 A Hard X-Ray Camera is Used For Determining the Location of the Fast Electrons and their Energy Distribution Diagnostic is chordal with a 3 channel pinhole camera using CZnT detectors and fast digitization techniques Spatial Resolution: Δr cm J. Liptac, PhD Thesis, 6

6 Simulation Model for Nonthermal Electron Distribution Function Evolution 3D (r, v, v // ) Fokker Planck Solver CQL3D f f 1 f f D ( p ) + C( f, p, p ) + ee + Γ δ( p ) + rχ = p p p r r r t e e e e rf // e // // s // f // // // Synthetic diagnostic codes use 3D distribution function f e (r, v, v // ) : Hard x-ray emission Nonthermal electron cyclotron emission (ECE) See Poster by R. W. Harvey UP8.55

7 Simulation Models for Wave Propagation Toroidal Ray Tracing Code GENRAY: Integrates the ray equations of geometrical optics. dx ε / k dk ε / x = =+ dt ε / ω dt ε / ω Full-wave electromagnetic field solver TORIC-LH: Solves Maxwell-Boltzmann system. Accounts for focusing and diffraction that can occur at caustic surfaces: ω i E + E J p iωμ c + = ωε See Poster by J. C. Wright GP8.15 J ant

8 Nearly Full Non-Inductive LH Current Drive has been Achieved on Alcator C-Mod B = 5.4 T, I p =.544 MA, P LH = 8 kw I p (MA) n e (1 m -3 ) P LH (kw) t (s) Zeff 1..5 See Oral by J. R. Wilson PO T e (kev) V Loop (V) t (s)

9 Waveguide Phasing (6 Degrees) Chosen to Maximize Driven LH Current in Lower Density Regime with a Launched n // = 1.55 Density (1 m-3) Density Profile n//crit Local wave accessibility is maintained with n // > n //crit Local n //crit 6 o with 1/R upshift in n //-Launch Normalized Radius (r/a) Major Radius [m] See Poster by G. M. Wallace NP8.69

10 Predicted HXR Spectra Agree Well with Measured Spectra Except Narrower Count Rate (s -1 kev -1 ) Measured and Simulated HXR Spectra Experiment x 1 4 Simulation - CQL3D 16 4 kev 34 kev kev Channel # No Normalization Used for Simulated Spectra γ v c.8.4 Contour plot of distribution function γ v // c Simulated results from CQL3D synthetic diagnostic were obtained neglecting spatial diffusion of fast electrons in the Fokker Planck solution (χ f = )

11 Approach for Treating Fast Electron Diffusion in CQL3D Use a velocity space dependent form for χ f following [Mynick and Strachan, Phys. Fluids (1981)]: Based on runaway electron confinement time measurements in PLT and a a theory of stochastic magnetic turbulence: χ fast = χ (v / v ) γ // te fast () 3 Vary χ fast () until the predicted current (OH + LH) from CQL3D matches the experiment. For the previous discharge we find χ fast ().4 m /s yields a predicted total current of about 5 ka, close to the experimental discharge (54 ka): Similar values of χ fast () were found on Alcator C [S. F. Knowlton et al, Phys. Plasmas (1994)]

12 Estimate the Effect of χ fast () =.4 m /s on the Fast Electron Distribution Function Assuming: χ τ fast fast τ ( Δr) 4τ LH fast ( ee / + ei / ) slow,, 19-3 Then: At n = 1.8, n 5 1 m, Z 3.5 E res // e ( ee / + ei / ) 3 14 kev and τ slow 1 sec. eff ( Δr) 1.8 cm LH Expect a local, rather than global spatial effect on fast electrons.

13 Spatial Diffusion of Fast Electrons is Found to Locally Smooth the Simulated J LH and S LH Profiles Current Density (MA / m ) Current Density Profiles (OH + LH) No Diff. Diffusion Normalized Radius (r/a) Power Density (MW / m 3 ) Power Deposition Profiles No Diff. Diffusion S LH (n // < ) Normalized Radius (r/a) Current density profile at r/a >.6 is also broadened

14 Spatial Diffusion Smooths Current Density Profile But Does Not Broaden Simulated Spectra Enough to Agree With Experimental HXR Measurements Count Rate (s -1 kev -1 ) Measured and Simulated HXR Spectra (39-48 kev) x Channel # Experiment CQL3D (No diffusion) CQL3D (Diffusion)

15 Pitch Angle (Deg.) Modification of the Current Profile by LHCD has been Measured with a Motional Stark Effect (MSE) Diagnostic on Alcator C-Mod B = 5.4 T, I p =.81 MA, P LH = 7 kw LH net power (kw) Ch (R = 81.8 cm) Ch 9 (R = 78. cm) t (s). 1. Loop Voltage (V) Ch 3 (R = 79.9 cm) Ch 4 (R = 76. cm) t (s) (Ohmic) Posters by: J. Ko NP8.86 S. Scott NP8.87 R. Parker NP8.68 Oral by: J. R. Wilson PO3. J φ obtained from pitch angle following C. Petty et al Nucl. Fusion 4, 114 ()

16 Waveguide Phasing of 75 Degrees Chosen to Guarantee Wave Accessibility to Higher Density Regime with Launched n // = 1.95 Density (1 m -3 ) Density Profile n //crit Local wave accessibility is maintained with n // > n //crit Local n //crit 75 o with 1/R upshift in n //-Launch Normalized Radius (r/a) Major Radius [m]

17 Simulated and Measured Current Density Profiles are in Good Agreement Current Density (MA / m ) Measured and Predicted Current Densities (φ tor-norm) 1/ ~ (r/a) J tot - CQL3D J LH - CQL3D (E // =) MSE J tot shown above also includes synergistic part of J LH due to finite E ll ( 3 ka). Count Rate (s-1 kev-1 ) Measured and Simulated HXR Spectra (39-48 kev) x Channel # Experiment CQL3D Simulated hard X-ray spectra agree much better in this case but are still narrower than measured spectra.

18 Full-wave effects due to Focusing and Diffraction Could Lead to Broader LHRF Wave Deposition [G. Pereverzev, NF (199)]. Calculation can be done with a version of the TORIC field solver, valid in the LHRF regime: Code couples the electrostatic slow wave polarization directly. For LH waves k (ω pe /ω)k // 3 cm -1 for [f = 4.6 GHz, n e () = m -3, B = 5.3 T, n // = 1.55]: k (m/r) -3 m +3 (poloidal mode resolution needed at r/a.5) Parallel field solver is needed and is now under development. Preliminary simulations have been performed with a serial field solver using a reduced (1/3 size) version of Alcator C-Mod. See Poster by J. C. Wright GP8.15

19 LH TORIC Solver was used to Simulate Full-Wave Effects in Alcator C-Mod [n e () = m -3, B = 5.4 T, T e () = 3.1 kev, n // () = 1.6] Simulation with TORIC LH solver using N r = 16 radial elements and N m = 17 poloidal modes (-63 m +63). Simulation used linear electron Landau damping (Maxwellian). Electric field pattern exhibits evidence of caustic formation where spectral broadening can occur.

20 Linear Damping Profiles Predicted by Full-Wave Solver and Ray Tracing are Qualitatively Different Suggesting Full-wave effects may be Important 15 Full-wave - TORIC Reduced Size C-Mod Plasma 6.8 Ray Tracing (CQL3D - GENRAY) S (MW / m3 / MW inc ) 1 5 Single Toroidal Mode (n // = 1.55) S (MW / m 3 / MW INC ) S (n // < ) r / a r / a

21 Conclusions Nearly full non-inductive operation of Alcator C-Mod has been achieved with LH current drive. Significant off-axis LH current drive has also been generated in the C-Mod device: Line integrated profiles of hard x-ray emissivity have been measured and compare favorably with a synthetic diagnostic code that uses the 3D distribution function from a CQL3D simulation. MSE measurements of J tot show evidence of off-axis current profile broadening. Simulated current density profile from CQL3D is in good agreement with MSE measurement.

22 Conclusions Measured profiles of hard x-ray emissivity are always found to be broader than the simulated profiles from a synthetic diagnostic code in CQL3D: Spatial diffusion effects (evaluated with χ fast ().4 m /s) have been found to locally modify the current density profile but cannot fully explain the broadening in the hard x-ray emissivity seen in the data. Currently we are evaluating full-wave field effects as a possible mechanism for the observed broadening in the hard x-ray profiles. Completion of parallel LH field solver and coupling to CQL3D will provide a definitive evaluation of full-wave effects on LHCD. LH power will be increased with the installation of a second LH launcher in FY9.