Particle Transport and Edge Dynamo in the ST RFP International RFP Workshop 28 February 2000, adison, WI D. J. Den Hartog Department of Physics University of Wisconsin adison In collaboration with J. K. Anderson, D. L. Brower, D. Craig, G. Fiksel, P. W. Fontana, Y. Jiang, N. E. Lanier, S. C. Prager, and J. S. Sarff Department of Physics, University of Wisconsin adison
Velocity fluctuations play a critical role in particle and current transport in the RFP Particle flux: Γ = nv r = γ n v r cosδnv must simultaneously measure density fluctuations, radial velocity fluctuations, and relative phase density fluctuations result from core tearing modes and can cause substantial particle transport in the core, but cannot explain particle transport in the edge Dynamo emf: E = d v B must measure all components of velocity and magnetic fluctuations, and relative phase edge dynamo results from m = 0 fluctuations and balances Ohm's law for >0.85a
Outline I. Particle transport character of density fluctuations phenomenology of ñ and ṽ r particle transport during standard and PPCD discharges summary II. First direct measurement of v H B in the edge of an RFP the sawtooth cycle in ST ( dynamo events ) v, B, and v H B peak during a sawtooth crash HD dynamo balances Ohm's law in the edge summary
Character of density fluctuations Advective or compressional? n Continuity equation: + nv t = S assume S 0, v0 0, but v 0, and nv, f ( re ) i kr ω t then n = advection non-radial compression i ( ) n0 ( ) ( ) v n kv r r rv n r r + r 0 k v 0 ω 0 ( ω kv0 ) radial compression +nonlinear Causes transport? Γ= nv r = γ n v r cosδnv π δ = nv no transport, but δ 2 = 0 π nv, transport ( )
9 Chord H Array α The Far-Infrared Interferometer * and H α array Waveguides Signal Beam CO 2 Pumping Laser 125W Continuous λ =10.6µm Reference Beam Wire esh BeamSplitters Twin Far Infrared Lasers 25mW Each λ 432µm Plasma Vacuum Duct Signal Channels Reference Channel Schottky Detectors * Developed with UCLA Plasma Diagnostics Group Volts Reference Signal Φ Time 750 khz The 11 Chords are split into 2 arrays, 5 o P28 P43 N02 P13 N32 N17 N24 N09 P06 = 1.5 m separated by 5 degrees. R o P21 P36 = a.52m
Core-Resonant Tearing odes Drive Density Fluctuations Fluctuation Power (a.u.) Fluctuation Power (a.u.) Fluctuation Power (a.u.) 2.0 1.5 1.0 0.5 Density Fluctuation Power r/a = 0.11 Total Coherent Incoherent 0.0 10 15 20 25 30 Frequency (khz) 20 15 10 5 Density Fluctuation Power r/a = 0.54 Total Coherent Incoherent 0 10 15 20 25 30 Frequency (khz) 20 15 10 5 Density Fluctuation Power r/a = 0.83 Total Coherent Incoherent 0 10 15 20 25 30 Frequency (khz) Correlation between core-resonant magnetic fluctuations and density fluctuations indicate: Core: density fluctuations are poorly coherent with the m = 1 magnetic fluctuations. At larger impact parameters: virtually all the power between 10 and 20 khz is coherent with the n = 5 to 15 modes. Edge: density fluctuations are less coherent with the core-resonant tearing modes relative contribution from smaller scale, higher frequency, fluctuations increase.
Density Fluctuations Display Both m=0 and m=1 Like Behavior Power (au) Power (au) 5 4 3 2 1 agnetic Fluctuation Spectrum n = 1 15 0 0 10 20 30 40 50 Frequency 5 4 3 2 1 0 Density Fluctuation Spectrum r/a = -0.49 r/a = 0.11 0 10 20 30 40 50 Frequency Phase Between Inboard and Outboard Chords agnetic fluctuation power shows a large peak between 10 20 khz dominated by m =1, n = 6 10 modes Density fluctuation power displays similar 15 khz peak in all but center chords. low frequency peak appears in all chords Density fluctuation m character Phase (π rad) 1.0 0.5 0.0 m = 0 m = 1 0 10 20 30 40 50 Frequency low frequency peak has m=0 character ~15 khz peak has m=1 character.
The Ion Dynamics Spectrometer (IDS) Radial Port Lens To Doppler Spectrometer R o a 20 Fiber optic coupling The IDS Radial View The IDS: custom designed Doppler Spectrometer fast time resolution 10 µs measures impurity ion flow fluctuations v Doppler Shift ~ i Radial View high light throughput impurity choice can enhance localization
easurements Indicate That ~ v r Flips Phase in the Core. Coherence Amplitude State Density (au).4.3.2.1 0 Computed Profiles for C V and He II Filtered He II C V 0.0 0.2 0.4 0.6 0.8 1.0 r/a n e v r HeII Amplitude He II measures significant coherence amplitude. Baseline 0 10 20 30 40 50 Frequency (khz) The edge peaked profile of He II weights the edge more heavily. The broad C V profile provides a more even weighting over the plasma radius. easurements with helium establish the existence radial velocity fluctuations in the plasma edge. Coherence Amplitude.4.3.2.1 0 Filtered n e v r CV Amplitude No significant coherence amplitude observed with C V. Baseline 0 10 20 30 40 50 Frequency (khz) easurements of C V ions show no significant coherence - implying a phase flip in the radial velocity fluctuations.
Phase Flip in ~ v r is Consistent With Tearing ode Picture q=m/n Tearing mode topology suggests that v should reverse across rational surface. ~ r ~ v r Since passive doppler spectroscopy measures Z Chord I () r ṽ r ()dr, r a π phase shift would explain how Radial Velocity (a.u.) + 0 ~ v (r) r - 0 rs Radius a Z Chord ṽ r () r finite but I () r ṽ r ()dr r 0.
Density Fluctuations in the Edge are Primarily Advective While in the Core are Compressional 1.0 Coherence Phase between ~ n and ~ v. r Edge: phase is ~ π/2 which is consistent with advection or radial compression Phase (π rad) 0.5 δ nvedge in edge the advection term dominates -0.0-60 -40-20 0 20 40 60 x (cm) easurements show: Core: phase is ~ 0,π and can only be explained by the non-radial compression term In the edge, density and velocity fluctuations are π/2 out of phase. Density fluctuation phase in the core is shifted by π/2 from that in the edge. Velocity fluctuation phase in the core is shifted by π from that in the edge. Therefore: we deduce that the density and velocity fluctuations are in phase in the plasma core.
Fluctuation-Induced Transport is Small at Edge, Large in Core Phase (π rad) 1.5 1.0 0.5 0.0 δ nvedge Phase of ñṽ redge Standard Density and Radial Velocity Fluctuations Out of phase at the edge In phase in the core -0.5-40 -20 0 20 40 60 Radial Position (cm) Standard Discharges Fluctuation-Induced Transport small in the edge. Fluctuation-Induced Transport large in the core.
1.5 1.0 Local Fluctuation Amplitudes Decrease During PPCD Local Fluctuation Profiles for m=1, n=6-9 Perturbations. Standard n=6 0.5 PPCD 17-3 (10 m ) Electron Density 1.2 0.8 0.4 1.2 0.8 0.4 Standard n=7 Standard n=8 PPCD PPCD Profile peaks farther out as n increases Fluctuation amplitudes are ~ 1.0 % Standard ~ 0.1 % PPCD 1.5 1.0 Standard n=9 0.5 PPCD 0.0 0.0 0.2 0.4 0.6 ra 0.8 1.0
PPCD Reduces Fluctuation-Induced Transport in the Core Phase (π rad) 1.5 1.0 0.5 0.0 δ nvedge Phase of ñṽ redge PPCD Phase shift in density vanishes during PPCD -0.5-40 -20 0 20 40 60 Radial Position (cm) PPCD Discharges Density and velocity fluctuations remain out of phase deeper into the plasma. Fluctuation-Induced Transport reduced in the core.
Fluctuation Reduction During PPCD is Accompanied by Similar Reductions in Equilibrium Radial Electron Flux Electron Density (10 19 m -3 ) Electron Source (m -3 s -1 ) Particle Flux (m -2 s -1 ) 1.2 0.8 0.4 0.0 23 10 22 10 21 10 20 10 22 10 21 10 20 10 Standard PPCD Standard Standard PPCD 19 10 PPCD 18 10 0.0 0.2 0.4 r a 0.6 0.8 1.0 In standard discharges: Density profiles are flat in the core with a steep edge gradient. Electron source is dominated by ionization of neutral hydrogen and is quite broad with substantial sourcing in the core. Radial Particle flux ranges from ~2E+20 to about 3E+21 at the edge. During PPCD discharges: Density profile hollows slightly in the core and gradient at the edge steepens. Electron source drops over an order of magnitude. Radial particle flux also decreases with the most dramatic reduction seen in the core.
Density fluctuation and particle transport summary Density fluctuations result mainly from the core-resonant tearing modes (m = 1, n = 6 10), and are advective in the edge and compressional in the core. Although large in the outer region of the plasma, the density fluctuations from core modes do not cause transport there. During PPCD, the measured radial particle flux decreases dramatically concurrent with similar reductions in density fluctuations. Phase measurements of density and radial velocity fluctuations indicate, that during PPCD, the region of vanishing fluctuation-induced transport extends deeper into the core.
Ohm s law requires the RFP to have a dynamo E 2 Ö η J 2 both in the core and edge current over-driven emf (arb) E 2 ηj 2 0.0 current under-driven 0.0 1.0 r/a need noninductive current drive to balance Ohm s law: 2 + v H B 2 = η J 2
The Ion Dynamics Spectroscopy Probe Support frame View dump 2.5 cm V y Vx Vz Vx α = 45.0 Prism Fiber bundle Vacuum Break BN housing Shaft
IDSP proof-of-existence
RFP dynamo events Regular discrete bursts of dynamo activity occur in ST
The HD dynamo balances Ohm's law Ohm's law balance is good at >0.85a - deteriorates for 0.85a
Velocity fluctuation spectra are dominated by n = 1 and 2, implying m = 0 dynamo in edge Numerical values represent the correlation (from 0 to 1) of the fluctuation with each mode resolved by the B t array
Summary of edge dynamo measurements The HD dynamo term balances mean-field Ohm's law in the edge of ST The edge dynamo is driven by m = 0 fluctuations which resonate at the reversal (q = 0) surface - dynamo in ST is a superposition of relatively localized reconnection events ay be a different current drive mechanism active inside 0.85a