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Characteristics of Biased Electrode Discharges in HSX S.P. Gerhardt, D.T. Anderson, J. Canik, W.A. Guttenfelder, and J.N. Talmadge HSX Plasma Laboratory, U. of Wisconsin, Madison 1. Structure of the Experiments 3. Two Time Scales Observed in Flow Damping General Structure of Experiments • • Mach Probes in HSX • • • 6 tip mach probes measure plasma flow speed and direction on a magnetic surface. 2 similar probes are used to simultaneously measure the flow at high and low field locations, both on the outboard side of the torus. Data is analyzed using the unmagnetized model by Hutchinson. • Looking To The Magnetic Surface • Convert flow magnitude and angle into flow in two directions: U t X t cos X t 2 • • 3 • • • B / Bo 1 H cos4 M cos4 Mirror : U Model Fits Flow Rise Well Mirror Tokamak Basis Vectors Can Differ from those in Net Current Free Stellarator. 3 • This allows the calculation of the radial electric field evolution: U 1 e t /1 S1e S3e 1 e t / 2 S2e S4e • 2. The Biased Plasma as a Capacitor Impedance in Smaller in the Mirror Configuration Bias Waveforms Indicate a “Capacitance” and an Impedance Decay Time: =33x10-6 seconds Impedance: R=V/I=36 C= /R=8.9x10-7F Acumulated Charge from “Charging Current”: Q=2.33 Coulombs Voltage: V=310 Volts C=Q/V=7.5x10-7F • • Impedance1/n consistent with radial conductivity scaling like n. Consistent with both neoclassical modeling by Coronado and Talmadge or anomalous modeling by,for instance, Rozhansky and Tendler. t 0 Current peaks at the calculated separatrix. Electrode Current Profile does not follow the density profileElectrode is not simply drawing electron saturation current. • • Linear I-V relationship Consistent with linear viscosity assumption. Very little current drawn when collection ions collect electrons in all experiments in this poster. • Mirror, F Mirror, slow rate QHS, F QHS, slow rate Two time scales/two direction flow evolution. 6. Observations of and Reductions in Turbulence With Electrode Bias. Vf Fluctuation Reduction with Bias • • “Forced Er” Plasma Response Rate is Between the Slow and Fast Rates. t 0 t / U t U E 1 e e BQ1 E 1 1 Q2 e F t Q2 e t / • Total Conductivity Combination of neutral friction and viscosity determines radial conductivity. Mirror agreement is somewhat better. Viscosity Only Neutrals Only The Coronado and Talmadge Model Overestimates the Rise Times By 2 Distinct Spectral Peaks in the Electrode Current r/a.7 r/a.9 QHS Configuration • 50 kHz mode remains unsuppressed by bias. See Poster by C. Deng • Electrostatic transport measurements soon. See Poster by W. Guttenfelder 1/in QHS Mirror Mirror Fast Rates, QHS and Mirror ExB flows and compensating Pfirsch-Schlueter flow will grow on the same time scale as the electric field. Parallel flow grows with a time constant F determined by viscosity and ion-neutral friction. d d QHS Assume that the electric field, d/d,is turned on quickly Er 0 Er 0 E 1 e t / • J 1/in Formulation #2: The Electric Field is Quickly Turned On. The “Forced Er” model Underestimates the QHS time • Measurements 4 d t d t 0 F1 1 et /1 F2 1 et / 2 d d • Define the radial conductivity as t / 2 • <B>=0 in net current free stellarator, but not a tokamak. 2*1e-7*48*14*5361 =.7205 2 t / 1 • Mirror 2 1 • QHS S1…S4, 1 (slow rate), and 2 (fast rate) are flux surface quantities related to the geometry. Break the flow into parts damped on each time scale: • Similar model 2 time scale / 2 direction fit is used to fit the flow decay. 1 QHS Modeled Radial Conductivity agrees to a Factor of 3-4 QHS Original calculation by Coronado and Talmadge After solving the coupled ODEs, the contravariant components of the flow are given by: <B>= Boozer g= t / t / S 1 e S S 1 e S 1 e QHS Flow Damps Slower, Goes Faster For Less Drive. R Use Hamada coordinates, using linear neoclassical viscosities. No perpendicular viscosity included. Predicted form off flow rise from modeling: U (t ) C 1 exp t / f fˆ C s 1 exp t / s sˆ U1, fit t C f 1 exp t / f cos f Cs 1 exp t / s cos s U1SS Symmetry Can be Intentionally Broken with Trim Coils U 1 e Fit flows to models U 2, fit t C f 1 exp t / f sin f Cs 1 exp t / s sin s U 2 SS Need quantities like <e·e >, <e·e >, <e·e >,<||>, <| · |>. Previous calculation used large aspect ratio tokamak approximations. Method involves calculating the lab frame components of the contravariant basis vectors along a field line, similar to Nemov. Solve these with Ampere’s Law t 4 J plasma J ext Formulation #1: The External Radial Current is Quickly Turned On. U 2,exp t X 2 t sin X 3 t Probe measures Vf with a proud pin. QHS : B / Bo 1 H cos4 • • • t B U B mi N iin B U As the damping is reduced, the flow rises more slowly, but to a higher value. Full problem involves two momentum equations on a flux surface2 time scales & 2 directions. 1,exp X I sat X 1 exp 2 .641 cos X 3 .71 cos X 3 2 • • 0 t0 U jB 1 exp t / nm t 0 • t c BP U J BP mi N iin BP U g B B mi N i Take a simple 1D damping problem: 0 t0 dU mn F U , F Has solution dt jB t 0 • Two time scales/directions come from the coupled momentum equations on a surface. mi N i Flow Analysis Method • We Have Developed a Method to Calculate the Hamada Basis Vectors Solve the Momentum Equations on a Flux Surface Simple Flow Damping Example • 5. Comparisons Between QHS and Mirror Configurations of HSX 4. Neoclassical Modeling of Plasma Flows r/a r/a r/a • 50 kHz peak becomes dominant as the probe moves in. • Do these simply reflect density fluctuations? 7. Computational Study: Viscous Damping in Different Configurations of HSX