1. Plasma Dynamics Lab HIBP E ~ 0 V/m in Locked Discharges Average potential ~ 580 V  ~ 500-600V less than in standard rotating plasmas Drop in potential possibly due to degradation of ion confinement, reduction in mode velocity or changes in bulk fluid rotation Scatter ~ ±100 V; reduced scatter likely due to uniformity of mode velocity ~ 0 km/s, variations in density remain Potential profile relatively flat, E r small/zero Biasing experiment 2 electrodes, inserted 8-10cm Negative biasing for 10ms with respect to MST wall Discharges lock then reaccelerate when biasing is turned off Density rises dramatically Unlike a standard locked discharge, sawteeth do not cease E ~ 0 V in Biased Discharges The potential is positive, but ~ 200-250V lower than in a standard locked discharge The potential profile is flat over the region sampled The lower  possibly due to: –higher n e (~20-40%) –better confinement of e - HIBP Measurements Facilitate Experimental Investigation of Ion Radial Force Balance Simplified equilibrium radial force balance for the ion species is given by: Quantities: –E r – HIBP – radial electric field –n e – FIR – electron density profile –v – IDS – ion toroidal and poloidal flow velocities (and m=1,n=6 mode velocity) –P – Rutherford, Thomson scattering – pressure gradient inferred from ion, electron temp. –B – MSTFit – reconstructed equilibrium field profile –Z – Assumed = 2 Assumptions -in equilibrium -incompressible plasma flows -isotropic pressure gradient Radial Force Balance in Low Current Standard Discharges HIBP measured E r is compared to the total computed, and individual RHS terms Agreement between measured and computed E r in the range of r = 16-27cm Contribution from v x B term 3- 6x greater than pressure gradient term in core, 2x greater toward edge The Computed Electric Field Incorporates Mid-Sawtooth Cycle Measured Quantities Measured ion and electron temperature profiles are similar in low current discharges For r < 23 cm,  n ~ 0 The ratio of toroidal to poloidal flow velocities is ~ 5-7. All quantities are from low current discharges, mid-cycle Limited Measurements Contribute to Uncertainty in E r Ion flow velocities –Chord localized (15 cm) rather than profile measurements –Past experimental measurements indicate that the flow velocity decreases toward the plasma edge (v x B in edge likely smaller than computed) –A 20% change in the flow velocity is enough to est. agreement between measured and computed E r Pressure Gradient –The uncertainty in the pressure gradient is < 3% –The uncertainty in the ion-temperature measurements is ~ 20-30% Due to lack of spatial resolution Uncertainty in  T i translates to an uncertainty of ~ 500 V/m at r~25-33cm Measured E r –Uncertainty in the measurement ~ 700 V/m Radial Force Balance in Low Current Locked Discharges Pressure profiles from standard discharges Ion temperature is assumed to be close to the impurity temperature measured mid-cycle; this is based on the similarity of measurements in a standard discharge near a sawtooth crash Calculated E r is negative The ratio of toroidal to poloidal flow velocities now ~ 1; decrease of the toroidal flow velocity from standard to locked discharges dramatically reduces computed E r The use of T impurity results in a pressure term that is 30% lower than in the standard discharge Radial Force Balance in Low Current Biased Discharges Suppression of electrostatic fluctuation induced transport has been observed with negative biasing The HIBP measurement of E r, while not shown, is close to zero over the range illustrated The electron temperature and density profiles were measured in the biased discharges. The n e profile is hollow and the gradient positive in the region investigated. The toroidal flow decreases and the ratio of toroidal to poloidal flow ~ 2 Low Current Force Balance Summary The computed electric field tends to agree with the measured electric field toward the core of the plasma, with greater deviation toward edge The v x B term increases with radius and is the dominant term in both standard and biased discharges The v x B term is reduced in both locked and biased discharges due to reduction in flow velocities The profile of the biased discharge pressure term is partly due to the hollow density profile and positive density gradient (transport barrier) Computation of the radial electric field would improve with –Profile measurements of flow velocities –Profile measurements of the ion temperature, mid-cycle in locked and biased discharges Experimental investigation of radial force balance in high current discharges Experimental Investigation of Radial Force Balance in High Current Discharges The radial electric field is computed during two intervals (after (a) and before (b)) The HIBP measured E r is shown for the same two time intervals Both calculated and measured show and increase in E r over the sawtooth cycle The n=6 phase velocity tends to be lower in the time window after the crash than the window before. The result, is a smaller contribution from v x B. Particle Drifts in MST Due to Radial Electric Field and Pressure Gradients Two drifts are considered: ExB and diamagnetic drift; E r and  P are both measured: Comparisons to IDS measurements are made (near r=20 cm) –  : v ExB + v  P ~ 8.6 km/s; v IDS = -4.5 km/s (sign error may exist) –  : v ExB + v  P ~ 8.6 km/s; v IDS = 22.5 km/s –The ExB drift dominates in the core, the diamagnetic toward the edge Radial Electric Field Predicted by Stochastic Field Theory Does Not Match Measurements Prediction from stochastic field theory (Harvey) is compared with measured E r and ion radial force balance This theory examines the relation between particle and heat flux, and the ambipolar electric field Ambipolar field is 1-2 orders smaller than either of the others Plasma rotation is not taken into account in the theory/eqn. Agree only when one considers that measured and predicted fields are both positive. Toroidal and Poloidal Flow Velocity Measurements Due to higher temperatures C-V emission moves outward to 30 < r < 40 cm. Thus, the measurement region is no longer coincident with the HIBP measurement of E r The global m=1,n=6 mode phase velocity is used instead Discharge Differences HIBP E r measurements are carried out in 383kA discharges, ion pressure gradients and phase velocities from 373 kA discharges Time Windows 1.5 - 2.5 ms after a sawtooth crash and 2-3 ms before a crash An m=0 perturbation applied by horizontal and vertical field error correction coils at the gap cause the n=6 mode to lock Sawteeth cease and local large amplitude density fluctuations decrease Confinement is poorer than in rotating plasmas The data are from two discharges, one realizationeach discharge (I p ~ 275 kA) The upper trace: n e ~ 0.5 x 10 13 cm -3 v n=6 ~ 32.5 km/s The lower trace: n e ~ 1.0 x 10 13 cm -3 v n=6 ~ 28 km/s Effect of Plasma Density and Rotation on Potential Measurements Locked Discharges