1. Plasma Dynamics Lab HIBP Abstract Measurements of the radial equilibrium potential profiles have been successfully obtained with a Heavy Ion Beam Probe (HIBP) in the core () of the Madison Symmetric Torus (MST) Reversed Field Pinch. Typically, has a magnitude of up to 1.0-2.0 kV in a standard 380 kA discharge. The core profile of the electrostatic potential fluctuations and electron density fluctuations have also been measured in MST. The measured ranges from 30-50 V rms and ranges from 10-20% for this same standard 380 kA discharge. While most of the data obtained thus far have been for standard discharges at a variety of plasma currents, preliminary measurements have also been obtained for other discharge conditions, including biased discharges and pulsed poloidal current drive (PPCD) discharges. Confinement is significantly improved in PPCD discharges and HIBP measurements obtained thus far show very distinct changes in, and. The general status of HIBP measurements on MST will be presented including representative data from all types of discharges and measurement development issues. I. Principle of Heavy Ion Beam Probing I 0 = initial primary current injected into the plasma  ion = ion cross-section for primary to secondary ions l sv = sample volume length n e (r sv ) =electron density at the sample volume k = a multiplying factor between 1~10 due to electrons emitted by the detector plates F p = primary beam attenuation F s = secondary beam attenuation q s = charge of the secondary beam q p = charge of the primary beam High Current Standard Plasmas RESULTS:  ~ 1700 - 2000V E r ~ 1.7 - 2 kV/m PLASMAS: I p ~ 380 kA,  ~ ±1% n e ~.95 x 10 13 cm -3,  ~ ±5% V n=6 ~ 30km/s,  ~±10% F ~ -0.22 T e ~ 300 eV Multiple Shot Analysis Three intervals, 1.5ms duration each ~1.5 ms after crash mid way between crashes ~2.5 ms before crash Potential is Positive Between Sawtooth Crashes After Crash –Phi ~ 1735 V –±125V scatter about trend- line Mid-cycle –Peak phi ~ 2kV –±125V scatter about trend Before Crash –Peak phi ~ 2kV –±150V scatter about trend Scatter may be due to Variations in density Variations in mode velocity Variations in magnetic profiles and thus sample volumes Potential Tracks the Mode Velocity Measured instantaneous potential tracks evolution of the mode velocity m=1, n=6 mode velocity Potential at which v n=6 = 40 km/s does not overlap  at v n=6 = 20 km/s Sample volume ~ r=22cm Data from over 50 shots Differences between  and v n=6 profiles may be due to evolution in B and motion of the sample location Potential and Electric Field Profiles in High I p Discharges Measurement locations determined for data in potential scatter plots Average sample position and potential computed from a 1- 1.6cm range Scatter in the potential and radial location are depicted by the vertical and horizontal ranges Electric field profiles computed from the average potentials and average sample volume spacing After Crash Mid-cycle Before Crash Potential Profile Measurements in Low Current Discharges Peak  ~ 1400 V Peak  ~ 500 V lower than in High I p discharges Measurements ~ 2 ms after crash Electric Field Profiles in Low Current Rotating Plasmas Average E r ~ 1.5kV/m The electric field is outwardly directed Recall, E ~ 2 kV/m in high I p discharges Large error bars on E r (neg. E r ) due to shot to shot scatter in potential and artifacts of data processing Singly charge heavy ions (primaries) are injected into the plasma Some primary ions are further ionized by collisions with plasma electrons The magnetic field separates the secondary ion trajectories from the primary ions. The combined primary and secondary ion trajectories appear as shown in the system figure above The secondary ions are detected by ion collection plates split vertically and horizontally so that four separate currents are monitored This permit measurements of the electric potential, fluctuations of potential and electron density, and magnetic vector potential, localized to the ionization position The secondary beam current I s ( the sum of the four split plate signals) is given by Assuming  ion is a weak function of plasma temperature T e, which is about a few hundred eV in the core of the MST plasma, I s is proportional to the density n e (r sv ) The relative density fluctuation level at the sample volume is then obtained from The currents on the top two plates are summed to produce i upper while the bottom two plates sum to i lower. The energy of the secondary ion leaving the plasma differs from that of the primary ion by the change in potential energy. Thus, to determine potential, we use a Proca and Green type energy analyzer and the following relationship G and F are geometric functions of the analyzer angle V AN is the analyzer voltage and V AC is the accelerator voltage

2. 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