2. Outline (HIBP) diagnostics in the MST-RFP Relationship of equilibrium potential measurements with plasma parameters Simulation with a finite-sized beam model  Description of the model and an example  Applications of the finite-sized beam model Simulation of detector currents during a sawtooth cycle Instrumental error analysis Numerical experiments Sources of uncertainty in potential measurements  Non-ideal fields in the energy analyzer  Secondary electron emission  Entrance angle of detected ions in the analyzer  Plasma and UV loading  Plasma density gradients  Beam attenuation Conclusion

3. MST HIBP Cross over sweeps to accommodate small ports Magnetic suppression structures to reduce plasma loading Magnetic field largely plasma produced (reconstructed from MSTFit) ion beam Na + or K + Na + enters plasma magetic field separates Na ++ from Na + Na ++ detected in the energy analyzer Na ++ in the split plate detector

4. Heavy Ion Beam Probing Quantities measured in MST  Potential  Potential fluctuations  Density fluctuations

5. Secondary Ion Currents Sources of uncertainty in potential measurements  variations in beam attenuation factors F p, F s  variations in sample volume length l sv  Gradient in local electron density n e C1C1 C3C3 C2C2 C4C4 Beam image on the split plates of the energy analyzer

6. Measurement of Electrostatic Potential Potential measurement is sensitive to  Entrance angles of ions into the analyzer  Calibration of the analyzer (X D, Y D, d, w)  Accuracy of analyzer voltages and detected current signals

7. Discharges in MST

8. HIBP Measurement Conditions Type of discharge Standard LockedPPCD Current I p (kA)350-380 (high I p ) 270-290 (low I p ) 260-290490-510 (high I p ) 370-400 (low I p ) Density n e (  10 13 cm 3 ) 0.8-1.2 (high I p ) 0.6-1.0 (low I p ) 0.5-1.00.8-1.2 (high I p ) 0.6-1.1 (low I p ) Temperature T e (eV)~ 300~ 350~<800 Reversal factor F~ -0.220~ -1.0 Velocity v m/n=1/6 (km/s) (mode) 20-40020-40(non-locked) 0 (locked) Potential  (kV) 1.2-2.1(high I p ) 0.9-1.2(low I p ) ~ 0.5~1.0 (non-locked) ~0 (locked)

9. Detected Currents During Standard 380kA Discharge c1c1 c3c3 c2c2 c4c4 sum IpIp F Potential nene Mode Speed

10. Sources of Sum Signal Variations Variation of sample volume size and location Variation of beam deflection due to evolution of magnetic fields Beam scrape-off Variation of plasma parameters

11. Plasma Profile for Standard Discharge

12. Sawtooth Cycle Potential Variation

13. Sources of Uncertainty in Potential Measurements Variations in plasma characteristics – rotation, density, current, etc. Evolution and fluctuations of magnetic and electric fields – affects location, size and orientation of sample volume Instrumental Effects  Beam scrape-off on apertures, sweep plates, etc.  Analyzer geometry  Detector noise due to plasma  Beam attenuation

14. Variation of Potential with Plasma Parameters Strongest correlation is with mode speed Only weakly dependent on other parameters Density BpBp Sawtooth Cycle Time Mode Speed F IpIp

15. Finite Beam Simulation

16. Description of the Model 8 secondary ion trajectories are generated to map the outer boundary of the probing ion beam A circular beam cross-section is assumed with either a uniform or Gaussian current profile Trajectories are followed until they intersect physical objects such as apertures, etc. to address scrape-off. Typical conditions  1.5cm diameter and Gaussian profile  Constant electron density and temperature profiles  380kA standard discharge

17. Sample Volume to centerline of the entrance aperture to bottom edge of the entrance aperture to top edge of the entrance aperture d sample volume 27 Trajectories are evaluated to represent the secondary ions originating in the sample volume.

18. Example – 380kA Standard Discharge Secondary TrajectoriesSample Volume

19. Example – 380kA Standard Discharge Secondary Beams at the Exit Port (Magnetic Aperture) Secondary Beams at the Analyzer Entrance Aperture

20. Example – 380kA Standard Discharge Secondary Beams at the Analyzer Ground Plane Secondary Beams at the Analyzer Detector Plates About half of secondary beam has been scraped-off largely by the sweep plates during the last half phase of a sawtooth cycle

21. Simulation of Secondary Currents During a 380kA Standard Discharge Sawtooth Cycle Typical secondary ion currents on the four plates of the center detector (c 1 - c 4 ), sum signal, and the measured plasma potential  c, during a 380 kA standard discharge with plasma current I p, electron density n 0, reversal factor F and dominant mode velocity. The vertical lines bracket the sawtooth cycle. A 10 kHz low-pass filter has been applied to the potential and mode velocity to remove the tearing mode fluctuations.

22. Detected Signals during Sawtooth Cycle Agreement between measured and simulated signals There is significant scrape off Sample volume position varies by up to 3.5cm HIBP: measurement Simu_in: simulation Simu_out: simulation after potential adjustment

23. Potential During Sawtooth Cycle output pot calculated currents consistent with measured HIBP signals? secondary beam energy = primary beam energy+ potential measured run finite-sized beam simulation calculate secondary currents on four slit plates of detector N adjust potential Y Simu_in Simu_out Signal scrape-off does not make a significant contribution to potential measurements because the up-down balance of the beam image on the detector is not affected.

24. Error Sources: Analyzer Characteristics Agreement between ideal and measured analyzer characteristics is excellent, but not perfect. Shown are characteristics for both bottom and center detectors. Non-ideal characteristics are typically non-uniform electric fields and slight variations in dimensions. G is more critical to potential measurements than F.

25. Error Sources: Analyzer Entrance Angle The variations of entrance angle are  0.45  (  )and 2.6  (  ) The potential uncertainty due to variations of G and F are   0.095 kV. Errors from simulation (due to scrape off and angles)   0.06 kV. entrance angle of beam in radial direction  and in toroidal direction  Potential variation due to the variation of beam angle 

26. Error Sources: Density Gradient The Electron density profile obtained from MSTFit over the sawtooth cycle during a typical 380 kA standard discharge. The thick lines along the density profiles show the simulated HIBP sample volume length when projected onto the horizontal axis. The potential uncertainty caused by the plasma density gradient in the sample volume is small ( < 0.01 kV ) in the interior of the plasma during a high current standard discharge, and becomes significant (0.05 - 0.11 kV) when the sample volume is moving to the outer area of the plasma.

27. Summary of Error Sources SourceUncertaintiesPotential Uncertainty (V) Calibration of F Measurement of entrance aperture width <  54 Beam angle, position and beam scrape-off Variation of beam entrance angles  < 0.45 ,  < 2.6  throughout a sawtooth cycle <  60 (simulation with finite-sized beam model) <  95 (calculated from equation) Plasma and UV loading ~ 0.9 nA (rms) of secondary currents noise loading,  1.7 V loading on V g  0.1 V loading on V a <  30.3 Plasma density gradient Varies with sample volume positions 0.1 ~ 10 ( r / a ~ 0.35) 50 ~ 110 ( r / a ~ 0.77) Beam attenuationVaries with sample volume positions < -0.43 ( r / a ~ 0.35) < -24.6 ( r / a ~ 0.77) Secondary electron emission Asymmetric electron currents due to magnetic fields in the analyzer Hard to quantify, but small – additional experiment required Sum of sources that may cause potential variation (1) – (3) <  144 (simulation) <  180 (w/o simulation) ( r / a ~ 0.35)

28. Numerical Experiment simulation of variation of secondary currents due to magnetic fluctuations Magnetic fluctuations are modeled as a small m / n = 1 / 6 mode in the plasma Simulation assumptions and parameters  Only m / n = 1 / 6 mode exists.  No potential and density gradients  Frequency is 20 kHz.  Perturbation amplitudes B r = 30 Gs, B  = 20 Gs, B  = 30 Gs.  Perturbation phases  r = 0,   =  /2,   = 3  /2.

29. Movement of the sample volumes during a rotation cycle Excursion of the center of sample volumesRadial movements of the sample volume The sample volume length remains relatively constant (~ 0.21 cm) during the cycle.

30. Secondary beam position and currents on the detector The toroidal position of the secondary beam center on the detector Secondary currents on the center split plates The width of the secondary beam fan on the detector is ~12 cm. The toroidal oscillations of the beam on the detector due the magnetic perturbation are within 2 cm and are correlated with B r and B . The simulation shows the about half of the secondary beam has been scraped-off by sweep plates.

31. The sum current, normalized top – bottom and normalized left – right signals on the center detector The variation of secondary current is produced by both magnetic fluctuation and beam scrape-off The insignificant variations of top – bottom signal (< 1% potential variation) are largely due to the variations of the beam angle onto the entrance aperture of the analyzer and to limitations in the simulation The left minus right signal demonstrates the correlation with the magnetic perturbation If we assume the potential profile is reasonably flat but becomes smaller at larger radii (as is almost always the case), the radial excursion of the sample volume would result in a potential fluctuation which is about 180 degrees out of phase with the density fluctuation.

32. Conclusion A new simulation tool is available to determine the quality of potential measurements Simulation shows that potential is determined with good accuracy – errors less than 10-15% Simulation can demonstrate the validity of the traditional (and much faster) data analysis method Simulation can be used to perform numerical experiments to predict signals for planned experiments