Analysis of instrumental effects in HIBP equilibrium potential profile measurements on the MST-RFP

1. Analysis of instrumental effects in HIBP equilibrium potential profile measurements on the MST-RFP Xiaolin Zhang Plasma Dynamics Lab, Rensselaer Polytechnic Institute MST Group, University of Wisconsin-Madison

2. Outline • Introduction to Heavy Ion Beam Probe (HIBP) diagnostics • Equilibrium potential measurements • Intrumental error analysis • Conclusion • Future work

3. Introduction to Heavy Ion Beam Probe (HIBP) HIBP can measure • electrostatic potential (r) • electron density ne(r) • electron temperature Te(r) • magnetic vector potential A(r) & their fluctuations HIBP applied in TEXT, MST, helicon plasma, etc

4. Introduction to Heavy Ion Beam Probe (HIBP) • Electron density measurement Is: secondary beam current Ip: primary beam current Fp, Fs: beam attenuation factors ion: ionization cross-section for primary to secondary ions lsv: sample volume length ne: local electron density Proca-Green parallel plate energy analyzer

5. C2 C1 C3 C4 Introduction to Heavy Ion Beam Probe (HIBP) • Plasma potential measurement q = Wd - Wp Wd: secondary beam energy Wp: sprimary beam energy gain factor off-line processing factor Beam image on the split plates of energy analyzer

6. ion beam Na+ or K+ Na+ enters plasma Na++ detected in the energy analyzer Na++ in the split plate detector magetic field separates Na++ from Na+ Introduction to Heavy Ion Beam Probe (HIBP)

7. Equilibrium potential measurements Raw data ( 380 kA standard discharge) • sawtooth crash indicated by the abrupt drop of signals • strong trend of potential with m/n = 1/6 mode velocity • the dominant tearing mode fluctuations eliminated by 10 kHz LP filter

8. Equilibrium potential measurements Calibration of the energy analyzer  good agreement between the calibration and theory  Beam entrance angle is centered at 30. Beam energy analyzer voltage detector signals

9. Equilibrium potential measurements Equilibrium potential profile measurements • Equilibrium potential is obtained by averaging within 0.2ms time window ensembles in 20~50 shots •  0.2 ~ 0.35 kV potential scattering (not shown) • potential profiles are obtained by changing the steering voltage from shot to shot • relatively flat profiles at r/a ~ 0.3 to 0.8, indicating weak Er • potential in PPCD discharges is smaller than in standard discharges, indicating improved electron confinement

10. Instrumental error analysis HIBP measurements in MST-RFP exhibit variations of currents on the detector during a sawtooth cycle unexplained shot to shot potential variations Possible reasons: evolution and fluctuation of fields variation of location, size and orientation of sample volume variation of other plasma parameters: electron density, plasma current, etc signal scrape-off effects (blocked by ports, apertures, structures in beamline) Potential profile during 25 standard discharge shots (ensembles are obtained during flattop period of discharge, away from sawtooth crashes)

11. Potential profile during 25 standard discharge shots (ensembles are obtained during flattop period of discharge, away from sawtooth crashes)

12. sample volume d to top edge of the entrance aperture to centerline of the entrance aperture to bottom edge of the entrance aperture Instrumental error analysis Finite-sized beam model • A beam trajectory code is used to compute the sample volumes within the plasma and their trajectories in HIBP beamlines. • Beam is emulated by several trajectories at the boundary traced to centerline and edges of the entrance aperture, respectively • The beam is assumed to have a circular-shaped cross-section and uniform or Gaussian current density profile • Including secondary beam scrape-off effects Schematic of primary beam and sample volume • Simulation parameters • 1.5 cm beam diameter& Gaussian profile • Constant electron density and temperature profile • 380 kA standard discharge

13. sample volume d to top edge of the entrance aperture to centerline of the entrance aperture to bottom edge of the entrance aperture Schematic of primary beam and sample volume

14. Instrumental error analysis Simulation at 3.7 ms after sawtooth crash Magnetic structure Sample volume Entrance aperture Primary and secondary beam in MST-HIBP system Detector plane About half of secondary beam scraped-off

15. Instrumental error analysis Simulation at 3.7 ms after sawtooth crash Primary and secondary beam in MST-HIBP system Sample volume About half of secondary beam scraped-off

16. Instrumental error analysis Simulation at 3.7 ms after sawtooth crash Primary and secondary beam in MST-HIBP system Magnetic structure About half of secondary beam scraped-off

17. Instrumental error analysis Simulation at 3.7 ms after sawtooth crash Primary and secondary beam in MST-HIBP system Entrance aperture About half of secondary beam scraped-off

18. Instrumental error analysis Simulation at 3.7 ms after sawtooth crash Primary and secondary beam in MST-HIBP system Detector plane About half of secondary beam scraped-off

19. Instrumental error analysis Simulation throughout a sawtooth cycle • significant signal scrape-off during a sawtooth cycle ( mostly by steering plates and grids on ground plate of the analyzer) • sample volume position varies up to 3.5 cm over a sawtooth cycle Sample volume position variation Secondary current signals on detector Good agreement of general trend of the signals between measurements and simulation

20. secondary beam energy = primary beam energy+ potential measured Simu_in run finite-sized beam simulation adjust potential calculate secondary currents on four slit plates of detector calculated currents consistent with measured HIBP signals? N Y output pot Simu_out Instrumental error analysis Potential estimation with iteration algorithm Potential variation • signal scrape-off has insignificant contribution to potential measurements due to the negligible slant angle of the beam images on the detector

21. signal scrape-off has insignificant contribution to potential measurements due to the negligible slant angle of the beam images on the detector

22. Instrumental error analysis Other factors including non-uniform electric field inside the analyzer, mechanical misalignment will contribute insignificantly to potential error.

23. Electron density profile obtained from MSTFit over the sawtooth cycle during a typical 380 kA standard discharge. The fat lines along the density profiles show the simulated HIBP sample volume length.

24. Conclusion • equilibrium potential profiles measured by HIBP are relatively flat, indicating weak radial electric field • finite-sized beam simulation shows good agreement with measurements. Signal scrape-off has insignificant effects on potential variations. • Other factors including UV loading, power supply ripples, density gradient and beam attenuation will contribute insignificantly to potential error in the interior region of the plasma.

25. Future work •improve beam focusing •real time feedback control of the secondary beam system to improve the beam alignment and reduce the beam scrape-off •numerical experiment by using finite-sized beam model to investigate the effects of magnetic fluctuations and other variations of plasma parameters on HIBP potential measurements.