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

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

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

Introduction to Heavy Ion Beam Probe (HIBP) Proca-Green parallel plate energy analyzer Electron density measurement I s : secondary beam current I p : primary beam current F p, F s : beam attenuation factors  ion: ionization cross-section for primary to secondary ions l sv : sample volume length n e : local electron density

Introduction to Heavy Ion Beam Probe (HIBP) C1C1 C3C3 C2C2 C4C4 Beam image on the split plates of energy analyzer Plasma potential measurement gain factor off-line processing factor q  = W d - W p W d : secondary beam energy W p : sprimary beam energy

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 Introduction to Heavy Ion Beam Probe (HIBP)

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

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

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 E r  potential in PPCD discharges is smaller than in standard discharges, indicating improved electron confinement

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

Instrumental error analysis to centerline of the entrance aperture to bottom edge of the entrance aperture to top edge of the entrance aperture d sample volume Finite-sized beam model Schematic of primary beam and sample volume  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 Simulation parameters  1.5 cm beam diameter& Gaussian profile  Constant electron density and temperature profile  380 kA standard discharge

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

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

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

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

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

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

Instrumental error analysis Simulation throughout a sawtooth cycle Secondary current signals on detector Sample volume position variation Good agreement of general trend of the signals between measurements and simulation 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

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 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 has insignificant contribution to potential measurements due to the negligible slant angle of the beam images on the detector

Instrumental error analysis sourceUncertainties of the sourcePotential uncertainty (KV) UV loading0.9 nA (rms) <  Power supply ripples~3.4 Vpp (V g ), ~ 0.2 Vpp (V a ) <  Density gradientDensity variation along the sample volume length ~ 0.01 ( r ~ 0.18m) 0.05 ~ 0.11 ( r ~ 0.4 m) Beam attenuationBeam intensity attenuated along sample volume by ionization V ( r ~ 0.18 m) –24.6 V ( r ~ 0.4 m) Other factors including non-uniform electric field inside the analyzer, mechanical misalignment will contribute insignificantly to potential error.

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.

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.

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.