Outline

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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

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MST HIBP

• Cross over sweeps to accommodate small ports
• Magnetic suppression structures to reduce plasma
  loading
• Magnetic field largely plasma produced
  (reconstructed from MSTFit)

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Heavy Ion Beam Probing

• Quantities measured in MST
• Potential
• Potential fluctuations
• Density fluctuations

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Secondary Ion Currents

• Sources of uncertainty in potential measurements
• variations in beam attenuation factors Fp, Fs
• variations in sample volume length lsv
• Gradient in local electron density ne

Beam image on the split plates of the energy
analyzer
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Measurement of Electrostatic Potential

• Potential measurement is sensitive to
• Entrance angles of ions into the analyzer
• Calibration of the analyzer (XD, YD, d, w)
• Accuracy of analyzer voltages and detected
  current signals

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Discharges in MST
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HIBP Measurement Conditions
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Detected Currents During Standard 380kA Discharge
c1
c2
c4
c3
sum
Potential
ne
Ip
F
Mode Speed
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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

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Plasma Profile for Standard Discharge
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Sawtooth Cycle Potential Variation
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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

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Variation of Potential with Plasma Parameters
Density
F
Ip
Bp
Sawtooth Cycle Time
Mode Speed
Mode Speed

• Strongest correlation is with mode speed
• Only weakly dependent on other parameters

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Finite Beam Simulation
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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

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Sample Volume
27 Trajectories are evaluated to represent the
secondary ions originating in the sample volume.
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Example 380kA Standard Discharge
Secondary Trajectories
Sample Volume
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Example 380kA Standard Discharge
Secondary Beams at the Exit Port (Magnetic
Aperture)
Secondary Beams at the Analyzer Entrance Aperture
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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
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Simulation of Secondary Currents During a 380kA
Standard Discharge Sawtooth Cycle
Typical secondary ion currents on the four plates
of the center detector (c1 - c4), sum signal, and
the measured plasma potential ?c, during a 380 kA
standard discharge with plasma current Ip,
electron density n0, 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.
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Detected Signals during Sawtooth Cycle
HIBP measurement Simu_in simulation Simu_out
simulation after potential adjustment

• Agreement between measured and simulated signals
• There is significant scrape off
• Sample volume position varies by up to 3.5cm

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Potential During Sawtooth Cycle
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.
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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.
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Error Sources Analyzer Entrance Angle
entrance angle of beam in radial direction ? and
in toroidal direction ?
Potential variation due to the variation of beam
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.

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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 (
lt 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.
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Summary of Error Sources
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Numerical Experimentsimulation 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 Br 30 Gs, B? 20 Gs,
  B? 30 Gs.
• ? Perturbation phases ?r 0, ?? ?/2, ??
  3?/2.

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Movement of the sample volumes during a rotation
cycle
Excursion of the center of sample volumes
Radial movements of the sample volume
The sample volume length remains relatively
constant ( 0.21 cm) during the cycle.
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Secondary beam position and currents on the
detector
Secondary currents on the center split plates
The toroidal position of the secondary beam
center on the detector
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 Br and B?. The simulation shows the about
half of the secondary beam has been scraped-off
by sweep plates.
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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
(lt 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.
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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