Ion Species: Cs-133

1
Simulation and Implementation of HIBP Electric
Field Measurements for the HSX Stellarator
Christopher Clark, Jon Hillesheim, David
Anderson, Paul Schoch1, Diane Demers1, Kenneth
Connor1, Michael Bingham1, Alex Dunckle1 HSX
Plasma Laboratory, Univ. of Wisconsin, Madison,
USA 1Rensselaer Polytechnic Institute, Troy, USA
Simulation Results
Overview

• A novel form of heavy ion beam probe is under
  development at HSX
• The deflection of a 10 keV beam of singly charged
  Cesium ions is used to infer the radial electric
  field
• Enabled by the equivalence of the HSX magnetic
  field with and without plasma
• Simulations of this novel technique have been
  performed using a realistic radial electric field
  model based on neoclassical calculations of the
  ambipolar condition
• These simulations suggest that this form of beam
  probe will be suitable for HSX
• Simulations also show that varying the insertion
  angle of the beam allows different radial
  locations in the plasma to be diagnosed

Optimization of Beam Parameters
Sensitivity to Electric Field Profile
Magnitude of Error Sources
The HSX boxports are the only feasible locations
at which to mount the beam and detector.
The projected peak deflections of about 1 cm are
relatively small, so it is important to know the
relative contributions of potential error sources.
Simulations of single particle trajectories show
that sweeping the beam insertion angle can
recover information about the electric field
profile.
Magnetic Field Strength
Beam Deflection
Ion Energy Error
Beam Deflection
/- 1 (.01T)
/- 2.2 mm
/- 1 (100 V)
/- 1.4 mm
2 ¾ Ports
/- 0.1 (.001T)
/- 0.6 mm
/- 0.1 (10 V)
/- 0.1 mm
Boxport Front Flange

• Beam hardware has been moved from RPI to HSX and
  set up on a test-stand
• Beam has been operated with Sodium ions on the
  test-stand

Simulate Sweep
Beam Divergence
It is difficult to predict the beam divergence,
so its effect was simulated to determine the
effect on the measurement.
Corresponding Deflections
Two Electric Field Profiles (At Mid-Plane)
.5 m
HSX Boxport Cross Section with Puncture Plot
Superimposed
Measurement of a Beam
-0.1 Degrees
Full three dimensional simulations were then
undertaken to maximize beam deflection, while
ensuring an accessible launch and detector
location based on the fixed parameters
Beam Hardware on.Test Beam-line at HSX
Simulations with a collimated truncated Gaussian
current density, show similar behavior to the
single particle simulations.
Conventional HIBP
Proposed HIBP
Nominal

• Magnetic Field on Axis 1.0 T
• Magnetic Configuration QHS
• Electric Field Model Peak Value 90 V/cm
• Electric Field Profile Shape Peaked around r/a
  0.2 - 0.4

• Measures energies of secondary ions

• Measures deflections of primary ions

Simulate Small Changes to Poloidal Launch Angle
Centroids
0.1 Degrees
The simulations found the following to be the
optimal trajectory, given the above criterion
Simulate Sweep
Launch Beam with Square Cross-Section
Centroid Shift at Point of Impact is Symmetric
A similar analysis holds for the case of changing
the toroidal launch angle. In general, so long
as the divergence is symmetric, the location of
the centroid will not exhibit a measurable shift
with respect to the centroid of a perfectly
collimated beam.
Sweep Insertion Angle
Two Electric Field Profiles (At Mid-Plane)
Simulated Current Density at Boxport Cover
Crowley, 1994

• Requires high enough density to produce large
  number of secondaries

• Requires low enough density for most primaries to
  traverse plasma

Using these results, the measurement of the beam
by a wire grid are simulated.
Boxport Front Flange
1 mm wide Conductor

Feasibility of Approach
Plan of Action

• Ion energies lower, as only primaries must
  traverse plasma

• Ion energies must be high enough for secondaries
  to have large rL

Micro-gap

• Develop inversion techniques to recover profile
  from deflections
• Develop error analysis techniques incorporating
  effects that have been simulated
• Construct mounting hardware and detector for HSX

• Based on a full, three dimensional particle orbit
  simulation
• Realistic electric field models incorporated
  results based on neoclassical calculations
• Deflections of up to 1 cm are predicted, which
  should be measurable
• Hardware parameters are compatible with the beam
  hardware provided by RPI
• Error sources and their relative magnitude have
  been identified

• A wire grid detector should be sufficient

• Requires energy analyzer

Compare Virtual Measurements at Maximum
Deflection

• Ion Species Cs-133
• Initial Energy 10 keV
• Launch and Detect on Boxport Front Flange
• Deviation from Plane Perpendicular to Axis 3 mm
• Projected Maximum Deflection in E-Field 1 cm

• Allows measurement of fluctuations

• Deflection due to fluctuations are too small to
  measure

Currents Expected on a Detector Grid
A Simple Grid of Wires as a Detector

• Results are a path effect, and must be inverted

• Sample volume can be selected by aperture angle