Irvine Field Reversed Configuration Ion Density and Flow

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Irvine Field Reversed Configuration Ion Density
and Flow

• T. Roche, F. Brandi, E. P. Garate, F. Giammanco,
  W. W. Heidbrink, W. Harris, R. McWilliams, E.
  Paganini, E. Trask
• Slides available at http//hal900.ps.uci.edu/aps20
  08/

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• ABSTRACT A mach probe has been used to measure
  the time-evolved, radial ion density profile and
  ion flow velocity in the Irvine Field Reversed
  Configuration (IFRC). The probe consisted of four
  tungsten tips 0.1mm in diameter and about 1.7mm
  long. An alumina barrier was placed between 2 of
  the tips to block ions impinging from opposite
  directions. The blocked tips were biased 30V
  negative with respect to the plasma floating
  potential to draw ion saturation current. The
  temperature of the ions was measured to be 10eV
  using doppler broadening spectroscopy. Peak
  densities were measured to be 1 x 1014 cm-3.
  Flow velocity was measured for the plasma source
  at 5 x 106 cm/s without the presence of magnetic
  fields. Data gathered during reversal were too
  noisy to measure the flow velocity of the FRC.
  These data were compared with two other methods
  for calculating the density. A NdYAG laser
  interferometer measured a line integrated density
  of 5 x 1015 cm-2 over an approximately 60 cm
  chord length. Previously gathered magnetic field
  data provided a radial density profile under the
  assumption of pressure balance. The combination
  of these two methods verifies both the shape and
  magnitude of the measured signals. An energy
  analyzer is being designed to measure the ion
  velocity distribution function in the IFRC.

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Irvine Field Reversed Configuration
Plasma Guns
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Brief Description of the Irvine Field Reversed
Configuration (IFRC)

• Coaxial Solenoid Configuration
• Inner Solenoid (Flux Coil) r 10.2 cm
• Outer Solenoid (Flux Limiter) r 38 cm
• Plasma Properties
• Cable gun source
• Peak density ni 1 x 1014 cm-3
• Plasma Current 10 kA
• Peak Field Reversal 250 Gauss

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Formation Uses Inner Flux Coil
plasma

• FRC with a Flux Coil configuration. The plasma
  forms around the inner coil instead of r0.

Pietrzyk, Vlases, Brooks, Hahn, Raman, Nuc. Fus.
1987
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Goals

• Measure the time-evolving density profile
• Measure Ion Flow Velocity
• Determine Ion Energy Distribution Function
• Classify orbit types
• Measure plasma drift

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Ion Saturation Current Measured With Floating
Double Probe
Stationary Plasma
Drifting Plasma
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Simple Circuit and Probe
4.2mm
1.7mm
0.9mm
40.0cm

• The signal tips are biased 35V negative with
  respect to the plasma floating potential.
• Reference tips float to the floating potential.
• The current flowing between the tips is measured
  with two Pearson probes.

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Some of the Mach Probe Revisions
Each Probe consists of 4 tips protruding from a
50cm shaft. Two of the tips are completely
exposed to the plasma. The other two are
separated from each other and only exposed to 180
degrees of theplasma.
The probe on the bottom is the final version. The
tips are much shorter, made out of tantalum
instead of platinum and have a radius of 0.4mm.
It is the only version that didnt suffer from
arcing.
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The Mach Probe Works
These shots exhibit functionality of the Mach
Probe. Probe is located at z-8cm with tips
facing opposite arrays of plasma guns. Flux will
be greater and arrive earlier on the tip closer
to guns. In all cases larger signal is from
expected tip. Here the plasma is not magnetized.
This probe works as expected in these conditions.
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Magnetic Field Evolves on 10ms Scale
Null
Bz at z 0 cm quickly reverses and maintains
reversal until it begins to decay around 70
micro-seconds.
Br at r 25 cm takes on the appropriate shape
and decays as the driving flux coil dies.
The field null, or B 0, forms around -10 cm z 12
Time evolution of density profile

• Ion saturation current reaches its maximum at r
  24 cm at 37 us.
• The density peak is at the magnetic null.
• In this sequence the plasma reaches an
  equilibrium and then quickly decays.
• These data are an average over both tips with 6
  shots at each of 10 radial positions.
• Ti and Te are assumed to be 10eV and 1eV
  respectively
• The density derived from the ion saturation
  current shows a peak at 1 x 1014 cm-3.

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Interferometer vs. Isat
The chord used to determine the line density from
the ion saturation current was the same for the
interferometer except that the laser also
traveled through the outer region of the
containment area. The density in that region is
assumed to be small. The features of these
methods are similar.
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The flow measurements are indeterminate
A and B refer to the two signal tips. When a tip
is faced Up it faced the direction of plasma
current. A ratio greater than 1 denoted a flow
velocity Up. This graph shows that the tips
gave conflicting results. After many iterations
it was determined that the environment during a
full shot was too noisy to make a precise enough
measurement to determine the flow velocity. It
became obvious that the probe tips do not agree
with each other.
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Magnetic Field Measurements Yield Density As Well
Using the argument of pressure balance, density
may be derived from the magnitude of the magnetic
field. There is an offset of a constant of
integration. Here pressure was set to zero at the
maximum of the magnetic field. At 40 ms the peak
of the density is at r 24 cm and ni 1.25 x
1014. Ti assumed to be 10eV.
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Comparing Magnetic data to Isat
Density profiles at 40us exhibit same features
and magnitudes.
These data show a similar density evolution. A
different series of shots were used which may
account for the discrepancies as the lifetime of
the plasma was longer for the magnetic shots.
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Large Floating Potential Makes Measurements
difficult
The spike to -1300V makes measuring anything
referenced to the plasma difficult. These signals
must be decoupled from our scope ground. In this
simple experimentcurrent on the line was
measured using a set of passive Pearson probes.
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Ion Energy Analyzer (IEA)

• The bias on the ion selection grid determines how
  much energy a particle must have to reach the
  collector.
• Sweeping the bias over a range of voltages will
  give an integrated distribution function. The
  derivative of the acquired data will yield the
  ion energy distribution function. From this the
  velocity distribution function can be determined.

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Theoretical Model of FRC Equilibrium

• The rigid rotor predicts the following plasma
  model

A. Qerushi, Doctoral Thesis,
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Choice of Distribution Function

• To perform this simulation a choice of
  distribution function must be made. A shifted
  maxwellian in canonical momentum space was
  selected.

Where
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Orbit Types
Betatron orbit and associated effective potential
Drift orbit and associated effective potential
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Generation of seed data

• The initial conditions of 20,000 particles were
  generated and stored for later use.
• Acquisition of these data was accomplished by
  generating random numbers using the rejection
  method to pick out particle locations and
  canonical momenta weighted by the distribution
  function.

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Verification of Seed Data
Theoretical
Randomly Generated
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Simulation Results

• The results indicate that a large population of
  betatron orbits exist, as expected, for this
  distribution.
• An interesting result of the simulation is that
  orbits can be differentiated from each other by
  the position of the detector with respect to the
  magnetic null surface.
• The following results will show
• The expected distributions of betatron and drift
  orbit particle in terms of pq
• The current obtained from the various orbit types
  versus radius

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Simulated collection rate decreases with
increasing bias voltage
Bias Voltage
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Simulated orbit collected depends on radial
position of probe
The number of betatron orbits leads us to believe
that we will not able to distinguish drift orbits
where betatron orbits are present. However, if
drift orbits exist in the region where betatron
orbits do not, they may be seen there.
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IEA Schematics
Differential signal amplifier. Placed as close as
possible to the collector and dummy.
Optical Isolation Amplifier Circuit. Its purpose
is to take the signal with a largeoffset from
scope groundand decouple it.
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Ion Energy Analyzer Schematic
Dummy
Collector
Axis of Symmetry
Electron Rejection
Ion Selection
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Conclusions Future Work

• Mach probe measurements have been successful
• Ion saturation current has given a reasonable
  number for the density
• Flow velocity is still unknown from a direct
  measurement
• IEA simulation suggests viability of probe
• Orbit classes may be distinguishable
• Current due to particle flux will be measurable
• Finish construction of Ion Energy Analyzer and
• Measure Ion energy distribution function
• Compare results with spectroscopy and Time Of
  Flight diagnostic