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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

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Irvine Field Reversed Configuration Ion Density and Flow

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irvine field reversed configuration ion density and flow

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

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 Nd:YAG 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.
brief description of the irvine field reversed configuration ifrc
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
formation uses inner flux coil
Formation Uses Inner Flux Coil


FRC with a Flux Coil configuration. The plasma forms around the inner coil instead of r=0.

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

  • Measure the time-evolving density profile
  • Measure Ion Flow Velocity
  • Determine Ion Energy Distribution Function
    • Classify orbit types
    • Measure plasma drift
simple circuit and probe
Simple Circuit and Probe





  • 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.
some of the mach probe revisions
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 didn’t suffer from arcing.

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.

The Mach Probe Works
magnetic field evolves on 10 m s scale
Magnetic Field Evolves on 10ms Scale


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


The field null, or B = 0, forms around -10 cm < z < 10 cm and r ~ 25 cm.

time evolution of density profile
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.
interferometer vs i sat
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.

the flow measurements are indeterminate
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.

magnetic field measurements yield density as well
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.

comparing magnetic data to i sat
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.

large floating potential makes measurements difficult
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.

ion energy analyzer iea
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.
theoretical model of frc equilibrium
Theoretical Model of FRC Equilibrium

The rigid rotor predicts the following plasma model

A. Qerushi, Doctoral Thesis,

choice of distribution function
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.


orbit types
Orbit Types

Betatron orbit and associated effective potential

Drift orbit and associated effective potential

generation of seed data
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.
verification of seed data
Verification of Seed Data


Randomly Generated

simulation results
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
simulated orbit collected depends on radial position of probe
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.

iea schematics
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.

ion energy analyzer schematic
Ion Energy Analyzer Schematic



Axis of Symmetry

Electron Rejection

Ion Selection

conclusions future work
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