FieldReversed Configuration Equilibrium

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Field-Reversed Configuration Equilibrium

• Thomas Roche

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Thanks to

• William Heidbrink, Roger McWilliams and Eusebio
  Garate
• Wayne Harris and Eric Trask

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Field-Reversed Configuration (FRC) Equilibrium

• Irvine FRC (IFRC)
• FRC Equilibrium Characterization
• Measurement Techniques
• Results
• Theory vs. Data
• Background Field Improvements
• Repeatability
• Field-Reversed Images
• Conclusions and Future Work

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Irvine FRC
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Irvine FRC
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FRC Equilibrium Characterization

• Magnetic Field Structure
• Pressure Balance
• Current Channel/Magnetic Field Null
• MHD Equilibrium Model

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Magnetic Field Structure
FRC Configuration with a Flux Coil
Redmond Plasma Physics Laboratory, University of
Washington
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Equilibrium Conditions
Global Equilibrium Condition Barnes, Seyler,
Anderson, 1979
where
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Coaxial Geometry Modifies Structure
plasma

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

Pietrzyk, Vlases, Brooks, Hahn, Raman, Nuc. Fus.
1987
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Separatrix Can Relocate

• Here the inner separatrix
• radius has moved away
• from the inner coil.
• We will see that the MHD
• equilibrium model
• predicts this as well.

rso
rsi
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Separatrix and Field Null
There are a few cases for the coaxial source
or
Axial View
Pietrzyk, et al. Nuc. Fus. 1987
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A Coaxial MHD Equilibrium
Choosing
And assuming the plasma is inside a conducting
toroidal chamber with rectangular cross section
(radii ri and ro and height L), we arrive at the
following flux function
Other relevant quantities can be written in terms
of this function
Where F0 and G0 are the regular and irregular
Coulomb Wave Functions and
Farengo and Brooks, Nuc. Fus. Vol.32, No.1, Jan.
1991
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MHD Equilibrium Fields
Field structure predicted by the previously
indicated MHD equilibrium model.
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MHD predictions of volume and current densities
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Techniques for Measurement of the
time-dependent, three-dimensional Magnetic field

• Axial B-Dot Arrays
• Radial B-Dot Arrays

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Axial B-Dots
Many windings
Z
Changing magnetic fields in the z direction
induce a current in the wire loops which can be
measured as a voltage.
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Radial B-Dot Probes
Each radial probe consists of 10 sets of 3
inductance coils. Each of the 3 coils are
arranged orthogonally to each other so all 3
components of the magnetic field can be measured
at each location. Each coil consists of 50
turns. Changing magnetic flux through a coil
induces a current which can be measured as a
voltage.
2.5 cm
Radial B-Dot array
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Magnetic Field Probes
3D radial array
3D radial array close-up
Outer axial array
Inner axial array
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Time Evolution of Axial Magnetic Fields During a
Plasma Shot
Inner and Outer Magnetic field traces show that
the fields do reverse and separate but provide no
information about field structure within the
plasma.
These traces represent the magnetic fields along
the internal and external axes of the plasma. The
Inner/Outer probes are placed symmetrically about
the midplane of the chamber. Outer 1 correlates
to Outer 8 and Inner 4 correlates to Inner 12
and so forth.
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Method for Mapping 3D B-Field
Z

• By placing the radial probes in various axial
  positions (as shown) it is possible to map out
  the magnetic field using many grid points.
  Interpolation is then used to find contours.

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Results

• MHD Comparison
• Field structure images from data
• Repeatability
• Azimuthal Symmetry
• Improvements due to improved background field
• Moving pictures of B-field profiles

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Early Field Reversal
Soon after formation with mirror coils left open.
Notice the good agreement with the MHD model
predictions.
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MHD Equilibrium Fields
Notice the striking similarity with the data.
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Side-by-side Comparison
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Time Evolution Along Chords
Current flows mostly where B is equal to zero,
density greatest there too.
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Shots Are Repeatable!
These traces represent the average Bz field over
5 shots given by 2 randomly selected probes. The
black regions show the standard deviation from
the mean.
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Limiter Field Improved
There was a large gradient in the magnetic field
before the limiter was modified.
The improvement in current distribution has
essentially removed the gradient in the
confinement region.
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Pre-modification Issue
A few micro-seconds later the plasma begins to
drift axially toward the wall.
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Drifting Plasma
The plasma is most-likely coming in contact with
the wall and soon dissipates. Notice that the
plasma may also have split in to two blobs. The
plasma drifts at 4 x 105 cm/s.
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Symmetric Formation
Near the early stages of formation. Limiter
improved and mirror coils shorted.
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Plasma is Azimuthally Symmetric
Radial array 1 at q -20º
Radial array 2 at q 70º
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Longer Confinement Times
Later in the shot with the mirror coils shorted
causing a cusp-like field structure. Field
reversal lasts much longer in this formation.
Plasma seems much more well behaved and no
longer drifts axially.
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Drifting Plasma Movie
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No Drift Plasma Movie
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Conclusions

• IFRC produces a repeatable and symmetric plasma
• Improvements in background fields have given rise
  to longer confinement times
• MHD model agrees with data

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Future Work

• B-Field map with symmetric limiter
• More detailed MHD analysis and comparison with
  kinetic models
• Analysis of particle orbits in the equilibrium