Irvine FRC Magnetic Field Structure

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Irvine FRC Magnetic Field Structure

• T. Roche, W. Harris, E. Trask E.P. Garate, W.W.
  Heidbrink, R. McWilliams
• Slides available at http//hal900.ps.uci.edu/aps20
  07/

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• ABSTRACT Magnetic probe arrays have been used
  to construct time-evolving images of the magnetic
  field structure in the Irvine Field Reversed
  Configuration (IFRC). Two radial arrays of ten
  probes each measure the field in all three
  directions within the interior of the plasma.
  Axial field arrays measure field strengths
  adjacent to inner/outer coils. Magnetic field
  maps are made by moving the radial probes to
  different axial and azimuthal positions over a
  series of shots. The map covers a grid of 30x50
  cm in the r-z plane with grid spacing 2.5x5 cm.
  Shot-to-shot variation is small enough (lt10) to
  use data from successive shots to interpolate
  magnetic field lines as they evolve in time.
  Reversed fields of 250 gauss have been measured
  with lifetimes of 80 ms. These data have been
  used to estimate essential IFRC equilibrium
  qualities/quantities such as mid-plane separatrix
  radii, major radius, field-null location and
  azimuthal symmetry. During this process the
  background fields also were measured. It has been
  found that some anisotropy in the background may
  have been the cause of undesired translational
  motion of the IFRC. Improvement of the background
  field symmetry may lead to longer lived
  equilibria in the desired location.

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Irvine FRC
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Expected B-Field Structure
FRC Configuration with a Flux Coil
Image used with permission from University of
Washington
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Coaxial Geometry Modifies Structure
rso
plasma
rsi

• FRC with a Flux Coil configuration. The plasma
  forms around the inner coil instead of r0. The
  inner separatrix radius can move away from the
  inner coil as predicted by the MHD model.

Pietrzyk, Vlases, Brooks, Hahn, Raman, Nuc. Fus.
1987
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Separatrix and Field Null Calculation w/ Inner
Solenoid
There are a few cases for the coaxial source
or
Axial View
Pietrzyk, et al. Nuc. Fus. 1987
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Simple Theoretical MHD Model
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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Model predicts this Field Structure
Field structure predicted by the previously
indicated MHD equilibrium model.
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and these flux surfaces
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Data gathering requires 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
3D radial array close-up
3D radial array
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and Axial B-Dots Probes
Many windings
Changing magnetic fields in the z direction
induce a current in the wire loops which can be
measured as a voltage.
Z
Probes
Outer axial array
Inner axial array
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Peering inside the plasmawith a 2D B-Field map
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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Typical results along the exterior 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.
Outer
Inner
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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Inside the plasma during shot
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.
Plasma current flows where B 0. Which occurs
from around -10 cm lt z lt 10 cm and r 25 cm.
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MHD Theory vs. Experimental datafor Magnetic
Field
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Earlier data showed the plasma was drifting
It starts out fairly well centered but as time
goes on
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The null has moved axially 15cm!
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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Background Field due to the flux limiter was
lopsided!
There was a large gradient in the magnetic field
before the limiter was modified.
The improvement in current distribution has
essentially removed the gradient from the center
of the confinement region.
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Now the Null forms in the center
Near the early stages of formation. Limiter
improved and mirror coils shorted. This caused a
large cusp-like field on the ends and improved
plasma lifetime.
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and remains there!
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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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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Plasma is Azimuthally Symmetric
Radial array 1 at q -20º
Radial array 2 at q 70º
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Tightly closed field lines contain the plasma
well
Separatrix determined by arbitrary integration
constant
Separatrix
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Most-recent measurements show good agreement with
classic FRCs

• In this data run the mirror coils were connected
  with 20 W
• producing a much small, faster-decaying cusp-like
  field.

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Conclusions and Future Work

• IFRC produces a repeatable and symmetric plasma
• Improvements in background fields have given rise
  to longer confinement times
• MHD model agrees with data
• More detailed MHD analysis and comparison with
  kinetic models
• Analysis of particle orbits in the equilibrium