Computational Modeling of Magnetic Intervention

1
Computational Modeling of Magnetic Intervention

• D. V. Rose, E. A. Madrid, R. E. Clark, C. Thoma,
  D. R. WelchVoss Scientific, LLC
• A. E. Robson, J. D. Sethian, and J. L. Giuliani
• Naval Research Laboratory
• High Average Power Laser Program Workshop
• Santa Fe, New Mexico
• April 8 and 9, 2008

2
Status report on computational modeling for
Magnetic Intervention (MI)

• Ion orbit analysis of the OCTACUSP MI concept
• No solution to the neutral line loss problem has
  been identified.
• A new variant of the conventional MI concept (the
  Bell Cusp) has been proposed (A. Robson) that
  reduces ion energy escaping from the point cusps
  and includes a more realistic scheme for handling
  the ring cusp ion pulse (A. Robson, J. Sethian,
  et al.)
• Ion orbit calculations are presented here,
  illustrating the main features.
• Refinements to the Lsp electromagnetic
  simulations of the Pechacek experiment result in
  improved comparisons with measurements.
• Accurate modeling of this experiment is an
  essential aspect of the MI scheme for
  laser-driven IFE.

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The Octacusp MI concept is being shelved

• The neutral line problem discussed at the last
  HAPL meeting (Oct. 2007) remains.
• These tapered neutral lines lead to losses
  between the eight point cusps.
• A number of coil configurations have been
  explored in an attempt to minimize these losses
• Various nested coil configurations with
  (analytically) graded currents were examined. We
  found ways to minimize but not eliminate the
  neutral line ion losses.

4
Nested coil configurations with graded coil
current magnitudes were studied
For N coils and N-1 field points
The as are the normalized magnetic at thefield
points due a coil in all octants.
The three pointsused to calculatethe relative
currents in the nested coils
A variety of coil configurationswere tried
(planar and spherical). All yielded some energy
deposition on the chamber wall.
5
We examined these Octacusp confinement geometries
using 3D orbit calculations and tracking the ion
energy deposited on the chamber wall
Neutral line intercept
Point cusp intercept
6
B contour levels at z0 plane illustrating
magnetic void at center of trap (left). 3D
representation of a single B iso-surface also
shown (right) illustrates location of the six
neutral lines.
B0.1T iso-surfaces
The long tube-like extensions away from the
center of the chamber at X-type neutral lines.
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Magnetic topology of a single tube orX-type
neutral line
Magnetic field at x200 cm plane
Chamber wall, r5 m
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Bell Cusp Concept (A. Robson)

• Berties design has two magnetic field
  modifications compared with the original MI cusp
  scheme
• Greatly increased coil currents at/near the point
  cusp to reduce the ion phase-space acceptance
• An addition coil modifying the planar ring cusp
  to form a bell cusp

z
This scheme opens up a number of possible ion
dump scenarios, includingliquid pools, water
(lead) falls, mists/vapors, etc.
9
Previously, we explored 5-coil designs in hopes
of spreading out the ring cusp ion deposition,
but with little success
Simply flipping this system poses several
problems, including laser line-sight issues,
structure support of a largeannular pool of
liquid lead, etc
up
WaterFall
Pool
10
We are beginning orbit calculations examining the
Bell Cusp using the Perkins ion spectrum
Contours of Aq
Contours of Log10 (nHe)
T10 ms
up
Greatly reduced point cuspion currents
z
11
Ion confinement periods are gt40 ms, with
highest energy ions escaping first.
Next, we will generate the time-dependent ion
energy deposition profiles on the
pool/water-fall surfaces
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EMHD modeling of the Pechacek experiment

• The Pechacek experiment is an important
  laboratory demonstration of the key principles of
  magnetic intervention.
• The experiment
• used a 2-coil arrangement to create a cusp
  magnetic field
• a two-laser illumination system to create
  thermal, high-density plasma from a 1-mm scale
  size deuterium pellet

R. Pechacek, et al., PRL 45, 256 (1980).
13
We have continued to refine the EMHD algorithm
for MI physics studies

• These refinements have lead to improvements in
• Numerical stability (simulations with higher
  conductivities are now possible)
• Energy conservation (reduction in the production
  of high energy ions at the plasma-vacuum
  interface, more consistent with fully EM PIC
  simulations)
• Improved agreement with experimental measurements
  (Pechacek), most significantly at times after the
  first magnetic field compression.

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Snapshots of vector potential and ion density
illustrate improved energy exchange between the
plasma and magnetic field
B-fieldenergyas a functionof time.
T0 ms, Aq
T2 ms, Aq
T3.8 ms, Aq
T0 ms, ni
T2 ms, ni
T3.8 ms, ni
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For the first time, this model gives a nearly
symmetric magnetic field energy bounce
The global ion kinetic energy
Ion charge leaves the systemafter 2 ms
The plasma ions drive a second bounce at 5.5
ms
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Another first the model now agrees with the
motion of the plasma/magnetic field interface
after peak compression
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With the present simulation model, we may now be
able to distinguish between the thermal and
non-thermal initial ion energy distribution
models
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Summary

• OctaCusp
• No solution to the ion losses due to existence of
  neutral lines has been found
• The Bell Cusp scheme has been proposed and offers
  a number of potential advantages
• The problem of the high intensity ion beams has
  been reduced somewhat with the use of high
  current point-cusp solenoids.
• The addition of a fifth coil creates the
  bell-like ion escape channel offering several
  possibilities for ion energy absorption
  (vapor/mist, liquids, etc.)
• Several details are being worked out (see R.
  Raffray presentation)
• New developments in the numerical modeling of the
  Pechacek experiment has resulted in better
  agreement between measurements and simulations
• These developments suggest a path forward for
  full-scale MI chamber modeling

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Backup slides
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Oct16.lsp
1-m radius solenoids at each point cusp, 2 kA/cm
(11 rings each carrying x MA) 5-meter radius
chamber Conformal Triangles on 6-m radius sphere,
3 MA 3 MeV He ion orbits followed Show
magnetic field topology Ion orbits Sample density
plot Energy deposition on surfaces.
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Cutaway view of an iso-surface of B illustrates
location of the neutral lines
B0.6 T iso-surfaces.
Neutral lines (6)lie along thecoordinate
axesin this orientation,and terminatenear the
chamberwall.
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Plots of the ion charge deposition on conducting
surfaces are used to guide the design of the
magnetic fields.
Ion Energy Delivery 20 in 8 tube ends 4 in
6 neutral line points 76 in the chamber wall
(flower petals)
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3D targets in drift tubes indicate a focused ion
beam
R 6 m
R 10 m
Additional diagnostics, not shown here, also
indicate an oscillating ion beam envelope.
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To zeroth-order, orbit calculations can be used
to conduct relevant design studies for ions
leaving the chamber

• We are continuing to develop new models that
  should lessen the discrepancies and handle the
  IFE chamber spatial temporal scales.
• The Pechacek experiment will continue to be the
  test case for all new algorithms.

t (ms)
t (ms)
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EMHD vs Orbit Calculation Ring cusp width and
transverse velocities compared
Ion channel width as a function of time at
r29 cm in the escape cusp.
Ion channel transverse momentum (vz) at r29 cm.
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Orbit Analysis of the duckbill dumps shows a
narrow and sharply peaked ion deposition pattern
HeliumDensity at25 ms

• The duckbill ion dump design does NOT look
  feasible for the ring cusp.
• 5th coil designs to spread the escaping ion
  ring have not been successful.

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OCTACUSP Primary Coil Configurations Include
Triangles
Circles
Conformal Triangles
28
3D view illustrates that the magnetic field lines
extend through the eight solenoids
Sample streamlines without conductor boundaries
Sample streamlines with conductor boundaries
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3D streamlines can aid in the analysis by looking
for critical field line intercept points
outside view
View from inside the chamber
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Sample Ion Orbit Calculation

• 5-meter radius vacuum chamber
• Four triangular main coils mapped onto a
  6-meter radius sphere
• each triangle carrys 6 MA
• Allows 1-meter for neutral shielding
• Eight 1.1-meter radius solenoids along ion drift
  tubes
• Drift tubes have an inner diameter of 0.9 meters
• Solenoids composed of 11 individual rings, each
  carrying 100 kA
• Only 3.0 MeV Helium ions (4He) followed here.

Oct17.lsp
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Individual particle and density plots are less
helpful here
Particle positions and densities at 5 ms
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Charge deposition on the chamber surfaces
(time-integrated) is being used to optimize the
magnetic field topology
Here, only surface cells with non-zerocharge
deposition are plotted.
All surface cells plotted
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Views of the charge deposition in a single octant
illustrate the three-fold symmetry in the
escaping ion distribution
For this case, about 40 of the ions reach
theends of the drift tubes. About 2 are
deposited at the neutral line points,and 58
are in the flowerpetals radiating out from the
entrance to the drift tubes.