Analysis of a Small-Scale Magnetic Deflection

Experiment*

D. V. Rose,** T. C. Genoni ATK Mission Research

A. E. Robson, J. D. SethianNaval Research Laboratory

HAPL Meeting, June 2005, LLNL

*R. E. Pechacek, et al., Phys. Rev. Lett. 45, 256 (1980).**David.Rose@atk.com

Experiment Description

• A two-stage laser system drives a 1-mm scale, solid D2 pellet forming a plasma.

• The plasma is created inside the void of a cusp magnetic field.

• The adiabatically expanding plasma compresses the cusp field lines.

• Plasma ions escape from the “point” and “ring” cusps in the field geometry.

• Plasma ions are “deflected” away from the chamber walls

Experimental Parameters

• Chamber wall radius is 30 cm (not shown)

• External field coils, 67 or 70 cm diam, 70 cm separation.

• |B| = 2.0 kG at ring cusp.

• 2x1019 D2 ions produced from cylindrical target of 1-mm diam., 1-mm length.

We have examined three different initialize plasma conditions:

1. A uniform density, thermal distribution of D2+

ions with an initial radius of 4 cm.

2. A non-Maxwellian energy distribution, estimated from experimental measurements, with a 2 cm initial radius and uniform density.

3. A non-Maxwellian energy distribution, with a 2.5 cm initial radius with radial energy and density distribution obtained from time-of-flight ballistic expansion from a 2-mm radius “pellet”.

1. Initialize with thermal ion cloud, uniform density, 4 cm radius

T=0 ns T=1000 ns T=2000 ns

At r=22 cm inside ring cusp, electron density was measured at 5 different

times.

Compare experimental data with an “orbit” calculation (no field pushing, no field-particle energy exchange) and EMHD simulation:

peak density unaffected, but FWHM of escaping ions closer to measured value.

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.62 4 6 8 10 12

Pe

ak

De

nsi

ty,

22

cm

in R

ing

Cu

sp (

10

15 c

m-3)

t (microsec)

PRL, 1980

LSP (bob3.lsp)

Orbit Calculation

0 2 4 6 8 100

2

4

6

8

102 4 6 8 10 12

FW

HM

(cm

), 2

2 c

m in

Rin

g C

usp

t (microsec)

??? PRL, 1980Electrons

LSP (bob3.lsp)Ions

OrbitCalculation

Plasma/Field boundary along 27 degree radial line from the cusp center:

2A. Estimate of Initial Energy Distribution in the Laser-Created D2

+ Plasma

Hand-digitize data from 1980 PRL to estimate initial ion energy distribution:

Measured J, no appliedB-field

Model calculation(Haught & Polk, 1970).

Use experimentally measured J from shot without applied B-field to determine approximate source distribution function:

0 1x107 2x107 3x107 4x1070.00E+000

1.00E+013

2.00E+013

3.00E+013

4.00E+013

5.00E+013

N(v

)

v (cm/s)

10 100 10001E8

1E9

1E10

1E11

1E12

N/E

(#

/eV

)

E (eV)

Sample from this calculated distribution in an LSP orbit calculation, assuming a 4-cm radius, uniform density ion cloud with radially directed

velocities.

2B. EMHD simulations with the non-Maxwellian distribution function, 2-cm

initial radius and uniform density

LSP run: bob9b.lspSigma = 1e14 (1/s)Ne-background=2e14 (cm-3)Non-Maxwellian ion distribution

2-cm initial plasmaradius (uniform density)

Initial magnetic fieldmagnitude

0.00015 s

1.5 s1.0 s0.5 s

3.0 s2.5 s2.0 s

4.0 s 4.5 s3.5 s

6.0 s5.5 s5.0 s

Magnetic field swept back too quickly, and takes too long to snap back into place.

0 1 2 3 4 5 60

5

10

15

20

r (c

m)

t (microsec)

bob9b.lsp

PRL data

3. Replace 2-cm radius, uniform density plasma blob with density distribution that results from time-of-flight expansion from 2-mm radius, uniform density blob. Use same non-Maxwellian speed distribution from previous simulation.

Field-free expansion of 2-mm radius ion cloud due to non-Maxwellian speed distribution at 75 ns.

Particle Positions Density Contours

Note reduced chamber dimensions for this “special” calculation.

No significant change to the answer with a non-uniform, pre-loaded plasma

0 1 2 3 4 5 60

5

10

15

20

r (c

m)

t (microsec)

bob9b.lsp - 2 cm uniform blob

PRL data

bob10.lsp - 2.5 cm non-uniform blob

Comparison between EMHD model and simple orbit calculation

Total ion charge inside 30 cmradius chamber vs. time

orbit

EMHD

orbit

EMHD

Total ion energy inside 30 cmradius chamber vs. time

Ion charge slower to leave chamber, due in part to energy exchange with magnetic field.

Status:

• Present simulation results suggest numerical (artificial) current & field diffusion into plasma volume.

• Recent tests suggest that this numerical diffusion can be significantly reduced with more conservative calculation of computational constraints.

• Reasonable agreement obtained between the Robson “shell” model and 1D LSP tests using the more conservative constraints.