![Page 1: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/1.jpg)
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).**[email protected]
![Page 2: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/2.jpg)
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
![Page 3: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/3.jpg)
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.
![Page 4: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/4.jpg)
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”.
![Page 5: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/5.jpg)
1. Initialize with thermal ion cloud, uniform density, 4 cm radius
![Page 6: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/6.jpg)
T=0 ns T=1000 ns T=2000 ns
![Page 7: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/7.jpg)
At r=22 cm inside ring cusp, electron density was measured at 5 different
times.
![Page 8: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/8.jpg)
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
![Page 9: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/9.jpg)
Plasma/Field boundary along 27 degree radial line from the cusp center:
![Page 10: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/10.jpg)
2A. Estimate of Initial Energy Distribution in the Laser-Created D2
+ Plasma
![Page 11: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/11.jpg)
Hand-digitize data from 1980 PRL to estimate initial ion energy distribution:
Measured J, no appliedB-field
Model calculation(Haught & Polk, 1970).
![Page 12: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/12.jpg)
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)
![Page 13: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/13.jpg)
Sample from this calculated distribution in an LSP orbit calculation, assuming a 4-cm radius, uniform density ion cloud with radially directed
velocities.
![Page 14: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/14.jpg)
2B. EMHD simulations with the non-Maxwellian distribution function, 2-cm
initial radius and uniform density
![Page 15: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/15.jpg)
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
![Page 16: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/16.jpg)
1.5 s1.0 s0.5 s
![Page 17: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/17.jpg)
3.0 s2.5 s2.0 s
![Page 18: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/18.jpg)
4.0 s 4.5 s3.5 s
![Page 19: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/19.jpg)
6.0 s5.5 s5.0 s
![Page 20: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/20.jpg)
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
![Page 21: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/21.jpg)
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.
![Page 22: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/22.jpg)
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.
![Page 23: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/23.jpg)
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
![Page 24: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/24.jpg)
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.
![Page 25: Analysis of a Small-Scale Magnetic Deflection Experiment *](https://reader036.vdocument.in/reader036/viewer/2022062309/56814eff550346895dbc8fc8/html5/thumbnails/25.jpg)
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.