プラズマ阻止能における強結合効果の実験的検証

Development of Thin Foil Plasma Target
for Beam-Plasma Interaction
Experiments
U.S.-Japan Workshop on Heavy Ion Fusion
and High Energy Density Physics, Sep 30,
2005
Academia Hall, Utsunomiya University
J. Hasegawa, S. Hirai, H. Kita, Y. Oguri, M. Ogawa
RLNR, TIT
Thin-foil-discharge was adopted to generate a plasma
target in warm-dense-matter (WDM) regime.
1000
•
 = 0.01
Temperature (eV)
100
 = 0.1
10
•
WDM
=1
1
0.1
0.01
0.001
•
•
Thin Foil
Discharge Plasma
0.01
0.1
1
10
•
100
1000
We have so far examined plasma
effects on stopping power using a ideal
plasma target (z-pinch plasma, laserproduced plasma)
Theory of plasma stopping well
reproduced experimental results.
EOS and conductivity model in WDM
regime has not been established.
Diagnostic of WD plasma by
conventional methods is very difficult.
Energetic ion beam can penetrate
dense (optically thick) plasma.
3
Density (g/cm )
Can we use a heavy ion beam as a diagnostic tool for WD plasma?
– Yes, but we have to care nonlinear effects on stopping.
Nonlinear effects on plasma stopping power strongly
depend on the projectile velocity.
e2
Plasma parameter: ee 
4 0 akT
Beam plasma coupling coefficient:  

3Z eff ee3 / 2
(1 (v 2 /v th2 ))3 / 2
 1
⇒ Nonlinear stopping
Zeff ~ 10, ee ~ 1, v/vth ~ 10 
⇒  ~10–5 !!

Typical beam energy in our beam-plasma experiment:
4.3 MeV/u ⇒ v/vth ~ 17
6 MeV/u ⇒ v/vth ~ 21
Nonlinear effects are
negligible!
By using fully-stripped ions as projectile, we can fix the
effective charge of the projectile in plasma target.
50
•
Equilibrium Charge
40
6 MeV/u
30
•
fully stripped
•
20
4.3 MeV/u
10
Equilibrium charge of projectile in a
plasma is larger than that in cold
matter because of suppression of
recombination process.
Zeff in plasma becomes the same as
that in cold matter.
In such a situation, the enhancement
of the stopping can be attributed to an
increase in Coulomb logarithm due to
plasma free electrons.
0
0
5
10
15 20 25
Atomic Number
30
Plasma stopping power:
35
40
2
e 4 Zeff
dE


N t qt L f  (Zt  qt )Lb 
2
2
dx 40 mvp
From the enhancement of the stopping power, we can extract
mean ion charge of target plasma.
Principle of Thin-Foil-Discharge (TFD) plasma
generation
Arrival Time of Rarefaction Wave
at Center of Foil (mm)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
A Half of Foil Width (mm)
Foil width >> Beam Diam.
• Areal density keeps constant in the early stage of discharge.
(before rarefaction waves reaches to the center of the foil.)
• High density is easily available. (~ 0.01 nsolid)
• Plasma effects on stopping power are directly observable.
10
For the first order estimation of TFD plasma parameters,
we used a 1D plasma expansion model with SESAME
EOS library.
• The LCR circuit solver includes
the change of the plasma
resistance.
• SESAME- EOS, Mean ion
charge, and electrical
conductivity are used.
• When temperature exceeds the
vaporization point, the plasma
starts its expansion with the
maximum escape velocity :
umax  4 /( 1)
• Plasma density distribution is
not considered. (Uniform)
Preliminary experiment on TFD plasma generation.
Thin Foil
Thin
Foil
Discharge
Current
Current
Transformer
Capacitors
0.3 µF
G.S.
High Voltage
0.3 µF
• Charged voltage: 10 kV
• Discharge current: ~ 10kA
• Thin foils: Al (12 µm), C (18 µm)
Time evolution of TFD plasma
（Aluminum, 12 µm）
Thin
foil ns
550
800 ns
750 ns
600 ns
750 ns
650 ns
700 ns
800 ns
820ns
870 ns
• The foil plasma expands with time.
• Until 750 ns, the plasma boundary looks stable.
• At 820 ns or later, the surface became jaggy.
The 1D plasma expansion model well reproduced
the observed plasma expanding velocity.
10
• Expansion velocity used
in the 1D model is
reasonable.
• We used this model to
estimate the TFD
plasma parameters.
Umax (calc.)  2.8 10 m/s
Foil Thickness (mm)
4

8
2.6 10 4 m/s
6
4

2
0
550
600
650
700
750
Time (ns)
800
850
In case of carbon (18µm), only the surface was
heated and ionized by discharge.
Cold core
2.2 µs
6.2 µs
10.2 µs
• Inhomogeneous heating due to a skin effect increase the surface
temperature.
• Electrical conductivity increases at surface.
• Discharge current selectively flows near the surface and deposits
the energy on the surface by Joule heating. (Positive feedback)
Preheating of the foil is
needed.
Electrical conductivity of carbon (graphite)
2.9×104 S/m at 0 ˚C
1.1×105 S/m at 2500 ˚C
A newly developed TFD plasma generator.
Multiple foil target
enabled us to change
foil without breaking
vacuum.
Thin foil
Target holder
Beam axis
Thin Foil
Discharge
electrodes
Electrodes
Required conditions for TFD aluminum plasma
2
Ionization Degree
1.5
2.8 eV 3.5 eV
1
•
Enhancement of stopping power
due to plasma effects is assumed
to be ~ 10%
•
Mean ion charge (Al) ~ 1.3
determined by the plasma stopping
fomula.
•
n~ 0.01-0.001nsolid
•
T~3 eV
•
Initial foil thickness ~ 0.8 µm
•
Capacitor voltage is determined to
be 25 kV.
2.2 eV
0.5
0
0.001
0.01
0.1
3
Density(Mg/m )
1
10
Time evolution of thin foil discharge plasma
(Al, 0.8 µm)
25 kV
Current
Thin Foil
330 ns
230 ns
280 ns
430 ns
480 ns
60
160
40
140
Input Energy (J)
Current (kA)
Energy deposited to the foil was evaluated from voltage
and current waveforms.
20
0
-20
-40
-60
-80
120
100
80
60
40
20
0
0
1
2
3
4
5
0
1
Time (µs)
4
3
4
5
Foil Thickness (mm)
2
3
Voltage (kV)
2
Time (µs)
2
1
0
-1
-2
-3
1.5
1
0.5
0
0
1
2
Time (µs)
3
4
5
0
0.05
0.1
0.15
0.2
0.25
Time (µs)
0.3
0.35
0.4
2
4
0.4

3.5
0.35
3
Temperature (eV)
Mass Density (mg/cm )
Obtained G value is much lower than expected. Energy
input efficiency
0.3
2.5
0.25
2
0.2
1.5
0.15
1
0.1
0.5
T
0.05
0
0
0.1
0.2
0.3
0
0.4
0.35
0.4

0.25
0.3
ee
ee
0.2
0.2
0.15
0.1
Z
0.05
0

Mean Ion Charge
0.5
0.3
0
0.1
0.1
i
0.2
Time (µs)
0.3
0.4
0
•
•
Time (µs)
0.4
•
Only 1~2% of the stored
energy was deposited at
330 ns.
Mean ion charge was only
0.35.
Energy deposition was not
efficient.
Beam-plasma interaction experiment was
performed using TFD plasma targets.
• Projectile: O8+
• Incident Energy: 4.3
MeV/u
• TOF distance: < 3.5 m
• Stop detector: MCP
MCP
Drift tube
TFD plasma
chamber
Beam
Preliminary results of energy loss measurement.
(O8+, 4.3 MeV/u -> Al, 0.8 µm)
2
Energy Loss (MeV)
Cold Eq.
• T < 300 ns, energy loss is
constant.
1.5
• T ~ 300 ns, when the
rarefaction wave reaches to
the center of the foil, the
energy loss began to
decrease with time.
1
0.5
4.3 MeV/u O
0
-200
0
200
8+
• Plasma effect could not be
observed. Higher ionization
degree will be needed.
-> Al
400
600
800
Time (ns)
1000 1200 1400
Summary
• A TFD plasma generator has been developed for beam-plasma
interaction experiments.
• One dimensionally expanding TFD plasmas were successfully
produced with Al foils.
• In case of using carbon foils, inhomogeneous plasma heating
occurred and TFD plasma was not produced successfully. However,
we expect that preheating of the foil will solve this problem.
• We succeed in measuring energy loss of 4.3-MeV/u oxgen ions in a
TFD Aluminum plasma.
• Due to low ionization degree of the plasma target, enhancement of the
energy loss has not been observed, yet. More efficient energy
deposition is needed for increase the ionization degree.
Future plan
• The discharge driving circuit will be upgraded.
• 1D-MHD code using more sophisticated EOS
and conductivity models will be developed
soon.
• Spectroscopic measurement will be
performed to determine surface temperature
of TFD plasma.

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