2004 international symposium on heavy ion inertial fusion 7 - 11 june 2004
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2004 International Symposium on Heavy Ion Inertial Fusion 7 - 11 June 2004Plasma Physics Laboratory,Princeton University
“Stopping of Low-EnergyHighly-Charged Ionsin Dense Plasmas”
Y. Oguri, J. Hasegawa, J. Kaneko and M. OgawaResearch Laboratory for Nuclear Reactors,Tokyo Institute of Technology,
K. HoriokaDepartment of Energy Sciences,Interdisciplinary Graduate School ofScience and Engineering,Tokyo Institute of Technology
1015 1020 1025
Te
mp
era
ture
kT(e
V)
Density ne (cm-3)
101
102
103
100
Degenerateplasma
Strongly-coupledplasma > 1
Weakly-coupledplasma < 1
HIF target(converter)
Tokyo Techlaser plasmatarget
Planneddense plasmatarget
Beam-plasma interaction experiments with dense plasma targets are being planned at RLNR/Tokyo-Tech.
Experiments performed so far using Tokyo-Tech 1.7 MV tandem accelerator:
Plasma target Li+ + H+ + 2e-,ne 1018 cm-3, kT 10 eV , 1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
Solid
Gas
t = 60 nsec
100 nsec
140 nsec
Charge state q
Cha
rge
fra
ctio
n F
(q
)
Plasma :
Cold matter :
225 keV/u 12C
0.05 0.1 0.5 10
20
40
60
80
100
Projectile energy (MeV/u)
Coldequivalent
Li+ + H+ + 2e-
Plasma target
Sto
pp
ing
po
we
r (M
eV
/(m
g/c
m2 ))
Calculation
ne = 1018 cm-3,Te = 20 eV
Enhanced-dE/dx in plasmas
Enhanced-dE/dx in plasmas
Enhancedcharge in plasmas
Enhancedcharge in plasmas
Dilute hot plasmas ・・・・・ Linear stopping :▬ Induced decelerating field Eind q
▬ -dE/dx = q Eind ∝ q q = q 2 ( q: projectile charge state ) Dense cold plasmas ・・・・・ Nonlinear stopping:
▬ Induced decelerating field Eind qm (m < 1)
▬ -dE/dx = q Eind ∝ q q m = q 1+m = q n (1 < n < 2)
Nonlinear effects are expected for projectile stoppingin HIF target with solid density ( ne 1022 cm-3 ).
q +
e-
e-e-
e-
e-
(( ))
(( )) e-
e-
e-
e-
e-
e-
e-
q +
e-
e-
e- (( ))
e-
(( ))
(( ))
(( ))
(( ))
(( ))
(( ))(( ))
((
))
Denseplasmas:
Diluteplasmas:
Eind Eind
q q q q
Energy loss measurement by Time-Of-Flight method:
Purpose of the research is to find appropriate experimental parameters to observe nonlinear effects.
Plasmadiagnostics
Plasma target
E E-E
Accelerator
Beam pulsingsystem
100 MHzDipolemagnet
Timedetector
Storageoscilloscope
Target : ne, kT, x ?Projectile: E, q?
Target : ne, kT, x ?Projectile: E, q?
Xq+
x
High density, low temperature and low projectile energy are needed to observe nonlinear effects.
Practically useful experimental conditions:▬ Low density : not so thin target thickness, easy diagnostics
▬ High temperature : high ionization degree of the target plasma
▬ High energy : high detection efficiency, good beam optics, long range in the target, high projectile charge state
Heavier projectiles will be more useful:▬ High charge states are available
at low velocities.
9341Nb is assumed to be the projectile:
▬ The heaviest element availablein the facility
▬ Available from the Cs-sputter source
▬ Projectile energy < 50 keV/u
Conditions for the nonlinear effects are not compatible with comfortable experimental conditions.
10 20 30 40
100
200
300
400
500
0
Terminal voltage = 1.6 MV
Projectile atomic number Z
Out
put
ener
gy (
keV
/u)
9341Nb
50 keV/u
Relationship between ionization degree and plasma coupling constant for hydrogen plasmas:
▬ 99.5% ionization at ne = 1020 cm-3 and kT = 10 eV, but 0.1 << 1 !
For hydrogen plasmas, strong coupling ( > 1) isnot compatible with high ionization degree ( 1).
kT
I
h
kTmπ
ne H
2
3
2
2
exp21
1
IH: Ionization potential of hydrogen
n: Hydrogen atomic density
0
0.2
0.4
0.6
0.8
1
Ioniza
tion d
eg
ree
natom = 1019 cm-3
0
0.2
0.4
0.6
0.8
1
Co
up
ling
co
nst
ant
natom = 1020 cm-3
2 4 6 8 10
0.2
0.4
0.6
0.8
1
0Temperature kT (eV )
Ioniza
tion d
eg
ree
natom = 1021 cm-3
2 4 6 8 100
0.2
0.4
0.6
0.8
1
0Temperature kT (eV )
Co
up
ling
co
nst
ant natom = 1022 cm-3
Sophisticated numerical / theoretical researches have been so far published by several authors.
A simple MD code was developed for rough estimation:▬ Target plasma confined in a test volume
▬ Coulomb forces between all particles
▬ Periodic boundary condition
▬ Equation of motion integrated by a leap-frog method
Energy loss of a single projectile in a fully-ionized densehydrogen plasma was calculated by an MD method.
● : Ions( H+ )● : electrons
10D
20D
+ +
E E+dE
dx
Plasma
Zwicknagel:Phys.Rep’99, Maynard:NIMB’98Gericke:LPB’02, Boine-Frankenheim:Phys. Plasma.’96, ▪ ▪ ▪ ▪ ▪
Zwicknagel:Phys.Rep’99, Maynard:NIMB’98Gericke:LPB’02, Boine-Frankenheim:Phys. Plasma.’96, ▪ ▪ ▪ ▪ ▪
-5 0 5
-5
0
5
x (nm)
y (n
m)
0 10 20 30
-5
0
5
z (nm)
y (n
m)
ne = 1020 cm-3, kT = 5 eV
ne = 1020 cm-3,kT = 5 eV
ne = 1020 cm-3,kT = 5 eV
The projectile is gradually decelerated in the plasma, repeating small acceleration and deceleration.
Evolution of kinetic energy of a 50 keV/u-93Nbq+ projectile in the plasma:▬ Large energy loss is observed for highly charged ions .▬ Constant deceleration except for a short transient region
Fit by a linear function Slope = Stopping power
0 10 20 30 40 50
4649.0
4649.5
4650.0
Depth in the plasma z (nm)
Pro
ject
ile e
nerg
y (k
eV)
q = 5+
10+
15+
ne = 1020 cm-3, kT = 10 eV
50 keV/u 93Nbq+
Relaxationlength ~ vproj/p
10 20 30 40
0.5
1
1.5[10-11]
0
Projectile charge q
-dE
/dx
(eV
/(el
ectr
ons/
cm2 )) BE
MD
ne = 1020 cm-3, kT = 2 eV
= 0.25, = 0.539
50 keV/u
= 0.1
Lower temperature induces strong coupling, leading to nonlinearity of the projectile stopping .
For low ne, high kT and high vproj, the results by LV(linearized Vlasov eq.), BE(binary encounter) and the MD calculation agree well each other.
The nonlinear effect was estimated using a projectile-plasma coupling parameter :
232thproj
2/3
/1
3/
vv
q
Γ Zwicknagel:Phys.Rep’99Gericke:LPB’02
Zwicknagel:Phys.Rep’99Gericke:LPB’02
Peter:PRE’91Peter:PRE’91
10 20 30 40
0.5
1
1.5[10-11]
0
Projectile charge q
-dE
/dx
(eV
/(el
ectr
ons/
cm2 ))
BE
MD
ne = 1020 cm-3, kT = 10 eV
= 0.995, = 0.108
50 keV/u
LV Temperaturedecreased
Temperaturedecreased
10 20 30 40
0.5
1
1.5[10-11]
0
Projectile charge q
-dE
/dx
(eV
/(el
ectr
ons/
cm2 ))
BE
MD
ne = 1021 cm-3, kT = 10 eV
= 0.96, = 0.232
50 keV/u
= 0.1
Nonlinear effects in –dE/dx are observed also forhigher electron densities.
Nonlinear stopping is observable for highly-charged ions, even if the plasma coupling constant 0.2
ne = 1021 cm-3 is not acceptable, because
▬ Ionization degree of the plasma is too low (0.96),
▬ Too short range R 100 m
▬ Very thin ( 10 m) target is needed.
Plasma life time 10 m / cs 1 ns Impossible !
Plasma life time 10 m / cs 1 ns Impossible !
10 20 30 40
0.5
1
1.5[10-11]
0
Projectile charge q
-dE
/dx
(eV
/(el
ectr
ons/
cm2 ))
BE
MD
ne = 1020 cm-3, kT = 10 eV
= 0.995, = 0.108
50 keV/u
LV Densityincreased
Densityincreased
10 20 30 40
0.5
1
1.5[10-11]
0
Projectile charge q
-dE
/dx
(eV
/(el
ectr
ons/
cm2 ))
BE
MD
ne = 1020 cm-3, kT = 10 eV
= 0.995, = 0.108
30 keV/u
= 0.1
~ q1.6
q ~ 8
30 keV/u is acceptable, although lower projectile energies are not preferable as practical experimental conditions.
q > 15+ may be necessary to clearly observe the nonlinear effects. For q = 40+, the decrease of the projectile effective charge is 8.
▬ At least 8 electrons are responsible to the screening ?
Nonlinear effect is remarkably increased by slightly decreasing the projectile velocity.
10 20 30 40
0.5
1
1.5[10-11]
0
Projectile charge q
-dE
/dx
(eV
/(el
ectr
ons/
cm2 ))
BE
MD
ne = 1020 cm-3, kT = 10 eV
= 0.995, = 0.108
50 keV/u
LV Velocitydecreased
Velocitydecreased
The projectile charge is partially screened by the freeelectrons in the cold dense plasma target.
Distribution of plasma electrons during the passage of the projectile:
High electron densities aroundthe projectile are observed alsoin the z-vz phase space:
▬ 10-20 electrons are closelyflying with the projectile.
0 5 10
-2
0
2
z (nm)
x (n
m)
z = 0.25Lbox
0 5 10z (nm)
z = 0.50Lbox
0 5 10z (nm)
z = 0.75Lbox
0 10 20 30 40-4
-2
0
2
4
z (nm)
30 keV/u, q = 40+
ne = 1020 cm-3, kT = 10 eV
Long
itugi
nal e
lect
ron
velo
city
v z
/ v
th
vproj / vth
z = 0.75Lbox
20 keV/u, q = 40+,ne = 1020 cm-3,kT = 10 eV
20 keV/u, q = 40+,ne = 1020 cm-3,kT = 10 eV
30 keV/u, q = 40+,ne = 1020 cm-3,kT = 10 eV
30 keV/u, q = 40+,ne = 1020 cm-3,kT = 10 eV
For very low projectile velocities, -dE/dx in a cold dense plasma dramatically decreases.
Strong electron trapping by slow projectiles→ partial screening of the projectile charge → reduction of –dE/dx
At 30 keV/u, q 15+ is not available by ordinary stripping processes:▬ e.g., stripping of 30 keV/u 92U by C-foil → q 7
▬ Experiments using the existing tandem accelerator are very difficult.
10 20 30 40 50
1
2
3
4[10-12]
0
Projectile energy (keV/u)
-dE
/dx
(eV
/(el
ectr
ons/
cm2))
BE
MD
ne = 1020 cm-3, kT = 10 eV
q = 15+ projectiles
0.5vth vth 1.5vth 2vth
Ionsource
Tandemaccelerator
(1st stripper)2nd stripper
93Nb2+ 93Nb15+
Impossible !Impossible !
Target
A calculation neglecting the trapped electrons shows that the q = 15+ state can survive up to the depth of 100 m.
▬ The atomic process is much slower than the classical electron “trapping”.
However, the loosely trapped electrons can enhancethe recombination rate by a factor of 4-5.
Evolution of charge state distribution of a 30 keV/u 93Nb projectile was calculated by a numerical method.
Zwicknagel:Fus.Eng.Des.’96
Zwicknagel:Fus.Eng.Des.’96
10-6 10-5 10-4 10-30
0.2
0.4
0.6
0.8
1
15+
14+
13+
12+
Depth in the plasma z (m)
Fra
ctio
n F
(q)
ne = 1020 cm-3,
kT = 10 eV
= 1.000
93Nb projectile
10-6 10-5 10-4 10-30
10
20
30
0
10
20
Depth in the plasma z (m)
Pro
ject
ile e
nerg
y E
(ke
V/u
)
E
qav
Ave
rage
d ch
arge
qav
0 20 40 60 80 10010
11
12
13
14
15
16
Depth in the plasma z (m)
Ave
rage
d ch
arge
qa
v
= 1.000
= 1.000,recombination x 10 = 0.995
ne = 1020 cm-3, kT = 10 eV
93Nb projectile
Effect of residual neutral species (atomic H) might be stronger than that of the trapped electrons.
In order to take into account the influence of the trapped electrons, the free electron capture rate was artificially increased by a factor of 10. (Red)
Capture of electrons bound in residual H atoms (0.5% by Saha equilibrium) was taken into account. (Blue)
Nonlinear effectscan be observed (?)
Sahaequilibrium
Sahaequilibrium
20 40 60 80 100
10
20
30
0
Pro
ject
ile e
nerg
y (k
eV/u
)
Depth in the plasma z (m)
= 1.00
= 1.00recombination x 10
= 0.995
93Nb projectile
ne = 1020 cm-3, kT = 10 eV
Nonlinear stopping was numerically verified by the MD calculation:▬ Partial neutralization of the projectile charge by plasma electrons
▬ Acceptable (?) condition: ne = 1020 cm-3, kT = 10 eV and E = 30 keV/u
Observed nonlinearity was explained by the projectile-plasma coupling constant :
▬ Nonlinear effects are observable for > 0.1.
Extremely high charge states are necessary for the projectile:▬ q > 15+ for ne = 1020 cm-3, kT = 10 eV and E = 30 keV/u
▬ Experiments using the tandem accelerator are very difficult.
▬ Alternative: small (100-200 kV) single-ended machine witha source of highly-charged ions.
Such highly charged ions rapidly disappear in the target:▬ Strong recombination of slow projectiles in the target plasma
▬ Effect on the recombination:loosely-trapped electrons around the projectile < residual atomic hydrogen
Summary andconclusions
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