+ +

++++

++

++

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