1. + + + + + + + + + + 2004 International Symposium on Heavy Ion Inertial Fusion 7 - 11 June 2004 Plasma Physics Laboratory, Princeton University “Stopping of Low-Energy Highly-Charged Ions in Dense Plasmas” Y. Oguri, J. Hasegawa, J. Kaneko and M. Ogawa Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, K. Horioka Department of Energy Sciences, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology

2. 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 -, n e  10 18 cm -3, kT  10 eV ， Enhanced -dE/dx in plasmas Enhanced -dE/dx in plasmas Enhanced charge in plasmas Enhanced charge in plasmas

3. Dilute hot plasmas ・・・・・ Linear stopping ： ▬Induced decelerating field E ind  q ▬-dE/dx = q  E ind ∝ q  q = q 2 （ q: projectile charge state ） Dense cold plasmas ・・・・・ Nonlinear stopping: ▬Induced decelerating field E ind  q m (m < 1) ▬-dE/dx = q  E ind ∝ q  q m = q 1+m = q n (1 < n < 2) Nonlinear effects are expected for projectile stopping in HIF target with solid density （ n e  10 22 cm -3 ）． q＋q＋ e-e- e-e- e-e- e-e- e-e- (( )) e-e- e-e- e-e- e-e- e-e- e-e- e-e- q＋q＋ e-e- e-e- e-e- e-e- Dense plasmas: Dilute plasmas: E ind  q q  q q   q  q   q  q

4. Energy loss measurement by Time-Of-Flight method: Purpose of the research is to find appropriate experimental parameters to observe nonlinear effects. Plasma diagnostics Plasma target E E-  E Accelerator Beam pulsing system 100 MHz Dipole magnet Time detector Storage oscilloscope Target : n e, kT,  x ? Projectile: E, q? Target : n e, kT,  x ? Projectile: E, q? Xq+Xq+ xx

5. 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. 93 41 Nb is assumed to be the projectile: ▬The heaviest element available in 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.

6. Relationship between ionization degree  and plasma coupling constant  for hydrogen plasmas: ▬99.5% ionization at n e = 10 20 cm -3 and kT = 10 eV, but  0.1 << 1 ！ For hydrogen plasmas, strong coupling (  > 1) is not compatible with high ionization degree (   1). I H :Ionization potential of hydrogen n:Hydrogen atomic density

7. 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 dense hydrogen plasma was calculated by an MD method. ● ： Ions （ H + ） ● ： electrons 10 D 20 D + + EE+dE dx Plasma Zwicknagel:Phys.Rep’99, Maynard:NIMB’98 Gericke:LPB’02, Boine-Frankenheim:Phys. Plasma.’96, ▪ ▪ ▪ ▪ ▪ Zwicknagel:Phys.Rep’99, Maynard:NIMB’98 Gericke:LPB’02, Boine-Frankenheim:Phys. Plasma.’96, ▪ ▪ ▪ ▪ ▪ n e = 10 20 cm -3, kT = 5 eV n e = 10 20 cm -3, kT = 5 eV

8. The projectile is gradually decelerated in the plasma, repeating small acceleration and deceleration. Evolution of kinetic energy of a 50 keV/u- 93 Nb q+ 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

9. Lower temperature induces strong coupling, leading to nonlinearity of the projectile stopping ． For low n e, high kT and high v proj, 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  : Zwicknagel:Phys.Rep’99 Gericke:LPB’02 Zwicknagel:Phys.Rep’99 Gericke:LPB’02 Peter:PRE’91 Temperature decreased Temperature decreased

10. Nonlinear effects in –dE/dx are observed also for higher electron densities. Nonlinear stopping is observable for highly-charged ions, even if the plasma coupling constant   0.2 n e = 10 21 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 / c s  1 ns  Impossible ! Plasma life time  10  m / c s  1 ns  Impossible ! Density increased Density increased

11. 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. Velocity decreased Velocity decreased

12. The projectile charge is partially screened by the free electrons in the cold dense plasma target. Distribution of plasma electrons during the passage of the projectile: High electron densities around the projectile are observed also in the z-v z phase space: ▬  10-20 electrons are closely flying with the projectile. 20 keV/u, q = 40+, n e = 10 20 cm -3, kT = 10 eV 20 keV/u, q = 40+, n e = 10 20 cm -3, kT = 10 eV 30 keV/u, q = 40+, n e = 10 20 cm -3, kT = 10 eV 30 keV/u, q = 40+, n e = 10 20 cm -3, kT = 10 eV

13. 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 92 U by C-foil → q  7 ▬Experiments using the existing tandem accelerator are very difficult. Ion source Tandem accelerator (1st stripper) 2nd stripper 93 Nb 2+93 Nb 15+ Impossible ! Target

14. 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 enhance the recombination rate by a factor of 4-5. Evolution of charge state distribution of a 30 keV/u 93 Nb projectile was calculated by a numerical method. Zwicknagel: Fus.Eng.Des.’96 Zwicknagel: Fus.Eng.Des.’96

15. 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 effects can be observed (?) Saha equilibrium Saha equilibrium

16. Nonlinear stopping was numerically verified by the MD calculation: ▬Partial neutralization of the projectile charge by plasma electrons ▬Acceptable (?) condition: n e = 10 20 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 n e = 10 20 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 with a 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 and conclusions