Nonlinear Effects in Stopping of Highly-Charged Ions in Dense Plasmas

1. + + + + + + + + + + 2004 International Symposium on Heavy Ion Inertial Fusion 7 - 11June 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: Enhanced -dE/dx in plasmas Enhanced chargein plasmas Plasma target  Li+ + H+ + 2e-, ne 1018 cm-3, kT 10 eV，

3. e- e- e- e- e- Nonlinear effects are expected for projectile stopping in HIF target with solid density （ne 1022 cm-3）． • 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) Dilute plasmas: Dense plasmas: (()) e- e- (()) (()) e- (()) e-  q   q q＋ Eind q＋ Eind (()) e- e- (()) (()) e- e- (()) (()) e- (()) e- (()) e-

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

5. Conditions for the nonlinear effects are not compatible with comfortable experimental conditions. • 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 availableat 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

6. For hydrogen plasmas, strong coupling (G > 1) is not compatible with high ionization degree (a 1). • Relationship between ionization degree a and plasma coupling constant Gfor hydrogen plasmas: • 99.5% ionization at ne = 1020 cm-3 and kT = 10 eV, but G 0.1 << 1！ IH: Ionization potential of hydrogen n: Hydrogen atomic density

7. Plasma 10lD + + E E+dE 20lD dx Energy loss of a single projectile in a fully-ionized dense hydrogen plasma was calculated by an MD method. • 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 Zwicknagel:Phys.Rep’99, Maynard:NIMB’98 Gericke:LPB’02, Boine-Frankenheim:Phys. Plasma.’96, ▪ ▪ ▪ ▪ ▪ ne = 1020 cm-3, kT = 5 eV ●： Ions（H+） ● ： electrons

8. 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

9. Lower temperature induces strong coupling, leading to nonlinearity of the projectile stopping． Peter:PRE’91 • 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 g: Zwicknagel:Phys.Rep’99 Gericke:LPB’02 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 G 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 mm • Very thin ( 10 mm) target is needed. Plasma life time  10 mm / cs  1 ns  Impossible ! Density increased

11. Nonlinear effect is remarkably increased by slightly decreasing the projectile velocity. • 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 ? 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 aroundthe projectile are observed alsoin the z-vz phase space: •  10-20 electrons are closelyflying with the projectile. 20 keV/u, q = 40+, ne = 1020 cm-3, kT = 10 eV 30 keV/u, q = 40+, ne = 1020 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 92U by C-foil → q  7 • Experiments using the existing tandem accelerator are very difficult. 93Nb2+ 93Nb15+ Ion source Tandem accelerator Target 2nd stripper (1st stripper) Impossible !

14. Evolution of charge state distribution of a 30 keV/u 93Nb projectile was calculated by a numerical method. • A calculation neglecting the trapped electrons shows that the q = 15+ state can survive up to the depth of 100 mm. • 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. 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

16. Summary and conclusions • 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 g: • Nonlinear effects are observable forg > 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