# Presentation: 802346

## “Stopping of Low-Energy

- 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*

## 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+ + 2*e*-,
*n**e*  1018 cm-3, *kT*  10 eV,

- Enhanced
*-dE/dx* in plasmas

- Enhanced
- charge in plasmas

## Nonlinear effects are expected for projectile stopping

- 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)

- in HIF target with solid density (*n**e*  1022 cm-3).

*q*+

- ((    ))

- ((    ))

*e*-

*e*-

*e*-

*e*-

*e*-

*e*-

*e*-

*q*+

*e*-

*e*-

*e*-

- ((    ))

*e*-

- ((    ))

- ((    ))

- ((    ))

- ((    ))

- ((    ))

- ((    ))

- ((    ))

- ((    ))

- Dense
- plasmas:

- Dilute
- plasmas:

*E*ind

*E*ind

-  *q*

-   *q*

## Purpose of the research is to find appropriate experimental parameters to observe nonlinear effects.

- Energy loss measurement by Time-Of-Flight method:

- 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*?

- X*q*+

***x*

## 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

## For hydrogen plasmas, strong coupling ( > 1) is

- Relationship between ionization degree ** and plasma coupling constant **for hydrogen plasmas:
- 99.5% ionization at* n**e* = 1020 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

## Energy loss of a single projectile in a fully-ionized dense

- 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

- hydrogen plasma was calculated by an MD method.

- ● : Ions(H+)
- ● : electrons

- Zwicknagel:Phys.Rep’99, Maynard:NIMB’98
- Gericke:LPB’02, Boine-Frankenheim:Phys. Plasma.’96, ▪ ▪ ▪ ▪ ▪

*n**e* = 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-93Nb*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

## Lower temperature induces strong coupling, leading to nonlinearity of the projectile stopping.

- 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

- Peter:PRE’91

- Temperature
- decreased

## Nonlinear effects in –dE/dx are observed also for

- 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* = 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 / *c*s  1 ns
-         Impossible !

- Density
- increased

## 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

## 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-v**z* phase space:
-  10-20 electrons are closelyflying with the projectile.

- 20 keV/u, *q* = 40+,
*n**e* = 1020 cm-3,
*kT* = 10 eV

- 30 keV/u, *q* = 40+,
*n**e* = 1020 cm-3,
*kT* = 10 eV

## For very low projectile velocities, -dE/dx in a cold dense plasma dramatically decreases.

- 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.

- Ion
- source

- Tandem
- accelerator

- (1st stripper)

- 2nd stripper

- 93Nb2+

- 93Nb15+

- Impossible !

- Target

## Evolution of charge state distribution of a 30 keV/u 93Nb projectile was calculated by a numerical method.

- 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

## 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

## Summary and

- Nonlinear stopping was numerically verified by the MD calculation:
- Partial neutralization of the projectile charge by plasma electrons
- Acceptable (?) condition: *n**e* = 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 *n**e* = 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

- conclusions