February 56, 2004

1
Survivable Target Strategy and Analysis

• Presented by A.R. Raffray
• Other Contributors
• B. Christensen, M. S. Tillack
• UCSD
• D. Goodin, R. Petzoldt
• General Atomics
• HAPL Meeting
• Georgia Institute of Technology
• Atlanta, GA
• February 5-6, 2004

2
Outline

• Survivable Target Strategy
• Accommodation and Sticking Coefficients
• Phase Change
• Summary

3
Overall Strategy to Develop a Survivable Target

• Uncertainty in chamber gas requirements and
  resulting heat flux on target
• - Min. gas density set by chamber wall
  protection
• - Max. gas density set by target placement and
  tracking accuracy
• - Uncertainty in accommodation and sticking
  coefficients for high temp. chamber gas on
  cryogenic target
• Prudent to consider dual target approach and
  address key issues
• - Basic target
• - Thermally robust target with insulated
  foam coating
• - Increase target heat flux accommodation
  through low temp. target and possible
  allowance of phase change
• Once sufficient information available
  down-select besttarget design
• Integrated team approach

4
Basic Target Strategy
Is Low Temperature Acceptable for DT Layering?
Outer Coat/DT Phase Change/DT Solid Interaction,
Vapor Growth, Impact on Target Symmetry
Vapor Bubble/Phase Change Exper.?
Will Liquid Layer/Vapor Bubbles Meet Physics
Requirements?
Physics Simulation
Which target design(s) fit within background gas
requirements?
Timeline(?) Downselect in mid-Phase II
5
Insulated Target Strategy
Which target design(s) fit within background gas
requirements?
Timeline(?) Downselect in mid-Phase II
Is Low Temperature Acceptable for Layering?
Experiment
Manufacturing Process and Cost Study?
Does Foam Insulator Meet Manufacturing and
Physics Requirements?
Physics Simulation
Does Liquid Layer/Vapor Bubbles Meet Physics
Requirements?
Numerical Model
Outer Coat/DT Phase Change/DT Solid Interaction,
Vapor Growth, Impact on Target Symmetry
Vapor Bubble/Phase Change Exper.?
DT/foam Mechanical Properties Exper.
6
Chamber Gas Density and Target Heat Flux
Downselect in mid-Phase II
Minimum Gas Density
Sufficient Chamber Wall Protection?
ArmorSystem Analysis
Which target design(s) fit within background gas
requirements?
Resulting heat flux on target based on gas
target surface conditions
Model expt. for sticking accomm. coeff.
Target Placement Tracking, and Repeatability
Maximum Gas Density
SPARTAN/ DSMC
7
Several Factors Influence the Heat Flux on the
Target from the Chamber Gas

• The condensation or sticking coefficient
• The accommodation coefficient ( fraction of
  energy transfer)
• Target shielding by cryogenic particles leaving
  the surface of the target
• Evaporation/sublimation of condensed background
  gas due to radiation heat transfer

Incoming High Temperature Background Gas (T
4000 K)
Radiation From Chamber Walls
Outgoing Cryogenic Gas
Condensed Material
IFE TARGET
8
Condensation (Sticking) Coefficient of High
Temperature Gas on Cryogenic Target(Very Little
Data Found, Applicable to our Prototypical
Conditions)
CO2 Beam on Cu Target
Condensation coefficient is a function of
several parameters, including - Ttarget,
Tgas, flux, angle of incidence...
Condensation coefficient decreases
rapidly with increasing Ttarget past a certain
point (Brown, et al., 1969) - No obvious
mechanisms causing the threshold (i.e melting
or boiling point of gas species) - MP
(Ar) 83.8 K - BP (Ar) 87.3 - MP (CO2)
194.6 K - BP (CO2) 217.5 K For an
insulated target the surface temperature
will increase rapidly thus the
condensation coefficient will decrease
rapidly
4 x 1016 s-1cm-2
Condensation Coefficient
2 x 1014 s-1cm-2
4 x 1015 s-1cm-2
Target Temperature (K)
1400 K
Ar Beam on Cu Target
Condensation Coefficient
300 K
Target Temperature (K)
9
DSMC Results of Heat Flux for No Sticking and
Complete Accommodation
Results shown in Frost (1975) indicates
accommodation close to unity for 1400K Ar over a
wide range of Cu target temperature and surface
conditions (77-280 K) Effect of shielding from
no sticking for accommodation of unity show a
slight reduction in heat flux due to
shielding effect
15-20 Maximum Reduction for High Density
Case, 100 mTorr Xe
Minor Effect for Low Density Case, 1 mTorr Xe
Xenon Gas _at_ 4000 K, vT 400 m/s Surface
Temperature 18 K (Constant) Complete
Accommodation
10
A Significant Reduction in Accommodation
Coefficient Would be Very Beneficial as the Heat
Flux on the Target Would Vary Accordingly

• Recent results from CERN indicate a possibility
  of much lower sticking coefficients for
  various gases (H2, CH4, CO, CO2) on
  cryogenic (5-300K) targets (and perhaps
  accommodation coefficient?)
• Experiments with prototypical materials and
  conditions would help better understand and
  estimate the actual accommodation and sticking
  coefficients
• In the mean time, for current analysis it seems
  prudent to assume unity for both coefficients
  until data become available

11
Modeling the Behavior of a Vapor Bubble
Simplified Target Cross Section

• Assumptions
• 1-D heat transfer
• DT liquid remains static
• The cryogenic polymer shell behaves according to
  the theory of elasticity
• Solid portion of DT is rigid
• Pre-existing bubble due to defect at plastic/DT
  interface or presence of 3He

ro
Preexisting Vapor Bubble
Plastic Shell
tv
DT Vapor Core
Rigid DT Solid
12
Deflection of the Plastic Shell due to DT Vapor
Pressure

• Two Possible Cases
• Membrane theory (valid for r/t 10) for a sphere
  with a uniform internal pressure
• From bending theory, max. deflection under the
  center of the load

- Where A is a numerical coefficient f (ro , R,
t, m)
- This equation is valid for any edge support
positioned 3 degrees or more from the center of
the load
Roarks Formulas for Stress Strain, 6th
Edition, p. 546
13
Comparison of the Calculated Deflection of the
Plastic Shell by Membrane and Bending Theory for
a Pressure of 104 Pa for Several Vapor Bubble
Sizes , ro
Bubble size for which bending theory approaches
membrane theory is independent of pressure, 37
mm in this case Would need much smaller bubble
size in target to avoid large membrane-like
deflections
14
Pre-existing Vapor Bubbles Could Close if Initial
Bubble is Below a Critical Size and the Heat Flux
Above a Critical Value
Encouraging results for self-healing Need
verification with 2-D model experimental data
Physics requirements (bubble has close but are
solidliquid layers ok?)
15
Summary

• A dual-target strategy is proposed basic target
  thermally robust target
• Converge on final target design once sufficient
  information is obtained on
• - Target fabrication and behavior
• - Heat loads on target (chamber gas density,
  sticking accommodation coefficients)
• - Physics requirements
• Small pre-existing vapor bubbles (defects) could
  be eliminated by solid to liquid phase change
  (self-healing)
• - Depends on heat flux and size of bubble
• - Based on 1-D model and assumptions such as
  rigid solid DT
• - Need experimental data and 2-D model to better
  understand
• - Is this acceptable based on target physics
  requirements?