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DAH, RRP, UW - FTI ARIES-IFE, January 2002, 1
Thin liquid Pb wall protection for IFE chambers
Time (s)
Ra
diu
s(c
m)
10-7 10-6 10-5 10-40
50
100
150
200
250
300
350
400
450
BUCKY Vaporization simulation: HIB targetin a 4.5m radius, 1mm Pb protected chamber, Tc=600C
D. A. Haynes, Jr. and R. R. PetersonFusion Technology Institute
Post-homogenization condensation1 mm Pb liquid wall, HIB target
0.0001
0.0010
0.0100
0.1000
1.0000
10.0000
0.00 0.05 0.10 0.15 0.20
Time post-homogenization (s)
Pb
De
ns
ity
(To
rr)
Radius = 4.5m,tbc=600C
Radius = 6.5m,tbc=600C
Radius = 6.5m,tbc=685C
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 2
Summary/Outline
We present results from vaporization and preliminary condensation calculations. BUCKY simulations are presented for the ~400MJ closely coupled HIB target and the laser direct-drive NRL target (160MJ) in a thin liquid wall (1mm Pb) chamber. For chambers with radii of 4.5m and 6.5m, and a starting chamber
pressure of 1mTorr, these preliminary results indicate that the chambers recover before the next shot, assuming a 5Hz rep. rate.
•Brief review of relevant processes and examples of BUCKY simulation of them.
•Vaporization results
•Preliminary condensation results
•Future work
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 3
Wetted-Wall Chamber Physics Critical Issues Involve Target Output, and First Wall Response
Target OutputSimulations
(BUCKY, etc) Target Disassembly
Energy Partition
Target OutputSimulations
(BUCKY, etc) Target Disassembly
Energy Partition
Liquid DynamicsSimulations(BUCKY)
X-ray DepositionVaporizationSelf-Shielding
Shocks in Liquid
Liquid DynamicsSimulations(BUCKY)
X-ray DepositionVaporizationSelf-Shielding
Shocks in Liquid
Chamber Recovery Simulations
(1-D: BUCKY,2, 3-D TSUNAMI, ?)
Re-condensation,Substrate Survival
Chamber Recovery Simulations
(1-D: BUCKY,2, 3-D TSUNAMI, ?)
Re-condensation,Substrate Survival
X-rays,Ion Debris,Neutrons
Vapor MassImpulse
Rep-Rate
Target Design
Wall Design
Low T,Hi
Opacity
LiquidProperties
BeamTransportCriteria
Vapor Opacity
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 4
We have obtained or generated relevant Pb properties
•Thermal properties linked by ARIES web site
•http://www.efunda.com/materials/elements/element_info.cfm?Element_ID=Pb
•Tmelt = 601K
•Tvap = 2022K
•Qvap = 866.31 J/g
•Heat capacity = 141.9 J/kg-K (@600K)
•Thermal conductivity = 31.4 W/m-K (@600K)
•Cold attenuation coefficients from Biggs and Lighthill
•EOS and Opacity for Pb calculated using FTI’s UTAOPA
EOSOPA results for Pb ionization
0
10
20
30
40
50
60
70
80
0.1 1.0 10.0 100.0 1000.0
Temperature (eV)
Ave
rag
e I
on
iza
tio
n S
tate
Ion density = 1e22/cc
Ion Density = 1.6e17/cc
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 5
BUCKY divides the mesh into two types of zones, vapor zones which participate in the hydrodynamic motion, and condensate zones which do not move. As
vaporization/condensation occurs, zones are dynamically reclassified.
Vapor Condensate
1
Initial condition (pre-shot)
2
After prompt x-rays from target strike the condensate,superheated vapor zones are created at high temperatures and densities
3
As the newly vaporized zones move out into the chamber,radiating and absorbing target ions
4
The heat and radiation from the newly created vapor zonesfurther vaporizes the condensate
5
As the vapor cools, zones re-condense,Leaving the hydridynamic mesh and re-joining the condensate
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 6
Of the two targets considered here, the HIB target is considerably more threatening
HIB (~400MJ) n
fusion products
x-rays
D
T
p
He
C
Au
Be
Fe
Br
Gd
NRL (154MJ)
nfusion productsx-raysDTpHeCAu
Target output x-ray spectra
0.0
0.2
0.4
0.6
0.8
1.0
0.01 0.1 1 10 100
Energy (keV)
Spe
ctra
(pe
ak n
orm
aliz
ed)
NRL165(LASNEX)
HIB (LASNEX)
2.14MJ
115MJ
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 7
Target x-ray deposition, initial vaporization, and shock
Target x-rays are rapidly deposited in the protecting liquid.
Vapor rapidly moves off of surface
t ~ 1-10 ns
Impulse launches shocks that might damage substrate and/or splash liquid.
4.5m radius, HIB target in 1mm Pb thin liquid wall protected chamber, Tcool=600C:
•The prompt x-rays heat the 1mTorr Pb gas to high temperatures and high ionization stages (~100eV at center of chamber).
•Of the 119MJ of target x-rays, 9MJ are deposited volumetrically in the liquid, and approximately 110MJ vaporize and ionize the first 4.6 microns (11.6kg) of Pb (vapor is heated to 10s of eV).
•Peak shock loading (over-pressure) of 1.5e4 J/cm3 occurs during this time.
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 8
Comparison of target x-ray spectra and Pb attenuation lengths
X-ray attenuation lengthsin cold, solid density Pb
(NIST: http://physics.nist.gov/PhysRefData)
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0.01 0.10 1.00 10.00 100.00
Photon Energy (keV)
Att
en
ua
tio
n le
ng
th (
cm
)
X-ray energy percentiles
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.01 0.10 1.00 10.00 100.00
Photon Energy (keV)
Fra
ctio
n of
tot
al x
-ray
ene
rgy
belo
w
HIB (115MJ x-rays)
NRL160(2.14MJ x-rays)
95% of the HIB target’s x-ray energy is emitted at energies where the attenuation length is less than 1 micron.
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 9
Snapshot: 4.5m radius chamber, HIB target, 10ns
BUCKY simulation: HIB target, 4.5m radius thin Pb liquid chamber, 10ns
0.1
1.0
10.0
100.0
1000.0
0 50 100 150 200 250 300 350 400 450
Radius (cm)
Te
mp
era
ture
(e
V)
1.00E+12
1.00E+13
1.00E+14
1.00E+15
1.00E+16
1.00E+17
1.00E+18
1.00E+19
1.00E+20
1.00E+21
1.00E+22
1.00E+23
Ion
de
nsi
ty (
/cc)
Temperature (eV)
Ion density (/cc)
Chamber gas (including blow-off from wall) conditions vary by many orders of magnitude 10ns after the target goes off.
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 10
Target ions are mostly stopped in the vapor, with only the most energetic particles reaching the liquid.
Debris Ions are stopped in vapor and the energy is re-radiated, some of it going to the liquid causing more vaporization.
t ~ 1-10 s 4.5m radius, HIB target in 1mm Pb thin liquid wall protected chamber, Tcool=600C:
•Of the 22MJ of energy in target ions, only 5.3 MJ are deposited in the wall, penetrating 0.646mm into the liquid.
•The remaining 16.7MJ of target ion energy is deposited in the chamber gas and the vaporized liquid. As the energy is re-radiated, the total vaporized mass increases to 20.94kg.
•By 10s, the target chamber gas and vapor have cooled to 1.4eV and less than 0.2eV, respectively.
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 11
For the 4.5m radius chamber with a thin Pb liquid wall, and the HIB target at around 100s, shock fronts from target blast and interact, and
blind continuation of 1-d simulation results deserves skepticism.
Time (s)
Ra
diu
s(c
m)
10-7 10-6 10-5 10-40
50
100
150
200
250
300
350
400
450
BUCKY Vaporization simulation: HIB targetin a 4.5m radius, 1mm Pb protected chamber, Tc=600C Plan of attack:
•“Homogenize” chamber, converting bulk kinetic energy into thermal energy.
•Start condensation run from these conditions.
•Geometry dependent uncertainty: how long does it take to homogenize, and will there be any x-ray pulse produced by stagnation on axis?
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 12
Preliminary modeling of the condensation phase (no effects from non-condensable target ions trapped in gas or vapor, lack of self-consistency
between starting vapor pressure (1mTorr) and final vapor pressure)
Condensation occurs as vapor atoms transit the Knudsen layer, which becomes filled with non-condensable gas.
t ~ 1-100 ms
Vapor atoms migrate towards Knudsen layer at thermal velocity
Post-homogenization condensation1 mm Pb liquid wall, HIB target
0.0001
0.0010
0.0100
0.1000
1.0000
10.0000
0.00 0.05 0.10 0.15 0.20
Time post-homogenization (s)
Pb
De
ns
ity
(T
orr
)
Radius = 4.5m, tbc=600C
Radius = 6.5m, tbc=600C
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 13
Re-establishment of conditions suitable for target injection
t ~ 100-500 ms
Vapor density and temperature are suitable for beam transport and target injection
Protecting liquid is re-established.
•We need to decide on the parameters space in which we want to identify operating windows, and what constitutes an acceptable design:
•Target Output
•Driver/Transport Method
•Radius
•Liquid
•Wall temperature
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 14
To obtain consistent chamber (pre-shot and post-condensation), the simplest “knob” is the temperature at the back of the thin liquid.
•In BUCKY, the vaporization and condensation rates are calculated using the kinetic theory model described by Labuntsov and Kryukov (Int. J. Heat Mass Transfer 22, 989 (1979).
•Vaporization rate is proportional to the saturation vapor pressure, which depends strongly on Tvap,0/Tcondensate.
•Condensation rate depends on vapor pressure of condensable material in the chamber.
Post-homogenization condensation1 mm Pb liquid wall, HIB target
0.0001
0.0010
0.0100
0.1000
1.0000
10.0000
0.00 0.05 0.10 0.15 0.20
Time post-homogenization (s)
Pb
De
ns
ity
(To
rr)
Radius = 6.5m, tbc=600C
Radius = 6.5m, tbc=685C
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 15
Summary of these preliminary results
1mm thick Pb liquid wall, starting Pb vapor density 1mTorr, all ions are stopped within chamber or within liquid
•HIB target
•4.5m chamber radius
•Amount of material vaporized: 21.4kg
•Maximum over-pressure: 1.4861E+04 (J/cm3)
•Time (post-homogenization) to reach vapor equilibrium: 0.15s (600C Tcool, 0.2mTorr)
•6.5m chamber radius
•Amount of material vaporized: 38.5kg
•Maximum over-pressure: 8.7121E+03 (J/cm3)
•Time (post-homogenization) to reach vapor equilibrium: 0.2s (600C Tcool, 0.2mTorr), 0.15s (685C Tcool, 1.4mTorr)
•NRL160 target
•4.5m chamber radius
•Amount of material vaporized: 9.2kg
•Maximum over-pressure: 1.7767E+03 (J/cm3)
DAH, RRP, UW - FTI ARIES-IFE, January 2002, 16
Conclusions/Summary
We present results from vaporization and preliminary condensation BUCKY simulations are presented for the ~400MJ closely coupled HIB target and the
laser direct-drive NRL target (160MJ) in a thin liquid wall (1mm Pb) chamber. For chambers with radii of 4.5m and 6.5m, and a starting chamber pressure of 1mTorr, these preliminary results indicate that the chambers recover before the
next shot, assuming a 5Hz rep. rate.
•1mm of liquid Pb protects permanent target chamber structures from x-ray and ion loads with a 1mTorr initial chamber gas pressure. We will investigate the effects of higher pressures before the next ARIES meeting
•Chamber conditions are re-established by 0.2s after homogenization. How long does that homogenization take? The transit time for the shock waves from the target and the flash vaporization is on the order of a few tenths of a millisecond. Are 5 of these periods enough? Are 1000 needed? Experiment or higher dimensional simulations may be required if the latter is more likely than the former.
•A self-consistent chamber pressure pre- and post-shot can be attempted to be achieved by varying Tcool.
•These results are preliminary. I’d like to benchmark the condensation part of the code with experiment, or at least with CONRAD, and also take into account the effects any non-condensable target material left in the chamber, and the thermal properties of the equilibrium liquid composition.