dah, rrp, uw - fti aries-ife, january 2002, 1 thin liquid pb wall protection for ife chambers d. a....

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




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


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


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


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


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


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.


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.


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.


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.


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?


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


0.0001

0.0010

0.0100

0.1000

1.0000

10.0000

0.00 0.05 0.10 0.15 0.20


Pb

De

ns

ity

(T

orr

)

Radius = 4.5m, tbc=600C



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


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.


0.0001

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0.1000

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0.00 0.05 0.10 0.15 0.20


Pb

De

ns

ity

(To

rr)




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)




•Time (post-homogenization) to reach vapor equilibrium: 0.2s (600C Tcool, 0.2mTorr), 0.15s (685C Tcool, 1.4mTorr)

•NRL160 target





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.

dah, rrp, uw - fti aries-ife, january 2002, 1 thin liquid pb wall protection for ife chambers d. a....

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