RRP:3/9/01Aries IFE 1 Parametric Results for Gas-Filled Chamber Dynamics Analysis Aries Workshop...

1RRP:3/9/01 Aries IFE

Parametric Results for Gas-Filled Chamber Dynamics Analysis

Aries WorkshopAries WorkshopMarch 8-9, 2001March 8-9, 2001Livermore, CALivermore, CA

Robert R. Peterson and Donald A. Haynes

Fusion Technology InstituteUniversity of Wisconsin-Madison


NRL

Sombrero

Target

Output

Gas

Protection

First Wall

T(t) Vaporization?

Gas

Species

Gas

DensityRadius Twall

T > 1.5 K?

Chamber Works!

Friction

T4

Velocity

Target

Injection

Distance in Chamber

Straight

Tube

MaterialOpacity

BUCKY

EOSOPA IONMIX

BUCKY BUCKY BUCKY

no

yes

yes

no

ANSYS

First Wall Erosion and Target Heating During Injection are Competing Concerns in Direct-Drive Laser Fusion Dry-Wall Target Chambers


•Check results for knock-on ions with finer time resolution for deposition. (cf. Raffray)

•deposited ion density/flux in useful form

•Wall load (total and differentiated as to source) as a function of time

•more snap shots of wall temperature as a function of depth

•W +SiC armor

•Scale up NRL target yield to SOMBRERO levels , for density-radius parameter space scan: warning: partitioning may not remain the same, can this be checked

•HI target: Threat spectrum still needed

•Au coated chamber for NRL Au-coated target, W coating for W coated NRL target

•Consider molecular buffer gases

•Re-visit 0 Torr case for NRL target (in particular, ion deposition depths)

•non-Au coated NRL target: need threat spectra

•Begin work on wetted wall?

Chamber Dynamics Action Items: From December 2000


Chamber Physics Critical Issues Involve Target Output, Gas

Behavior and First Wall Response

Design,Fabrication,

Output Simulations,(Output Experiments)

Design,Fabrication,

Output Simulations,(Output Experiments)

Gas Opacities,Radiation Transport,

Rad-Hydro Simulations

Gas Opacities,Radiation Transport,

Rad-Hydro Simulations

Wall Properties,Neutron Damage,

Near-Vapor Behavior,Thermal Stresses

Wall Properties,Neutron Damage,

Near-Vapor Behavior,Thermal Stresses

X-rays,Ion Debris,Neutrons

Thermal Radiation,

Shock

Target Output Gas Behavior Wall Response

UW uses the BUCKY 1-D Radiation-Hydrodynamics Code to Simulate Target, Gas Behavior and Wall Response.


• 1-D Lagrangian MHD (spherical, cylindrical or slab).

BUCKY, a Flexible 1-D Lagrangian Radiation-Hydrodynamics Code; Useful in Predicting Target Output and Target Chamber

Dynamics

• Thermal conduction with diffusion.

• Applied electrical current with magnetic field and pressure calculation.

• Equilibrium electrical conductivities

• Radiation transport with multi-group flux-limited diffusion, method of short characteristics, and variable Eddington.

• Non-LTE CRE line transport.• Opacities and equations of state from EOSOPA or SESAME.


BUCKY, a Flexible 1-D Lagrangian Radiation-Hydrodynamics Code; Useful in Predicting Target Output and Target Chamber

Dynamics

• Thermonuclear burn (DT,DD,DHe3) with in-flight reactions.

• Fusion product transport; time-dependent charged particle tracking, neutron energy deposition.

• Applied energy sources: time and energy dependent ions, electrons, x-rays and lasers (normal incidence only).

• Moderate energy density physics: melting, vaporization, and thermal conduction in solids and liquids.

• Benchmarking: x-ray burn-through and shock experiments on Nova and Omega, x-ray vaporization, RHEPP melting and vaporization, PBFA-II K emission, …

• Platforms: UNIX, PC, MAC


Radiation Transport and Hydrodynamics are Crucial to IFE Fill-Gas Calculations: Validated for BUCKY and

EOSOPC

•EOSOPC represents an improvement over IONMIX for LTE plasmas:•Atomic Physics: multi-electron wavefunctions (UTA)•Degeneracy lowering: Hummer-Mihalas formalism is implemented•Additional effects in EOS: (partial degeneracy, modified Debye-Hückel interaction)•Results from EOSOPC have been benchmarked against burnthrough experiments, and compared with other major opacity codes, such as STA.

X-Ray Burnthrough of Au

Nova Experiments vs. BUCKY simulations assuming 150 TW/cm^2 Laser

Bur

nthr

ough

tim

e (n

s)

Slab Thickness (mm)1 2 3

0.5

1.0

1.5

2.0430-570 eV SXI210-240 eV SXI208-236 eV BUCKY451-537 eV BUCKY


Direct-Drive Targets Under Consideration Have Different Output

DT Vapor

DT Fuel

Foam + DT

1 CH + 300 Å Au

0.265g/cc

0.25 g/cc1.50 mm

1.69 mm

1.95 mm

DT Vapor

DT Fuel

Foam + DT

1 CH

0.265g/cc

0.25 g/cc1.22 mm

1.44 mm

1.62 mm

Direct-drive Laser Targets

CH

SOMBRERO (1990) NRL (1999) NRL (1999)

Laser Energy: 1.3 MJLaser Type: KrFGain: 127Yield: 165 MJ

Laser Energy: 1.6 MJLaser Type: KrFGain: 108Yield: 173 MJ

Laser Energy: 4 MJLaser Type: KrFGain: 100Yield: 400 MJ

Debris Ions 94 keV D - 5.81 MJ141 keV T - 8.72 MJ138 keV H - 9.24 MJ188 keV He - 4.49 MJ 1600 keV C - 55.24 MJTotal - 83.24 MJ per shot

Standard Direct-Drive Radiation Tailored-Wetted Foam Wetted Foam

DT Vapor

DT Fuel3.0 mm

2.7 mm2.5 mm

Spectra:•Calculated with BUCKY•Calculated by NRL•Calculated with Lasnex

Spectra:•Not Yet Calculated

The energy partition and spectra for SOMBRERO were supplied by DOEand need to be calculated.


Time (ns)

Po

sitio

n(c

m)

0 10 20 300

0.1

0.2

0.3

0.4

0.5

NRL DD-43

Au

CH

DT-wetted foam

DT

Implosion, Burn and Explosion of NRL Radiation Smoothed Direct-Drive Laser Fusion Target

•22% of DT ice is burned; NRL and LLNL get about 32 %, though peak R (LLNL) and bang time (NRL) do agree.

•This calculation yielded 115 MJ; another, 200 MJ

•Very little DT in wetted foam is burned.

•Other yields would be achieved with further tuning.

•Target expands at a few time 108 cm/s and radiates.


We Have Isolated the Differences Between the UW and NRL Target Implosion and Burn Calculations: Laser

Deposition

Radius (cm)

Ma

ssD

en

sity

(g/c

c)

0 0.01 0.02 0.03 0.04 0.050

25

50

75

100

125

150

175 NRL (AS)UW (RRP)

Mass Density at 27 ns

Subtle differences in implosion geometry at ignition. •UW BUCKY calculation from UW designed laser pulse gives green curve and 115 MJ. •NRL calculation from NRL designed laser pulse give red curve and 160 MJ.•UW BUCKY calculation starting from red curve give 158 MJ.•Therefore the burn in the two calculations agrees and it is subtle differences in the implosion caused by differences in the laser deposition that leads to the differences in yield.•UW and NRL are working on importing NRL laser deposition model into BUCKY.

BUCKY NRL =>BUCKY


Ion Spectrum for NRL Radiation Pre-Heated Target Depends on Yield

Ion Energy (eV)

Nu

mb

er

of

Ion

s

103 104 105 106 107 108 1091016

1017

1018

1019

1020 DTHCAuHe

NRL-DD-43

Ion Spectrum from 115 MJ NRL Laser Target

Wetted Foam

Plastic

Au

DT Ice

DT Gas

SOMBRERO

Ion Energy (eV)

Nu

mb

er

of

Ion

s

103 104 105 106 107 108 1091016

1017

1018

1019

1020 DTHCAuHe

NRL-DD-49

Ion Spectrum from 160 MJ NRL Laser Target

Wetted Foam

Plastic

Au

DT Ice

DT Gas

SOMBRERO

•The particle energy of each species in each zone is then calculated as mv2/2 on the final time step of the BUCKY run. This time is late enough that the ion energies are unchanging. The numbers of ions of each species in each zone are plotted against ion energy.•The spectra from direct fusion product D, T, H, He3, and He4 are calculated by BUCKY but they don’t make it out of the target. Knock-ons not included.•The ion spectra is more energetic for 200 MJ yield

Ion Spectrum for 115 MJ Yield NRL Target Ion Spectrum for 200 MJ Yield NRL Target


Ions from Hydro Expansion (18% of Yield) Knock-on Ions (12% of Yield)

John Perkins (LLNL) has Performed Target Output Calculations

Perkins’ calculations of ion spectra from NRL radiation pre-heated target have been used to analyze dry-wall gas-protected chambers.

Eion= mionu2/2 n + ion => n´ + ion´


Open collimator LOS 1/2 8” from Z

Pin Hole Camera10 degrees tilt to center. 9” from center of camera hole plate to blast shield.

L I D

CR39 film measures ion energy through damage track lengths.

Z-pinch x-ray source

Ion Spectrum Experiments on Z are in Progress to Validate Target Output Calculations

SHOT # 603 06/26/00 16:13

Damage by ions

Z X-rays

CR39detector

Ablator Material

Concept

Ion track analysis and supporting BUCKY simulations are in progress.


BUCKY-Produced X-ray Spectra from Targets Are Used; They are Changed by High Z

Components and Yield

•X-ray spectra are converted to sums of 3 black-body spectra.

•Time-dependant spectra are in Gaussian pulses with 1 ns half-widths and are used in chamber simulations.

• Time-integrated fluences are shown for 115 MJ and 200 MJ NRL and 400 MJ SOMBRERO.

•The presence of Au in the NRL targets adds emission in spectral region above a few keV.

•At higher yield the Au is more important.

Photon Energy (eV)

No

rma

lize

dX

-ra

yF

lue

nce

101 102 103 104 105 10610-7

10-6

10-5

10-4

10-3

10-2

10-1

160 MJ115 MJSOMBRERO

NRL-DD-43NRL-DD-49

X-ray Spectrum from 115 MJ and 160 MJ NRL and SOMBRERO Laser Targets

Time (ns)

X-r

ay

Po

we

r(T

W/c

m2)

0 10 20 3010-1

100

101

102

103

NRL-DD-43

X-ray Emission from 115 MJ NRL Laser Target

NRL 116 MJ

NRL 200 MJ

SOMBRERO 400 MJ


LLNL-Produced X-ray Spectra from Targets Show How Direct and Indirect-Drive Differ


The threat spectrum can be thought of as arising from three contributions: fast x-rays, unstopped ions, and

re-radiated x-rays

Some debris ions are deposited in chamber gas, which re-radiates the energy in the form of soft x-rays

The x-rays directly released by the target are, for Xe at the pressures contemplated for the DD target, almost all absorbed by the wall.

Some debris ions are absorbed directly in the wall.

The wall (or armor) reacts

to these insults in a

manner largely

determined by it’s

thermal conductivity and stopping

power.


1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

1e-8 1e-7 1e-6 1e-5 1e-4 1e-3

Time (s)

Wa

ll S

urfa

ce T

em

pe

ratu

re (

C)

Prompt X-rays 9MJ

Ions absorbed by the wall (1.2MJ)+Re-radiated

energy (27MJ)

For example, the first wall does not vaporize for the SOMBRERO target in a 6.5m radius chamber filled with 0.1

torr Xe and a wall equilibrium temperature of 1450C.

•The separation in time of the insults from the prompt x-ray, the ions, and the re-radiated x-rays is crucial to the survival of the wall.

•The Xe serves to absorb the vast majority of the ion energy and almost half of the prompt x-rays and slowly re-radiates the absorbed energy at a rate determined by the Plank emission opacity of the Xe.

Neutrons

•Neutron deposition begins after 1st peak but continues into 2nd.•Enhanced neutron sputtering?


For the current calculations, IONMIX has been used to generate Non-LTE Xe opacity tables

Xe Average charge state, n_i = 1e16/cc

0

10

20

30

40

50

0.1 1 10 100 1000 10000Electron Temperature (eV)

Ave

rage

Cha

rge

Sta

te

IONMIX

LTE

EOSOPA (LTE) / IONMIX COMPARISON: Xe 1e16/cc

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

Photon Energy (eV)

Ro

sse

lan

d G

rou

p O

pa

city

(cm

^2/g

)

IONMIX 1 eV

EOSOPA 1 eV

IONMIX 100 eV

EOSOPC 100 eV

•Xe gas at or below 0.5 Torr in Density is not in LTE.

•The Xe opacity can differ substantially between LTE (EOSOPC) and Non-LTE (IONMIX).•IONMIX opacities are used in this study.

•Non LTE (IONMIX) ionization is substantially below the LTE (Saha) ionization.


A scan of Xe density holding the first wall equilibrium temperature fixed at 1450C was performed to examine the onset of vaporization.

SOMBRERO TARGET in 6.5m C Chamber, Equilibrium Wall Temperature of 1450C

2500

2600

2700

2800

2900

3000

3100

3200

0.05 0.06 0.07 0.08 0.09 0.1

Xe Density (Torr)

Tem

pera

utre

(C

)

1st Peak T_wall (C)

2nd Peak T_wall (C)

T_sublimination att_vap

Initial SublimationTemperature (C)

Direct Energy Deposition on Wall, SOMBRERO Target in 6.5m C Chamber, Equilibrium Wall Temperature of 1450C

0

2

4

6

8

10

12

14

0.05 0.06 0.07 0.08 0.09 0.1

Xe Density (Torr)

Ene

rgy

(MJ)

or

Ma

ss (

g) X-ray EnergyDeposited in Wall(MJ)

Ion EnergyDeposited in Wall(MJ)

Amount Vaporized(g)

•For the SOMBRERO target in a 6.5m graphite chamber, the prompt x-rays are the major threat.

•Even at 0.05 Torr Xe, 78MJ of the 83MJ of ion energy is absorbed by the gas, slowly re-radiated to contribute to the second peak in temperature.

•The sublimation threshold occurs when the prompt x-rays loading is above 1.88 J/cm2 for x-rays with the SOMBRERO spectrum, for this equilibrium wall temperature.


0

20

40

60

80

100

120

SOMBRERO NRL 400MJ "NRL"

No

n-n

eutr

on

ic T

arg

et O

utp

ut

(MJ) IONS

X-rays

The SOMBRERO and NRL targets differ significantly in yield, partitioning, and spectra. These differences lead to very

different target chamber dynamics.

•Even if the NRL spectra are scaled up by the ratio of the total yields (400/165), it poses considerably less threat to the target chamber.

• It has fewer of the dangerous, prompt x-rays and a different ion spectrum.

• For instance, the first wall survives at conditions where the SOMBRERO target vaporizes 6.7g of wall material per shot. (This assumes that the energy is increased by increasing the flux, and not the shape, of the spectra..)

Surface Temperature as a Function of Time, 0.05 Torr Xe, T_equilibrium = 1450C

1400

1800

2200

2600

3000

3400

1.00E-08 1.00E-07 1.00E-06 1.00E-05

Time (s)T

em

pe

ratu

re (

C)

SOMBRERO SCALED NRL


Wall temperature as a function of depth at the times of the first and second peaks of surface temperature, and at the local minimum

between.

SOMBRERO Target

1450

1950

2450

2950

3450

1.E-04 1.E-03 1.E-02 1.E-01

Depth (cm)T

empe

ratu

re (

C) Time of first peak

(~20ns)Time of second peak(~400ns)Time of 'dip' (100ns)

Scaled NRL Target

1450

1550

1650

1750

1850

1950

1.E-04 1.E-03 1.E-02 1.E-01Depth (cm)

Tem

pera

ture

(C

)

Time of firstpeak (~20ns)Time of secondpeak (~300ps)Time of dip(100ns)

0.05 Torr Xe, T_equil. = 1450C, Radius = 6.5m, Graphite Wall

Note the differences in temperature scales!


1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0.1 1 10 100 1000

Photon Energy (keV)

X-r

ay

Sp

ect

rum

(J/

keV

)

SCALED NRL (5.6MJ X-rays)

SOMBRERO (22.5MJ X-rays)

Detail: Carbon and deuterium deposition and X-ray spectra for SOMBRERO and Scaled NRL Targets in 6.5m Radius C Chamber

SOMBRERO

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Depth (cm)

Num

ber

of D

epos

ited

Ions

D Hydro

C Hydro

Scaled NRL

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Depth (cm)

Num

ber

of D

epos

ited

Ions

D_Hydro

C_Hydro

D_Knockon

The spectra differ primarily due to the Au and knock-ons in the NRL spectrum and the 55MJ of 1.6MeV C ions in the SOMBRERO spectrum. The NRL knock-ons heat the 1st mm of the wall volumetrically.

Xe density is 50 mtorr and wall temperature is 1450 ° C.


A C-C Target Chamber Can Survive, with Proper Gas Protection and Wall Temperature

0

500

1000

1500

2000

2500

3000

3500

0 0.1 0.2 0.3 0.4 0.5 0.6

Xe Density (Torr)

Max

.Equ

ilibr

ium

Wal

l Tem

p. to

Avo

id

Vap

oriz

atio

n (C

)

SOMBRERO Target

NRL Target

Chamber Radius of 6.5m

•A series of BUCKY calculations have been performed of the response of a 6.5 m radius graphite wall to the explosions of SOMBRERO and NRL targets. Time-of-flight dispersion of debris ions is important, especially for low gas density.

•The gas density and equilibrium wall temperature have been varied to find the highest wall temperature that avoids vaporization at a given gas density.

•Vaporization is defined as more than one mono-layer of mass loss from the surface per shot.

•The use of Xe gas to absorb and re-emit target energy increases the allowable wall temperature substantially.

160 MJ

400 MJ

W

NRL 400 MJ


Region Excluded due to Radiation Damage Accumulation

0

500

1000

1500

2000

2500

3000

3500

0 0.1 0.2 0.3 0.4 0.5 0.6

Xe Density (Torr)

Ma

x.

Eq

uil

ibri

um

Wa

ll T

em

p.

to A

vo

id

Va

po

riza

tio

n (

C)

SOMBRERO WALL ConstraintNRL WALL ConstraintSOMBRERO TARGET (200 m/s, 6.5m, 0.2 Reflectivity)NRL TARGET (400 m/s, 2m, 0.99 Reflectivity)NRL TARGET (400 m/s, 6.5m, 0.99 Reflectivity)

Chamber radius of 6.5mTumbling Target

When Considering Target Heating and Graphite Neutron Damage, Wall Temperature and Gas Density Constraints are

More Restrictive

160 MJ

400 MJ

Chamber radius of 6.5 mTumbling target


SOMBRERO

Graphite Tungsten

Mass Density (g/cc) (at STP) 2.26 19.3 Tvap (eV) (at 1 bar)

Tmelt (eV)

0.338

N/A

0.51

0.32

Heat Capacity (J/g-eV) (at 1450C) 23200 1940

Thermal Conductivity (W/g-eV) (1450C) 13344 11532

Latent Heat of Vaporization (J/g)

Latent Heat of Fusion (J/g)

59730

N/A

4800

220

Nuclear Charge 6 74

Stopping e-fold length for 1keV photons 5 microns 0.12 microns

Tungsten armor has been considered. There are at least two major differences between it and graphite: melting, and x-ray stopping length


The decreased stopping length of W requires a lower equilibrium wall temperature for operation with no Xe than does Graphite, if

vaporization is to be avoided. For the NRL target and no Xe, the W wall starts to vaporize for Tequil of 1450C, to be compared with the

1570C for the C-C wall

Surface Temperature as a function of time, NRL target, 6.5m radius chamber, no Xe

1400

1900

2400

2900

1.E-08 1.E-07 1.E-06 1.E-05

Time (s)

Su

rfa

ce T

(C

)

Tungsten Wall

Graphite Wall


The shorter x-ray deposition depths of Tungsten lead to both a higher peak surface temperature and a sharper temperature

gradient.

1450

1650

1850

2050

2250

2450

2650

2850

3050

1.0E-04 1.0E-03

Depth (cm)

Tem

pera

ture

(C

)

1450

1550

1650

1750

1850

1950

Tem

per

atu

re (

C)

Tungsten Wall Graphite Wall

T_equil. = 1450CNo Xe

Radius = 6.5mNRL Target

N.B.-Note Different

Scales


Though the x-rays are the dominant threat, we note that the ion energy is deposited closer to the surface in a W wall than in a C wall.

Graphite Wall

1.E+141.E+151.E+161.E+171.E+181.E+191.E+20

0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04

Depth (cm)

Num

ber

of d

epos

ited

ions

D Hydro

C (Hydro)

D (Knock-on)

Tungsten Wall

1.E+14

1.E+15

1.E+161.E+17

1.E+18

1.E+19

1.E+20

0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04

Depth (cm)

Num

ber

of d

epos

ited

ions

D Hydro

C (Hydro)

D (Knock-on)

•NRL target

•No Xe

•T_equil. = 1450C

•6.5 meter radius


•Done knock-on ions with finer time resolution for deposition.

•Deposited ion density/flux in useful form ?

•Have shown wall load as a function of time.

•Have shown more snap shots of wall temperature as a function of depth.

•Have studied W armor but not SiC armor.

•Scaled up NRL target yield to SOMBRERO levels, for density-radius parameter space scan: warning: partitioning may not remain the same.

•HI target have threat spectrum but haven’t done calculations yet.

•Have not considered Au coated chamber for NRL Au-coated target, W coating for W coated NRL target

•Have not considered molecular buffer gases.

•Have found that Vacuum chamber works for NRL target at reduced wall temperature.

•Need threat spectra for non-Au coated NRL target

•Begin work on wetted wall?

Chamber Dynamics Action Items: Status March 2001


Status of Aries Dry-Wall Chamber Dynamics: Baseline C-C Composite Work is Complete

•Maximum wall operating temperatures have been found for C-C composite chambers at various Xe fill-gas densities.

•Three targets were considered; 165 MJ NRL target, 400 MJ SOMBRERO target, and scaled 400 MJ NRL target.

•Kr fill-gases were found to be less effective in protecting the first wall, requiring 10% more gas than Xe.

•Tungsten walls were found to have no advantage over C-C composites.

•Consistency between chamber survival, target injection and optimum neutron damage condition is difficult to achieve.

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RRP:3/9/01Aries IFE 1 Parametric Results for Gas-Filled Chamber Dynamics Analysis Aries Workshop...

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