Relevant one dimensional simulations of prompt physics in thick liquid design

Presented by

D. A. Haynes, Jr.

for the staff of the

Fusion Technology Institute

University of Wisconsin•BUCKY treats superheated liquid in a manner which conserves energy at the cost of redistributing it.

•Importance of plasma shielding demonstrated by varying void radius: there is more vaporized material for a 90cm void radius than for a 50cm void radius, though the ratio is less than that of the surface areas.

•Amount of vaporized material does not depend strongly on void fraction in jet in one dimensional simulation.

•BUCKY treats superheated liquid in a manner which conserves energy at the cost of redistributing it.

•Importance of plasma shielding demonstrated by varying void radius: there is more vaporized material for a 90cm void radius than for a 50cm void radius, though the ratio is less than that of the surface areas.

•Amount of vaporized material does not depend strongly on void fraction in jet in one dimensional simulation.

•C/C HIB target

•50, 90cm radius voids (1Torr FLiBe vapor)

•void fraction (0%, 50%)

•Initial Temperature: 600C

BUCKY does treat explosive boiling, in a non-explosive sense.

• Region A– Specific Energy > Specific

Vaporization Energy– Zones join hydrodynamic mesh as

plasma with T>=T_vap• Region B

– Vaporization Energy > Specific Energy > Sensible Heat

– Energy is redistributed such that plasma facing zones are brought up to vaporization energy and vaporized, while others remain at T_vap at sensible heat.

• Region C– Sensible heat > specific energy– Hotter liquid.

Thus energy is conserved, and after each time step, there is no super-heated liquid. What is missing, however, is the effect of exploding

bubbles spewing liquid drops into the chamber.

50cm void radius results (from last time) Soon after 1 microsecond, the shock from the blowoff will interact with the shock from center of the

chamber, and we should hand off to a higher dimensional code which encompasses aerosolization and

dynamic jet location.

Vaporized mass amount due to target ions and x-rays: starting at 600C with 1Torr

vapor.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1.E-09 1.E-08 1.E-07 1.E-06

Time (s)

Vap

oriz

ed m

ass

(g)

Velocity profile at 1 microsecond

-6.E+06

-4.E+06

-2.E+06

0.E+00

2.E+06

4.E+06

6.E+06

0 10 20 30 40 50

Radius (cm)

Vel

oci

ty (

cm/s

)

Temperature profile at 1 microsecond

0.E+00

1.E+01

2.E+01

3.E+01

4.E+01

5.E+01

0 10 20 30 40 50

Radius (cm)

Tem

per

atu

re (

eV)

Density profile at 1 microsecond

1.E-061.E-051.E-041.E-031.E-021.E-011.E+00

0 10 20 30 40 50

Radius (cm)

Den

sity

(g

/cc)

Increasing the initial void radius to 90cm from 50cm results in more vaporization and lower plasma

temperatures.

Velocity profile at 1 microsecond

-6.E+06

-4.E+06

-2.E+06

0.E+00

2.E+06

4.E+06

6.E+06

0 20 40 60 80

Radius (cm)

Vel

oci

ty (

cm/s

)

Temperature profile at 1 microsecond

0.E+00

1.E+01

2.E+01

3.E+01

4.E+01

5.E+01

0 20 40 60 80

Radius (cm)

Tem

per

atu

re (

eV)

Density profile at 1 microsecond

1.E-061.E-051.E-041.E-031.E-021.E-011.E+00

0 20 40 60 80

Radius (cm)

Den

sity

(g

/cc)

Vaporized mass amount due to target ions and x-rays: starting at 600C with 1Torr

vapor.

0

2000

4000

6000

8000

10000

12000

1.E-09 1.E-08 1.E-07 1.E-06

Time (s)

Vap

oriz

ed m

ass

(g)

Void Radius = 50cm

Void Radius = 90cm

Increasing the void radius from 50cm to 90cm increases the amount of vaporized mass, but by

significantly less than 81/25

Vaporized mass amount due to target ions and x-rays: starting at 600C with 1Torr

vapor.

0

2000

4000

6000

8000

10000

12000

1.E-09 1.E-08 1.E-07 1.E-06

Time (s)

Vap

oriz

ed m

ass

(g)

Void Radius = 50cm

Void Radius = 90cm

•This behavior is consistent with that found for thin liquid walls.

•Practically all of the absorption of x-rays is done by vaporized wall rather than the initial contents of the “void” (18g in the 90cm case).

In BUCKY’s one dimensional approximation, varying the void fraction leads to little change in amount of material

vaporized or in the conditions of the resulting plasma

•For this case, a 90cm “void” (1Torr FLiBe vapor) radius, the C/C HIB target output, the vaporization depth differs for void fractions from 50% to 0%, but the total vaporized mass is relatively invariant.

• However, increased surface area of jets may lead to increased vaporization for 3-d geometry.

Vaporized mass as a function of time, C/C HIB target, 90cm 1Torr FLiBE, FLiBe liquid walls, T_0 =

600C

0.0E+00

2.0E+034.0E+03

6.0E+03

8.0E+031.0E+04

1.2E+04

1.E-09 1.E-08 1.E-07 1.E-06

Time (s)

Va

po

riz

ed

ma

ss

(g

)

LiquidDensity

50% voidfraction

Are these one dimensional simulations even relevant?

•Does the enormous surface area of the flapping and crossing jets assure that any aerosol, plasma, or shock-induced droplets will be swept up by the next shot?

•If not, what fraction of aerosol and plasma from the void gets out and stays in the critical driver target injection paths?

•Let’s take a moment now to discuss this.

Outstanding issue, conclusions

• Do vaporization amount, plasma charge state, aerosol amount, aerosol size matter?

• If so, increasing the void size will effect:– amount of plasma/aerosol (increase, though less

than surface area), – conditions (cooler, less dense),– importance of edge effects (increase surface to

edge).

OLD SLIDES FOR

BACKUP

BUCKY can treat “walls” in two modes, each of which has advantages and disadvantages

• “Heat capacity” EOS– Advantages:

• Latent heats easily incorporated

• Bookkeeping

– Disadvantages:• Inconsistent EOS/Opacity

as zone moves from wall to vapor.

• No shock tracking within wall.

• Only current surface zone can vaporize

• “Plasma” EOS– Advantages:

• Consistent EOS/Opacity• Shock tracking within the

wall• “Buried” “evaporation”

– Disadvantages• Currently: no latent heats

in FLiBe tables• Bookkeeping (plasma/wall

distinguished only by density)

Soon after 1 microsecond, the shock from the blowoff will interact with the shock from center of the chamber, and we should hand off to a higher

dimensional code which encompasses aerosolization and

dynamic jet location.

Vaporized mass amount due to target ions and x-rays: starting at 600C with 1Torr

vapor.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1.E-09 1.E-08 1.E-07 1.E-06

Time (s)

Vap

oriz

ed m

ass

(g)

Velocity profile at 1 microsecond

-6.E+06

-4.E+06

-2.E+06

0.E+00

2.E+06

4.E+06

6.E+06

0 10 20 30 40 50

Radius (cm)

Vel

oci

ty (

cm/s

)

Temperature profile at 1 microsecond

0.E+00

1.E+01

2.E+01

3.E+01

4.E+01

5.E+01

0 10 20 30 40 50

Radius (cm)

Tem

per

atu

re (

eV)

Density profile at 1 microsecond

1.E-061.E-051.E-041.E-031.E-021.E-011.E+00

0 10 20 30 40 50

Radius (cm)

Den

sity

(g

/cc)

Time (s)

Ra

diu

s(c

m)

10-9 10-8 10-7 10-6 10-5 10-4

25

50

75

100

125

150

175

FLiBeInitially in 1Torr Vapor

FLiBeInitially in Thick Liquid Walls

BUCKY "plasma" simulation

The shocks rattling around the central void render 1 dimensional simulations suspect after 20

microseconds.

•For an initial void radius of 90cm, the outward moving shock interacts with the wall blowoff around 10 microseconds.

•Note the outer wall movement at late times.

C/C HIB target, 90cm radius void, 600C, FLiBe

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 50 100 150 200

Radius (cm)

Ch

arg

e s

tate

t=1 microsecond

t=10 microseconds

As the wall blowoff moves in the chamber, it cools but remains significantly ionized as aerosolization initiates.

Initially in vapor Initially in “wall”

Does this ionization inhibit aerosol formation?

Time

Ra

diu

s(m

icro

ns)

0 50000 100000 1500000

50000

100000

150000

Log10 (T)0.50.3692160.2384330.107649

-0.0231341-0.153918-0.284701-0.415485-0.546268-0.677052-0.807835-0.938619-1.0694-1.20019-1.33097-1.46175

(ns)

A narrow band of the blowoff plasma shields the rest of the liquid from the target emissions, slowly re-radiating and

causing the rest of the wall to simmer.

BUCKY simulation of 90cm radius, 1 Torr FLiBe void, wall at 600C

•For FLiBe, with its simple atomic physics, EOS/Opacity tables can be created in DCA/NLTE with accurate emissivity values.

•For Pb, LiPb, LiSn, an alternative procedure can be employed.

Evolution of the Transition Patterns from Low Z to High Z

30 35 40

Mo (Z=42)

60 70 80 90 100

Pr (Z=59)

16 18 20 22 24 26

Kr (Z=36)

Transition: pdsd 4343 88 Cowan’s Code RSSUTA

• Under jj coupling, the initial configuration is split into:

2/16

2/52

2/3 433 sdd

2/15

2/53

2/3 433 sdd

2/14

2/54

2/3 433 sdd

• For each subconfiguration, there are two transitions:

2/12/1 44 ps

2/32/1 44 ps

• Spin orbital integrals4*)(Z

are greater than Slaterintegrals *Z

(Examples from C. Bauche-Arnoult, et al., Phys. Rev. A, 31, 2248, 1985)

Ion distributions under LTE and Non-LTE and Busquet Method

Temperature (eV)

Zbar

0 100 200 300 4005

10

15

20

25

30

35LTENonLTE

2.17)200()58( eVZeVZ LTEnonLTE

Ion Stage Population Fractions, Kr, 1e18/cc

0

0.1

0.2

0.3

0.4

0.5

0.6

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Ionization Stage

Fra

ctional Popula

tion

LTE200

LTE58

NLTE200

•What needs to be done?•Identification of variables for operating window studies•Combination of validated, relevant prompt physics simulation (rad. transport, ionization, evaporation) with validated, relevant aerosol model, and validated, relevant 3-d hydrodynamics code.•Validation of combination!•Addition of latent heat to plasma modeling of liquid wall phenomena (combine the best parts of BUCKY’s split personality)•Post-vaporization/ionization chemistry before/during/after aerosolization. •Comparison of initial vaporization phase in spherical (chamber-centric) and cylindrical (jet-centered) geometries

Path forward: prompt chamber response for thin and thick liquid wall protected IFE chambers

•Importance of results to feasibility of HIB concept•Assuming the “protection part” of the schemes work, then the key from the point of prompt chamber response is providing the correct source term for aerosolization and 3d hydrodynamic simulations.•Target conditions pre-target and pre-beam injection are crucial in determining feasibility of HIB concept.•We need a soup-to-nuts exercise of the combination mentioned previously to determine importance of prompt response to pre-next-shot conditions

•Paper study vs experimental work to get results

Path forward: prompt chamber response for thin and thick liquid wall protected IFE chambers

•Paper study versus experimental work to get results:•Wrong way to phrase the item.

•Experimental validation of models used in predictive design codes:

•Need experimental validation of evaporation, ionization, explosive evaporation.•Need aerosolization studies at extremely high temperatures with appropriate nozzles to simulate density profile (iterative).•Shock-tube work for jet array reaction to shock wave.

•RESULTS ARE VALIDATED PREDICTIVE CODES/SUITES AND THE RESULTS TEY PRODUCE.

Path forward: prompt chamber response for thin and thick liquid wall protected IFE chambers