IFE Chamber Dynamics

Presented by Mark S. Tillack

DOE Budget Planning MeetingGermantown, MDMarch 12, 2002

contributors: F. Najmabadi, A. R. Raffray, S. S. & Bindhu Harilal,

D. Blair, A. Gaeris, S. Krasheninnikov (UCSD),C. Olson, T. Renk (SNLA), T. Knowles (ESLI), D. Haynes (UWisc),

J. P. Sharpe (INEEL), J. Latkowski, D. Blackfield (LLNL)

ESLI

Background

neutrons & gammas

x-rays

ions

• Following target explosions, several distinct stages of chamber response occur:

1. Prompt transport of energy through and deposition into materials (ns-s)

2. Radiation fireball & shock propagation, mass ejection from walls (1-100 s)

3. Afterglow plasma & transport processes (1-100 ms)4. Liquid wall dynamics (ms-s)5. Long-term changes in materials (days-months)

• A better understanding of chamber physics is neededin order to make progress on key IFE technology issues:

Wall protectionChamber clearing for target and driver injection

• This presentation focuses on the underlying science of IFE chambers in a generic sense (i.e., without ties to a specific chamber design concept), using results from OFES IFE Technology, DP-HAPL and ARIES-IFE programs

Outline

1. Surface modification from pulsed ion flux

2. Fireball dynamics in a gas-protected chamber

3. Plume ejection dynamics

4. Aerosol and dust generation and transport

5. Magnetic diversion of expanding plasma

6. Ion stopping by beam-plasma instabilities

NRL Direct-Drive Target

DT Vapor0.3 mg/cc

DT Fuel

CH Foam + DT

1 m CH +300 Å Au

.195 cm

.150 cm

.169 cm

CH foam = 20 mg/cc

LLNL/LBNL HIF Target

458154

26.5 (6%) 43 (28%)

316 (69%) 109 (71%)

115 (25%) 2.14 (1%)

Indirect Drive Target (MJ)

Direct Drive Target (MJ)

Total

Ions

Neutrons

X-rays

EnergySplit

Details of target emissions have a strong impact on chamber and wall responses

High Yield

DD Target

397

112 (28%)

279 (70%)

6.07 (1%)

X-ray spectra

Time-of-flight spreading allows significant thermal penetration during energy deposition

Ion power at chamber wall (R=6.5 m)

Photon and ion attenuation in C and W slabs

NRL direct drive target spectrum (154 MJ)

1x106

1x107

1x108

1x109

1x1010

1x1011

1x10-8 1x10-7 1x10-6 1x10-5 1x10-4 1x10-3 1x10-2

Debris ions, C

Debris ions,W

Fast ions, C

Photons, W

Photons, C

Fast ions, W

Penetration depth (m)

(1 s~1 m thermal penetration depth)

100 ns

Modeling and simulation experiments are being used to improve our understanding of chamber dynamics

Pulsed ion sources (e.g., RHEPP)

Pulsed x-ray sources (e.g., Z)

Pulsed e-beam facilities (DTRA)

Lasers:1–2 J materials response,

laser propagationdiagnostic development

100–200 J rep-rated chamber dynamics1–2 kJ IRE (integrated effects)

Ignited targets (ETF)

Facilities: Rad/hydro (LASNEX, BUCKY)

Surface responses (SRIM, Ablator)

Mass ejection and recondensation

Gasdynamics (CFDSTARS)

Ion transport (LSP)

Atomic physics

Modeling tools:

1. Surface modification from pulsed ion flux

• 0.5 MeV ions C+, H+

– Range ~ 1 m

• 150-300 ns pulse – Thermal penetration ~ microns

• 10 J/cm2 fluence – Similar to IFE

• Repeating – 1000 shots max

Ion exposure experiments are being performed at the RHEPP pulsed ion source

IFE Materials Test Matrix:° W alloys° C-graphite, Ceramic fiber composites° Innovative architectures

e.g., fiber flocked, functionally graded, nano-engineered

° Flibe

Magnetically confined Anode Plasma

Severe carbon erosion and roughening are observed above 2–3 J/cm2

Mechanically polished Poco graphite exposed to 75 pulses of 70% C/30% H beam at average dose of 5.5 J/cm2

0.1

1

10

100

0 1 2 3 4 5 6

Ablation Step

Ra (treated)

Ra (untreated)

Ion Beam Fluence (J/cm2)

(mic

ron

s)

Profilometer scan across interface:~ 20 micron step (0.27 µm/pulse)Ra (original) = 0.23 micronsRa (treated) = 3.6 microns

Step measurement accuracy ~ 0. 4 µm reached below ~ 3 J/cm2

ESLI engineered wall exhibits much less net erosion Each pulse is spread over 15x more area The ablated material may redeposit on the nearby fibers:

recycling Thermal penetration into vertical fibers may be providing

effective cooling on this time scale

Specimen fractured to reveal interior

IBEST (Ion Beam Surface Treatment) uses intense ion beams to melt and modify surfaces

IONS

MeltRegion

Cooling byThermalDiffusion

IonRange

T. Renk et al., “Improvement of surface properties by modification and alloying with high-power ion beams,” Phys. Plasmas 5(5), May 1998.

Tribometer wear tracks in Pt-Ti cosputtered layer without and with surface treatment (2000 wear cycles)

• 500-750 keV N+ ions• Range ~ 2–10 m• 109 K/s cooling rate due to

thermal diffusion • 2–8 J/cm2 fluence to melt

2. Fireball dynamics in a gas-protected chamber

The dominant threat for the indirect-drive target is from soft x-rays created by debris ions

This would be deposited in the first micron of the wall effectively instantaneously, causing the graphite to sublimate

at a rate incompatible with rep-rated reactor concepts.

Nearly half of the 115MJ of prompt x-ray energy comes in the form of sub-keV photons

Simulating the protection of a dry first wall with a buffer gas requires:

• Radiative hydrodynamics (BUCKY)

• EOS/opacity data from the coronal to the collisional regimes (IONMIX)

For the HIB target in a 4.5m radius graphite chamber, 1 Torr of Xe is sufficient to prevent first wall sublimation

Ion temperature (eV) contours from BUCKY simulation

Fireball forms from captured x-ray and ion

energy

Fireball forms from captured x-ray and ion

energy

Fireball propagates and slowly re-radiates

energy, allowing wall to conduct energy away from surface, avoiding

sublimation

Fireball propagates and slowly re-radiates

energy, allowing wall to conduct energy away from surface, avoiding

sublimation

• The simulation proceeds by instantly depositing the prompt target x-rays through the gas and the wall.

• The ions from the target then traverse the ionized gas, depositing their energy through a stopping power formalism, while the gas dynamics are tracked using 1d Lagrangian radiative-hydrodynamics.

HIB target output energy deposited in the gas and wall of a 4.5m radius graphite walled chamber filled with 960mTorr of Xe starting at 1000C.

6 (knock-ons only)

10Wall

19105Gas

Ion energy (MJ)

X-ray energy

(MJ)

3. Plume ejection dynamics

Processes present in IFE mass ejection and transport are analogous to laser micromachining

• Energy absorption in surface

• Prompt thermal response of surface

• Liquid hydrodynamics

• Evaporation

• Unsteady gas dynamics

(including chamber environment)

• Radiation transport

• Condensation

• Laser-plume interaction

Table-top experiments with extensive diagnosticsare being developed to explore chamber responses

Modeling and experiments are being performed for both liquid and solid surfaces

1.E+17

1.E+18

1.E+19

10 100 1000 10000Time [ns]

Electron density of Si ablation plume measured by Stark broadening

at 390 nm, 1e9 W/cm2

Ele

ctro

n D

ensi

ty [

cm-3]

0.15 Torr

100 Torr

Expansion velocity = 4.5e6 cm/s (300 eV)

4. Aerosol and dust generation and transport

Aerosol and dust generation and transport are important for both chamber clearing and safety

Homogeneous Nucleation (Becker-Doring model)

∂n∂t[ ]growth,

homo=

Psat

kT

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2 2σmπ

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1/ 2 S2

ρl

exp−πσdcrit

2

3kT

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ δ Vcrit( ),

#

m3s

1

m3

⎡ ⎣ ⎢

⎤ ⎦ ⎥ dcrit =

4σmρlkTlnS

, and Vcrit =π6dcrit

3

∂n∂t[ ]growth,

hetero=−∂I

∂ V( ) =−∂∂ V( ) n∂

∂t V( )( ), #

m3s

1

m3

⎡ ⎣ ⎢

⎤ ⎦ ⎥ ∂

∂t V( ) =2π π6( )

1/ 3 S−K( )PsatDdp

kTVmolF,

m3

s

⎡

⎣ ⎢

⎤

⎦ ⎥

Condensation Growth

Coagulation

∂n∂t[ ]coag

=12

β V*,V−V *( )n(V*)n(V−V*)dV*0

V

∫ − β V,V*( )n(V)n(V*)dV*0

∞

∫

β V,V*( ) =2π D+D*( ) dp +dp*

( )Fcoagwhere the coagulation kernel is given by

Convective Diffusionand Transport

∂n

∂t+∇ • nv v ( ) −∇ • D∇n( ) +∇ •

v c n= ∂n

∂t[ ]growth,homo

+ ∂n∂t[ ]growth,

hetero+ ∂n

∂t[ ]coag

Particle Growth Rates

Growth Rate Models:Nova dust

Opportunities and challenges for IFE research on aerosol and dust generation and transport

10 14

10 16

10 18

10 20

10 22

10 24

10 26

10 28

10 30

10 32

10 34

10 36

10 38

0.01

0.1

1

10

1 10 100

Critical Radius (nm)(dashed curves)HMG Nucleation Rate (#/m

3/s)

(solid curves)

Saturation Ratio

1500 K

2000 K

2500 K

3000 K

1000 K

1500 K

2000 K2500 K

3000 K

3500 K

3500 K

Formation Rate and Size of Pb droplets in an IFE System

0

0.2

0.4

0.6

0.8

1

0.1 1 10

Button 1 data

Region I Predicted

Particle Diameter (µm)

Particle Distribution (frac/ln(µm))

typical value for a bubble chamber

• Computational improvements to solve stiff integro-differential transport equations• Plasma effects on dust growth and transport mechanisms (e.g., dusty plasmas)• In-situ particle diagnostics for determining fundamental mechanisms of nucleation

and growth in fusion, space, and industrial plasma environments• Development of nanoparticle generation systems for industrial and medical uses

SIRENS simulator vs. TopGun model

J.P. Sharpe, B.D. Merrill, D.A. Petti, "Modeling of Particulate Production in the SIRENS Plasma Disruption Simulator," J. Nuclear Materials, vol.290-293, 1128-1133 (2001).

Cu plasma5.2 kJ, 120 s450 mg particulate70% melt blowoff

5. Magnetic diversion of expanding plasma

Magnetic deflection is being studied forprotection of the first wall against ions

L. A. Booth and T. G. Frank, “Commercial Applications of Inertial Confinement Fusion,” LA-6838-MS, May 1977.

Three configurations are currently under consideration:

– Uniform field

– Mirror arrangement

– Cusp arrangement

Cusp configuration is simply a mirror with the field reversed in one of the coils.

Uniform field configuration would

require more magnets but lower (~2 T) fields.

PIC simulations have been initiated using LSP code (MRC) developed for HIF

• Ions only in these two movies

• Field strength ~8 T, 14 m diameter coils

• Red particles are DT (mass=2.5, charge=1) at 250 keV; blue particles are alphas at 1 MeV; Total plasma energy is 113 MJ

Mirror Cusp

Inclusion of electrons is computationally very challenging, but necessary

• Red particles are DT (mass=2.5, charge=1) at 250 keV; green particles are alphas, blue particles are electrons

• Key issues include stability, collisions, charge exchange, Bremsstrahlung & synchotron radiation, cost of magnets & shielding, recirculating power for magnet cooling

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

6. Ion stopping by beam-plasma instabilities

Residual plasma persists longer than the dwell time

T / npl 1018 m–3 1019 m–3 1020 m–3

0.2 eV ~ 0.1 s ~ 3x10–3 s ~ 10–4 s

0.6 eV ~ 1 s ~ 0.1 s ~ 2x10–3 s

1.2 eV ~ 3 s ~ 0.4 s ~ 10–2 s

Characteristic plasma recombination time, rec

10-28

10-27

10-26

10-25

1 10 100 1000

BeBoronCarbonNeonArgon

LZ(T

e

) (watts cm

3)

Te (eV)

Chamber gas/plasma temperature stops falling below ~1 eV

Recombination becomes ineffective below npl~1019/m3

τrad(T ˜ > feweV) ~T

L(T)npl

~10−3 s<<f −1

for Lrad(t)~10–25 W-cm3

Impact of residual plasma on ion stopping

• For reasonable chamber gas density the impact of binary collisions on stopping of energetic (~ 1 MeV) ions is small

(e.g., for H on Xe at 10 mTorr, dE/dx=87 MeV-cm2/g = 0.05 MeV/m)

• However, collective effects of the interactions of the beam of energetic ions with residual plasma can significantly alter the population of energetic ions

γi−beam~ωpi ni−beam/npl( )1/ 3

• Total number of fast ions per pellet, ni-fast~1020 m–3, results in average ion

beam density ni-beam~1016 m–3

• During pellet explosion the electron temper-ature of residual plasma can be quickly heated up by electron heat conduction, so that the electron temperature of residual plasma exceeds the ion temperature.

Impact of residual plasma on ion stopping

Li−beam~Vi−beam

γ i−beam

~10cm<<R

• Further study of the impact of collective effects on fast ion stopping is needed:

– a more accurate description of the evolution of residual plasma parameters

– a more detailed evaluation of collective interactions of fast components (both electron and ion) with the background gas/plasma

• For ni-beam~1016 m–3 and, npl~1018 m–3, we find i-beam~108 s–1

• Assuming the effective collision frequency of the beam with residual plasma is of the order of i-beam , we find a crude estimate of stopping distance of fast ions caused by collective effects, Li-beam:

• Free expansion into an ambient plasma is also a subject of astrophysical interest

D. S. Spicer, R. W. Clark and S. P. Maran, “A model of the pre-Sedov expansion phase of supernova remnant-ambient plasma coupling and x-ray emission from SN1987A,” The Astrophysical Journal 356 (1990) 549.

Closing Remarks

• IFE chamber dynamics encompasses a wide variety of phenomena with numerous opportunities for fundamental scientific investigations

• A better understanding of IFE chamber dynamics is needed in order to make progress toward an IFE power plant

• IFE chamber dynamics shares many features in common with MFE and non-fusion sciences

• A multi-institutional program of theory, modeling and experiments is being developed through a combination of DP & OFES support