robust heavy ion fusion target

33
Robust Heavy Ion Fusion Target Shigeo KAWATA Utsunomiya Univ. Japan U.S.-J. Workshop on HIF December 18-19, 2008 at LBNL & LLNL

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Robust Heavy Ion Fusion Target. Shigeo KAWATA Utsunomiya Univ. Japan U.S.-J. Workshop on HIF December 18-19, 2008 at LBNL & LLNL. Acknowledgments Thanks for Collaborations with Grant, John & Friends in VNL for WDM/HEDM physics + HIF with wobblers! Colleagues in HIF Japan, Sasho, Jacob - PowerPoint PPT Presentation

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Page 1: Robust Heavy Ion Fusion Target

Robust Heavy Ion Fusion Target

Shigeo KAWATA

Utsunomiya Univ. Japan

U.S.-J. Workshop on HIF

December 18-19, 2008

at LBNL & LLNL

Page 2: Robust Heavy Ion Fusion Target

Acknowledgments

Thanks for Collaborations with Grant, John & Friends in VNL

for WDM/HEDM physics + HIF with wobblers!Colleagues in HIF Japan,

Sasho, JacobJSPS & MEXT, Japan

Page 3: Robust Heavy Ion Fusion Target

/ High d ~ 30~40%/ Robust driver with a high rep. / Beam handling/ Spherical target with a hybrid implosion/ Robust implosion

Page 4: Robust Heavy Ion Fusion Target

Advantages of HIF Scheme

/ High efficiency ~30~40% => Gain~30 with ~10Hz operation/ Simple energy deposition/ Robust against R-T instability <= large density gradient

Large scale

Small scale

0

20

40

60

80

1.5 2.5 3.5 4.5 5.5r [mm]

[g

/cm

3 ]

Without foam in 25.2nsecWith foam in 25.1nsec

Page 5: Robust Heavy Ion Fusion Target

0

20

40

60

80

1.5 2.5 3.5 4.5 5.5r [mm]

[g

/cm

3]

Without foam in 25.2nsec

With foam in 25.1nsec

Without foamIncident beam

: 34 [ns] 7 [MJ]Nonunifomity

: 2.0 [%]Maximum incidence angle

: 30 [degree]

With foamIncident beam

: 34 [ns] 7 [MJ]Nonunifomity

: 4.0 [%]Maximum incidence angle

: 40 [degree]

No 11

Comparison of space profiles of density

The Density Valley is Widened by inserting the foam.

Page 6: Robust Heavy Ion Fusion Target

Histories of growth rate   of the R-T instability with foam

No 20

With foamIncident beam

: 34 [ns] 7 [MJ]Maximum incidence angle

: 40 [degree]

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35Time [nsec]

Gro

wth

Rat

e

[1/n

sec]

012345678

Growth Rate [1/nsec]

Estimation of the R-T Instability growth

gk

Page 7: Robust Heavy Ion Fusion Target

Introduction - Problems of ICF -

Wobbling HIBs => time-dependent energy deposition E=> time-dependent non-uniform acceleration: g

Flow of inertial confinement fusion

7

Page 8: Robust Heavy Ion Fusion Target

The Rayleigh-Taylor Instability (RTI)

• When a low density fluid supports a high density one under gravity, the fluid instability is caused.

• This instability is so called the Rayleigh-Taylor Instability (RTI).

12

12

+−

= gk

The growth rate of the RTI is

density

namberwavek

gravityg

rategrowth

:

:

:

:

gravity

ρ1<ρ2

high density

low density

2π/k 2π/k

8

Page 9: Robust Heavy Ion Fusion Target

RTI induced by non-uniform gravity

xg

gravity

g

ggg += 0

gravityuniformnong

gravitytconsg

Å@−:tan:0

A non-uniform acceleration (gravity) is generated by non-uniform illumination of heavy ion beams.

Because the beam number is finite.

9

The gravity is expressed by the constant term and the non-uniform term, in this study.

ion beam

target

Page 10: Robust Heavy Ion Fusion Target

RTI induced by non-uniform gravity

x

g

orv

ggg += 0

10

time

Page 11: Robust Heavy Ion Fusion Target

Simulation model - constant gravity -

density

gravity

gravity

0.0

5.0

10.0

ρ

( )kxgggLow

High

sin1.0:

3:

10:

00 +

ρ

ρ

1:

1:0

k

gThe calculation parameters are

Page 12: Robust Heavy Ion Fusion Target

Simulation result - constant gravity -

0.0 1.00.0

1.0

x [2π]

y [2

π]

density

3

10ρ

t=0~6 [1/γ]

gravity

12

The RTI is grown by the initial unstable density and the non-uniform gravity distributions.

Page 13: Robust Heavy Ion Fusion Target

HIB axis can be oscillated with a high frequency-> Control of RTI - Oscillating gravity -

w0 ∝δgΔt

Ω = 2πf

x

grav

ity

Oscillation Gravity

timetgravityuniformnongvelocityinitialw

frequencyfrategrowthvelocityw

:::

:::

0 −

13

From the equation, when the gravity oscillation frequency f increases, the RTI perturbation velocity w decreases.

g x,y,z,t( ) = g0 +δg x,y,z,t( )

= g0 + g1 f1 x,y( ) exp −β z( ) exp iΩt( )

w =γ + iΩ

γ 2 + Ω 2g1 exp(ikx + iky )[exp(γt)− exp iΩt( )]

Page 14: Robust Heavy Ion Fusion Target

Control of RTI - Oscillating gravity -

| w |≈1

Ωg1 exp γ t( ) Ω<<for

x

grav

ity

Oscillation Gravity

timetgravityuniformnongvelocityinitialw

frequencyfrategrowthvelocityw

:::

:::

0 −

14

The RTI perturbation velocity is approximately written by <-.

From the equation, when the gravity oscillation frequency f is increased, the RTI perturbation velocity w decreases.

w =γ + iΩ

γ 2 + Ω 2g1 exp(ikx + iky )[exp(γt)− exp iΩt( )]

| w |≈1

2γg1 exp γ t( ) Ω=for

Page 15: Robust Heavy Ion Fusion Target

0.0 1.00.0

1.0

x [2π]

y [2

π]

0.0 1.00.0

1.0

x [2π]

y [2

π]

vorticitydensity

Single Mode Simulation [constant gravity]

t=0~6 [1/γ]

Page 16: Robust Heavy Ion Fusion Target

t=5 [1/γ]density vorticity

Single Mode Simulation [constant gravity]

Page 17: Robust Heavy Ion Fusion Target

x [2π]

grav

ity

1.0

1.1

0.9

0.0 0.5 1.0

gravity

[ ] [ ] [ ]Hzfmmksmgex 92150 10/11,/10. =→==

Single Mode Simulation [oscillation gravity]

( ) ( )tf2sinkxsing1.0g:g

3:

10:

00

Low

High

π

ρ

ρ

+ ( )kg:f

1:k

1:g

0

0

=γγ

parameter

density

gravity

Page 18: Robust Heavy Ion Fusion Target

density

vorticity

Single Mode Simulation oscillation (γ[Hz])

t=5 [1/γ] t=9 [1/γ]t=7 [1/γ]

Page 19: Robust Heavy Ion Fusion Target

Single Mode Comparison (γt=5)density vorticity

oscillation (γ[Hz])

constant

Page 20: Robust Heavy Ion Fusion Target

constant

f=1[γ]

f=10[γ]

constant

f=1[γ]

f=10[γ]

constant

f=1[γ]

f=10[γ]

[ ]( )( ) [ ]

[ ]( )( ) [ ]

[ ]( )( ) [ ]%58.15100

tan

1

%02.55100tan

1

%40.15100tan

1

=×Δ

=×=

=×=

tcons

f

tcons

f

tconsv

fv

γ

ω

γω

γ

[ ] 5:/1time γ

Single Mode Comparison   (passage of time)

Page 21: Robust Heavy Ion Fusion Target

Multi Mode Simulation [oscillation gravity]

( ) ( )[ ] ( )tf2sinckxsinkxsing210

1g:g

3:

10:

00

Low

High

π

ρ

ρ

++ ( )kg:f

1:k

1:g

0

0

=γγ

parameter

[ ] [ ] [ ]Hz10fmm/11k,s/m10g.ex 690 =→==

0.0 1.00.5

0.9

1.0

1.1

x [2π]

grav

ity

gravitygravity

Page 22: Robust Heavy Ion Fusion Target

Multi Mode Comparison (t=5 [1/γ])density vorticity

oscillation (γ[Hz])

constant

Page 23: Robust Heavy Ion Fusion Target

Al pellet structure

Al 1.00mm2.69g/cm3

Illumination of WobblersParameters

Pb+ ion beam

Beam number : 12, 32

Beam particle energy : 8GeV

Beam particle density distribution : Gaussian

Beam temperature of projectile ions : 100MeV with the

Maxwell distribution

Beam emittance : 1.0 mm-mrad

External pellet radius : 4.0mm

Pellet material : Al

Page 24: Robust Heavy Ion Fusion Target

1.5~3.0mm

Rotation radiusPellet radius 4.0mm

Beam radius 1.5~4.0mm

Rotation radius 1.5mm Rotation radius 2.0mm

Rotation radius 3.0mm

Page 25: Robust Heavy Ion Fusion Target

Rotation radius 1.9mmBeam radius 2.6mm 2.3 %rmsσ

Rotation radius 3.0mmBeam radius 3.2mm 3.2 %rmsσ

Page 26: Robust Heavy Ion Fusion Target

32 beamsRotation radius 1.9mmBeam radius 2.6mm 2.32% z

x

y-4

-3

-2

-1

0

1

2

34

-4 -3 -2 -1 0 1 2 3 4 -4-3

-2-1

01

23

4

32-HIBs illumination system

32-beam

x

y

z

-4-3

-2

-1

0

1

2

3

4

-4-3

-2-1

0

23

4

-4 -3 -2 -1 0 1 2 3 4

12-beam12 beamsRotation radius 1.9mmBeam radius 2.6mm 8.29%rmsσ

rmsσ

mm

mm

12-HIBs illumination system

Page 27: Robust Heavy Ion Fusion Target

Mode(2,0)

Mode(1,0) Mode(1,1)

Mode(2,1) Mode(2,2)

Page 28: Robust Heavy Ion Fusion Target

Summary• The Rayleigh-Taylor Instability growth can be reduced by

the oscillating gravity (acceleration), that may be realized by wobbling HIBs.

• The reduction ratio of the RTI growth depends on the frequency of the gravity oscillation.

• Even in the case of the multi mode gravity perturbation, the RTI growth is reduced by the wobbler.

28

Page 29: Robust Heavy Ion Fusion Target

Wobblers may bring a robust uniform target implosion.

Page 30: Robust Heavy Ion Fusion Target

Issues in HIF/ Particle Accelerator (Scale, Cost, Energy, etc..)/ Physics of Intense Beam (Focusing & Compression, Emittance growth, etc..)/ Beam Final Transport (Stable transportation, Interaction with gas, etc..)/ Target-Plasma Hydrodynamics, stability, beam illumination scheme, robustness, ignition, burning, … / Reactor design, wall, T breeding, molten salt, material, neutronics, …etc..

Proposal of a Conceptual Design of International HIF Reactor?!?

International Collaborative Work!

i-HIF Reactor

AcceleratorIon Beam

chamber

target

Page 31: Robust Heavy Ion Fusion Target

31

IFE reactor

HIB illumination non-uniformity

< a few %

Pellet injector

Fusion reactor

Reactor chamber center

Displacement dz

3.00×1048.14×1041.33×1051.84×1052.36×105

(a) dz = 0[m]

(b) dz = 100[m]

[J/mm3] Fuel Pellet

Conventional illumination pattern => ~ 50-100m => non-uniformity > 3.0%Our results => ~ 300-400m is allowable

Previous work on uniform HIB illumination

dvr

Rbea

mFuel pellet

Rch ffmin

fmax

Rf

Focal Spot

Forward focal positionBackward focal position

Ren

Page 32: Robust Heavy Ion Fusion Target

Sample (beam profile) Simulation [constant]gravity

[ ][ ]

[ ][ ]Hzf

smg

mkg

mkg

Low

High

7

2110

3

3

10:

/10:

/300:

/1000:

ρ

ρparameter beam profile Pn

gravity

1.1e+11

1.0e+11

0.9e+11grav

ity

[m/s

2 ]

0.0 0.90.3 0.6x [mm]

Page 33: Robust Heavy Ion Fusion Target

density vorticity

oscillation (γ[Hz])

constant

Sample (beam profile) Comparison (t=0.2 [μsec])