Upload
imogen-carr
View
215
Download
1
Tags:
Embed Size (px)
Citation preview
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, JacobJSPS & MEXT, Japan
/ High d ~ 30~40%/ Robust driver with a high rep. / Beam handling/ Spherical target with a hybrid implosion/ Robust implosion
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
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.
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
Introduction - Problems of ICF -
Wobbling HIBs => time-dependent energy deposition E=> time-dependent non-uniform acceleration: g
Flow of inertial confinement fusion
7
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
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
RTI induced by non-uniform gravity
x
g
orv
ggg += 0
10
time
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
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.
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( )]
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
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]
t=5 [1/γ]density vorticity
Single Mode Simulation [constant gravity]
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
density
vorticity
Single Mode Simulation oscillation (γ[Hz])
t=5 [1/γ] t=9 [1/γ]t=7 [1/γ]
Single Mode Comparison (γt=5)density vorticity
oscillation (γ[Hz])
constant
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
=Δ
=×=
=×=
tcons
f
tcons
f
tconsv
fv
γ
ω
γω
γ
[ ] 5:/1time γ
Single Mode Comparison (passage of time)
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
Multi Mode Comparison (t=5 [1/γ])density vorticity
oscillation (γ[Hz])
constant
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
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
Rotation radius 1.9mmBeam radius 2.6mm 2.3 %rmsσ
Rotation radius 3.0mmBeam radius 3.2mm 3.2 %rmsσ
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
Mode(2,0)
Mode(1,0) Mode(1,1)
Mode(2,1) Mode(2,2)
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
Wobblers may bring a robust uniform target implosion.
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
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
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]
density vorticity
oscillation (γ[Hz])
constant
Sample (beam profile) Comparison (t=0.2 [μsec])