Transcript Gain Issues for Fast Ignition

Gain Issues for Fast Ignition
Heavy Ion Fusion Symposium
Princeton,NJ
Max Tabak and Debra Callahan
Lawrence Livermore National Laboratory
7 June,2004
This work was performed under the auspices of the U.S. Department of
Energy by the University of California Lawrence Livermore National
Laboratory under contract No. W-7405-Eng-48.
A/XDiv-IDMARKING–1
We constructed a Fast Ignitor gain model based
on a few ingredients
•
•
Atzeni ignition power,intensity,energy model
•
•
Ponderomotive EK scaling model
•
Found dependence of gain on IFAR, total laser energy, drive intensity,
ignition laser energy, ignition spot size, laser wavelength, short pulse
coupling efficiency, short pulse laser cost, compression laser
coupling efficiency for laser direct drive targets
•
•
Fast Ignition gain curves driven by distributed radiator HIF target given
Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket
equation using degenerate gas DT EOS(summarized in Lindl’s book)
“Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell selfsimilar stagnation model
Detailed calculations are required to validate these optima
–2
The burn efficiency depends on the fuel adiabat
and is one factor in Fast Ignition gain

R
R  6
 R
For uniform sphere
E m  
2
3
R  3 M 2
    1.5  R   1
 the adiabat was entirely set by careful
It was thought that
pulseshaping during the implosion

Modest increases in shock pressure
and proper timing
Wrong!
Significant jump in adiabat during stagnation
For implosions with uniform M,g=5/3 jumps by M1/2
M-t-V and Schalk, Kemp and M-t-V
But story a little more complicated:implosion doesn’t produce
self-similar shape
–4
There are four stages in an implosion
Uniform M~10 at end
Ignore convergence

P
2 a
1.5
   (R  R0 )
5 

R0
R
Uniformly accelerated
equilibrium 
R
Adiabat shaping
P
~3x in P
Ablation
pressure
R
Convergence harvests
kinetic energy and
breaks self-similarity
10x
 jump
Convergent
amplification
Hollow
shell

R
R
stagnation
–5
The gain at fixed total energy(3 MJ) is
determined by the IFAR and the compression
intensity
I
I,IFAR
Vimpl,cs
Vimpl,IFAR,vabl
M
M,inflight
stag
Eigni,igni
=> vabl,Pabl,
inflight,cs
=>vimpl
=>M
=>hydro
=>
=>stag
=>Eigni
=>Eigni-
laser
Etotal, Eigni-laser
Ecomp-laser, hydro
Ecomp, stag, 
Mass, stag
R
,mass =>yield
=>Ecmp-las
=>Ecomp
=> mass
=> R
=>
=>gain
100
200.
100.0
50.
400
200
IFAR
20.
10.0
0.01
50
0.1
1.0
Intensity(1014W/cm2)
10.0
–6
How do maximum gain quantities depend on
implosion laser intensity and total laser energy?
Intensity(1014W/cm2)
IFAR
10.0
10.0
160
10.0
100
40
80
1.0
1.0
30
30
1.0
0.1
0.1
0.1
Energy(MJ)
100
300
120
0.01
0.01
gain(IFAR<100)
gain
1.0
0.01
0.01
300
0.1
0.1
Energy(MJ)
1.0
0.01
0.01
0.1
1.0
Energy(MJ)
–7
There are satisfactory design points for IFAR
under 100
Implosion velocity
107cm/sec
300
300
Implosion intensity
1014W/cm2
gain
300
3.
6
0.9
200
200
IFAR
4
200
0.3
100
100
100
2
1
100
2
Energy(MJ)
3
1
2
Energy(MJ)
3
300
1
2
3
Energy(MJ)
–8
Low required convergence ratios will allow
relaxed illumination symmetry
Convergence ratio
Convergence ratio is
measured after adiabat
setting shocks have
passed
200.
40
100.0
20
IFAR
50.
10
20.
10.0
0.01
0.1
Energy(MJ)
1.0
–9
Maximum gains correspond to large ignition
laser energies
Fraction of energy in ignition laser
Ignition laser energy(MJ)
300
300
0.03
200
IFAR
200
0.1
0.1
100
0.3
100
0.4
1.0
1
2
Energy(MJ)
3
0.2
1
2
Energy(MJ)
3
–10
Low IFAR’s and high system energies lead to
large spots and long stagnation and ignition
energy delivery times
Spot radius()
300
Ignition time(ps)
Stagnation time(ps)
300
300
30
200
200
10
IFAR
30
100
100
2
Energy(MJ)
100
300
100
30
60
1
200
10
60
3
1
2
Energy(MJ)
900
3
1
2
3
Energy(MJ)
–11
We explore the sensitivity of the optima to a
number of model uncertainties and
experimental details
Nominal model
Laser wavelength
m laser spot
Maximum IFAR
100
Short pulse laser coupling efficiency
Compression laser coupling 
Ignition energy
Particle range(gm/cm2)
0.33
10
0.25
hydro model
Atzeni model
0.6 E/MeV
–12
How does the wavelength of the implosion laser
affect the gain curve?
No restriction
on ignition laser
Eign-laser < 100 kJ
300

1.0,0.5
400 0.33,0.25
200

1.0,0.5
0.33,0.25
gain
200
0
100
1
2
Elaser(MJ)
3
0
1
2
Elaser(MJ)
3
–13
How do the gain curves depend on the
minimum radius of the ignition spot?
No restriction
on ignition laser
Eign-laser < 100 kJ
400
200
spot radius()
10,20,30,40,50
gain
200
100
spot radius()
10,20,30,40,50
0
1
2
Elaser(MJ)
No solution for
R > 10!
3
0
1
2
3
Elaser(MJ)
Current experiments show e- spreading to 20 spot from
much smaller laser spot!
–14
Limiting the energy supplied by the ignition
laser affects the total system gain
No limitation
400 kJ
200 kJ
100 kJ
400
gain 200
0
1
2
Elaser(MJ)
3
–15
The system gain depends strongly coupling
efficiency from laser to ignition region
E ign < 100kJ
No restriction on ignition laser
400
600
300
gain

0.5
0.25
0.12
0.06
400
200
200
0
100
0
1
Elaser(MJ)
2
3
1
2
3
Elaser(MJ)
–16
The system gain depends on the range of the
relativistic electrons
No restriction on ignition laser
gain
Range
multiplier
400 0.5 1.0
2.0 3.0
E ign < 100kJ
300
200
Range
multiplier
0.5 1.0
2.0 3.0
200
100
0
1
2
Elaser(MJ)
3
0
1
Elaser(MJ)
Nominal range(gm/cm2) = 0.6 T(MeV)
T=(I/1.2*1019W/cm2 )1/2
2
3
–17
What is the effect of reducing the coupling
between the compression laser and the fuel?
No restriction
on ignition laser
H multipliers
1.
0.75
0.5
0.25
Eign-laser < 100 kJ
400
200
200
100
gain
0
1
2
Elaser(MJ)
3
0
1
2
3
Elaser(MJ)
Indirect drive has lower H but smaller adiabat jump
Cone focus implosions forming high  core may have reduced H
–18
Current techniques to deflate imploded
capsules expel significant energy
•It is natural for implosion of shell to lead to low density-high
entropy hotspot
•About half of stagnated energy resides in hotspot
•Eliminating low density core by “flatulent stagnation” wastes
this energy and can halve gain
•Need to lower “hotspot” by factor 100 before final stagnation
•Options
•Radiative cooling
•Holey shell so low density core can escape early. Tricky
implosion calculation
•Have low Mach # implosion so hollow core doesn’t form; e.g.,
bare drop driven at high intensity. Use large short pulse laser
to compress and light ignition region
–19
How would the gain curves change if
requirements could be reduced below Atzeni’s
fit?
Atzeni fit ~ 6x ignition
energy in isobaric
model
No restriction
on ignition laser
Eign-laser < 100 kJ
600
Recent calculations
gain
500
show 2x reduction for
cylindrical implosion
driven by short pulse
How well can we do?
0
400
200
1
2
Elaser(MJ)
3
0
Atzeni
x 0.5
x 0.25
x 0.125
1
2
3
Elaser(MJ)
–20
Original Fast Ignitor paper had suprathermal
electrons drive implosion with most of yield
coming at stagnation
•Similar effect rediscovered in 2-D
calculations by Herrmann and Hatchett
with a cylindrical reimplosion of original
blob
•Factor 2 reduction of ignition
energy relative to direct core heating
•Probably room for further
optimization
–21
How does the cost of ignition laser joules
relative to compression driver joules affect the
optima in yield/cost ?
Fractional cost of
Ignition driver
Yield/cost
1.0
600
Ignition driver
(MJ)
Relative cost/J
0.5 1.0
3.0 10.
400
1.0
0.5
0.5
200
0
1
Cost*
2
3
0.0
0.0
0
1
2
3
0
Cost*
*MJ equivalent of compression driver
1
2
3
Cost*
–22
What happens when we Fast Ignite an ion
distributed radiator target
2-sided illumination scaled from normal DRT
Eescape
Ion
beam
2rbeam
rh
t~rb/vimp
rb
Pr~3T3.5
Econv~rh2 T
Ewall~rh2T3.3t0.62
laser
Identifying Marker. 23
Gain distribution and short pulse laser
requirements
Short pulse energy(MJ)
Gain
3.0
3.0
TR(100 eV)
0.95
0.95
260260
200
2.5
0.1
2.5
0.3
100
180180
0.5
2.0
2.0
0.65
0.65
0.35
0.35
1.5
100100
30
1.5
0.05
0.05
20 20
1.0
1
2
Total input energy(MJ)
3
1.0
1
2
3
Total input energy(MJ)
Short pulse energy can be reduced with small gain
reduction
Identifying Marker. 24
We obtain the spot size and pulse length
dependence of gain
Gain
Gain
0.3
Pulse length(10-8sec)
Spot radius(cm)
2.0
260
260
0.2
260260
1.5
30
180
180
30
0.1
100
20
20
0.0
1
2
1.0
100
100
200
Total input energy(MJ)
3
180180
100100
200
0.5
100
20 20
0.0
1
2
Total input energy(MJ)
3
Hybrid target has ~3-4X beam spot with 25%lower coupling efficiency
Identifying Marker. 25
We constructed a Fast Ignitor gain model based
on a few ingredients
•
•
Atzeni ignition power,intensity,energy model
•
•
Ponderomotive EK scaling model
•
Found dependence of gain on IFAR, total laser energy, drive intensity,
ignition laser energy, ignition spot size, laser wavelength, short pulse
coupling efficiency, short pulse laser cost, compression laser
coupling efficiency for laser direct drive targets
•
•
Fast Ignition gain curves driven by distributed radiator HIF target given
Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket
equation using degenerate gas DT EOS(summarized in Lindl’s book)
“Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell selfsimilar stagnation model
Detailed calculations are required to validate these optima
–26
We constructed a Fast Ignitor gain model based
on a few ingredients
•
•
Atzeni ignition power,intensity,energy model
•
“Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell
self-similar stagnation model
•
Found dependence of gain on IFAR, total laser energy, drive
intensity, ignition laser energy, ignition spot size, laser
wavelength, short pulse coupling efficiency, short pulse laser
cost, compression laser coupling efficiency
•
•
Detailed calculations are required to validate these optima
Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from
rocket equation using degenerate gas DT EOS(summarized in
Lindl’s book)
Suggested options to increase fast ignition gain
–27
We constructed a Fast Ignitor gain model based
on a few ingredients
•
•
Atzeni ignition power,intensity,energy model
•
•
Ponderomotive EK scaling model
•
Found dependence of gain on IFAR, total laser energy, drive intensity, ignition
laser energy, ignition spot size, laser wavelength, short pulse coupling efficiency,
short pulse laser cost, compression laser coupling efficiency for laser direct drive
targets
•
•
Fast Ignition gain curves driven by distributed radiator HIF target given
Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using
degenerate gas DT EOS(summarized in Lindl’s book)
“Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell self-similar
stagnation model
Detailed calculations are required to validate these optima
–28
–29
–30
–31
–32
–33
LSP calculations showing electron transport in
cones
Spatial distributions shown:
Hot electron temperature
Thermal electron temperature
Ion temperatures
Particle densities
Magnetic field
Electrical current
Electric field
–34
–35
Lasnex calculations showing laser propagation
in cone and intensity distribution
–36
Rays injected from f/5 focus into 30o cone have
only one bounce
R(cm)
Fraction of ray power
Ray paths
Z(cm)
Ray pathlength
Try other acceptor shapes or incident angles to get more
bounces
Increase roughness at micron scale--ponderomotively formed
bubbles have much higher absorption in PIC calculations
–37
The implicit,hybrid PIC code LSP from MRC was
used to calculate the transport of hot electrons
in a cone to high density fuel
Au Z*=30
100 TW e- power
2MeV drift in z
1 MeV temperature
H ne=1026
–38
Hot electron current flows along inner edge of
cone*
Density of relativistic electrons
Temperature of hot electrons
*Consistent with Sentoku collisionless lower density PIC simulations
–39
Heating is mainly on inner edge of cone
Te-thermal
TAu
Te-thermal
t
H
H
Electron
thermal wave
begins to
penetrate
dense(1026/cc)
H
–40
The surface fields and currents are very large
Eradial
Ez
rBq
–41
For 3 MJ total laser energy, the optima depend
most strongly on the in-flight-aspect-ratio(IFAR)
Implosion
Velocity
(107cm/sec)
Hydrodynamic
efficiency(%) is a
function of IFAR,I
(gm/cc)
6
200.
200.
200.
900
4.5
IFAR
100.0
50.
0.11
0.15
3.
50.
100.0
300
50.
120
1.5
20.
10.0
0.01
0.08
100.0
20.
0.04
0.1
1.0
10.0
10.0 0.01
laser intensity
1014W/cm2
60.
20.
0.1
1.0
laser intensity
1014W/cm2
10.0
10.0
0.01
0.1
1.0
10.0
laser intensity
1014W/cm2
–42
Optimized designs show tradeoffs among
hydroefficiency, density,column density and
IFAR
(%)
300
R(gm/cm2)
(gm/cm3)
300
200.
100.0
200
IFAR
300
8
6
100
200
50.
100
12
4
40
20.
6
9
1
10.0
2
Laser energy(MJ)
3
100
1
2
Laser energy(MJ)
2
3
1
2
3
Laser energy(MJ)
–43
Through Innovative Laser Pulse Shaping we have
Significantly Improved the Stability of High-Gain
Direct-Drive Targets for Inertial Fusion Energy
KrF or DPSSL
laser
Laser Power Pulse Shape
1.0
2.38mm
DT ablator
(+ CH foam)
DT fuel
DT gas
0.1
Standard
0.01
0.001
Yield 350MJ
Elaser 2.9MJ
Gain 120
Shell breakup fraction:
-Standard pulse ~1.8
- Picket pulse ~0.15
IFSA_03_Haan–44
“Picket stake”
prepulse
Time
Picket fence pulse shape
drives decaying through
shell
High adiabat in ablator
Low adiabat in fuel
IFAR 100 => 40 without loss
of fuel density
Comparable to indirect drive
Long pulse plastic slab coupling efficiencies
were used*
1.0
Absorption
fraction
0.5

1.0,0.5
0.33,0.25
0.0
10+11 10+12 10+13 10+14 10+15
Laser intensity(W/cm2)
* See W.L.Kruer,ThePhysics of Laser Plasma Interactions,Westview Press, Boulder,CO
–45
Are small laser focal spots consistent with final
optics protection?
•1 cm thick SiO2 at 15m from capsule will become opaque due to neutron
loading after 2 months of reactor yields
•Thin films may tolerate longer exposures
•200 kJ at 2J/cm2 => 105cm2 => 3m final optic =>f/5
•Diffraction limit allows small spot
•Pointing accuracy ~ 1 microradian for a moving target!
•G.Logan suggested 1 cm scale conical plasma mirror at 1015W/cm2 to
focus light from large area
•Scanning the surface maintains a smooth surface for long pulse
•High intensity simulations show absorption between 30-90% (Sentoku
small scale, LASNEX--preliminarylarge scale)
•Electron transport calculations have begun
–46