Gain Issues for Fast Ignition

1
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.
2
We constructed a Fast Ignitor gain model based on
a few ingredients

• Atzeni ignition power,intensity,energy model
• Hydrodynamic efficiency, in-flight-aspect-ratio(IF
  AR) from rocket equation using degenerate gas DT
  EOS(summarized in Lindls book)
• Ponderomotive EK scaling 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 for laser
  direct drive targets
• Fast Ignition gain curves driven by distributed
  radiator HIF target given
• Detailed calculations are required to validate
  these optima

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The burn efficiency depends on the fuel adiabat
and is one factor in Fast Ignition gain
For uniform sphere
It was thought that the adiabat was entirely set
by careful pulseshaping during the
implosion Modest increases in shock pressure and
proper timing Wrong! Significant jump in adiabat
during stagnation For implosions with uniform
M,g5/3 a jumps by M1/2 M-t-V and Schalk, Kemp
and M-t-V But story a little more
complicatedimplosion doesnt produce
self-similar shape
5
There are four stages in an implosion
Uniform M10 at end Ignore convergence
P
r
R0
R
R
Uniformly accelerated equilibrium
Adiabat shaping
Convergent amplification
3x in P
10x
Hollow shell
Ablation pressure
a jump
P
r
R
R
R
Convergence harvests kinetic energy and breaks
self-similarity
stagnation
6
The gain at fixed total energy(3 MJ) is
determined by the IFAR and the compression
intensity
100
I gt vabl,Pabl,
?inflight,cs I,IFAR
gtvimpl Vimpl,cs
gtM Vimpl,IFAR,vabl gt?hydro M
gt? M,?inflight
gt?stag ?stag
gtEigni Eigni,?igni
gtEigni-laser Etotal, Eigni-laser
gtEcmp-las Ecomp-laser, ?hydro gtEcomp Ecomp,
?stag, ? gt mass Mass, ?stag gt
?R ?R gt? ?,mass gtyield
gtgain
400
200
IFAR
50
Intensity(1014W/cm2)
7
How do maximum gain quantities depend on
implosion laser intensity and total laser energy?
gain(IFARlt100)
gain
IFAR
100
30
160
40
30
80
100
Intensity(1014W/cm2)
300
120
300
Energy(MJ)
Energy(MJ)
Energy(MJ)
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There are satisfactory design points for IFAR
under 100
Implosion intensity 1014W/cm2
Implosion velocity 107cm/sec
gain
3.
6
100
0.9
IFAR
4
0.3
300
2
Energy(MJ)
Energy(MJ)
Energy(MJ)
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Low required convergence ratios will allow
relaxed illumination symmetry
Convergence ratio
Convergence ratio is measured after
adiabat setting shocks have passed
40
20
IFAR
10
Energy(MJ)
10
Maximum gains correspond to large ignition laser
energies
Fraction of energy in ignition laser
Ignition laser energy(MJ)
0.03
IFAR
0.1
0.1
0.3
0.2
0.4
1.0
Energy(MJ)
Energy(MJ)
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Low IFARs and high system energies lead to large
spots and long stagnation and ignition energy
delivery times
Spot radius(?)
Ignition time(ps)
Stagnation time(ps)
30
10
10
100
IFAR
300
30
30
60
900
60
Energy(MJ)
Energy(MJ)
Energy(MJ)
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We explore the sensitivity of the optima to a
number of model uncertainties and experimental
details

• Nominal model
• Laser wavelength 0.33?
• ??????m laser spot 10?
• Maximum IFAR 100
• Short pulse laser coupling efficiency 0.25
• Compression laser coupling ? hydro model
• Ignition energy Atzeni model
• Particle range(gm/cm2) 0.6 E/MeV

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How does the wavelength of the implosion laser
affect the gain curve?
No restriction on ignition laser
Eign-laser lt 100 kJ
????? 1.0,0.5 0.33,0.25
????? 1.0,0.5 0.33,0.25
gain
Elaser(MJ)
Elaser(MJ)
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How do the gain curves depend on the minimum
radius of the ignition spot?
Eign-laser lt 100 kJ
spot radius(?) 10,20,30,40,50
No solution for R gt 10?!
Elaser(MJ)
Current experiments show e- spreading to 20m spot
from much smaller laser spot!
15
Limiting the energy supplied by the ignition
laser affects the total system gain
No limitation 400 kJ 200 kJ 100 kJ
gain
Elaser(MJ)
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The system gain depends strongly coupling
efficiency from laser to ignition region
E ign lt 100kJ
No restriction on ignition laser
gain
???????? 0.5 0.25 0.12 0.06
Elaser(MJ)
Elaser(MJ)
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The system gain depends on the range of the
relativistic electrons
No restriction on ignition laser
E ign lt 100kJ
Range multiplier 0.5 1.0 2.0 3.0
gain
Range multiplier 0.5 1.0 2.0 3.0
Elaser(MJ)
Elaser(MJ)
Nominal range(gm/cm2) 0.6 T(MeV) T(I/1.21019W/
cm2 )1/2
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What is the effect of reducing the coupling
between the compression laser and the fuel?
No restriction on ignition laser
Eign-laser lt 100 kJ
?H multipliers 1. 0.75 0.5 0.25
gain
Elaser(MJ)
Elaser(MJ)
Indirect drive has lower ?H but smaller adiabat
jump Cone focus implosions forming high ? core
may have reduced ?H
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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 a 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 doesnt
  form e.g., bare drop driven at high intensity.
  Use large short pulse laser to compress and light
  ignition region

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How would the gain curves change if requirements
could be reduced below Atzenis fit?
No restriction on ignition laser
Eign-laser lt 100 kJ
Atzeni fit 6x ignition energy in
isobaric model Recent calculations show 2x
reduction for cylindrical implosion driven by
short pulse How well can we do?
gain
Elaser(MJ)
Atzeni x 0.5 x 0.25 x 0.125
Elaser(MJ)
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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

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How does the cost of ignition laser joules
relative to compression driver joules affect the
optima in yield/cost ?
Fractional cost of Ignition driver
Ignition driver (MJ)
Yield/cost
Relative cost/J 0.5 1.0
3.0 10.
Cost
Cost
Cost
MJ equivalent of compression driver
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What happens when we Fast Ignite an ion
distributed radiator target
2-sided illumination scaled from normal DRT
Eescape
2rbeam
Ion beam
rh
Pr3T3.5
rb
trb/vimp
Econvrh2 T
Ewallrh2T3.3t0.62
laser
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Gain distribution and short pulse laser
requirements
Short pulse energy(MJ)
Gain
0.1
200
0.3
100
0.5
TR(100 eV)
30
Total input energy(MJ)
Total input energy(MJ)
Short pulse energy can be reduced with small gain
reduction
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We obtain the spot size and pulse length
dependence of gain
Gain
Gain
30
Spot radius(cm)
Pulse length(10-8sec)
30
200
100
200
100
Total input energy(MJ)
Total input energy(MJ)
Hybrid target has 3-4X beam spot with 25lower
coupling efficiency
26
We constructed a Fast Ignitor gain model based on
a few ingredients

• Atzeni ignition power,intensity,energy model
• Hydrodynamic efficiency, in-flight-aspect-ratio(IF
  AR) from rocket equation using degenerate gas DT
  EOS(summarized in Lindls book)
• Ponderomotive EK scaling 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 for laser
  direct drive targets
• Fast Ignition gain curves driven by distributed
  radiator HIF target given
• Detailed calculations are required to validate
  these optima

27
We constructed a Fast Ignitor gain model based on
a few ingredients

• Atzeni ignition power,intensity,energy model
• Hydrodynamic efficiency, in-flight-aspect-ratio(IF
  AR) from rocket equation using degenerate gas DT
  EOS(summarized in Lindls book)
• 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
• Suggested options to increase fast ignition gain

28
We constructed a Fast Ignitor gain model based on
a few ingredients

• Atzeni ignition power,intensity,energy model
• Hydrodynamic efficiency, in-flight-aspect-ratio(IF
  AR) from rocket equation using degenerate gas DT
  EOS(summarized in Lindls book)
• Ponderomotive EK scaling 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 for laser
  direct drive targets
• Fast Ignition gain curves driven by distributed
  radiator HIF target given
• Detailed calculations are required to validate
  these optima

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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
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Lasnex calculations showing laser propagation in
cone and intensity distribution
37
Rays injected from f/5 focus into 30o cone have
only one bounce
Ray paths
Fraction of ray power
R(cm)
Ray pathlength
Z(cm)
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
38
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 Z30
100 TW e- power 2MeV drift in z 1 MeV temperature
H ne1026
39
Hot electron current flows along inner edge of
cone
Temperature of hot electrons
Density of relativistic electrons
Consistent with Sentoku collisionless lower
density PIC simulations
40
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
41
The surface fields and currents are very large
rBq
Eradial
Ez
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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
900
4.5
300
0.11
3.
0.15
IFAR
120
0.08
1.5
60.
0.04
laser intensity 1014W/cm2
laser intensity 1014W/cm2
laser intensity 1014W/cm2
43
Optimized designs show tradeoffs among
hydroefficiency, density,column density and IFAR
?()
?R(gm/cm2)
?(gm/cm3)
300
8
6
100
IFAR
4
12
40
2
6
9
Laser energy(MJ)
Laser energy(MJ)
Laser energy(MJ)
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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 0.1 0.01 0.001
Picket stake prepulse
Standard
2.38mm
DT ablator ( CH foam)
DT fuel
Time
DT gas

• Yield 350MJ
• Elaser 2.9MJ
• Gain 120
• Shell breakup fraction
• Standard pulse 1.8
• - Picket pulse 0.15

Picket fence pulse shape drives decaying through
shell High adiabat in ablator Low adiabat in
fuel IFAR 100 gt 40 without loss of fuel
density Comparable to indirect drive
45
Long pulse plastic slab coupling efficiencies
were used
Absorption fraction
????? 1.0,0.5 0.33,0.25
Laser intensity(W/cm2)
See W.L.Kruer,ThePhysics of Laser Plasma
Interactions,Westview Press, Boulder,CO
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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 gt 105cm2 gt 3m final optic
  gtf/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