# Presentation: 544732

## 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.

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

**Atzeni ignition power,intensity,energy model**
**Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book)**
**Ponderomotive E****K**** 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**

## Slide 3

## 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,********=5/3  ********jumps by M****1/2**
**M-t-V and Schalk, Kemp and M-t-V**
**But story a little more complicated:implosion doesn’t produce self-similar shape **

## There are four stages in an implosion

**P**

**R**

**Adiabat shaping **

****

**R**

**Uniformly accelerated equilibrium**

**Uniform M~10 at end**
**Ignore convergence**

**R****0**

**P**

**R**

**Ablation pressure**

**Convergent amplification**

**Convergence harvests kinetic energy and breaks self-similarity**

****** ****jump**

**R**

****

**R**

**Hollow shell**

**stagnation**

**10x**

**~3x in P**

## The gain at fixed total energy(3 MJ) is determined by the IFAR and the compression intensity

**The gain at fixed total energy(3 MJ) is determined by the IFAR and the compression intensity**

**I                         => v****abl****,P****abl****,                 ****	****	****    ********inflight****,c****s**
**I,IFAR                 =>v****impl**
**V****impl****,c****s****                =>M**
**V****impl****,IFAR,v****abl       ****=>********hydro             **
**M                        =>******
**M,********inflight                     ****=>********stag**
******stag****                     =>E****igni**
**E****igni****,********igni                     ****=>E****igni-laser**
**E****total****, E****igni-laser****      =>E****cmp-las**
**E****comp-laser****, ********hydro   ****=>E****comp**
**E****comp****, ********stag****, ********      => mass**
**Mass, ********stag****          => ********R**
******R                       =>******
******,mass =>yield  =>gain       **

**IFAR**

**Intensity(10****14****W/cm****2****)**

**50**

**100**

**200**

**400**

## How do maximum gain quantities depend on implosion laser intensity and total laser energy?

**How do maximum gain quantities depend on implosion laser intensity and total laser energy?**

**IFAR**

**gain(IFAR<100)**

**gain**

**40**

**80**

**120**

**160**

**30**

**100**

**300**

**30**

**100**

**300**

**Intensity(10****14****W/cm****2****)**

**Energy(MJ)**

**Energy(MJ)**

**Energy(MJ)**

## There are satisfactory design points for IFAR under 100 

**There are satisfactory design points for IFAR under 100 **

**Implosion velocity**
**10****7****cm/sec**

**Implosion intensity**
**10****14****W/cm****2**

**gain**

**IFAR**

**Energy(MJ)**

**Energy(MJ)**

**Energy(MJ)**

**2**

**4**

**6**

**0.3**

**0.9**

**3.**

**100**

**300**

## Low required convergence ratios will allow relaxed illumination symmetry

**Low required convergence ratios will allow relaxed illumination symmetry**

**Convergence  ratio**

- 10

**20**

- 40

**Energy(MJ)**

**IFAR**

**Convergence ratio is **
**measured after adiabat**
**setting shocks have **
**passed **

## Maximum gains correspond to large ignition laser energies

**Maximum gains correspond to large ignition laser energies**

**Ignition laser energy(MJ)**

**Fraction of energy in ignition laser**

**IFAR**

**Energy(MJ)**

**Energy(MJ)**

**0.03**

**0.1**

**0.3**

**0.1**

**0.2**

**0.4**

**1.0**

## Low IFAR’s and high system energies lead to large spots and long stagnation and ignition energy delivery times

**Low IFAR’s and high system energies lead to large spots and long stagnation and ignition energy delivery times**

**Spot radius(********)**

**Ignition time(ps)**

**Stagnation time(ps)**

**Energy(MJ)**

**Energy(MJ)**

**Energy(MJ)**

**IFAR**

**30**

**100**

**300**

**900**

**10**

**30**

**10**

**30**

**60**

**60**

## 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/cm****2****)****	****	****0.6 E/MeV**

## How does the wavelength of the implosion laser affect the gain curve?

**How does the wavelength of the implosion laser affect the gain curve?**

**E****laser****(MJ)**

**E****laser****(MJ)**

**gain**

**No restriction**
**on ignition laser**

**E****ign-laser**** < 100 kJ**

****
**1.0,****0.5**
**0.33****,****0.25**

****
**1.0,****0.5**
**0.33,****0.25**

## How do the gain curves depend on the minimum radius of the ignition spot?

**E****ign-laser**** < 100 kJ**

**E****laser****(MJ)**

**spot radius(********)**
**10,****20****,****30****,****40****,****50**

**No solution for **
**R > 10********!**

**Current experiments show e****-**** spreading to 20******** spot from much smaller laser spot!**

## Limiting the energy supplied by the ignition laser affects the total system gain 

**Limiting the energy supplied by the ignition laser affects the total system gain **

**No limitation**** **
**400 kJ**
**200 kJ**
**100 kJ**

**E****laser****(MJ)**

**gain**

## The system gain depends strongly coupling  efficiency from laser to ignition region

**The system gain depends strongly coupling  efficiency from laser to ignition region**

**No restriction on ignition laser**

**E ****ign**** < 100kJ**

**E****laser****(MJ)**

**E****laser****(MJ)**

**gain**

************
**0.5**
**0.25**
**0.12**
**0.06**

## The system gain depends on the range of the relativistic electrons

**The system gain depends on the range of the relativistic electrons**

**No restriction on ignition laser**

**E ****ign**** < 100kJ**

**E****laser****(MJ)**

**E****laser****(MJ)**

**gain**

**Nominal range(gm/cm****2****) = 0.6 T(MeV)**
**T=(I/1.2*10****19****W/cm****2**** )****1/2**

**Range**
**multiplier**
**0.5**** ****1.0**
**2.0**** ****3.0**

**Range**
**multiplier**
**0.5**** ****1.0**
**2.0**** ****3.0**

## What is the effect of reducing the coupling between the compression laser and the fuel?

**What is the effect of reducing the coupling between the compression laser and the fuel?**

**No restriction**
**on ignition laser**

**E****ign-laser**** < 100 kJ**

**Indirect drive has lower ********H ****but smaller adiabat jump**
**Cone focus implosions forming high ******** core may have reduced ********H**

**E****laser****(MJ)**

**E****laser****(MJ)**

******H**** multipliers**
**1.**
**0.75**
**0.5**
**0.25**

**gain**

## 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**

## How would the gain curves change if requirements could be reduced below Atzeni’s fit?

**How would the gain curves change if requirements could be reduced below Atzeni’s fit?**

**No restriction**
**on ignition laser**

**E****ign-laser**** < 100 kJ**

**gain**

**E****laser****(MJ)**

**E****laser****(MJ)**

**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? **

**Atzeni**
**x 0.5**
**x 0.25**
**x 0.125**

## 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 **

## How does the cost of ignition laser joules relative to compression driver joules affect the optima in yield/cost ?

**How does the cost of ignition laser joules relative to compression driver joules affect the optima in yield/cost ?**

**Yield/cost**

**Cost***

***MJ equivalent of compression driver**

**Cost***

**Cost***

**Fractional cost of **
**Ignition driver**

**Ignition driver**
**(MJ)**

**Relative cost/J**
**           ****0.5  ****1.0**
**           ****3.0  ****10.**

## What happens when we Fast Ignite an ion distributed radiator target 

- rb

- rh

**E****wall****~r****h****2****T****3.3********0.62**

**E****conv****~r****h****2**** T**

- Eescape

**Pr~3T****3.5**

**2r****beam**

******~r****b****/v****imp**

**2-sided illumination scaled from normal DRT**

**laser**

**Ion**
**beam**

## Gain distribution and short pulse laser requirements

**Total input energy(MJ)**

**T****R****(100 eV)**

- 30

- 100

- 200

- 0.1

- 0.3

- 0.5

**Total input energy(MJ)**

**Gain**

**Short pulse energy(MJ)**

**Short pulse energy can be reduced with small gain reduction**

## We obtain the spot size and pulse length dependence of gain

**Total input energy(MJ)**

**Total input energy(MJ)**

**Gain**

**Gain**

**Spot radius(cm) **

**Pulse length(10****-8****sec)**

**Hybrid target has ~3-4X beam spot with 25%lower coupling efficiency**

**30**

**30**

**100**

**100**

**200**

**200**

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

**Atzeni ignition power,intensity,energy model**
**Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book)**
**Ponderomotive E****K**** 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**

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

**Atzeni ignition power,intensity,energy model**
**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**
**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**

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

**Atzeni ignition power,intensity,energy model**
**Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book)**
**Ponderomotive E****K**** 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**

## 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**

## Lasnex calculations showing laser propagation in cone and intensity distribution

## Rays injected from f/5 focus into 30o cone have only one bounce

**R(cm)**

**Z(cm)**

**Ray paths**

**Ray pathlength **

**Fraction of ray power**

**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 **

## 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**

**H  n****e****=10****26**

**100 TW e- power**
**2MeV drift in z**
**1 MeV temperature**

## 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**

## Heating is mainly on inner edge of cone

**T****Au**

**H**

**T****e-thermal**

**t**

**T****e-thermal**

**H**

**Electron thermal wave begins to penetrate dense(10****26****/cc) H**

## The surface fields and currents are very large

**E****radial**

**E****z**

**rB******

## For 3 MJ total laser energy, the optima depend most strongly on the in-flight-aspect-ratio(IFAR) 

**For 3 MJ total laser energy, the optima depend most strongly on the in-flight-aspect-ratio(IFAR) **

**Hydrodynamic**
**efficiency(%) is a **
**function of IFAR,I**

**Implosion **
**Velocity**
**(10****7****cm/sec)**

******(gm/cc)**

**IFAR**

** ****laser intensity**
**10****14****W/cm****2**

**laser intensity**
**10****14****W/cm****2**

**laser intensity**
**10****14****W/cm****2**

**0.04**

**0.08**

**0.15**

**1.5**

**3.**

**4.5**

**6**

**60**.

**120**

**300**

**900**

**0.11**

## Optimized designs show tradeoffs among hydroefficiency, density,column density and IFAR

**Optimized designs show tradeoffs among hydroefficiency, density,column density and IFAR**

******(%)**

******R(gm/cm****2****)**

******(gm/cm****3****)**

**40**

**100**

**300**

**2**

**4**

**6**

**8**

**6**

**9**

**12**

**IFAR**

**Laser energy(MJ)**

**Laser energy(MJ)**

**Laser energy(MJ)**

## Through Innovative Laser Pulse Shaping we have Significantly Improved the Stability of High-Gain Direct-Drive Targets for Inertial Fusion Energy

**Yield****	*****350MJ******	***
**E****laser****	*****2.9MJ******	***
**Gain****	*****120******	***
**Shell breakup fraction:**
***Standard pulse******	******~1.8***
***- Picket pulse   ~0.15***

- DT gas

- DT fuel

- 2.38mm

- DT ablator
- (+ CH foam)

- 1.0
- 0.1
- 0.01
- 0.001

- Time

- KrF or DPSSL laser

- “Picket stake” prepulse

**Laser Power Pulse Shape**

- Standard

**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,****0.5**
**0.33****,****0.25**

**Laser intensity(W/cm****2****)**

**Absorption fraction **

- * See W.L.Kruer,_ThePhysics of Laser Plasma Interactions,_Westview Press, Boulder,CO

## Are small laser focal spots consistent with final optics protection?

**1 cm thick SiO****2**** 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/cm****2 ****=> 10****5****cm****2****  => 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 10****15****W/cm****2**** 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**