1. Target Gain Curves for Systems Modeling*
Wayne R. Meier
Lawrence Livermore National Lab
ARIES IFE Meeting
PPPL
Sept 19-20, 2000
* 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. There are many possible laser-driven gain curves to use
NRL direct drive design
Low alpha with zooming
G = 135 at E = 1.2 MJ 

3. Simple fits have been used in past studies
Gain Curves
Line of constant yield

4. Fitting equations for laser gain curves
Fast Ignitor
Gfi = ln(Ed)
Direct drive, low a with zooming (includes NRL design point)
G1 = ln(Ed)
Direct drive, a = 2
G2 = ln(Ed)
Direct drive, a = 3
G3 = ln(Ed)

5. Heavy ion gain curves
Based on scaling equations from Debbie Callahan-Miller, “Progress in target physics and design for heavy ion fusion,” Physics of Plasmas, 7, No. 5 (May 2000)
Miller’s equations depend on three primary variables:
Energy absorbed by fuel capsule, Ecap
Ratio of hohlraum radius to capsule radius, CCR = Rhohl/Rcap
Hohlraum temperature, Tr
Driver systems model calculates driver cost and performance as a function of total driver energy (Ed) and other design variables (e.g., number of beams, quad field, etc.)
Systems model also calculates achievable spot size as a function of these variables
Therefore, must relate Ed and achievable rspot to target gain scaling parameters

6. Heavy ion gain curves for distributed radiator targets
240 eV
Hohlraum temperature varies, 250 eV
Ecap, Rcap, Yield = constant, CCR varies
CCR = constant, Ecap, Rcap, Yield vary

7. Beam spot size requirements vary with capsule radius and case-to-capsule radius ratio, CCR
End view of target showing how beams are positioned (one of many shown)
Spot size required for “conventional” target, CCR = 2.14

8. Heavy ion gain curve calculations
Yield scales with Ecap
Y ~ (Ecap)5/3
Gain is ratio of yield to driver energy, G = Y/Ed
Driver energy is calculated as sum of the following
Ed = Ecap + Ewall + Econverter + Ebeamblock + Eescape
I find that the ratio of Ed to Ecap is nearly constant for a given CCR (moving along one of Miller’s curves)
Since Rcap scales with Ecap and Rspot is a function of Rcap and CCR, can now find Rspot for a given Ed and CCR
Or for a given Ed and achievable Rspot , can find the corresponding CCR, Ecap, yield and gain

9. Example result of gain vs driver energy for different spot sizes and case-to-capsule ratios
Target gain vs driver energy, MJ
(Tr = 250 eV)
Fixed spot size curves: Rspot = 2.7 mm
Rspot = 1.7 mm
Fixed CCR curves:
CCR = 2.14 (Standard)
CCR = 1.57 (Close-coupled)

10. Next steps on target gain curves
Get target size info corresponding to laser direct-drive targets (input to laser focusing, target injection and tracking designs)
Do we want to consider laser indirect drive at this point?
Review the HI target scaling assumptions with Debbie and incorporate in power plant systems code