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Target Gain Curves for Systems Modeling*

Explore various gain curves for system modeling, including direct-drive and heavy ion targets, with equations and parameters. Learn to calculate driver cost, performance, and achievable spot size based on design variables.

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Target Gain Curves for Systems Modeling*

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  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 = 300+144 ln(Ed) • Direct drive, low a with zooming (includes NRL design point) G1 = 119.3 + 86.0 ln(Ed) • Direct drive, a = 2 G2 = 47.2 + 48.0 ln(Ed) • Direct drive, a = 3 G3 = 25.0 + 36.1 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

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