Cone-Guided Fast Ignition with Imposed Magnetic Fields

Transcription

1 Cone-Guided Fast Ignition with Imposed Magnetic Fields D. J. Strozzi Lawrence Livermore National Laboratory 7 th International Conference on Inertial Fusion Sciences and Applications Bordeaux France September 12-16, 211 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-7NA Supported by OFES HEDLP project FI-HEDS, and LDRD project 11-SI-2. LLNL-CONF

2 Fast igni)on modeling at LLNL Explicit PIC for short- pulse laser- plasma interaceon: A. J. Kemp, L. Divol Rad- hydro: fuel assembly in hohlraum, around cone: H. D. Shay, M. Tabak, D. Ho laser laser intensity Au C DT Transport modeling hybrid PIC code Zuma fast electrons, E/B fields coupled to Hydra: rad- hydro, burn, radiaeon fast electron injected source Zuma domain plasma condieons at Eme of ignitor pulse Subject of this talk DJS: IFSA 211 p. 2

3 A device is needed to achieve fast igni)on with a realis)c, divergent electron source we explore imposed magne)c fields Fast electron source from PIC sims of short- pulse laser- plasma interaceon: Energy spectrum has two temperature components, many electrons too energeec to stop in DT hotspot Angle spectrum is divergent serious challenge! Transport modeling: hybrid PIC code Zuma coupled to rad- hydro code Hydra Imposed uniform axial magneec fields 3-5 MG miegate divergence Can be produced in an implosion with seed field ~ 5 kg MagneEc mirroring in non- uniform field prevents fast electrons from reaching fuel Especially if fast electrons generated in uncompressed seed field Hollow magneec pipe can prevent mirroring: no field within spot radius Co- authors: M. Tabak, D. J. Larson, M. M. Marinak, M. H. Key, L. Divol, A. J. Kemp, C. Bellei, H. D. Shay DJS: IFSA 211 p. 3

4 Fast electron source distribu)on found from explicit PIC laser- plasma simula)ons with PSC code (A. Kemp, L. Divol) 4 3 Electron density (ripples due to laser absorp)on) +," #"+ -." *$$" )$" ExtracEon box: all fwd- going electrons with kin. en. >.5 MeV %"#"! $" 2 ($" '$" Source box: fast electrons excited here in equivalent Zuma simulaeon k laser !"#"! $" $" &$" f(e,θ) = f E (E) * f θ (θ) factorized I fast (r,t) =.52 * I las (r,t) 3D Cartesian run, pre- plasma with n e ~ exp[ z / 3.5 λ ] Big run: 6 million cells, 1 billion parecles, 16, cpu*hrs! Intensity at vacuum focus (z = 1 λ ): I las (r) = I exp[- (r/18.3 λ ) 8 ] Normalized vector poteneal: a = 1 DJS: IFSA 211 p. 4

5 PIC fast electron energy spectrum is quasi two- temperature 1..5 E*dN/dE ε = E / T p running integral dn d! =.82exp[!! /1.3]+ 1! exp[!! /.19]!!!!!!! = E T p hot: from pre- plasma cold: from criecal density We scale dn/de with ponderomoeve temperature 1 T pond m e c! 1+ a " " 2 2 # $ I %1/2 &1 ~ a! sqrt las! 2 $ ( ) # 1.37'1 18 W cm -2 µm 2 % For our PIC run: a = 1, T pond = 4.63 MeV DT hot spot: ρδz ~ 1.2 g/cm 2 removes 1.4 MeV from a fast electron (negleceng angular scaher) Spectrum is too energeec to stop in hot spot 1 S. C. Wilks et al., Phys. Rev. Leh. (1992) DJS: IFSA 211 p. 5

6 PIC fast electron angle spectrum is divergent source solid-angle spectrum: Δθ = 9 o agrees with PIC results dn / dω [ µc / sterad ] Solid angle spectrum Zuma source box, Δθ = 9 o PIC extraceon box Zuma extraceon box θ [deg] dn d! = exp $ %"(! / #!)4& ' <θ> [deg] Δθ <θ> Zuma- Hydra runs used for o 6.9 o areficially collimated source 9 o 52 o realisec PIC source Average polar angle Δθ [deg] θ <θ> = Δθ! p ẑ DJS: IFSA 211 p. 6

7 Zuma: Hybrid PIC code (D. J. Larson) Reduced dynamics removes light, plasma waves: ω << ω plasma, ω laser k << k laser, 1/λ Debye!!Relativistic fast electron advance: F = - e( E! + v!! B)!!Fast e- energy loss and angular scattering: formulas of Solodov, Davies!! J return = -! J fast + µ "1 #!! B!!!Ampere's law without displacement current!electric field given by massless momentum equation for background electrons: d v! m eb e dt!=!"e E! +...!=!!!!! $!!!!!!! E! = E! C + E! NC! E C =!!i! " J! return " e " "1!!i!#T e!!!!!!!!!! E! NC = " #p e " v! eb! B! en eb "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!,!!! from Lee-More-Desjarlais and Epperlein-Haines!! J return i! E C! %! B %t collisional heating = - #!! E Faraday's law Complete E field results can differ from E = η*j return (c.f. Nicolai et al., APS DPP 21) DJS: IFSA 211 p. 7

8 Hybrid PIC code Zuma coupled to rad- hydro code Hydra (M. M. Marinak, D. J. Larson, L. Divol) Both codes run in cylindrical R- Z geometry on fixed Eulerian meshes (which can differ) Typical run: 2 ps transport (Zuma + Hydra), then 18 ps burn (just Hydra) 2-3 wall- Eme hours on 48 cpu s Hydra 1: plasma condieons to Zuma (densiees, temperatures, Z) Zuma t coupling step 4: hydro Hydra steps Zuma steps t 1 3: B field, energy/momentum deposieon rates t 2 2: hybrid transport energy, momentum deposieon Hydra details: IMC photonics, no MHD used yet. DJS: IFSA 211 p. 8

9 igni)on- scale idealized target with carbon cone Cone: 8 g/cc carbon DT fuel e- beam source Ideal burn- up fraceon f = ρr/(ρr+6) = 1/3 Ideal fusion yield = 338 MJ * Mass [mg] * f = 64.4 MJ OpEmal e- beam ignieon energy [Atzeni et al., PoP 27]: E ig = 14 kj / (ρ/1 g/cc) 1.85 = 8.7 kj in ρr =.6, or r = 13.3 µm 527 nm (2ω) wavelength laser: lowers T pond ~ λ DT density ρ > 1 g/cc: ρr = 3. g/cm 2 mass =.572 mg fast e power [a. u.] Fast electron Eme pulse time [ps] DJS: IFSA 211 p. 9

10 Ar)ficially collimated source ignites with 132 kj of fast electrons; PIC- based divergence gives prohibi)ve igni)on energies fusion yield [MJ] Ar)ficially collimated source: Δθ=1 o ideal yield r spot = 1 µm = 14 µm = 18 µm = 23 µm Beam intensity = I exp(-.5*(r/r spot ) 8 ) fusion yield [MJ] E fast = 132 kj: 15x ideal value: spectrum too energeec to stop in hot spot; further opemizaeon may lower PIC- based source: Δθ=9 o r spot = 36 µm width > depth regime r spot = 18 µm DJS: IFSA 211 p. 1

11 Adding an ini)al, uniform, axial magne)c field B z reduces igni)on energy to roughly that of ar)ficially collimated beam B z = 5 MG ignites with 158 kj of fast electrons, similar to Δθ=1 o 1 +2 e- Larmor radius: r Le!!" B = 33.4 µm B MG " # W 2 MV +1.2W MV 1/2 $ % fusion yield [MJ] B z =, Δθ = 1 o B z = 1 MG 3 MG 5 MG B z =, Δθ = 9 o For 2 MeV e- (deposits well in hot spot): r Le = spot radius (18 µm) for B = 4.6 MG: lower bound on when B fields maher 2 4 Rad- hydro- MHD studies of B field compression are underway (H. D. Shay, M. Tabak) Omega experiments show compression of 5 kg seed B field in cylindrical implosions 1 to 3-4 MG, and in spherical implosions 2 to 2 MG 1 J. P. Knauer, Phys. Plasmas 17, (21) 2 P. Y. Chang et al., Phys. Rev. Leh 17(3):356 (211) DJS: IFSA 211 p. 11

12 Implosion can compress magne)c field in DT, but short- pulse LPI will likely happen in the seed field conductors Flux B z *r 2 conserved inside conductor, negleceng resiseve moves diffusion fixed Nested conductors: Field compressed between conductors, but not inside inner one B not compressed B compressed Cone outer surface compressed Cone inner surface doesn t move shock break- out would fill cone B field in vacuum region is uncompressed, negleceng diffusion LPI region seed B z max. volume compression field line DJS: IFSA 211 p. 12

13 Magne)c mirroring issue 1: axial increase in magne)c field strength Bz [MG] Ini)al B z profiles fast e- source DT fuel fusion yield [MJ] Fusion yield Bz5 Bz5-75 Bz3 Bz energy fraction Fast e- energy reflected to lec edge.4.2. B z ramp B z flat z [µm] Ini)al B z : 5-75 MG B field lines φ 15 fast e- source fuel r 1 db z /dz requires B r for div B = mirror force F z = e v φ B r 5 fast e- source fuel z DJS: IFSA 211 p. 13

14 Magne)c mirroring issue 2: field low in electron source region Ini)al B z profiles 8 1. Fusion yield Fast e- energy reflected to lec edge.4 Bz [MG] fast e- source sharp rise near source DT fuel fusion yield [MJ] 1..1 sharp B z rise energy fraction z [µm] DJS: IFSA 211 p. 14

15 Mirroring avoided with magne)c pipe: B z peaks off- axis Pipe with B z = 5 MG ignites for E fast = 158 kj ArEfically collimated beam (Δθ = 1 o ) ignites for E fast = 132 kj r [µm] 5 Ini)al B z (max = 5 MG) fast e- source DT fuel 5-5 z [µm] 5 1 fusion yield [MJ] energy fraction B z = 5 MG pipe B z = 5 MG uniform B z = 5-75 MG B z = - 5 MG Fast e- energy reflected to lec edge DJS: IFSA 211 p. 15

16 r [µm] Summary: imposed magne)c fields can overcome electron source divergence; magne)c pipe avoids mirroring in non- uniform field Δθ = 1 o : 132 kj e- 1 5 reflected current e- source DT fuel Δθ = 9 o : igni)on > 1 MJ e- B z = 5 MG: 158 kj e z [µm] B z = to 5 MG: igni)on > 211 kj e- magne)c pipe, 2 µm radius: 158 kj e- Possible pipe approach: mid- Z wire on axis, not compressed in implosion J fast at 1 ps (mid ignitor pulse) 5e+1 5E17 A/m 2 DJS: IFSA 211 p. 16