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R. J. Kingham, C. Ridgers Plasma Physics Group, Imperial College London

Recent developments in Vlasov-Fokker-Planck transport simulations relevant to IFE capsule compression. R. J. Kingham, C. Ridgers Plasma Physics Group, Imperial College London 9 th Fast Ignition Workshop, Boston, 3 rd —5 th Nov 2006. Outline.

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R. J. Kingham, C. Ridgers Plasma Physics Group, Imperial College London

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  1. Recent developments in Vlasov-Fokker-Planck transport simulations relevant to IFE capsule compression R. J. Kingham, C. Ridgers Plasma Physics Group, Imperial College London 9th Fast Ignition Workshop, Boston, 3rd—5th Nov 2006

  2. Outline • We are coupling our electron transport code, IMPACT, to an MHD code (previously, IMPACT used static density) • Example of enhanced code in use  Froula (LLNL) & Tynan’s (USD) expt.effect of B-fields on non-local transport in hohlraum gas-fill context • We are starting to investigate transport & B-field generation on outside wall of cone, during implosion • Preliminary results  B-field of wt > 1 in 0.5ns  affects lateral Te profile next to cone (beneficial?)  lateral heat flow non-local

  3.  T qRL Righi-Leducheat flow Nernst effect Convection of B-field with heat flow Interested in departures from Braginskii transport……even in classical transport, B-fields add complexity Braginskii’s transport relations (stationary plasma)

  4. First 2-D FP code for LPI with self consistent B-fields fo can be non-Maxwellian  get non-local effects IMPACT – Parallel Implicit VFP code • Implicit finite-differencing  very robust + large Dt (e.g. ~ps for Dx~1mm vs 3fs) • Solves Vlasov-FP + Maxwell’s equations for fo, f1, E & Bz Kingham & Bell , J. Comput. Phys. 194, 1 (2004) IMPLICT LAGGED EXPLICIT

  5. Compressional heating - from bulk plasma compression/rarefaction Fictitious forces - we are no longer in an inertial frame Moving with ion fluid - include bulk convection. VFP equation for isotropic component f0 f(v) f(w) c

  6. Bulk flow terms - Bulk momentum flow Fictitious Forces Moving with ion fluid Ist velocity moment of this yields VFP equation for “flux” component f1 [ Chris Ridgers’ PhD project ] (4)

  7. B=0 nonlocal heat wave B=12T local heat wave • Strong B-field  expected to “localize” Te (eV) lmfp rge wt >> 1 means krge << klmfp LASER D ~ l2mfp / t  D ~ r2ge / t Radius (mm) Using IMPACT with MHD to model magnetized transport experiments 1, 1J, 1ns laser beam • Experiment of D. Froula (LLNL), G. Tynan (UCSD) and co. N2 gas jet 2, 1J, 200ps probe beam - Thompson scattering • Effect of B-fields on non-local transport in hohlraum gas-fill context • No B-field: k lmfp > 0.03 non-local [ Tynan et al. submitted to PRL ] [ Divol et al. APS2006 Z01.0014 ]

  8. “Bottling up” of Te for wt>1 seen in VFP simulation too No B-field 12T B-field 200 mm • Simulations start at Te=100eV + heating via inverse bremsstrahlung • See “bottling up” of temperature in VFP sims with B-field • 1D problem with cylindrical symmetry  code 2D Cartesian so do 2D calc

  9. VFP suggests heat flow is marginally non-local at 12T Radial heat flow

  10. VFP code successfully moving plasma & B-field wt electron pressure blowing out plasma • Magnetic Reynold’s # large  resistive diffusion small • B-field convecting with plasma… • … Nernst covection responsible for majority of central B-field reduction

  11. Allowing for plasma motion affects evolution Te(r) Heat flow - |q| (r) e Bz(r) / meteio with hydro w/o hydro • Simulations starts at Te= 20eV • B = 12T

  12. n , T rcrit r qRL rq B  (T)q (n) r • Could be susceptible to n x T B-fields? qRL rq B  (T)r  (n)q rn  Radial Te & Lateral ne gradients ? qT rT r Lateral Te & Radial ne gradients ? qn r “What does the gold cone do to thermal transport in the vicinity of ncr in the adjacent shell?” • Focusing on critical surface 0.25 ncr < ne <4 ncr

  13. Peak heating: ~8 keV / ns I ~1.5 x 1014 W/cm2~ 4 x10-4 (neTeo/ tei)cr 24 log10( n/ncr , Z) ne 4 Heating Rate log10( ne /cm3 ) 22 Z Te / keV ni y / lmfp Gold cone: Lni ~ 80mm Z ~ 50 Te ~ 3 keV !!! 2 20 r / mm r / mm y / mm 0 0 4000 4000 x / lmfp Simulation set up – region from 0.25 ncr < ne < 4 ncr • DRACO ‘snapshot’ of ne(r,q) , Te(r,q), dU(r,q)/dt used as init. cond. for IMPACT [ … as used in APS talk on PDD. DRACO data courtesy Radha & McKenty ] Radial densprofile lei = 5.5 mm Radial Te profile tei = 0.17 ps

  14. Simulation details Dx = 2.5 lei (nx = 56) fixed x-bc Dy = 7.5 lei (nx = 40) refl. y-bc Dt = 0.5 tei B-fields strong enough to magnetize plasma develops via n x  T wt t = 85ps wt ~ 1.3 t = 500ps y / lmfp x / lmfp (n)r  (T)q (n)q (T)r log10(ne) lei = 5.5 mm tei = 0.17 ps

  15. Flattening due to Righi-Leducheat flow fromB-field (?) t = 1ns t = 85ps (n)r  (T)q Lowering due to Righi-Leducheat flow fromB-field (?) with B-field with B-field (n)q (T)r no B-field no B-field Large heat capacity -1 T5/2 (Z lnL) • Virtually no change in Te in cone  k~ Low thermal cond. 1 + c1 (wt)2 B-field does affect lateral Te profile dTe = Te(y) - Tey at ne = 2 ncr t = 8.5ps dTe / eV with B-field no B-field y / lmfp

  16. Braginskii heat flow Classical heat flow into cone up to 4x too large qx qy t = 0.5ns y / lmfp VFP heat flow x / lmfp Units qfso= neo mevTo3

  17. B-field alters lateral heat flow in VFP sims qy – with B-field t = 500ps qy – B=0

  18. Transport & B-field generation on outside wall of cone during CGFI implosion • Preliminary results B-field of wt > 1in 0.5ns  flattens lateral Te profile next to cone (beneficial?)  lateral heat flow non-local Au too hotLn to large?  no radiation transp., ionization (yet) + • Future: use enhanced code + working on adding f2 + f3 Conclusions • IMPACT (VFP code) + MHD moving plasma + B-field in 2D • Fielded on Froula & Tynan’s experiment; B-field suppr. of non-local effects  still some non-locality at 12 Tesla B-field cavity, primarily due to Nernst advection

  19. Simulation: Teo = 100eV (Au), 500eV (shell) T = 17ps Radial dens. gradient ~ 3x shorter than before Lni ~ 20mm

  20. No flux limiter used in classical simulation --> dTe(y) smaller --> less B-field • Collapse of dTe(y) outweighs tendancy for Braginskii to overestimate E ? VFP predicts 5x larger B-field than with Classical sim • Used an equivalent non-kinetic transport simulation • Solves 1) Elec. energy equation 2) Ohm’s law 3) heat-flow eqn 4) Ampere-Maxwell 5) Faraday’s law • Transport coeffs. k, b, a [ Epperlein & Haines, Phys. Fluids 29, 1029 (1986) ] Classical VFP t = 510ps Bz

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