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Recent Developments in Vlasov-Fokker-Planck Transport Simulations for IFE Capsule Compression

This study focuses on the advancements in transport simulations, exploring effects of magnetic fields on heat flow, plasma motion, and radial gradients during compression in IFE capsules. The research findings indicate complexities in classical transport, especially with high-intensity magnetic fields.

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Recent Developments in Vlasov-Fokker-Planck Transport Simulations for IFE Capsule Compression

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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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