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Electron transport in the shock ignition regime Tony Bell University of Oxford Rutherford Appleton Laboratory Acknowledgements: Guy Schurtz, Xavier Ribeyre et al (CELIA, Bordeaux) Robert Kingham, Alex Robinson, Mark Sherlock (Imperial/RAL) Michail Tzoufras (Oxford/RAL) Key papers: Betti et al PRL 98 155001 (2007) Theobald et al Phys Plasmas15 056306 (2008) Ribeyre et al PPCF (in press)

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Shock ignition Compress target on low isentrope Final laser spike launches ignition shock Figures from: Betti et al (2008) JPhys conf series 112 022024 Pressure (Gbar)

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Starting point: work at CELIA on off-axis drive Does electron transport increase symmetry? Benefits of going to higher laser intensity (‘fast shock ignition’) Ribeyre et al PPCF 51 015013 (2009)

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Gitomer et al Phys Fluids 29 2679 (1986) I 2 =10 16 Wcm -2 m 2 : T~10-30keV I 2 =10 17 Wcm -2 m 2 : T~10-100keV Fast electrons produced by ignition pulse Beg et al 1997: T hot = 100 (I 2 /10 17 Wcm -2 ) 1/3 keV Can heat with 100keV electrons without excessive preheat Pressure at critical: 0.32 (T/10keV) (n e /10 22 cm -3 ) Gbar need strong shock convergence high T at critical Pressure in core: 800 (T/5keV) (n e /5x10 25 cm -3 ) Gbar Fast electron range Betti et al PRL 98 155001 (2007): Ignition shock pressure ~ 1Gbar Laser spike: ~ 6x10 15 Wcm -2, 47kJ, 540TW, 100-300psec, 3 10% 100keV electrons from instabilities - beneficial

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Explore shock ignition driven by high energy electrons using KALOS electron transport code

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Features of non-local transport: Reduced heat flow for scalelengths < 30 x mfp (‘flux limiter’) Increased heat flow at base of heat front Heat flow at angle to T Magnetic field where n x T = 0 mfp of 10keV electron at critical density ~ 80 m ( laser =0.33 m) transport is non-local Non-local electron transport

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deflected heat flow Non-local mag feld Epperlein et al (1988) Heat flow at angle to - T Extra heat flow at base of heat front Nishiguchi et al (1992) Kingham & Bell (2002) Reduced heat flow L < 30 mfp Bell et al (1981)

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Other ‘non-(non-local)’ effects Borghesi et al (1998) n x T source of magnetic field Guerin et al PPCF 41 285 (1999) Resistive electric field inhibition with collisions without collisions

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Electron transport model requirements Kinetic: non-Maxwellian, anisotropic Energy range: 100 eV – 100 keV Density range: less than critical – more than solid Collisional to collisionless Magnetic field Implicit on electron plasma frequency timescale Unified treatment of thermal (0.1-30keV) with hot (10-1000keV) electrons

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KALOS code Expand velocity dist n in spherical harmonics f(x,y,v, , ,t) = f nm (x,y,v,t) P n |m| (cos ) e im Any degree of anisotropy by expanding to any order Without collisions operates as efficient Vlasov code Collisions and B easily included E calculated implicitly Equations simple – efficient despite small explicit timestep velocity coordinates in 3D Kinetic a Laser-plasma o Simulation PPCF 48 R37 (2006)

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collisions magnetic field advection electric field

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20 grid-points in magnitude of momentum Spherical harmonics up to 10 th order No collisions ExB drift & rotation KALOS as a pure Vlasov code

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pxpx pypy 20 grid-points in magnitude of momentum Spherical harmonics up to 10 th order No collisions ExB drift & rotation 0 0

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pxpx pypy 0 0 After nearly one rotation

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Tests: Collisions Advection Electric field Reproduce Spitzer conductivity KALOS as a Fokker-Planck code Uses an approximate electron-electron collision term

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Epperlein & Haines Phys Fluids 29 1029 (1986) KALOS time-dependent calculation for T proportional to sin(kx) x x x x Comparison with Spitzer conductivity x Spitzer applies in limit of: long scalelength small temperature variation steady state (long times)

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Simulations to test effect of varying hot electron temperature Parameters relevant to possible expts (not fusion targets)

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n=10 22 cm -3 100 micron T=3keV T=150eV Initial conditions at start of ‘ignition pulse’ density temperature Cylindrical target Polar drive, absorbed intensity = 8x10 16 cos 2 Wcm -2 Absorption at n = 10 22 cm -3 Constant for 32psec T hot =100keV n=3x10 23 cm -3 n=5x10 21 cm -3

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Electron pressure (Mbar) 800 0 t = 0 psec

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Electron pressure (Mbar) 800 0 t = 32 psec P max =640Mbar at edge of high density lower pressure at absorption surface symmetric pressure central preheat (but not for fusion R) coronal heating

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n=10 22 cm -3 100 micron T=3keV T=150eV Reduced intensity: initial conditions density temperature Cylindrical target Polar drive I absorbed = 8x10 15 cos 2 Wcm -2 Absorption at critical: n = 10 22 cm -3 Constant for 28psec T hot =10keV n=3x10 23 cm -3 n=5x10 21 cm -3

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Electron pressure (Mbar) 400 0 t = 28 psec Polar drive I absorbed = 8x10 15 cos 2 Wcm -2 T hot =10keV

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Electron pressure (Mbar) 400 0 t = 28 psec Polar drive I absorbed = 8x10 15 cos 2 Wcm -2 T hot =10keV Pressure lower by only 50% Less energy into corona Less energy into core: Stronger shock Less symmetric Lack of symmetry compensated for by hydro? (Ribeyre et al)

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n=3x10 23 cm -3 n=5x10 21 cm -3 n=10 22 cm -3 100 micron T=1keV T=50eV density temperature Cylindrical target Polar drive I absorbed = 1.5x10 15 cos 2 Wcm -2 Absorption at n = 10 22 cm -3 Constant for 32psec T hot =3keV Further reduce intensity & larger scalelength larger scalelength

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Electron pressure (Mbar) 80 0 t = 32 psec Polar drive I absorbed = 1.5x10 15 cos 2 Wcm -2 T hot =3keV Large pressure asymmetry Much lower pressure in core Max pressure occurs at critical

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-0.16 to 0.85 MG Magnetic field Electron pressure up to 330 Mbar Electron density 0.5 to 30x10 22 cm -3 Q radial -6.7x10 15 to.3x10 15 Wcm -2 Q theta -2.5x10 15 to 4.5x10 15 Wcm -2 |Q Spitzer | up to 41x10 15 Wcm -2 I absorbed = 8x10 15 cos 2 Wcm -2, T hot =10keV, t=28psec More details of calculation at intermediate intensity

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Electron densityElectron pressure Heat flow into target I absorbed = 8x10 15 cos 2 Wcm -2, T hot =10keV, t=28psec Planar target 5x10 21 cm -3 3x10 23 cm -3 240 Mbar 120 Mbar (T=250eV) 5x10 15 Wcm -2 3x10 15 Wcm -2 300 m 75 m Magnetic field 480 kG Electric field along surface 3x10 7 Vm -1 Heat flow along surface

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Conclusions Energetic electrons are useful: Deposit energy at high density - giving high pressure Spread energy around target allowing uneven irradiation Preheat not a problem Crucial parameter: electron range compared with ablation scalelength & target radius Prospect of integrated simulation of transport expts relevant to shock ignition

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