Suprathermal electron pressure and K  generation

1. Suprathermal electron pressure and K generation Presented to: International Fusion Science and Applications Conference Kobe,Japan Max Tabak Lawrence Livermore National laboratory September 13,2007

2. Are there parasitic channels that have been neglected in previous analyses of Kexperiments? • The superthermal pressure can directly couple the kinetic energy of hot electrons to bulk motion via ambipolar fields • Plasma motion approximately given by self-similar solution with sound speed given by: cs=(ZTHot/m nh/ne)1/2 • This process leads to the well-known proton acceleration • Lasnex was used to model this process • 1D Fokker-Planck treatment with lowest order moments(MG relativistic collisional electron diffusion) (Kershaw,1979) • Similar to treatment Glinsky(1995) used to model proton acceleration • First prediction of • Compared collisionless results with recent work by Mora

3. 100 80 500J, 1 PW Laser 200 to 800 mm Al 50 mm Mo 2 mm CH 0.5 ps 0.7 – 1.0 PW 60 50 40 30 5 ps 60 TW 20 20 ps 0.5 ps 20 TW 5 ps 20 ps 10 2 4 6 8 2 4 6 8 2 4 6 8 1018 1019 1020 1021 Laser intensity(W/cm2) -2 Laser intensity ( I ) [W cm ] Mo Ka Previously published results show high conversion efficiency from laser light to hot electrons Conversion* efficiency(%) Coupling may actually be higher--analysis does not yet include self-consistent E,B fields But K yields from recent experiments imply lower coupling *K.Yasuike,et.al.,Rev.Sci.Inst 72,1(2001)1236.

4. We studied the expansion of a thin slab where the electrons had a two temperature distribution Mora,(PRE 72,056401) Lasnex collisionless V(108cm/sec) (cs0~5.8) We can now use Lasnex to predict K production from a thin slab

5. 10 5 0 Now turn on e-I collisions and Lee-More conductivity • When injecting from a preheated surface,this model shows significant transport inhibition. • Need runaways? • Electron spectrum?Angular Dist? • Diffusion treatment not good enough? • Less important for low mass exps Inject hot electrons uniformly in slab Ti or cu r~30-80m Beg and Yasuike scalings assumed z~1-30m 60J z=1m 12.5J 400 keV e- Kinetic energy(J) .7 ps Potential(keV) z=1m 10 ps drive z(cm) Lagrangian mass(g)

6. We post-processed LASNEX distribution functions to produce K emission rates K(from Hares’ thesis and Green and Cosslett(1961): ~ (E EK)-1log(E/EK) And  is the fraction of radiative decay EK(eV) PKkeV/s) t(10-8s)

7. The K cross section for Cu

8. We made 1D Lasnex models of 10ps(Akli) and 0.7ps(Theobald) exposures We assumed the intensity dependent coupling efficiency found in Yasuike and ponderomotive scaling for the electron energy Because the electrons spread from the laser spot we varied the electron spot radius trying to be consistent with images if available The hot electrons were usually sourced uniformly(by mass) into the slabs over the irradiation duration. Sometimes the energy was injected into a 1 micron thick surface layer The simulations were forced to be 1-D(the sides of the slabs were held). If the sides were released, more hydrodynamic work was done and the Kradiation was reduced Cold K cross sections were used. We ignored rate reductions due to L or K shell being burned out. Simulations were run freezing or allowing hyhdrodynamics

9. Modeling hot electron driven hydrodynamic expansion produced good agreement between model and experiment for the 10 ps exposures *inject into outer micron

10. Shorter exposures in thick slabs have worse agreement *energy loaded into surface micron ;**surface 1/2 micron Experiment 629 produces less radiation than 628, although there is 3 times as much laser energy Superthermal driven expansion is less important in thicker slabs--closer to hydro-off case Relying on transport to reduce hot electron flow into the interior improves agreement

11. Why is there less Kradiation in surface driven slab even though there is less parasitic hydro? The density of hot electrons is reduced by the expansion =>The flux of hot electrons incident on any given ion is reduced Volume injection Surface micron injection Ion number*hot electron density mass

12. What can explain the good agreement for thin targets driven for long duration and poor agreement for thick targets driven quickly? • Transport • Assumption that hot electron transport can be ignored and we can assume that the hot electrons are deposited uniformly into the slab is no longer adequate • When slabs are driven by sources that deposit the hot electrons at the critical surface, the electrons do not cross the thickness of the slab of the Theobald experiment during the irradiation period. • N.B. Remember caveats about Lasnex model • A mystery • Analysis of Yasuike experiment used ITS(MC collisional code) to model K emission and ignored transport inhibition • Why did that experiment report such high absorption fractions even for sub-picosecond irradiations? • In apparent contradiction with more recent experiments