suprathermal electron pressure and k generation

This work was performed under the auspices of the U.S. Department of Energy by the University of CaliforniaLawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.

Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-0808

Identifying Marker. 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


Are there parasitic channels that have been neglected in previous analyses of Kexperiments?

•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


Previously published results show high conversion efficiency from laser light to hot electrons

500J, 1 PWLaser

200 to 800 m Al 50 m Mo

2 mm CH

Mo K

Coupling may actually be higher--analysis does not yet include self-consistent E,B fieldsBut K yields from recent experiments imply lower coupling

Laser intensity (I ) [W cm-2

]

Conversion* efficiency(%)

1019 1020 10212 4 6 8 2 4 6 8 2 4 6 8

1018

0.5 ps

5 ps

20 ps

20 ps20 TW

5 ps60 TW

0.5 ps0.7 – 1.0 PW

10

20

30

40

50

60

80

100

Laser intensity(W/cm2)

*K.Yasuike,et.al.,Rev.Sci.Inst 72,1(2001)1236.


We studied the expansion of a thin slab where the electrons had a two temperature distribution

V(108cm/sec) (cs0~5.8)

Mora,(PRE 72,056401) Lasnex collisionless

We can now use Lasnex to predict K production from a thin slab


Now turn on e-I collisions and Lee-More conductivity

Inject hot electrons

uniformly in slab

Ti or cu

r~30-80m

z~1-30m

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

10

5

0

Kinetic energy(J)

Lagrangian mass(g)

12.5J 400 keV e-

Beg and Yasuike scalings assumed

z=1m

z(cm)

Pot

entia

l(keV

)

10 ps drive

60Jz=1m.7 ps


We post-processed LASNEX distribution functions to produce K emission rates

€

dProbKαdt

= dEhotdVσ Kvhotd2NhotdVdEhot

∫∫ dN iondV

K(from Hares’ thesis and Green and Cosslett(1961):~ (E EK)-1log(E/EK)And is the fraction of radiative decay

EK(eV)

PKkeV/s)

t(10-8s)


The K cross section for Cu

€

= f /(1+ f )

f = (aa+ bb ⋅Z + cc ⋅Z 3)4 ,where

aa = 0.015,bb = 0.0327,cc = −0.64e −6,Z = 29

EKi = 8.979(keV ),EKα = 8.012(keV )

σ K =7.9e −20 ⋅ccc1/2mev

2

1.

EKilog

EeEKi,where

ccc = 0.85 + 0.0047 ⋅Z


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 Kradiation was reduced

Cold Kcross sections were used. We ignored rate reductions due to L or K shell being burned out.

Simulations were run freezing or allowing hyhdrodynamics


Run# Thot

(keV)

Dt(ps) Dz() Dr() Elas

(J)

E elec

(J)

Direct Hydro(J)

Kyield

(keV)

Exp

keV

625c 400 10 1 50 75 12.5 0 4.1e14 6e13

625b 400 10 1 50 75 12.5 9.4 8.2e13 6e13

626c 400 10 1 30 75 12.5 0 3.4e14 6e13

626d 400 10 1 30 75 12.5 9.2 7.4e13 6e13

627c 400 10 1 20 75 12.5 0 3.1e14 6e13

627d 400 10 1 20 75 12.5 10.2 5.7e13 6e13

628e 400 10 10 20 75 12.5 0 4.e14 3e14

628f 400 10 10 20 75 12.5 4.9 2.6e14 3e14

628g* 400 10 10 20 75 12.5 5. 1.5e14 3e14

Modeling hot electron driven hydrodynamic expansion produced good agreement between model and experiment for the 10 ps exposures

*inject into outer micron


Run# Thot

(keV)

Dt(ps) Dz() Dr() Elas

(J)

E elec

(J)

Direct Hydro(J)

Kyield

(keV)

Exp

keV

629c 400 .7 20 80 200 40 12.8 1.9e15 2.1 e14

629d* 400 .7 20 80 200 40 21.8 1.1e15 2.1e14

630p 1300 .7 20 35 200 60 0 2.3e15 2.1e14

630q 1300 .7 20 35 200 60 27 1.4e15 3.e14

630r* 1300 .7 20 35 200 60 41 6.2e14 3.e14

631i* 4000 .7 20 25 200 120 71 3.6e14 3.e14

631k** 4000 .7 20 25 200 120 80 2.6e14 3.e14

631j 4000 .7 20 25 200 120 88 1.2e15 3.e14

Shorter exposures in thick slabs have worse agreement

*energy loaded into surface micron ;**surface 1/2 micronExperiment 629 produces less radiation than 628, although there is 3 times as much laser energySuperthermal driven expansion is less important in thicker slabs--closer to hydro-off caseRelying on transport to reduce hot electron flow into the interior improves agreement


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

mass

Ion number*hot electron density

Surface micron injection

Volume injection


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

suprathermal electron pressure and k generation

Documents