suprathermal electron pressure and k generation
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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
Identifying Marker. 2
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
Identifying Marker. 3
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.
Identifying Marker. 4
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
Identifying Marker. 5
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
Identifying Marker. 6
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)
Identifying Marker. 7
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
Identifying Marker. 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 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
Identifying Marker. 9
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
Identifying Marker. 10
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
Identifying Marker. 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
mass
Ion number*hot electron density
Surface micron injection
Volume injection
Identifying Marker. 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
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