a Numerical study of K energetic charged particles · 2005. 10. 5. · Ground & Singly excited ions 1s-vacant ions Cl8+: 1s22s22p5, 1s22s22p4nll Population kinetics modeling on K

T. Kawamura1, H. Nishimura2, F. Koike3, T. Johzaki2, Th. Schlegel4,5,D. H. H. Hoffmann4,5, K. Horioka1

1Tokyo Institute of Technology, Yokohama, Kanagawa, Japan2Institute of Laser Engineering, Osaka University, Osaka, Japan3Physics Laboratory, School of Medicine, Kitasato University, Kanagawa, Japan4Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany5Gesellschaft für Schwerionenforschung, Darmstadt, Germany

U.S.-Japan Workshop onHeavy Ion Fusion and High Energy Density Physics28(Wed.)-30(Fri.) September, 2005,Utsunomiya University.

Numerical study of Kaaaa radiation from high density plasma byenergetic charged particles

Motivation & Outline

In the fast ignition research,fast electrons play an essential role in the viewpoint of energy transport.

With the use of Kaaaa radiation,

1.) Distribution of Kaaaa spectra gives bulk-plasma temperature information. Fast electrons contribute to ionize the K-shell. Cold bulk electrons mainly ionize the outer-shell bound electrons.

2.) Potentiality of sub pico-second x-ray source.

Outline

Motivation

1.) Present status of development of the corresponding kinetics codefor fast ignition research with CHCl plastic targets.

2.) Consideration of Kaaaa radiation by energetic heavy ions.

Related papers:T. Kawamura, et al., PRE, Vol.66, 016402,(2002)H. Nishimura, et al., JQSRT, Vol.81, pp. 327,(2003), Erratum:Vol87,pp.211,(2004)T. Kawamura, et al., JQSRT, Vol.81, pp. 237,(2003)IFSA2003 proceedings, pp.1022,(2003)

Tokyo Institute of Technology

1s-vacant ionsGround & Singly excited ions

Cl8+ : 1s22s22p5, 1s22s22p4nllll

Population kinetics modeling on Kαααα emission.1s-vacant ions are created via inner-shell ionizationby fast electrons.

Radiative & Auger decays

Population : PGnd & PExc P1s-vacant>>


Cl10+ : 1s22s22p3, 1s22s22p2nllll

••

Recombination & Ionization

••




••

••

Recombination & Ionization

Recombination & Ionization Radiative & Auger decays

Radiative & Auger decaysRecombination & Ionization

Inner shellionization

DielectronicCapture


1011

1012

1013

1014

1015

2600 2650 2700 2750 2800Emission Energy(eV)

Rad

iati

ve D

ecay

Rat

e(1/

sec)

HeααααCl14+

Cl12+

Cl13+Cl11+

Cl10+Cl9+Cl1+

Cl8+-

Transition energies and radiative decay rates for Kαααα lines ofpartially ionized chlorine atoms are calculatedwith GRASP-code.

Cl+ : 1s22s22p53s23p5-1s2s22p63s23p5

Cl2+ : 1s22s22p53s23p4-1s2s22p63s23p4

Cl8+ : 1s22s22p5-1s2s22p6

Cl9+ : 1s22s22p4-1s2s22p5

Cl10+ : 1s22s22p3-1s2s22p4

Cl11+ : 1s22s22p2-1s2s22p3

Cl12+ : 1s22s22p -1s2s22p2

Cl13+ : 1s22s2 -1s2s22pCl14+ : 1s22s -1s2s 2pCl15+ : 1s2 -1s 2p (Heαααα)

∆∆∆∆E from primary Kαααα (Cl+)is large!!

Information of Plasma Temperature can be obtained.


Number of transitions of 1s2s22pNnllll(n=3-4,N=1-5)are 15100.

Kαααα transition rates are 1013-1014 1/sec.

Kαααα-lines of excited states completely overlap withthose of the ground state of the next charge state.

1014

2600 2650 2700 2750 2800

1013

1013

1013

1013

1013

1013

1014

1014

1014

1014

1014

Cl10+ : 1s2s22p4

Cl10+ : 1s2s22p33

Cl11+ : 1s2s22p3

Cl11+ : 1s2s22p23

llll

llll

Cl10+ : 1s2s22p34llll

Cl11+ : 1s2s22p24llll

Rad

iaiv

e D

ecay

Rat

e(1/

sec)

Emission Energy(eV)


1013

1014

1015

1016

0

0.05

0.1

Ave

rag

e A

ug

er R

ate

(1/s

ec)

Flu

orescen

ce Yield

Charge State

KLL AugerKLM Auger

8 9 10 11 121012

1013

1014

1015

1016

0

0.2

0.4

0.6

0.8

0 5 10 15F

luo

rescence Y

ield

Charge State

Ave

rag

e A

ug

er R

ate

(1/s

ec) KLL Auger

KLM AugerKMM Auger

KLL-Auger is the most dominant process of all the Augertransitions for 1s-vacant ions.

Each Auger transition is calculated by "Auger code".S.Fritzsche, B.Fricke, Phys. Scr.T41,45(1992)

Average Auger rate of partially ionized Cl is about 1014-1015 1/sec.

Excited states of 1s-vacant ions:1s2s22pN3llll(N=1-5, llll=s,p,d)

Ground states of 1s-vacant Ions


0

4

8

12

16

101 102 103

C:H:Cl=Fast Electron:

Ion Density:A

vera

ge

Ion

izai

ton

Sta

te

Bulk Electron Temperature(eV)

Fraction ofFast Electrons5%:1%:0%:

9X1022c m-3

1:1:1100keV

Average charge state is mostly governed by bulk electrontemperature.

Total Ion Density : 9X1022cm-3

Bulk e- : Fast e- = 99:1(C:H:Cl = 1:1:1)

6.0

6.1

6.2

6.3

103 104 105

8.1

8.2

8.3

8.4

103 104 105

7.0

7.1

7.2

7.3

103 104 105

Bulk Electron:

C:H:Cl=Bulk:Fast=

Ni=9X1022c m-3

Ni=9X1022c m-3

Fast Electron Temperature (eV)

Ave

rag

e Io

niz

atio

n S

tate

Ni=9X1022c m-3

75eV99:1

1:1:1

Bulk Electron:

C:H:Cl=Bulk:Fast=

100eV99:1

1:1:1

Bulk Electron:

C:H:Cl=Bulk:Fast=

50eV99:1

1:1:1

No Opacity effect


Inte

nsity

( x10

7 erg/

sec/

cc/H

z )

0

1.0

1.5 Cl9+

(Ground)

Cl8+

(n=3)Cl

8+(n=4)

Cl10+

(Ground)

Cl9+

(n=3)Cl

9+(n=4)

Cl11+

(Ground)Cl

10+(n=4)

Cl10+

(n=3)

Cl12+

(Ground)

Cl11+

(n=3)Cl

11+(n=4)

Bulk Temperature : 100 eVPlasma thickness : 0.1 µµµµm

0.5

Cl13+

(Ground)

Cl12+

(n=3)Cl

12+(n=4)

2.0

TotalGround StateExcited States(n=3)Excited States(n=4)

Inte

nsi

ty(

x107 er

g/s

ec/c

c/H

z )

0

1.0

1.5 Cl9+

(Ground)

Cl8+

(n=3)Cl

8+(n=4)

Cl10+

(Ground)

Cl9+

(n=3)Cl

9+(n=4)

Cl11+

(Ground)Cl

10+(n=4)

Cl10+

(n=3)Cl

12+(Ground)

Cl11+

(n=3)Cl

11+(n=4)


0.5

2.0

Satellites of excited states Cl(n-1)+ overlap withparent lines of ground states Cln+.

Fast Electron Temperature : 40 keV, Bulk e-: Fast e- = 99:1Ion Density Ni=9x1022cm-3 (C2H3Cl)

2640 2660 2680 2700 2720 2740 2760

Inte

nsi

ty(

x107 er

g/s

ec/c

c/H

z )

1.0

1.5

Emission Energy(eV)

Cl9+

(Ground)

Cl8+

(n=3)Cl

8+(n=4)

Cl10+

(Ground)

Cl9+

(n=3)Cl

9+(n=4)

Cl11+

(Ground)Cl

10+(n=4)

Cl10+

(n=3)

Cl12+

(Ground)

Cl11+

(n=3)Cl

11+(n=4)


0.5

Cl13+

(Ground)

Cl12+

(n=3)Cl

12+(n=4)

2.0


ILE OSAKA

Experimental setup on T6

T6 laser:@ 800 nm, ####100 mJ (on T)132 fs, P-pol.S= 15x21 µµµµm @ 70%contrast >10 -6

IL=2x1017 W/cm2 (Th=50 keV)

2D curved crystal spectrograph1:

Quartz [10.-1], 2d=6.6864 A

εεεε=2.44-2.85 keV, M= 1/8

1D curved crystal spectrograph2:PET[002], 2d=8.742 Aεεεε=1.48-1.73 keV, M=1

x-ray CCD

45 deg

d (µµµµm)

A B 200µµµµm

A d (µµµµm) B

target 1 CH 0~2 CHCltarget 2 Mg 0~2.2 Al

x-ray

9 µµµµm

(a)

(b)

spot-size

H.Nishimura, et al., JQSRT, Vol.81, pp.327, (2003)Erratum : Vol.87, pp.211, (2004)

photon energy (eV)

2600 2700 28002650 2750 2850

PVC-bare

PVC+ Pa 0.12 um

inte

nsity

(a.u

.)

ClK

αααα Cl

9+

Cl

(N-li

ke)

10+

Cl

(C-li

ke)

11+

Cl

(B-li

ke)

Cl

(Be-

like)

Cl

(Li-l

ike)

12+

13+

14+

Cl

(He

αααα )15

+

ClK

ββββ

experimental result 1

ILE OSAKA

The Kαααα lines from partially ionized plasma decease drastically withincrease in thickness of over-coatin g, inferrin g energy localization.

H.Nishimura, et al., JQSRT, Vol.81, pp.327, (2003)Erratum : Vol.87, pp.211, (2004)

Ion density(C2H3Cl) : Solid densityFast electron temperature : 50 keVIncident laser energy absorption : 15%

Assumptions:

Bulk electron temperature : 140 eVLife-time of fast electron : several ps

Result:

Neglecting advection term in the F-P equation.

Time evolution of bulk electron temperature and fractional number of fastelectrons are obtained from Fokker-Planck code.- Simulation was done in the region near target surface. -

Local deposition near target surface.Heat transport in the axial direction is inhibited.

10- 3

10- 2

10- 1

100

Bu

lk E

lect

ron

Tem

per

atu

re (

eV)

Time (ps)1.0 2.0

50

150

100

0 3.0 4.0 5.0 6.0 7.0

laser pulse


Time dependent properties of Kαααα radiation combined with Fokker-Planckcode are obtained.- Simulation was done in the region near target surface. -

0 0.5 1 1.5 2 2.5 3

Inte

gra

ted

Kαααα

Inte

nsi

ty

Time (ps)

(x1

017 e

rg/s

ec/c

m2)

2.0

1.5

1.0

0.5

laser pulse

Cl9 +

Cl1 0 +

Cl1 1 +

Cl1 2 +

Cl1 3 +

Cl8 +

0 1 2 3 4 5Time (ps)

0.2

0.15

0.1

0.05

laser pulse

Cl1 3 +

Cl1 4 +

Cl1 5 +

(Heαααα)

X 10


Comparison between simulation and experiment is madein the framework of intensity ratio for time-integrated data.

2.) Intensities of excited states Cln+ are grouped together with that of ground state Cl(n+1)+.

1.) Intensities of Cl+ - Cl8+ are grouped together as cold Kαααα emissions.

Cold Kαααα emission(Cl+ - Cl8+) Hot Kαααα emission

(Cl9+ - Cl15+)

Because of unresolved properties;

Hot Kαααα emissions show good agreement betweensimulation and experiment results.


Consideration of Kα-radiation by ion beams for plasmadiagnosis. With spatial resolved observation of Kα-radiation,plasma heating process can be understood clearer than thetraditional way of “TOF”.


~100µm

~1cmIon beam

hν hν hν hν hν

High Z plasma

Kα from low charge state Kα from high charge state

Spatial resolved diagnosis of heating process is possible.

For chlorine plasmas, ion energy of more than few tens MeVis necessary to occur the K-shell ionization.


10-22

10-21

10-20

10-19

10-18

10-17

103

104

105

106

107

108

109

Cro

ss S

ecti

on

of

K-s

hell Io

niz

ati

on

(cm

2)

Energy(eV)

e- --> Cl

He2+

--> Cl

Ne10+

--> Cl

Ar18+

--> ClIon impact K-shell ionization:ADNDT, Vol.20, pp.503,(1977)

Electron impact ionization:J. Phys. B: Atom. Molec. Phys.,Vol.11, pp.541,(1978),and related papers.

In the calculation, ion energies are set so that the maximumcross sections can be obtained with the energy-spread of0.1 %, 1%, and 10%.


10-21

10-20

10-19

10-18

10-17

106

107

108

109

K-s

hell Io

niz

ati

on

Cro

ss S

ecti

on

(cm

2)

Energy(eV)

25MeV 150MeV

400MeV

He2+

--> Cl

Ne10+

--> Cl

Ar18+

--> Cl

0 50 100 150 200

Electron Temperature(eV)

Cl6+

Cl5+

Cl4+

K!

em

iss

ion

(W

/cc

)

108

106

104

102

For chlorine plasmas, temperature diagnosis by Kα-radiationwith ion beams is suitable for electron temperature Te < 100 eV .


Kα due to Dielectronic CaptureKα due to the K-shell Ionization by He2+ Impact

He2+ current : 1 kA/cm2

Enegry : 25 MeV (±0.1%)

0 50 100 150 200

K!

em

issio

n (

W/c

c)

Electron Temperature(eV)

Cl7+

Cl8+

Cl9+

Cl10+

1014

1012

1010

108

106

104

For chlorine plasmas, temperature diagnosis by Kα-radiationwith ion beams is suitable for electron temperature Te < 100 eV .


Kα due to Dielectronic CaptureKα due to the K-shell Ionization by He2+ Impact

He2+ current : 1 kA/cm2

Enegry : 25 MeV (±0.1%)

40 50 60 70 80 90 100

Electron Temperature (eV)

K! dominated byInnershell Ionization

Cl9+

Cl10+

Cl11+

Cl9+

Cl10+

Cl11+

Laser-producedfree electrons

(50 keV,Fraction:1%)

1016

1014

1012

1010

108

106

(1kA/cm2

,1GeV:"E=10%)

Kr ions

(1kA/cm2

,1GeV:!E=10%)

40 50 60 70 80 90 100

Electron Temparture (eV)

K"

em

iss

ion

(W

/cc

)

K" dominated byInnershell Ionization

Cl3+

Cl2+

Cl+

Cl3+

Cl2+

Cl+

Laser-producedfree electrons

(50 keV,Fraction:1%)

Kr ions

1014

1012

1010

108

106

104

102

100

Emission density of Kα-radiations is very small in comparisonwith that by fast electrons generated by sub-ps laser pulses.


Kα-radiation by ion beams is about 10-8 of that by LPP-scheme.

To get the same order of Kα-radiation by LPP-scheme,the difference of Kα yield must be covered by a large plasma.


Kα-radiation by energetic heavy ions scheme:

1.) Ionization cross-section: 10~100 times larger than energetic electrons’.

2.) Ion beam density : ~1012 cm-3 at 1 kA/cm2 with He2+ beams. (cf.) Energetic electrons by laser-produced plasma scheme: ~ 1021 cm-3

Resultant plasma volume to get Kα-radiation by Ion beams:1.) Ion beam cross section : ~1cm2

2.) Ion Stopping range : ~100 µmon the assumption that plasma is heated up uniformly.

(cf.) With LPP-scheme :1.) e- beam cross section ~ laser spot size : ~ < 100 µm2

2.) heated depth ( in the T6-experiments ) : ~ < 0.1 µm

--> 10-2 cm3

--> 10-11 cm3

There may be potentiality to get Kα-radiation by ion beams.

Summary & Plans

Population kinetics and spectral synthesis codes of Kaaaa-emission ofpartially ionized Cl atoms has been developed.

Plans

Summary

1.) Code development for fast ignition:--> Code extension to cover polarized x-ray for the diagnosis of velocity distribution function ( in progress now ).

--> Comparing with experimental results, a plasma temperature of 100~150 eV on the target surface is deduced, and showing the potentiality for the generation of sub-ps x-ray.


1.) Present status of development of the corresponding kinetics codefor fast ignition research with CHCl plastic targets.

2.) Consideration of Kaaaa radiation by energetic heavy ions.

Kaaaa radiation by high intense, energetic ( ~MeV, or GeV ) heavy ionbeams may be useful for the diagnosis of heated plasma.

2.) Consideration of Kaaaa radiation by intense heavy ion beams--> To proceed it further for purpose of plasma diagnostics.

Documents

a Numerical study of K energetic charged particles · 2005. 10. 5. · Ground & Singly excited ions 1s-vacant ions Cl8+: 1s22s22p5, 1s22s22p4nll Population kinetics modeling on K