Excitation and Ionisation in High Energy Density Plasmas Steven Rose - - PowerPoint PPT Presentation

Excitation and Ionisation in High Energy Density Plasmas Steven Rose Imperial College London University of Oxford, UK

• Laser-produced plasmas can produce the highest laboratory thermal radiation

fields (i.e. excluding laser fields).

• We consider in these lectures the direct effect of those radiation fields on the

excitation and ionisation of high energy density plasmas (not the indirect effect

• f heating by the radiation field).
• We describe the theory describing excitation and ionisation in HED plasmas,

particularly the contribution from the radiation field.

• We discuss experiments which test models with little or no radiation field, with

a narrow-band radiation field and with a broad-band radiation field.

• We finish with some recent work that links laboratory HED plasmas with

astrophysical plasma physics and spectroscopy.

• Conclusions

Overview

(energy in a Planckian radiation field)/(total energy)

4 4

aT T C aT

V energy

+ = ρ ε

(pressure from a Planckian radiation field)/(total pressure)

rad mat rad pressure

P P P + = ε

free electrons ions radiation e-i ff s Radiation interacts with bound electrons through free electrons bound electrons e-i bb bf

free electrons ions radiation e-i ff s bound electrons e-i bb bf Radiation interacts with bound electrons directly

β’ β α

c

R

α β → ′ c

R

β α ′ → c

R

β α→ c

R

α β →

Collisional and radiative rates

α β β’

r

R

β α ′ → r

R

α β → ′ r

R

β α→ r

R

α β →

c

R

α β → ′ c

R

β α ′ →

c

R

β α → c

R

α β →

Collisional rates Electron collisional excitation (~ne) Electron collisional de-excitation (~ne) Electron collisional ionisation (~ne) + Autoionisation Three-body recombination (~ne

2) + Dielectronic recombination (~ne)

Radiative rates

r

R

β α ′ → r

R

α β → ′ r

R

β α→ r

R

α β →

Photoexcitation - stimulated absorption Photo de-excitation – spontaneous and stimulated emission Photoionisation – stimulated absorption Photorecombination (~ne) – spontaneous and stimulated emission

Level of detail describing atomic states

Detailed Configuration Accounting DCA Detailed Term Accounting DTA

Rate equations

∑ ∑

→ → → →

+ + + − =

β α β α β β β α β β α α α

) )( ( ) ( ) ( ) (

r c r c

R R t n R R t n dt t dn

∑

=

α α α e

n t n t Z ) ( ) (

) ( = dt t dnα

The rate equations governing the populations are for each level α which have the constraint and for the case of the system having come to a steady-state

Photo excitation / de-excitation rates

∫

∞ → → =

) / ) ( ) ( ( 4 ν ν ν ν σ π

β α β α

d h I Rr

∫

∞ − → →

+         Ω Ω =

→

/ 2 3

)) ( ) / 2 )(( / ) ( ( 4 ν ν ν ν ν σ π

ν β α β α α β

β α

d e I c h h e R

e

kT h U r e

kT E E U

      →

− = ) ( ) ( α β

β α

        − = 1 ) / exp( 1 ) / 2 ( ) (

2 3 r

kT h c h I ν ν ν

( ) ( )

ν φ π ν σ

β α β α β α → → →

= f mc e2 Both rates involve an integral over the line shape and the radiation field

Photopumping

( ) ( )

ν ν δ ν φ

β α

− =

→

R A n R A n

r ph r ph α β β α β α β α → → → →

= = + ( ) 1

1 1

/

− =

b

kT h ph

e n

ν

β α β α α β

ε π

→ →

Ω Ω = f mc h e A

3 2 2 2 2

8

If photon intensity is roughly constant over the line shape then we can approximate it as a delta function which leads to the radiative excitation and de-excitation rates being

Photoionisation / photorecombination rates

∫

∞ ′ → ′ →

= ) / ) ( ) ( ( 4 ν ν ν ν σ π

β α β α

d h I Rr

∫

∞ − ′ → ′ → ′

+         Ω Ω         =

′ →

/ 2 3 2 / 3 2

)) ( ) / 2 )(( / ) ( ( 2 2 4 ν ν ν ν ν σ π π

ν β α β α α β

β α

d e I c h h e T k m h n R

e

kT h U e e e r

e

kT E E U

      ′ →

− ′ = ) ( ) ( α β

β α

        − = 1 ) / exp( 1 ) / 2 ( ) (

2 3 r

kT h c h I ν ν ν

Both rates involve an integral over the photoionisation cross-section and the radiation field

Radiative rates - no radiation field

∫

∞ − ′ → ′ → ′

        Ω Ω         =

′ →

/ 2 3 2 / 3 2

) / 2 )( / ) ( ( 2 2 4 ν ν ν ν σ π π

ν β α β α α β

β α

d e c h h e T k m h n R

e

kT h U e e e r

α β α β → →

= A Rr

If there is no ambient radiation field only spontaneous de-excitation and radiative recombination remain

No external radiation field – optical depth

R R A g

r r α β β α β α

τ

→ → →

= = ( )

τ π φ ν

α β α α β β 2

= −

→

e mc f n n y ( )( ) Ω Ω φ ν π ν ( ) =

−

1

2

∆

D x

e

x

D

= − ( ) / ν ν ν ∆

∆ν ν

D i

kT m c = ( ) / 2

1 2

But even if no radiation is incident on the plasma from outside, internally generated radiation from transitions can influence the populations. This introduces the photon escape probability

dx e g

x ))

exp( 1 ( 1 ) (

2

− ∞ ∞ −

− ∫ − = τ τ τ

For a Doppler lineshape this is given by Optical depth

) ( 0 τ g

Cauchy (Dirac-Fuchs) mean chord theorem

surface area A volume V For any convex shape, the mean chord length is given by the Dirac-Fuchs theroem as y = 4V/A

Dirac P A M, Technical Report MS-D-5, part I, Public Records Office, Kew (1943). Dirac PAM, Fuchs K, Peierls R and Preston P, Technical Report MS-D-5, part II, Public Records Office, Kew (1943).

600 z0 For a slab geometry, the mean chord length y = 4V/A = 2z0

Level of detail describing atomic states

Detailed Configuration Accounting DCA Average-atom Detailed Term Accounting DTA

Average-atom model

c r n m

c n c

R →

c c n

R →

c r n

R →

c n r

R →

c m n

R →

c n m

R →

c r n m

r n c

R →

r c n

R →

r r n

R →

r n r

R →

r m n

R →

r n m

R →

Collisional and radiative rates

NIMP – equations and solutions − − − + +         − + − − − =

→ →

) ( 1

r n m c n m n n m n

R R P P dt dP ω ) , ,...., ( ) , ,...., (

max 1 max max max 1 1 1

R P P f dt dP R P P f dt dP

n n n n

= = 

max 1,...., n

P P

sum of radiative and collisional rates from shell m to n number of probability of a electrons hole in shell n in shell m solved for screened-hydrogenic excitation and ionisation energies, collisional and radiative rates used

Reconstruction of individual level populations from the average shell populations

i n i i i i n i i i i i i i

P P n n P

−

        − ∏         − =

ω

ω ω ω ω α 1 ! )! ( ! ) (

( )

) ( ! )! ( ! / 1 2 ) ( α ω ω P n n J a P

i i i i a

              − + =

From the average populations (P1,….,Pnmax) the fraction of ions in a real configuration α(n1,….,nnmax) can be calculated assuming that the orbitals are not statistically correlated The fraction of ions in level a, degeneracy 2Ja+1, which is derived from the configuration α, is then

Photoionisation cross sections

FeXXIII (1s22s2) FeXXIV (1s22s)

dt dP

n

dt dP

m

dt dP

g

) ( mn gf W Q Q P Z

dr n m g

→

∗ m g m g

R Q P

→

) ( mn gf W Q Z R

dr n m g

→ =

∗ →

) ( ) ( gf mn W Q P P mn gf W Q Q P Z

a g m n dr n m g

→ = →

∗

• f

___________________________ limit _______________ n _______________ m _______________ g with

detailed balance

Dielectronic recombination / autoionisation rates

• Albritton and Wilson, Phys Rev Letts, 83, 1594 (1999); JQSRT, 65, 1 (2000)

22 23 24 25 26 27 28 29 0.01 0.1 1 B C N O F Ne Na Mg Z

*

fraction DCA - no DR NIMP - no AI/DR DCA - DR NIMP - AI/DR

Comparison of NIMP and detailed (DCA) models with / without DR Se ne=5x1020cm-3, Te=1000eV

Lee, JQSRT, 38, 131 (1987)

Comparison between theory and experiment No or small radiation field

Non-LTE ionisation distribution measurement

Foord, Glenzer, Thoe, Wong, Fournier, Wilson, Springer, Phys Rev Letts, 85, 992 (2000). Foord, Glenzer, Thoe, Wong, Fournier, Albritton, Wilson, Springer, JQSRT, 65, 231 (2000).

Conditions in the gold plasma were characterised by Thompson scattering, radiography and X-ray spectroscopy.

47 48 49 50 51 52 0.0 0.1 0.2 0.3 0.4 Z

*=53.7

Z

*=49.3

Z

*=48.6

Co Ni Cu Zn Ga Ge fraction Z

*

(experiment -Foord et al) (NIMP - AI/DR) (NIMP - no AI/DR)

Charge state distributions for Au ne=6x1020cm-3, Te=2200eV

Charge state distributions for Au ne=1.4x1021cm-3, Te=2600eV

Glenzer, Fournier, Wilson, Lee and Suter Phys Rev Letts, 65, 045002 (2001).

46 47 48 49 50 51 52 53 54 0.0 0.1 0.2 0.3 0.4

fraction Z

*

experiment (Glenzer et al) NIMP (AI/DR), no Tr) NIMP (AI/DR, Tr=210eV) NIMP (no AI/DR, no Tr)

21 22 23 24 25 26 27 28 29 30 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Z

*=26.8

Z

*=25.0

fraction Z

*

experiment (Popovics et al) NIMP (AI/DR) NIMP (no AI/DR) Z

*= 26.5

Charge state distributions for Xe ne=1.3x1020cm-3, Te=415eV

Chenais-Popovics, Malka, Gauthier, Gary, Peyrusse, Rabec-Le Gloahec, Matsushima, Bauche-Arnoult, Bachelier and Bauche Phys Rev E, 65, 046418 (2002).

43 44 45 46 47 48 49 50 51 52 0.00 0.05 0.10 0.15 0.20 0.25 0.30

Z

*=53.2

Z

*= 46.4

fraction

Z

*

experiment (Wong et al) NIMP (AI/DR) NIMP (no AI/DR) Z

*= 47.4

Charge state distributions for Au ne=1012cm-3, Te=2500eV

Wong, May, Beiersdorfer, Fournier, Wilson, Brown, Springer, Neill and Harris, Phys Rev Letts, 90, 235001 (2003).

Ionisation in Au, ne=1021cm-3 with and without a radiation field

Heeter, Hansen, Fournier, Foord, Froula, Mackinnon, May, Schneider and Young Phys Rev Letts, 99, 195001 (2007).

1000 1500 2000 2500 30 35 40 45 50 55

experiment, no Tr experiment, Tr=185eV

Z

*

electron temperature (eV)

AI/DR, no Tr AI/DR, Tr=175eV AI/DR, Tr=190eV no AI/DR, no Tr no AI/DR, Tr=175eV no AI/DR, Tr=190eV

Comparison between theory and experiment Broad-band radiation field Photoionised plasmas

Accretion-powered objects

Photoionised plasmas (radiation- dominated plasmas) scale with the ionisation parameter ξ=4πF/ne

Tarter, Tucker and Salpeter, ApJ, 156, 943,(1969) Tarter and Salpeter, ApJ, 156, 953 (1969)

EXO 0748-676 Low mass X- ray binary ξ=30 ergcms-1 NGC 4593 Seyfert galaxy ξ=300 ergcms-1

Spectral interpretation needs reliable models

β’ α

c

R

α β → ′ c

R

β α ′ →

Ionisation / recombination rates

α β’

r

R

β α ′ → r

R

α β → ′ ai

R

β α ′ → dr

R

α β → ′

Ionisation / recombination rates

r

R

β α ′ → r

R

α β → ′

Electron collisional ionisation (~ne) Three-body recombination (~ne

2)

Autoionisation Dielectronic recombination (~ne) Photoionisation – stimulated absorption Photorecombination (~ne) – spontaneous and stimulated absorption

c

R

β α ′ → c

R

α β → ′

ai

R

β α ′ → dr

R

α β → ′

Ionisation / recombination rates

r

R

β α ′ → r

R

α β → ′

Electron collisional ionisation (~ne) Three-body recombination (~ne

2)

Autoionisation Dielectronic recombination (~ne) Photoionisation – stimulated absorption Photorecombination (~ne) – spontaneous and stimulated absorption

c

R

β α ′ → c

R

α β → ′

ai

R

β α ′ → dr

R

α β → ′

In the limit of high radiation field and low electron density

Photoionised plamsas

) (

e e r

T n n R n

α β β β α α

α

→ ′ ′ ′ →

=

) ( ) / ) ( ) ( ( 4

e e

T n d h I n n

β α β α α β

α ν ν ν ν σ π

′ → ∞ ′ → ′

∫

= ) ( ) / ) ( ) ( ( 4

e e

T d h p n F n n

β α β α α β

α ν ν ν ν σ π

′ → ∞ ′ → ′

∫ =

e

n F π ξ 4 =

Tarter, Tucker and Salpeter, ApJ, 156, 943,(1969) Tarter and Salpeter, ApJ, 156, 953 (1969) r dr e

R R T

α β α β α β

α

→ ′ → ′ → ′

+ = ) (

ignoring stimulated radiative recombination take out shape function p(ν) from the flux F

collapsed Z-pinch pinhole camera flux and spectral measurements absorption spectrum emission spectrum 1000Å CH 500Å NaF/Fe

Experiment on Z-pinch at Sandia generates ξ=20ergcms-1

Foord, Heeter, van Hoof, Thoe, Bailey, Cuneo, Chung, Liedahl, Fournier, Chandler, Jonauskas, Kisielius, Mix, Ramsbottom, Springer, Keenan, Rose and Goldstein, Phys Rev Letts, 93, 055002 (2004)

sample bathed in radiation from pinch over 4πα steradians

5 6 7 8 9 0.0 0.2 0.4 0.6 0.8 1.0

experiment NIMP with radiation field NIMP without radiation field

fraction Z

*

F photoionised plasma ionisation distribution ne=2x1019, Te=150eV, Tr=165eV (α=0.01), ξ=20ergcms-1

Rose, vanHoof, Jonauskas, Keenan, Kisielius, Ramsbottom, Foord, Heeter and Springer, J Phys B, 37, L337 (2004)

6 7 8 9 10 11 0.0 0.2 0.4 0.6 0.8 1.0

experiment NIMP with radiation field NIMP without radiation field

fraction Z

*

Na photoionised plasma ionisation distribution ne=2x1019, Te=150eV, Tr=165eV (α=0.01), ξ=20ergcms-1

Rose, vanHoof, Jonauskas, Keenan, Kisielius, Ramsbottom, Foord, Heeter and Springer, J Phys B, 37, L337 (2004)

Fe photoionised plasma ionisation distribution ne=2x1019, Te=150eV, Tr=165eV (α=0.01), ξ=20ergcms-1

Rose, vanHoof, Jonauskas, Keenan, Kisielius, Ramsbottom, Foord, Heeter and Springer, J Phys B, 37, L337 (2004)

13 14 15 16 17 18 19 0.0 0.2 0.4 0.6 0.8 1.0

fraction Z

*

experiment NIMP with radiation field NIMP without radiation field CLOUDY with radiation field

Z*(Br) in C500H470Br27 0.001gcm-3

Rose, JQSRT (1995)

Z*(Br) in C500H470Br27 0.1gcm-3

C500H470Br27 opacity 0.001gcm-3

Comparison between theory and experiment Narrow-band radiation field Line-coincidence photopumping

Simplified diagram of the Bowen resonance fluorescence mechanism

Bowen, Publ. Astr. Soc. Pac.(1934)

• ptical
• ptical

Astrophysical line-coincidence photopumping and lasing

Johanssen and Letokhov,, Astrophysical Lasers, CUP (2009)

Accidental line coincidences H-like and He-like ions

Alley, Chapline, Kunasz and Weisheit, JQSRT(1982)

Calculation of line coincidences

Na → Ne E(Na; ) - E(Ne; ) Dirac-Fock SCF 0.11eV Dirac-Fock SCF + Breit

• 0.01eV

Dirac-Fock SCF + Breit +QED

• 0.06eV

Experiment

• 0.25eV

1 1 1 2

2 1 1 P p s S s −

1 1 1 2

4 1 1 P p s S s −

Transition energies ~ 1.13keV

1 1 1 2

2 1 1 P p s S s −

1 1 1 2

4 1 1 P p s S s −

Sr → Br E(Sr; ) - E(Br; ) Dirac-Fock SCF 9.0eV Dirac-Fock SCF + Breit 5.1eV Dirac-Fock SCF + Breit +QED 1.9eV Dirac-Fock SCF + Breit +QED + finite nucleus 1.7eV

1 3 1 2

2 1 1 P p s S s −

1 1 1 2

3 1 1 P p s S s −

Transition energies ~ 14.6keV

1 3 1 2

2 1 1 P p s S s −

1 1 1 2

3 1 1 P p s S s −

Rose, JQSRT(1985)

H-like and He-like K / H-like Cl line-coincidence photopumping

Line coincidence photopumping in a laboratory plasma

Beer, Patel, Rose and Wark, JQSRT (2000)

Line coincidence photopumping in a laboratory plasma Modal photon density nph in the frame of the Cl ions at 3.3507Å (Cl 1s1/2 – 4p3/2) at distance x and velocity v(x) at the peak of the laser pulse.

Beer, Patel, Rose and Wark, JQSRT (2000)

Line radiation transport in a velocity gradient

Wark, Djaoui, Rose, He, Renner, Missalla, Foerster, Physical Review Letters (1994)

Line radiation transport in a velocity gradient

Patel, Wark, Renner, Djaoui, Rose, Heading, Hauer, JQSRT (1997)

Experimental evidence for XUV/X-ray line-coincidence photopumping

There are only a few experiments in which line-coincidence photopumping has been demonstrated in the XUV / X-ray range through measurement of enhanced fluorescence: Monier et (1988) Al/Si Back et al (1991) Al/Al O’Neill et al (1990) Mn/F Gouveia et al (2003) Al/Fe One experiment has measured population inversion: Porter et al (1992) Na/Ne There is no experimental evidence for lasing in the XUV or X-ray range through line-coincidence photopumping.

Porter et al, Phys Rev Letts (1992)

Na / Ne line coincidence photopumping scheme

1 1 1 2

2 1 1 P p s S s − Na Ne

Na / Ne line coincidence photopumping scheme

Porter et al, Phys Rev Letts (1992)

Population inversion measured

Sako et al, ApJ (2003)

Proposed astrophysical line coincidence photopumping

XUV

Na / Ne line coincidence photopumping astrophysical scheme

H / He / Ne / Na plasma with astrophysical Ne and Na abundances (0.68637 / 0.3113 / 1.3831x10-4 / 2.9461x10-6)

Na / Ne line coincidence photopumping astrophysical scheme

H / He / Ne / Na plasma with astrophysical Ne and Na abundances (0.68637 / 0.3113 / 1.3831x10-4 / 2.9461x10-6) ne = 1010-1013 cm-3 l = 109 – 1013 cm T

e = 100 – 200 eV

Internal ‘Bowen’ pumping of lines by accidental line-coincidence The radiative excitation and de-excitation rates for the pumped ion are:

( )

) 1 (

ph r ph r

n A R n A R + = Ω Ω =

→ → → → α β α β α β α β β α

n n n

ph =

− 1 1

χ δ δ χ

Ω Ω

‘Bowen’ pumping of transition α→β by χ↔δ (Judge, MNRAS,1988)

Rose, JPhysB (1998)

Porter et al, Phys Rev Letts (1992)

Na / Ne line coincidence photopumping laboratory scheme

Na / Ne line coincidence photopumping astrophysical scheme

82.76Å 81.58Å 233.52Å 224.34Å Keenan et al, MNRAS (2018)

Acton et al, Ap J (1985)

On July 13th 1982 a rocket-borne spectrograph that measured the 10 - 100Å emission from an M- class flare on the Sun with 0.02Å resolution. Spectroscopy of the Sun

Na / Ne line coincidence photopumping astrophysical scheme

82.76Å 81.58Å 233.52Å 224.34Å

In solar flare spectra, the NeIX 224.34Å and 233.52Å lines are blended with the strong FeXIV 224.35Å and OIV 233.55Å features.

Keenan et al, MNRAS (2018)

Na / Ne line coincidence photopumping astrophysical scheme

82.76Å 81.58Å 233.52Å 224.34Å

NeIX 81.58Å line has predicted enhancement which is too small even under optimal conditions to detect the feature.

Keenan et al, MNRAS (2018)

Na / Ne line coincidence photopumping astrophysical scheme

82.76Å 81.58Å 233.52Å 224.34Å Keenan et al, MNRAS (2018)

109 1010 1011 1012 1013 1 10 100 1000

Ratio of line intensity pumping / no-pumping for NeIX 1s3s - 1s2p 82.76A line electron temperature 150eV

line intensity ratio (pump/no pump) path length (cm)

1010 cm-3 1011 cm-3 1012 cm-3 1013 cm-3

Keenan et al, MNRAS (2018)

100 125 150 175 200 1 10 100 1000

Ratio of line intensity pumping / no-pumping for NeIX 1s3s - 1s2p 82.76A line, l=1011cm

line intensity ratio (pump/no pump) electron temperature (eV)

1010 cm-3 1011 cm-3 1012 cm-3 1013 cm-3

Keenan et al, MNRAS (2018)

• CHIANTI gives the electron density of the flare to be ne = 1011cm−3.
• CHIANTI gives the electron temperature of the flare to be 150eV.
• CHIANTI predicts that in the absence of photopumping, the 82.76Å

line feature is at least 50% NeIX 1s3s 1S1 – 1s2p 1P1 with the other intensity arising from Fe transitions.

• Maximum flare loop length is about 1010cm (Shibata and Magara

2011). CHIANTI modelling of the spectroscopy of the Sun

Dere et al, Astron Astrophys Suppl (1997), Del Zanna et al, Astron Astrophys (2015) Keenan et al, MNRAS (2018)

Acton et al, Ap J (1985)

• CHIANTI analysis predicts line intensity ratios (in photon units) with

NeIX lines at 13.45 and 13.70 to be 82.76/13.45 = 0.019 and 82.76/13.70 = 0.020, compared to measured values of 0.20 and 0.24, respectively.

• These imply enhancements in in 82.76Å line intensity of about a

factor of 5.

• CHIANTI analysis predicts line intensity ratios (in photon units) with

Fe XV and Fe XVI lines at 73.47A and 76.80A to be 82.76/73.47 = 0.16 and 82.76/76.80 = 0.30, compared to measured values of 0.52 and 0.19, respectively.

• These imply enhancements in 82.76Å line intensity of factors of 3.25

and 1.6 respectively. CHIANTI modelling of the spectroscopy of the Sun

Keenan et al, MNRAS (2018)

109 1010 1011 1 2 3 4 5 6 7 8 9 10

Ratio of line intensity pumping / no-pumping for NeIX 1s3s - 1s2p 82.76A line

line intensity ratio (pump/no pump) path length (cm)

1010 cm-3 1011 cm-3 1012 cm-3

Keenan et al, MNRAS (2018)

XUV photopumping in the Sun’s corona

• First tentative evidence for X-ray line coincidence photopumping in an

astrophysical source.

• However the evidence must be treated with some caution:

The flare spectrum was recorded on photographic film and is no longer accessible and hence the quality of the 82.76Å line measurement (and indeed those of other transitions) cannot be confirmed. The 13.45Å and 13.70Å and the 82.76Å features lie close to

• pposite ends of the flare wavelength coverage (10 – 100Å), so that

instrument sensitivity calibration may be an issue.

• We would like to extend our observations to CHANDRA satellite data –

access to database required.

• We have started a programme of experiments on the ORION laser to

test our modelling of internal ‘Bowen’ line-coincidence photopumping.

Conclusions The theory of direct excitation and ionisation by an ambient radiation field is well established. The modelling involves atomic data and coverage uncertainties. Comparison between experiment and theory even for no radiation field shows differences. Broad-band pumping experiments show reasonable agreement with theory. Narrow-band pumping experiments show poor agreement with theory, although there is fairly good agreement in line radiation transfer. This is an area in which modelling still has a long way to go.