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

Transcription

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

2 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 of 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

3 (energy in a Planckian radiation field)/(total energy) ε energy 4 at = ρ C T + at V 4

4 (pressure from a Planckian radiation field)/(total pressure) ε pressure = P mat Prad + P rad

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

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

7 Collisional and radiative rates c c c c r r r r

8 Collisional rates c c c c Electron collisional excitation (~n e ) Electron collisional de-excitation (~n e ) Electron collisional ionisation (~n e ) + Autoionisation Three-body recombination (~n e2 ) + Dielectronic recombination (~n e )

9 adiative rates r r r r Photoexcitation - stimulated absorption Photo de-excitation spontaneous and stimulated emission Photoionisation stimulated absorption Photorecombination (~n e ) spontaneous and stimulated emission

10 Level of detail describing atomic states Detailed Configuration Accounting DCA Detailed Term Accounting DTA

11 ate equations The rate equations governing the populations are for each level dn t ( ) c r c r = n ( t) ( + ) + n ( t)( + dt which have the constraint ) Z ( t) n ( t) = e n and for the case of the system having come to a steady-state dn ( t) dt = 0

12 Photo excitation / de-excitation rates = 0 ) ) / ( ) ( ( 4 ν ν ν ν σ π d h I r + Ω Ω = 0 / 2 3 )) ( ) / )((2 ) / ( ( 4 ν ν ν ν ν σ π ν d e I c h h e e kt h U r kt e E E U = ) ( ) ( = 1 ) / exp( 1 ) / (2 ) ( 2 3 kt r h c h I ν ν ν ( ) ( ) ν φ π ν σ = f mc e 2 Both rates involve an integral over the line shape and the radiation field

13 φ Photopumping If photon intensity is roughly constant over the line shape then we can approximate it as a delta function ( ν ) = δ ( ν ) which leads to the radiative excitation and de-excitation rates being r = A n ph 1 r nph = hν 0 / kt = A ( 1 + n ) e b 1 ph ν π e ε 0 Ω A = f 2 3 h mc Ω

14 Photoionisation / photorecombination rates = 0 ) ) / ( ) ( ( 4 ν ν ν ν σ π d h I r + Ω Ω = 0 / / 2 )) ( ) / )((2 ) / ( ( ν ν ν ν ν σ π π ν d e I c h h e k T m h n e kt h U e e e r kt e E E U = ) ( ) ( = 1 ) / exp( 1 ) / (2 ) ( 2 3 kt r h c h I ν ν ν Both rates involve an integral over the photoionisation cross-section and the radiation field

15 adiative rates - no radiation field Ω Ω = 0 / / 2 ) / )(2 ) / ( ( ν ν ν ν σ π π ν d e c h h e k T m h n e kt h U e e e r = A r If there is no ambient radiation field only spontaneous de-excitation and radiative recombination remain

16 No external radiation field optical depth 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 r = 0 r = A g( ) τ0 g( τ 0 ) φ( ν) = 1 2 π ν D e x For a Doppler lineshape this is given by g( τ ) 0 1 = (1 exp( τ 0e τ 0 2 x )) dx x ν = ( ν ν ) / ν D 0 kt = ( 2 ) / i m 1 2 D ν 0 c Optical depth τ 0 2 πe = φ ν 0 mc f ( )( n Ω Ω n ) y

17 Cauchy (Dirac-Fuchs) mean chord theorem volume V surface area A For any convex shape, the mean chord length is given by the Dirac-Fuchs theroem as y = 4V/A For a slab geometry, the mean chord length y = 4V/A = 2z z 0 Dirac P A M, Technical eport MS-D-5, part I, Public ecords Office, Kew (1943). Dirac PAM, Fuchs K, Peierls and Preston P, Technical eport MS-D-5, part II, Public ecords Office, Kew (1943).

18 Level of detail describing atomic states Average-atom Detailed Configuration Accounting DCA Detailed Term Accounting DTA

19 Average-atom model

20 Collisional and radiative rates c n c c c n c n r c r n c r n r n c r c n r n r c r r r n n c m n c n m m r m n r n m m

21 dp dt n NIMP equations and solutions P = + c r P 1 n m ( m n + m ωn number of electrons in shell m n) probability of a hole in shell n + sum of radiative and collisional rates from shell m to n screened-hydrogenic excitation and ionisation energies, collisional and radiative rates used dp dt 1 = dp dt f n max 1 ( P = solved for 1 f P1,..., Pnmax,..., P n max n max ( P 1, ),..., P n max, )

22 econstruction of individual level populations from the average shell populations From the average populations (P 1,.,P nmax ) the fraction of ions in a real configuration (n 1,.,n nmax ) can be calculated assuming that the orbitals are not statistically correlated ωi! Pi Pi P i i ni n ( ) = 1 ( ω )! i! ωi ωi ni ωi ni The fraction of ions in level a, degeneracy 2J a +1, which is derived from the configuration, is then ω! P( a) = a ( ωi ni )! ni! ( 2J + 1) / i P( )

23 Photoionisation cross sections FeXXIII (1s 2 2s 2 ) FeXXIV (1s 2 2s)

24 Dielectronic recombination / autoionisation rates f limit dp n dt n - dp m dt m - dp g dt g Z P g Q m Q W n dr ( gf mn) P Q Z Q W ( gf mn) g m g m with g m = n dr detailed balance Z 0 P 0 g Q 0 m Q 0 n W dr ( gf mn) = P 0 n P 0 m Q 0 g W a ( mn gf ) Albritton and Wilson, Phys ev Letts, 83, 1594 (1999); JQST, 65, 1 (2000)

25 Comparison of NIMP and detailed (DCA) models with / without D Se n e =5x10 20 cm -3, T e =1000eV 1 fraction 0.1 DCA - no D NIMP - no AI/D DCA - D NIMP - AI/D Mg Na Ne F O N C B Z * Lee, JQST, 38, 131 (1987)

26 Comparison between theory and experiment No or small radiation field

27 Non-LTE ionisation distribution measurement Conditions in the gold plasma were characterised by Thompson scattering, radiography and X-ray spectroscopy. Foord, Glenzer, Thoe, Wong, Fournier, Wilson, Springer, Phys ev Letts, 85, 992 (2000). Foord, Glenzer, Thoe, Wong, Fournier, Albritton, Wilson, Springer, JQST, 65, 231 (2000).

28 Charge state distributions for Au n e =6x10 20 cm -3, T e =2200eV Z * =48.6 Z * =49.3 fraction 0.2 Z * = (experiment -Foord et al) (NIMP - AI/D) (NIMP - no AI/D) Ge Ga Zn Cu Ni Co Z *

29 Charge state distributions for Au n e =1.4x10 21 cm -3, T e =2600eV experiment (Glenzer et al) NIMP (AI/D), no T r ) NIMP (AI/D, T r =210eV) NIMP (no AI/D, no T r ) fraction Z * Glenzer, Fournier, Wilson, Lee and Suter Phys ev Letts, 65, (2001).

30 Charge state distributions for Xe n e =1.3x10 20 cm -3, T e =415eV Z * = 26.5 experiment (Popovics et al) NIMP (AI/D) NIMP (no AI/D) 0.4 fraction 0.3 Z * =25.0 Z * = Z * Chenais-Popovics, Malka, Gauthier, Gary, Peyrusse, abec-le Gloahec, Matsushima, Bauche-Arnoult, Bachelier and Bauche Phys ev E, 65, (2002).

31 Charge state distributions for Au n e =10 12 cm -3, T e =2500eV fraction Z * = 46.4 Z * = 47.4 Z * = experiment (Wong et al) NIMP (AI/D) NIMP (no AI/D) Wong, May, Beiersdorfer, Fournier, Wilson, Brown, Springer, Neill and Harris, Phys ev Letts, 90, (2003). Z *

32 Ionisation in Au, n e =10 21 cm -3 with and without a radiation field experiment, no T r experiment, T r =185eV 45 Z * electron temperature (ev) AI/D, no T r AI/D, T r =175eV AI/D, T r =190eV no AI/D, no T r no AI/D, T r =175eV no AI/D, T r =190eV Heeter, Hansen, Fournier, Foord, Froula, Mackinnon, May, Schneider and Young Phys ev Letts, 99, (2007).

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

34 Accretion-powered objects EXO Low mass X- ray binary Photoionised plasmas (radiationdominated plasmas) scale with the ionisation parameter ξ=4πf/n e ξ=30 ergcms -1 Tarter, Tucker and Salpeter, ApJ, 156, 943,(1969) Tarter and Salpeter, ApJ, 156, 953 (1969) NGC 4593 Seyfert galaxy ξ=300 ergcms -1

35 Spectral interpretation needs reliable models

36 Ionisation / recombination rates c c ai dr r r

37 Ionisation / recombination rates c c ai dr r r Electron collisional ionisation (~n e ) Three-body recombination (~n e2 ) Autoionisation Dielectronic recombination (~n e ) Photoionisation stimulated absorption Photorecombination (~n e ) spontaneous and stimulated absorption

38 Ionisation / recombination rates In the limit of high radiation field and low electron density c c ai dr r r Electron collisional ionisation (~n e ) Three-body recombination (~n e2 ) Autoionisation Dielectronic recombination (~n e ) Photoionisation stimulated absorption Photorecombination (~n e ) spontaneous and stimulated absorption

39 Photoionised plamsas ( e ) e r T n n n = ) ( ) ) / ( ) ( ( 4 0 n e T e d h I n n ν ν ν ν σ π = ) ( ) ) / ( ) ( ( 4 0 e e T d h p n F n n ν ν ν ν σ π = n e πf ξ 4 = Tarter, Tucker and Salpeter, ApJ, 156, 943,(1969) Tarter and Salpeter, ApJ, 156, 953 (1969) r dr e T + = ) ( ignoring stimulated radiative recombination take out shape function p(ν) from the flux F

40 Experiment on Z-pinch at Sandia generates ξ=20ergcms -1 sample bathed in radiation from pinch over 4π steradians 1000Å CH flux and spectral measurements absorption spectrum emission spectrum 500Å NaF/Fe pinhole camera collapsed Z-pinch Foord, Heeter, van Hoof, Thoe, Bailey, Cuneo, Chung, Liedahl, Fournier, Chandler, Jonauskas, Kisielius, Mix, amsbottom, Springer, Keenan, ose and Goldstein, Phys ev Letts, 93, (2004)

41 F photoionised plasma ionisation distribution n e =2x10 19, T e =150eV, T r =165eV (=0.01), ξ=20ergcms experiment NIMP with radiation field NIMP without radiation field 0.6 fraction Z * ose, vanhoof, Jonauskas, Keenan, Kisielius, amsbottom, Foord, Heeter and Springer, J Phys B, 37, L337 (2004)

42 Na photoionised plasma ionisation distribution n e =2x10 19, T e =150eV, T r =165eV (=0.01), ξ=20ergcms fraction experiment NIMP with radiation field NIMP without radiation field Z * ose, vanhoof, Jonauskas, Keenan, Kisielius, amsbottom, Foord, Heeter and Springer, J Phys B, 37, L337 (2004)

43 Fe photoionised plasma ionisation distribution n e =2x10 19, T e =150eV, T r =165eV (=0.01), ξ=20ergcms experiment NIMP with radiation field NIMP without radiation field CLOUDY with radiation field fraction Z * ose, vanhoof, Jonauskas, Keenan, Kisielius, amsbottom, Foord, Heeter and Springer, J Phys B, 37, L337 (2004)

44 Z * (Br) in C 500 H 470 Br gcm -3 ose, JQST (1995)

45 Z*(Br) in C500H470Br27 0.1gcm-3

46 C500H470Br27 opacity 0.001gcm-3

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

48 Simplified diagram of the Bowen resonance fluorescence mechanism optical optical Bowen, Publ. Astr. Soc. Pac.(1934)

49 Astrophysical line-coincidence photopumping and lasing Johanssen and Letokhov,, Astrophysical Lasers, CUP (2009)

50 Accidental line coincidences H-like and He-like ions Alley, Chapline, Kunasz and Weisheit, JQST(1982)

51 Calculation of line coincidences Na 1 P 1 1 s 2 S 1s2 p Ne Dirac-Fock SCF Dirac-Fock SCF + Breit Dirac-Fock SCF + Breit +QED Experiment 1 s p P s S 1 1 E(Na; 1s 2 S ) - 0 1s2 p P1 1 1 E(Ne; 1s 2 S 1s4 p P ) 0.11eV -0.01eV -0.06eV -0.25eV 0 1 Transition energies ~ 1.13keV Sr 1 P s S 1s2 p Br s S 1s3 p P E(Sr; 1s S ) - 0 1s2 p P E(Br; 1s S 1s3 p P ) 0 1 Dirac-Fock SCF Dirac-Fock SCF + Breit Dirac-Fock SCF + Breit +QED Dirac-Fock SCF + Breit +QED + finite nucleus 9.0eV 5.1eV 1.9eV 1.7eV Transition energies ~ 14.6keV ose, JQST(1985)

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

53 Line coincidence photopumping in a laboratory plasma Beer, Patel, ose and Wark, JQST (2000)

54 Beer, Patel, ose and Wark, JQST (2000) Line coincidence photopumping in a laboratory plasma Modal photon density n ph in the frame of the Cl ions at Å (Cl 1s 1/2 4p 3/2 ) at distance x and velocity v(x) at the peak of the laser pulse.

55 Line radiation transport in a velocity gradient Wark, Djaoui, ose, He, enner, Missalla, Foerster, Physical eview Letters (1994)

56 Line radiation transport in a velocity gradient Patel, Wark, enner, Djaoui, ose, Heading, Hauer, JQST (1997)

57 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.

58 Na / Ne line coincidence photopumping scheme Ne Na s S0 1s2 p P1 Porter et al, Phys ev Letts (1992)

59 Na / Ne line coincidence photopumping scheme Population inversion measured Porter et al, Phys ev Letts (1992)

60 Proposed astrophysical line coincidence photopumping XUV Sako et al, ApJ (2003)

61 Na / Ne line coincidence photopumping astrophysical scheme H / He / Ne / Na plasma with astrophysical Ne and Na abundances ( / / x10-4 / x10-6 )

62 Na / Ne line coincidence photopumping astrophysical scheme H / He / Ne / Na plasma with astrophysical Ne and Na abundances ( / / x10-4 / x10-6 ) n e = cm -3 l = cm T e = ev

63 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 n A + = Ω Ω = n n n ph = 1 1 χ δ δ χ Ω Ω Bowen pumping of transition by χ δ (Judge, MNAS,1988) ose, JPhysB (1998)

64 Na / Ne line coincidence photopumping laboratory scheme Porter et al, Phys ev Letts (1992)

65 Na / Ne line coincidence photopumping astrophysical scheme Å Å 82.76Å 81.58Å Keenan et al, MNAS (2018)

66 Spectroscopy of the Sun On July 13 th 1982 a rocket-borne spectrograph that measured the Å emission from an M- class flare on the Sun with 0.02Å resolution. Acton et al, Ap J (1985)

67 Na / Ne line coincidence photopumping astrophysical scheme Å Å 82.76Å 81.58Å In solar flare spectra, the NeIX Å and Å lines are blended with the strong FeXIV Å and OIV Å features. Keenan et al, MNAS (2018)

68 Na / Ne line coincidence photopumping astrophysical scheme Å Å 82.76Å 81.58Å NeIX 81.58Å line has predicted enhancement which is too small even under optimal conditions to detect the feature. Keenan et al, MNAS (2018)

69 Na / Ne line coincidence photopumping astrophysical scheme Å Å 82.76Å 81.58Å Keenan et al, MNAS (2018)

70 line intensity ratio (pump/no pump) atio of line intensity pumping / no-pumping for NeIX 1s3s - 1s2p 82.76A line electron temperature 150eV cm cm cm cm path length (cm) Keenan et al, MNAS (2018)

71 line intensity ratio (pump/no pump) atio of line intensity pumping / no-pumping for NeIX 1s3s - 1s2p 82.76A line, l=10 11 cm cm cm cm cm electron temperature (ev) Keenan et al, MNAS (2018)

72 CHIANTI modelling of the spectroscopy of the Sun CHIANTI gives the electron density of the flare to be n e = cm 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 1 S 1 1s2p 1 P 1 with the other intensity arising from Fe transitions. Maximum flare loop length is about cm (Shibata and Magara 2011). Keenan et al, MNAS (2018) Dere et al, Astron Astrophys Suppl (1997), Del Zanna et al, Astron Astrophys (2015)

73 CHIANTI modelling of the spectroscopy of the Sun CHIANTI analysis predicts line intensity ratios (in photon units) with NeIX lines at and to be 82.76/13.45 = 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. Keenan et al, MNAS (2018) Acton et al, Ap J (1985)

74 line intensity ratio (pump/no pump) atio of line intensity pumping / no-pumping for NeIX 1s3s - 1s2p 82.76A line cm cm cm path length (cm) Keenan et al, MNAS (2018)

75 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 opposite 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 CHANDA satellite data access to database required. We have started a programme of experiments on the OION laser to test our modelling of internal Bowen line-coincidence photopumping.

76 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.