Chapter 6. Atomic Physics and Process in Partially Ionized Plasma

Transcription

1 Chapter 6 Atomic Physics and Process in Partially Ionized Plasma

2 6.1 Fundamentals of Atomic Physics Hydrogen Atom E m a n

3 Photon(Radiation) Emission from H Atom

4 Opacity Photon Energy

5 Energy Splitting of Alkali Atom

6

7

8 Argon Atom Energy Level nl 3p 6 C w 2(2l ) C 4 p 6 C w 1

9 6.2 Screened Hydrogen Model Z n E n I H n 2 E n 0 Z n Z n,m P m 1 n,n P n 2 E n mn e 2 r n n,n P n mn e 2 P m r m m,n Z is the ion nuclear charge, P n is the number of electrons in the eigen-state n. n,m is the screening constant r n =a 0 n 2 / Z n, where a 0 = 0.529Å is the Bohr radius. E ion P n E n E ion is the total energy of the bound electrons in the ion E ion n I H Z n / n 2

10

11 Energy level 2 2 Qn e In 2 2na0 1 Q Z n, m P n, n P 2 n m n mn P n is the occupation number of the level n Screened Hydrogenic model Figure shows the comparison of ionization energy with corresponding data from NIST in case of Ar. More R. M. (1991) Atomic Physics of Laser-Produced Plasmas, Handbook of Plasma Physics, eds. M. N. Rosenbluth and R. Z. Sagdeev

12 6.3 Detail Configuration Accountings

13 Rate Coefficients and Detail Configuration Accounting

14 F-f(conti.) Free-bound (conti.) B-b (line)

15 Atomic processes in present model Resonant Photoabsorption Photo-Ionization Electron Impact Excitation Electron Impact Ionization Spontaneous Decay Stimulated Emission Radiative Recombination Electron Impact De-Excitation (E) 3-body Recombination

16

17

18

19

20

21

22 Analytical approximation to calculate rates RP PI fea h n P A( n' n) f ( n n') P 1 n' 2 n 2 ' 2 n' EA n E 4 2 A 32 QQ n n' f ( n n') n n' En' E PI 4 Bd R c c h na B QE 1 n A n, h E f P, if h > E 2 2 n n 3 3 Qn 2n h n 3 EIE R EIE mn u 5 (, ) mn ne f m n e g 1 3 mn u 2 sec mn mm n u g u e nm 1 u 20 Z nm nm nm EII EI R N v E f E de a ln E e ( ) e( ) cm 1 E Atzeni and Meyer-Ter-Vehn, The physics of inertial fusion, Clarendon Press, Oxford Lokke and Grasberger, Lawrence Livermore National Lab. Internal Report UCRL Lotz, ApJS, 14, 207

23 With the detail balance relation, the rate of Reverse Process could calculated from rate of Process in the last slide. RP-SD B n' n 2 ch 2 2 h 3 A n' n PI-RR E n, h n h ev 2 2 n, h E mec E ev EIE-EIDE T mn g n Em E n exp T gm kte nm EII-E3R 3 (3) 2 2 R 1, m', m; T g, m e n e mc Te e 2 c 2, m 1, m'; T 2 g 1, m' e E E 1, m', m T e

24 6.4 Average Atom Model Case of LTE P n g n 1 exp E n T e Z * n i 2m e T e 2 Fermi-Dirac distribution 1 3/ 2 I 1/ 2 T e µ is the chemical potential and determined to satisfy the relation I 1/ 2 x Z Z * 0 n P n y 1/ 2 1 exp x y dy

25 Rate equation for Average Atom Population dp n dt T cn V n T nc P n G T mn mn P m V n T nm P n V m mn L V n = 1-P n / g n is the fraction of vacancy In CRE model, T cn and T nc are given to be T cn T cn CD Tcn RD Tcn DD CU T nc T nc G T mn T CD RD mn T mn CU T mn m n m n T L nm T nm CD Tnm RD CU T mn n m n m

26 Charge State Distribution of Aluminum with CRE How to calculate with AAM

27 n n n g P x g g k g k k g g g g k x x x x C x x x f Averaged population gives us the probability of an electron in n-state in the form Then, the fraction of the ion with full in n=1,2,and 3 and k in n=4 and no electron for n > 5 is calculated to be

28

29

30

31

32

33

34 6.5 Multi-Electron System Hamiltonian for N-electron system How to solve: MCHF, HF, Para-potential Method OPAL at LLNL

35 Term-splitting makes a line a group of many lines

36 Unresolved Transition Array (UTA)

37 OPAL

38 38

39 6.6 Opacity of Partially Ionized Plasmas 1 c t I r I 1 2 r 0 n m,m' i m,m' m,m' I I

40 Emissivity Opacity Einstein Rel. at LTE.

41 Fe Opacity: OPAL

42

43 6.7 Opacity Experiment

44 Shingang II (Shanghai, China) 44

45 Experiment Arrangement on Shengang II Crystal spec. Pinhole camera 2 Target Transmission Grating Pinhole camera 1 Target Backlighter Pinhole + streak camera 4 laser beams 4 laser beams 45

46 Japan-China Collaboration supported by JSPS, Japan, and NSFC, China. 8 laser beams for radiation field (1ns) X-ray radiation temp. (T R ~ 80 ev) Shingang II (China) Au Backlighter 3, 130ps, 100J (9th beam) 800 m SiO2 gel(40mg/cc) Absorption Spectra Dog-bone cavity 8 laser beams (0.35um,1ns,2000J) were incident to the dog-bone Au cavity to produce a 80 ev x-ray radiation field. The 40mg/cc SiO2 gel were photoionized by the radiation field. An additional Au x-ray source produced by the 9th laser beam was used as backlighter. Absorption (with backlighter) or self-emission spectra were measured in the experiment. 46

47 Temperature Dependence of Silicon Charge State with LTE Assumption F O N C B Be Li He H 47

48 Model Dependence of Absorption Spectrum 70 % due to n =2, 20% due to n =3-6, less than 5% due to n =8 48

49 Transmission Spectra from Photo-ionized SiO2 Plasma 1 ns Experimental Data are Dotted Lines Theoretical Results are Solid Lines (LTE, Saha) 1 ns: Te=65 ev 1.5 ns: Te=55 ev 2 ns: 52eV+34eV 1.5 ns 2 ns 1700eV eV 49

50 Theoretical Model Detailed term accounting (DTA) model J. L. Zeng et al. Phys. Rev. E (2004); and references therein. Flexible Atomic Code (FAC) M. F. Gu, Astrophys. J. 597, 832(2003). Line Profile Voigt Profile Natural, Doppler(0.2eV), Stark, and Autoionization resonance (~0.3eV) + Instrumental (0.89eV) See Poster 8HE91 by Yutong Li et al. 50

51

52 6.8 Importance of Opacity in Astrophysics

53 Cygnus Loop( 網状星雲 ) Cygnus Loop (Old SNR) 月 kev ROSAT 53

54

55 Metal disperses into Space by SN Explosion

56 56

57 57

58 58

59 Opacity is the most important ingredient to study NOVA light curve 59

60 60

61

62 The First Supernova-Explosion Gas density E SN ~10 53 ergs ~ 1 kpc Complete Disruption (PISN)