Chapter 6 Atomic Physics and Process in Partially Ionized Plasma
6.1 Fundamentals of Atomic Physics Hydrogen Atom E 2 1 1 2 2 2m a n
Photon(Radiation) Emission from H Atom
Opacity Photon Energy
Energy Splitting of Alkali Atom
Argon Atom Energy Level nl 3p 6 C w 2(2l 5 5 36 1) C 4 p 6 C w 1
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 0 1 2 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
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
6.3 Detail Configuration Accountings
Rate Coefficients and Detail Configuration Accounting
F-f(conti.) Free-bound (conti.) B-b (line)
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
Analytical approximation to calculate rates RP PI 2 3 2 2 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') 2 5 3 3 3 n n' En' E PI 4 Bd R c c h 2 2 3 64 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 1.5810 g 1 3 mn u 2 sec mn mm n 0.19 1 0.9 1 1 1 2 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( ) 1 1 2 1 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-52276 Lotz, ApJS, 14, 207
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 2 2 2 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
6.4 Average Atom Model Case of LTE P n g n 1 exp E n T e Z * 1 2 2 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
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
Charge State Distribution of Aluminum with CRE How to calculate with AAM
n n n g P x... 1 1 1 6 5 4 3 2 1 6 5 4 4 4 3 2 1 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
6.5 Multi-Electron System Hamiltonian for N-electron system How to solve: MCHF, HF, Para-potential Method OPAL at LLNL
Term-splitting makes a line a group of many lines
Unresolved Transition Array (UTA)
OPAL
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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
Emissivity Opacity Einstein Rel. at LTE.
Fe Opacity: OPAL
6.7 Opacity Experiment
Shingang II (Shanghai, China) 44
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
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
Temperature Dependence of Silicon Charge State with LTE Assumption F O N C B Be Li He H 47
Model Dependence of Absorption Spectrum 70 % due to n =2, 20% due to n =3-6, less than 5% due to n =8 48
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 - 1900eV 49
Theoretical Model Detailed term accounting (DTA) model J. L. Zeng et al. Phys. Rev. E 70 027401(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
6.8 Importance of Opacity in Astrophysics
Cygnus Loop( 網状星雲 ) Cygnus Loop (Old SNR) 月 0.1 0.6 kev ROSAT 53
Metal disperses into Space by SN Explosion
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Opacity is the most important ingredient to study NOVA light curve 59
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The First Supernova-Explosion Gas density E SN ~10 53 ergs ~ 1 kpc Complete Disruption (PISN)