等离子体中自由—自由吸收的扭曲波研究
|
摘要
自由-自由吸收(free-free absorption)的精确研究对惯性约束核聚变、核物理、天体物理和X射线激光等领域非常重要。由于光谱探测技术的发展,人们对自由-自由吸收的进行了进一步的精确测量和研究,对其采用经典的Kramers截面公式和类氢近似已显然不能满足研究的需求。特别是随着实验技术的发展,实验中能够产生的等离子体密度越来越大,离子与离子之间、电子与电子之间、离子与电子之间表现出强的耦合效应,对自由-自由吸收的深入研究日益迫切。
我们成功的实现了扭曲波框架下自由-自由吸收的偶极近似计算。首先得出了扭曲波理论框架下自由-自由过程的截面公式,化简了相应的矩阵元,然后针对变形后的自由-自由积分应用了“对相位积分法”进行积分,并讨论了相应的分点选取原则。通过计算对比发现,除频率较低处,分波求和的截断引入了一些偏差外,其余均能给出正确的计算结果。
对一些实例的计算结果表明:对于类氢情形,在被吸收的光的频率不是很低的情形,我们的程序能反映经典的Kramers截面公式到精确的量子公式的修正。而对于非类氢离子,计算结果表明,它们的截面与类氢情形除了在低频率修正较小外,其它差异较大,使用类氢进行近似是不精确的。
Free-free absorptions play important roles in inertial confinement fusion, nuclear physics, astrophysics and X ray laser, etc. As the advancement of spectrum detection, more accurate measurement can be made for free-free absorptions. The classical Kramers formula and hydrogenic approximation are not enough to obtain accurate atomic data for the free-free processes. With the development of experimental technology, hot dense plasmas can be generated in laboratory, where strong coupling appears between ions and ions, electrons and electrons, ions and electrons. More accurate theoretical methods should be developed to meet this challenge.
Dipole approximation calculation of free-free absorption cross section was carried out based on the distorted wave approximation. The formulae of free-free absorption cross section were deduced according to the perturbation theory of quantum mechanics and then the formulae were simplified to calculate the reduced matrix elements. The integration on phase method was apllied to calculate the free-free integrals. The standard of dividing points chosen was discussed. The reliability and correctness of the present procedure is verified by comparing the thermal averaged gaunt factor with the results of classical and close-coupling methods. It is found that our program can provide correct result except for energy of the photon absorbed is small. The partial wave summation converged very slowly at low photon energy and therefore the cut off of partial wave summation will result in inaccuracy.
The calculation for specific cases showed that for hydrogenic system, the present theoretical method agrees well with accurate quantum treatment except at low photon energy. For non-hydrogenic system, calculations show that the cross section deviate evidently from the hydrogenic approximation, and thus the hydrogenic and Kramers formula is inappropriate.
我们成功的实现了扭曲波框架下自由-自由吸收的偶极近似计算。首先得出了扭曲波理论框架下自由-自由过程的截面公式,化简了相应的矩阵元,然后针对变形后的自由-自由积分应用了“对相位积分法”进行积分,并讨论了相应的分点选取原则。通过计算对比发现,除频率较低处,分波求和的截断引入了一些偏差外,其余均能给出正确的计算结果。
对一些实例的计算结果表明:对于类氢情形,在被吸收的光的频率不是很低的情形,我们的程序能反映经典的Kramers截面公式到精确的量子公式的修正。而对于非类氢离子,计算结果表明,它们的截面与类氢情形除了在低频率修正较小外,其它差异较大,使用类氢进行近似是不精确的。
Free-free absorptions play important roles in inertial confinement fusion, nuclear physics, astrophysics and X ray laser, etc. As the advancement of spectrum detection, more accurate measurement can be made for free-free absorptions. The classical Kramers formula and hydrogenic approximation are not enough to obtain accurate atomic data for the free-free processes. With the development of experimental technology, hot dense plasmas can be generated in laboratory, where strong coupling appears between ions and ions, electrons and electrons, ions and electrons. More accurate theoretical methods should be developed to meet this challenge.
Dipole approximation calculation of free-free absorption cross section was carried out based on the distorted wave approximation. The formulae of free-free absorption cross section were deduced according to the perturbation theory of quantum mechanics and then the formulae were simplified to calculate the reduced matrix elements. The integration on phase method was apllied to calculate the free-free integrals. The standard of dividing points chosen was discussed. The reliability and correctness of the present procedure is verified by comparing the thermal averaged gaunt factor with the results of classical and close-coupling methods. It is found that our program can provide correct result except for energy of the photon absorbed is small. The partial wave summation converged very slowly at low photon energy and therefore the cut off of partial wave summation will result in inaccuracy.
The calculation for specific cases showed that for hydrogenic system, the present theoretical method agrees well with accurate quantum treatment except at low photon energy. For non-hydrogenic system, calculations show that the cross section deviate evidently from the hydrogenic approximation, and thus the hydrogenic and Kramers formula is inappropriate.
引文
[1] M J Seaton.Free free transitions and spectral-line broadening[J].J. Phys. B: At. Mol. Opt. Phys.,2000,33:2677~2704
[2] M J Seaton . Atomic data for opacity calculations:Ⅰ.General description[J].J. Phys. B: At. Mol. Phys., 1987,20:6371~6377
[3] Brussard P J and van de Hulst H C.Rev. Mod. Phys., 1962,34:1643
[4] K L Bell and K A Berrington.Free-free absorption coefficient of the negative hydrogen ion[J].J. Phys. B: At. Mol. Phys,1987,20:801~806
[5]王福恒,王嵩薇.近代科学技术中的原子分子辐射理论[M].成都:成都科技大学出版社,1991.
[6] H. A. Kramers and W. Heisenberg.Z. Phys.,1925,31:681
[7] G. Breit.Rev. Mod. Phys.,1932,4:504
[8] P. A. M. Dirac.Proc. R. Soc. Lond. A,1927,114:710
[9] P. A. M. Dirac.The Principles of Quantum Mechanics[M].Clarendon, Oxford,1958
[10] S. Geltman . Continuum States of H and the Free-Free Absorption Coefficient[J].Astrophys. J.,1964,141:376~394
[11] N. A. Doughty and P. A. Fraser.The free-free absorption coefficient of the negative hydrogen ion[J].Mon. Not. R. Astron. Soc.,1966,132:267~282
[12] G. Peach.A general formula for the calculation of absorption cross sections for free-free transitions in the field of positive ions[J].Mem. R. astr. Soc.,1965,130: 361~377
[13] G. Peach . Free-fee absorption coefficients for non-hydrogenic atoms [J].Mem. R. astr. Soc.,1967 ,71:1~11
[14] G. Peach.Total continuous absorption coefficients for complex atoms [J].Mem. R. astr. Soc.,1967,71:29~45
[15] J. L Stilley and J. Callaway.Free- free absorption coefficient of the negative hydrogen ion[J].Astrophys. J.,1970,160:245-260
[16] K. L Bell, A. E. Kingston and W. A. McIlveen.The total absorption coefficient of the negative hydrogen ion[J].J. Phys. B: At. Mol. Phys.,1975,8:358~364
[17] Michael S. Pindzola and Hugh P. Kelly.Free-free radiative absorption coefficient for the negative argon ion[J].Phys. Rev. A,1976,14:204~210
[18] K. L Bell, P. G. Burke and A. E Kingston.Free-free transitions of an electron in the presence of an atomic system[J].J. Phys. B: At. Mol. Phys.,1977,10:3117~3127
[19] Bell K L, Berrington K A and Croskery P J.J. Phys. B: At. Mol. Phys.,1982,15:977
[20] Bell K L, Hibbert A and Berrington K A.J. Phys. B: At. Mol. Opt. Phys.,1988,21:2319
[21] C. A.Iglesias, F. J. Rogers and R. G. Wilson.Spin-Orbit Interaction Effects on the Rosseland Mean Opacity [J].Astrophys. J.,1992,397:717~728
[22] A. Grinenko and D.O. Gericke.Nonlinear Collisional Absorption of Laser Light in Dense Strongly Coupled Plasmas[J].Phys. Rev. L.,2009,103:065005
[23] Paul Hilse and Manfred Schlanges.Collisional absorption of dense plasmas in strong laser fields: Quantum statistical results and simulation[J].Phys. Rev. E, 2005,71:056408
[24] S. M. Vinko et al.Free-free opacity in warm dense aluminum[J].High Energy Density Physics.,2009,5:124~131
[25] Massey.Electronic and Ionic Impact Phenomena vol 2[M].Oxford: Oxford University Press,1969
[26] Geltman S. J..Quant. Spectrosc[J].Radiat. Transfer,1973,13:601~613
[27] B. Wallbank V. W. Connors J. K. Holmes and A. Weingartshofer . Experimental differential cross sections for one-photon free-free transitions[J].J. Phys. B: At. Mot. Phys.,1987,20:L833~L838
[28] J.P.Matte and T.W.Johnston . Electron Heat Flow with Inverse Bremsstrahlung and Ion Motion[J].Phys. Rev. L.,1984,53:1461~1464
[29] D.Hulin and M.Combescot.Energy transfer during silicon irradiation by femtosecond laser pulse[J].Phys. Rev. L.,1984,52:1998~2001
[30] T.A.Hall A.Djaoui R.W.Eason et . Experimental observation of ion correlation in a dense laser produced plasma[J].Phys. Rev. L.,1988,60:2034-2037
[31] D.F.Price R.M.More R.S.Walling G.Guethlein.Absorption of ultra short laser pulses by solid targets heated rapidly to temperatures 1-1000eV[J].Phys. Rev. L.,1995,75:252~255
[32] K. Krushelnick et.Effect of Relativistic Plasma on Extreme-Ultraviolet Harmonic Emission from Intense Laser-Matter Interactions[J].Phys. Rev. L.,2008,100:125005
[33]曾交龙.使用细致谱项模型研究铝等离子体的辐射不透明度[M].国防科技大学出版社.2005
[34]姜明.非理想氩等离子体电子密度和不透明度理论研究[博士学位论文],2004
[35]高城.铁等离子体辐射不透明度的细致能级模型研究[硕士学位论文],2007
[36]方泉玉,颜君.原子结构、碰撞与光谱理论[M].国防工业出版社,2006
[37] Robert D. Cowan.The theory of atomic structure and spectra[M].University of California Press,1981
[38] Condon and Shortley.The Theory of Atomic Spectra[M].Cambridge at the University Press,1959
[39]李世昌.高温辐射物理与量子辐射理论[M].国防工业出版社,1992
[40]徐锡申,张万箱等.实用物态方程理论导引[M].科学出版社,1986
[41] Harald Friedrich.Theoretical atomic physic[M].Springer-Verlag Berlin Heidelberg New York,1991
[42] Gu MingFeng.“Flexible Atomic Code”.http://kipac-tree.stanfordedu/fac/
[43] M J. Seaton.Contributions to radiative transition probabilities from the asymptotic region[J].J. Phys. B: At. Mol. Phys.,1981,14:3827~3837
[44] M J. Seaton . Outer-region contributions to radiative transition probabilities[J].J. Phys. B: At. Mol. Phys.,1986,19:2601~2610
[45] M. Edwards, X. Tang, P. Lambmpoulis, and R. Shakeshaft.Multiphoton absorption by alkali-metal atoms above the ionization threshold[J].Phys. Rev. A.,1986,33:4444~4445,
[46] M. Edwards, X. Tang, and R. Shakeshaft.Multiphoton absorption by alkali-metal atoms above the ionization threshold. II. Further results on Cs and Rb ionization[J].Phys. Rev. A.,1987,36:3758~3767
[47] Bo Gao and A. F. Staracey.Numerical methods for free-free radiative transition matrix elements[J].COMPUTERS IN PHYSICS.,1987,NOV/DEC:70~73
[48] J. Vackár,A. smünek and O. sipr.Integration of free-free radiative-transition matrix elements[J].Computer Physics Communications,1991,66:259-265
[49] M J. Seaton.Integrals involving products of Coulomb functions and inverse powers of the radial coordinate[J].J. Phys. B: At. Mol. Phys.,1984,17:1~19
[50] A. Burgess, D. G. Hummer, J. A. Tully.Electron impact excitation ofpositive ions[J].Phil. Trans. R. Soc.,1970,266:225~279
[51] M J. Seaton.Quantum defect theory[J].Rep. Prog. Phys..1983,46:167~257
[52] Jwei-Jun Chang.The R-matrix theory of electron-atom scattering using the Dirac Hamiltonian[J].J. Phys. B: Atom. Molec. Phys.,1975,8:2327~2335
[53] K A Berrington, P G Burke, K Butler, M J Seaton, P J Storey, K T Taylor and Yu Yan . Atomic data for opacity calculations: II. Computational methods[J].J. Phys. B: At. Mol. Phys.,1987,20:6379~6397
[54] I P Grant.Gauge invariance and relativistic radiative transitions[J].J. Phys. B: Atom. Mol. Phys.,1974,12:1458~1475
[55] Ralph S. Sutherland.Accurate free–free Gaunt factors for astrophysical plasmas[J].Mon. Not. R. Astron. Soc.,1998,300:321~330
[56]周世勋.量子力学教程[M].高等教育出版社,2006
[57] A. Burgess, Coulomb integrals: tables and sum rules[J].J. Phys. B: At. Mol. Phys.,1974,L364-L367
[2] M J Seaton . Atomic data for opacity calculations:Ⅰ.General description[J].J. Phys. B: At. Mol. Phys., 1987,20:6371~6377
[3] Brussard P J and van de Hulst H C.Rev. Mod. Phys., 1962,34:1643
[4] K L Bell and K A Berrington.Free-free absorption coefficient of the negative hydrogen ion[J].J. Phys. B: At. Mol. Phys,1987,20:801~806
[5]王福恒,王嵩薇.近代科学技术中的原子分子辐射理论[M].成都:成都科技大学出版社,1991.
[6] H. A. Kramers and W. Heisenberg.Z. Phys.,1925,31:681
[7] G. Breit.Rev. Mod. Phys.,1932,4:504
[8] P. A. M. Dirac.Proc. R. Soc. Lond. A,1927,114:710
[9] P. A. M. Dirac.The Principles of Quantum Mechanics[M].Clarendon, Oxford,1958
[10] S. Geltman . Continuum States of H and the Free-Free Absorption Coefficient[J].Astrophys. J.,1964,141:376~394
[11] N. A. Doughty and P. A. Fraser.The free-free absorption coefficient of the negative hydrogen ion[J].Mon. Not. R. Astron. Soc.,1966,132:267~282
[12] G. Peach.A general formula for the calculation of absorption cross sections for free-free transitions in the field of positive ions[J].Mem. R. astr. Soc.,1965,130: 361~377
[13] G. Peach . Free-fee absorption coefficients for non-hydrogenic atoms [J].Mem. R. astr. Soc.,1967 ,71:1~11
[14] G. Peach.Total continuous absorption coefficients for complex atoms [J].Mem. R. astr. Soc.,1967,71:29~45
[15] J. L Stilley and J. Callaway.Free- free absorption coefficient of the negative hydrogen ion[J].Astrophys. J.,1970,160:245-260
[16] K. L Bell, A. E. Kingston and W. A. McIlveen.The total absorption coefficient of the negative hydrogen ion[J].J. Phys. B: At. Mol. Phys.,1975,8:358~364
[17] Michael S. Pindzola and Hugh P. Kelly.Free-free radiative absorption coefficient for the negative argon ion[J].Phys. Rev. A,1976,14:204~210
[18] K. L Bell, P. G. Burke and A. E Kingston.Free-free transitions of an electron in the presence of an atomic system[J].J. Phys. B: At. Mol. Phys.,1977,10:3117~3127
[19] Bell K L, Berrington K A and Croskery P J.J. Phys. B: At. Mol. Phys.,1982,15:977
[20] Bell K L, Hibbert A and Berrington K A.J. Phys. B: At. Mol. Opt. Phys.,1988,21:2319
[21] C. A.Iglesias, F. J. Rogers and R. G. Wilson.Spin-Orbit Interaction Effects on the Rosseland Mean Opacity [J].Astrophys. J.,1992,397:717~728
[22] A. Grinenko and D.O. Gericke.Nonlinear Collisional Absorption of Laser Light in Dense Strongly Coupled Plasmas[J].Phys. Rev. L.,2009,103:065005
[23] Paul Hilse and Manfred Schlanges.Collisional absorption of dense plasmas in strong laser fields: Quantum statistical results and simulation[J].Phys. Rev. E, 2005,71:056408
[24] S. M. Vinko et al.Free-free opacity in warm dense aluminum[J].High Energy Density Physics.,2009,5:124~131
[25] Massey.Electronic and Ionic Impact Phenomena vol 2[M].Oxford: Oxford University Press,1969
[26] Geltman S. J..Quant. Spectrosc[J].Radiat. Transfer,1973,13:601~613
[27] B. Wallbank V. W. Connors J. K. Holmes and A. Weingartshofer . Experimental differential cross sections for one-photon free-free transitions[J].J. Phys. B: At. Mot. Phys.,1987,20:L833~L838
[28] J.P.Matte and T.W.Johnston . Electron Heat Flow with Inverse Bremsstrahlung and Ion Motion[J].Phys. Rev. L.,1984,53:1461~1464
[29] D.Hulin and M.Combescot.Energy transfer during silicon irradiation by femtosecond laser pulse[J].Phys. Rev. L.,1984,52:1998~2001
[30] T.A.Hall A.Djaoui R.W.Eason et . Experimental observation of ion correlation in a dense laser produced plasma[J].Phys. Rev. L.,1988,60:2034-2037
[31] D.F.Price R.M.More R.S.Walling G.Guethlein.Absorption of ultra short laser pulses by solid targets heated rapidly to temperatures 1-1000eV[J].Phys. Rev. L.,1995,75:252~255
[32] K. Krushelnick et.Effect of Relativistic Plasma on Extreme-Ultraviolet Harmonic Emission from Intense Laser-Matter Interactions[J].Phys. Rev. L.,2008,100:125005
[33]曾交龙.使用细致谱项模型研究铝等离子体的辐射不透明度[M].国防科技大学出版社.2005
[34]姜明.非理想氩等离子体电子密度和不透明度理论研究[博士学位论文],2004
[35]高城.铁等离子体辐射不透明度的细致能级模型研究[硕士学位论文],2007
[36]方泉玉,颜君.原子结构、碰撞与光谱理论[M].国防工业出版社,2006
[37] Robert D. Cowan.The theory of atomic structure and spectra[M].University of California Press,1981
[38] Condon and Shortley.The Theory of Atomic Spectra[M].Cambridge at the University Press,1959
[39]李世昌.高温辐射物理与量子辐射理论[M].国防工业出版社,1992
[40]徐锡申,张万箱等.实用物态方程理论导引[M].科学出版社,1986
[41] Harald Friedrich.Theoretical atomic physic[M].Springer-Verlag Berlin Heidelberg New York,1991
[42] Gu MingFeng.“Flexible Atomic Code”.http://kipac-tree.stanfordedu/fac/
[43] M J. Seaton.Contributions to radiative transition probabilities from the asymptotic region[J].J. Phys. B: At. Mol. Phys.,1981,14:3827~3837
[44] M J. Seaton . Outer-region contributions to radiative transition probabilities[J].J. Phys. B: At. Mol. Phys.,1986,19:2601~2610
[45] M. Edwards, X. Tang, P. Lambmpoulis, and R. Shakeshaft.Multiphoton absorption by alkali-metal atoms above the ionization threshold[J].Phys. Rev. A.,1986,33:4444~4445,
[46] M. Edwards, X. Tang, and R. Shakeshaft.Multiphoton absorption by alkali-metal atoms above the ionization threshold. II. Further results on Cs and Rb ionization[J].Phys. Rev. A.,1987,36:3758~3767
[47] Bo Gao and A. F. Staracey.Numerical methods for free-free radiative transition matrix elements[J].COMPUTERS IN PHYSICS.,1987,NOV/DEC:70~73
[48] J. Vackár,A. smünek and O. sipr.Integration of free-free radiative-transition matrix elements[J].Computer Physics Communications,1991,66:259-265
[49] M J. Seaton.Integrals involving products of Coulomb functions and inverse powers of the radial coordinate[J].J. Phys. B: At. Mol. Phys.,1984,17:1~19
[50] A. Burgess, D. G. Hummer, J. A. Tully.Electron impact excitation ofpositive ions[J].Phil. Trans. R. Soc.,1970,266:225~279
[51] M J. Seaton.Quantum defect theory[J].Rep. Prog. Phys..1983,46:167~257
[52] Jwei-Jun Chang.The R-matrix theory of electron-atom scattering using the Dirac Hamiltonian[J].J. Phys. B: Atom. Molec. Phys.,1975,8:2327~2335
[53] K A Berrington, P G Burke, K Butler, M J Seaton, P J Storey, K T Taylor and Yu Yan . Atomic data for opacity calculations: II. Computational methods[J].J. Phys. B: At. Mol. Phys.,1987,20:6379~6397
[54] I P Grant.Gauge invariance and relativistic radiative transitions[J].J. Phys. B: Atom. Mol. Phys.,1974,12:1458~1475
[55] Ralph S. Sutherland.Accurate free–free Gaunt factors for astrophysical plasmas[J].Mon. Not. R. Astron. Soc.,1998,300:321~330
[56]周世勋.量子力学教程[M].高等教育出版社,2006
[57] A. Burgess, Coulomb integrals: tables and sum rules[J].J. Phys. B: At. Mol. Phys.,1974,L364-L367