Analytical evaluation of the plasma dispersion function for a Fermi–Dirac distribution

doi:10.1088/1674-1056/21/5/055204

Abstract An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi--Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

Keywords: Fermi--Dirac distribution plasma dispersion function binomial coefficients incomplete gamma functions

Received: 12 September 2011
Revised: 27 April 2012
Accepted manuscript online:

PACS:	52.35.Mw	(Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))
	52.25.Dg	(Plasma kinetic equations)
	52.27.-h	(Basic studies of specific kinds of plasmas)

Cite this article:

B.A. Mamedov Analytical evaluation of the plasma dispersion function for a Fermi–Dirac distribution 2012 Chin. Phys. B 21 055204

[1]	Melrose D B and Mushtag A 2009 Phys. Plasmas 16 094508
[2]	Melrose D B and Mushtag A 2010 Phys. Rev. E 82 056402
[3]	Fried B D and Conte S D 1961 The Plasma Dispersion Function (New York:Academic)
[4]	Melrose D B and Mushtag A 2010 Phys. Plasmas 17 122103
[5]	Lindhard D J 1954 Mat. Fys. Medd. K. Dan Vidensk. Selsk. 28 8
[6]	Silin V P 1952 Zh. Eksp. Teor. Fiz. 23 641
[7]	McOrist J, Melrose D B and Weise J I 2007 J. Plasma Phys. 73 495
[8]	Hoover B G and Gamiz V L 2006 J. Opt. Soc. Am. A 23 314
[9]	Stijns E 1977 Opt. Commun. 23 155
[10]	Mamedov B A 2009 Contrib. Plasma Phys. 49 36
[11]	Gradshteyn I S and Ryzhik I M 1980 Tables of Integrals, Sums, Series and Products, (4th Edn.) (New York:Academic Press)
[12]	Guseinov I I and Mamedov B A 2004 J. Math. Chem. 36 341

[1]	Effect of kinetic ions on the toroidal double-tearing modes Ruibo Zhang(张睿博), Lei Ye(叶磊), Yang Chen, Nong Xiang(项农), and Xiaoqing Yang(杨小庆). Chin. Phys. B, 2023, 32(2): 025203.
[2]	Phase-matched second-harmonic generation in hybrid polymer-LN waveguides Zijie Wang(王梓杰), Bodong Liu(刘伯东), Chunhua Wang(王春华), and Huakang Yu(虞华康). Chin. Phys. B, 2022, 31(10): 104208.
[3]	Parametric decay instabilities of lower hybrid waves on CFETR Taotao Zhou(周涛涛), Nong Xiang(项农), Chunyun Gan(甘春芸), Guozhang Jia(贾国章), and Jiale Chen(陈佳乐). Chin. Phys. B, 2022, 31(9): 095201.
[4]	Observation of V-type electromagnetically induced transparency and optical switch in cold Cs atoms by using nanofiber optical lattice Xiateng Qin(秦夏腾), Yuan Jiang(蒋源), Weixin Ma(马伟鑫), Zhonghua Ji(姬中华),Wenxin Peng(彭文鑫), and Yanting Zhao(赵延霆). Chin. Phys. B, 2022, 31(6): 064216.
[5]	Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas Hui Li(李慧), Jiquan Li(李继全), Zhengxiong Wang(王正汹), Lai Wei(魏来), and Zhaoqing Hu(胡朝清). Chin. Phys. B, 2022, 31(6): 065207.
[6]	The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge Zhao-Yang Liu(刘朝阳), Yang-Zhong Zhang(章扬忠), Swadesh Mitter Mahajan, A-Di Liu(刘阿娣), Chu Zhou(周楚), and Tao Xie(谢涛). Chin. Phys. B, 2022, 31(4): 045202.
[7]	Determine the physical mechanism and source region of beat wave modulation by changing the frequency of high-frequency waves Zhe Guo(郭哲), Hanxian Fang(方涵先), and Farideh Honary. Chin. Phys. B, 2022, 31(2): 024103.
[8]	Optimization of the beam quality in ionization injection by a tailoring gas profile Ye Cui(崔野), Guo-Bo Zhang(张国博), Yan-Yun Ma(马燕云), Xiao-Hu Yang(杨晓虎), Jia-Yin Mu(牟佳胤), Hai-Bo Yao(姚海波), Ming Zi(资明), Jie Zhou(周洁), Jing-Qi Yang(杨静琦), Li-Xiang Hu(胡理想), and Li-Chao Tian(田立朝). Chin. Phys. B, 2021, 30(10): 105201.
[9]	Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice Ji-Li Ma(马吉利), Xiao-Xun Li(李晓旬), Rui-Jin Cheng(程瑞锦), Ai-Xia Zhang(张爱霞), and Ju-Kui Xue(薛具奎). Chin. Phys. B, 2021, 30(6): 060307.
[10]	An easily-prepared impedance matched Josephson parametric amplifier Ya-Peng Lu(卢亚鹏), Quan Zuo(左权), Jia-Zheng Pan(潘佳政), Jun-Liang Jiang(江俊良), Xing-Yu Wei(魏兴雨), Zi-Shuo Li(李子硕), Wen-Qu Xu(许问渠), Kai-Xuan Zhang(张凯旋), Ting-Ting Guo(郭婷婷), Shuo Wang(王硕), Chun-Hai Cao(曹春海), Wei-Wei Xu(许伟伟), Guo-Zhu Sun(孙国柱), and Pei-Heng Wu(吴培亨). Chin. Phys. B, 2021, 30(6): 068504.
[11]	Nonlinear propagation of an intense Laguerre-Gaussian laser pulse in a plasma channel Mingping Liu(刘明萍), Zhen Zhang(张震), and Suhui Deng(邓素辉). Chin. Phys. B, 2021, 30(5): 055204.
[12]	Breather solutions of modified Benjamin-Bona-Mahony equation G T Adamashvili. Chin. Phys. B, 2021, 30(2): 020503.
[13]	Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas Rong-An Tang(唐荣安), Tiao-Fang Liu(刘调芳), Xue-Ren Hong(洪学仁), Ji-Ming Gao(高吉明), Rui-Jin Cheng(程瑞锦), You-Lian Zheng(郑有莲), and Ju-Kui Xue(薛具奎). Chin. Phys. B, 2021, 30(1): 015201.
[14]	Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation Xiao-Bo Wang(王晓波), Man Jia(贾曼), and Sen-Yue Lou(楼森岳). Chin. Phys. B, 2021, 30(1): 010501.
[15]	Propagation properties of the chirped Airy-Gaussian vortex electron plasma wave Lican Wu(吴利灿), Jinhong Wu(吴锦鸿), Yujun Liu(刘煜俊), and Dongmei Deng(邓冬梅). Chin. Phys. B, 2020, 29(12): 125202.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Analytical evaluation of the plasma dispersion function for a Fermi–Dirac distribution

Cite this article:

Online attention