New views of the solar wind with the Lambert W function

被引:97
作者
Cranmer, SR [1 ]
机构
[1] Harvard Smithsonian Ctr Astrophys, Cambridge, MA 02138 USA
关键词
D O I
10.1119/1.1775242
中图分类号
G40 [教育学];
学科分类号
040101 ; 120403 ;
摘要
This paper presents closed-form analytic solutions to two illustrative problems in solar physics that have been considered not solvable in this way previously. Both the outflow speed and the mass loss rate of the solar wind of plasma particles ejected by the Sun are derived analytically for certain illustrative approximations. The calculated radial dependence of the flow speed applies to both Parker's isothermal solar wind equation and Bondi's equation of spherical accretion. These problems involve the solution of transcendental equations containing products of variables and their logarithms. Such equations appear in many fields of physics and are solvable by use of the Lambert W function, which is briefly described. This paper is an example of how new functions can be applied to existing problems. (C) 2004 American Association of Physics Teachers.
引用
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页码:1397 / 1403
页数:7
相关论文
共 31 条
[1]  
[Anonymous], 1997, SOLAR CORONA
[2]  
[Anonymous], W OLOGY SOME EXACTLY
[3]   The new solar corona [J].
Aschwanden, MJ ;
Poland, AI ;
Rabin, DM .
ANNUAL REVIEW OF ASTRONOMY AND ASTROPHYSICS, 2001, 39 :175-210
[4]  
Banaszkiewicz M, 1998, ASTRON ASTROPHYS, V337, P940
[5]   ON SPHERICALLY SYMMETRICAL ACCRETION [J].
BONDI, H .
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 1952, 112 (02) :195-204
[6]   Some applications of the Lambert W function to classical statistical mechanics [J].
Caillol, JM .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (42) :10431-10442
[7]  
Chakrabarti S. K., 1990, Theory of Transonic Astrophysical Flows
[8]   On the Lambert W function [J].
Corless, RM ;
Gonnet, GH ;
Hare, DEG ;
Jeffrey, DJ ;
Knuth, DE .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 5 (04) :329-359
[9]   Coronal holes and the high-speed solar wind [J].
Cranmer, SR .
SPACE SCIENCE REVIEWS, 2002, 101 (3-4) :229-294
[10]   Acceleration of the solar wind as a result of the reconnection of open magnetic flux with coronal loops [J].
Fisk, LA .
JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS, 2003, 108 (A4)