A class of exact two‐dimensional kinetic current sheet equilibria

Abstract

1] The present paper discusses a class of exact two-dimensional kinetic current sheet equilibria. The general solution to the two-dimensional Grad-Shafranov equation was first obtained by Walker in 1915 in terms of the generating function g(z) (z = X + iZ), where X and Z are two dimensionless spatial coordinates. There are infinite choices of g(z), but not every solution yields physically meaningful or mathematically useful form. The known solutions to date with geophysical application include those by Harris [1962], Fadeev et al. [1965], Kan [1973], Manankova et al. [2000], and Brittnacher and Whipple [2002]. In this paper, these solutions are reviewed systematically, and several new solutions are proposed. These include a generalization of the Harris-Fadeev-Kan-Manankova line of model, a model for an isolated X-line alternative to that of Brittnacher-Whipple, and finally a model which represents an isolated magnetic island. Citation: Yoon, P. H., and A. T. Y. Lui (2005), A class of exact two-dimensional kinetic current sheet equilibria,

Comment on “A class of exact two‐dimensional kinetic current sheet equilibria” by Peter H. Yoon and Anthony T. Y. Lui

“…With this in mind, it appears that equation (3) gives a way to locate the singularities directly from properties of the generating function g; therefore one does not need to find them from the final expression of É which was done in sections 3.3 to 3.9 of Yoon and Lui [2005]. It is particularly convenient when É takes a rather complicated form.…”

“…This class is a 2-D extension of the initial 1-D work of Harris which itself has been extended in different papers (in addition to those presented by Yoon and Lui [2005], see Channell [1976], Mottez [2003], and Génot et al [2005]). This class of equilibria includes results derived by other authors (termed the Harris-Fadeev-Kan-Manankova solution), a generalization of this solution, and new configurations for isolated X line and isolated magnetic island.…”

“…is obtained in terms of the generating function g(z) with z = X + iZ, where X and Z are two dimensionless spatial coordinates (we respect notations used by Yoon and Lui [2005]). The formal solution to equation (1) is given by…”

“…[1] In a recent article, Yoon and Lui [2005] discuss a class of two-dimensional (2-D) kinetic current sheet equilibria. This class is a 2-D extension of the initial 1-D work of Harris which itself has been extended in different papers (in addition to those presented by Yoon and Lui [2005], see Channell [1976], Mottez [2003], and Génot et al [2005]).…”

Thin current sheets with strong bell-shape guide field: Cluster observations and models with beams

“…Sitnov et al (2000) and Zelenyi et al (2000) have developed a 1-D thin CS (TCS) model assuming that the current is provided by transient (or Speiser) ions (Speiser, 1965). In contrast to 2-D models with an isotropic pressure tensor (Birn et al, 2004;Yoon and Lui, 2005;Nickeler and Wiegelmann, 2010;Vasko et al, 2013) in the TCS model the magnetic field tension along the x axis is balanced by the ion pressure anisotropy (Eastwood, 1972(Eastwood, , 1974. Detailed comparisons with spacecraft observations have shown that the TCS model well describes the CS structure .…”