@Article{OjedaGonzalezDomiKaibPres:2015:OvImNu,
author = "Ojeda Gonzalez, Arian and Domingues, Margarete Oliveira and
Kaibara, M. K. and Prestes, Alan",
affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Instituto
Nacional de Pesquisas Espaciais (INPE)} and {Universidade Federal
Fluminense (UFF)} and {Instituto Nacional de Pesquisas Espaciais
(INPE)}",
title = "Grad-shafranov reconstruction: overview and improvement of the
numerical solution used in space physics",
journal = "Brazilian Journal of Physics",
year = "2015",
volume = "45",
number = "5",
pages = "493--509",
month = "Oct.",
keywords = "Grad-Shafranov equation, Magnetic flux-ropes, Cauchy problem,
Space plasmas, Kinetic theory.",
abstract = "The Grad-Shafranov equation is a Poisson's equation, i.e., a
partial differential equation of elliptic type. The problem is
depending on the initial condition and can be treated as a Cauchy
problem. Although it is ill-posed or ill-conditioned, it can be
integrated numerically. In the integration of the GS equation,
singularities with large values of the potential arise after a
certain number of integration steps away from the original data
line, and a filter should be used. The Grad-Shafranov
reconstruction (GSR) technique was developed from 1996 to 2000 for
recovering two-dimensional structures in the magnetopause in an
ideal MHD formulation. Other works have used the GSR techniques to
study magnetic flux ropes in the solar wind and in the magnetotail
from a single spacecraft dataset; posteriorly, it was extended to
treat measurements from multiple satellites. From Vlasov equation,
it is possible to arrive at the GS-equation in function of the
normalized vector potential. A general solution is obtained using
complex variable theory. A specific solution was chosen as
benchmark case to solve numerically the GS equation. We propose
some changes in the resolution scheme of the GS equation to
improve the solution. The result of each method is compared with
the solution proposed by Hau and Sonnerup (J. Geophys. Res.
104(A4), 6899-6917 (1999)). The main improvement found in the GS
resolution was the need to filter B (x) values at each y value.",
doi = "10.1007/s13538-015-0342-y",
url = "http://dx.doi.org/10.1007/s13538-015-0342-y",
issn = "0103-9733",
language = "en",
targetfile = "ojeda gonzalez_grad.pdf",
urlaccessdate = "03 dez. 2020"
}