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 
                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"