publication . Article . Preprint . 2014

Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

Kaneko, Yuta; Yoshida, Zensho;
Open Access
  • Published: 21 Jan 2014 Journal: Physics of Plasmas, volume 21, page 32,103 (issn: 1070-664X, eissn: 1089-7674, Copyright policy)
  • Publisher: AIP Publishing
Abstract
Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the acti...
Subjects
free text keywords: Condensed Matter Physics, Laplace operator, Physics, Nonlinear system, Symplectic geometry, Vorticity equation, Euler's formula, symbols.namesake, symbols, Classical mechanics, Numerical analysis, Hamiltonian system, Euler system, Physics - Plasma Physics

[1] B. B. Kadomtsev and O. P. Pogutse, Sov. Phys. JETP 38, 283 (1974).

[2] M. N. Rosenbluth, D. A. Monticello, H. R. Strauss, and R. B. White, Phys. Fluids 19, 198 (1976).

[3] H. R. Strauss, Phys. Fluids 19, 134 (1976).

[4] H. R. Strauss, Phys. Fluids 20, 1354 (1977).

[5] P.J. Morrison and J.M. Greene, Phys. Rev. Lett. 45, 790 (1980).

[6] P.J. Morrison and R.D. Hazeltine, Phys. Fluids 27, 886 (1984).

[7] P.J. Morrison, Rev. Mod. Phys. 70 467-521 (1998).

[8] A. Clebsch, J. Reine Angew. Math. 56, 1 (1859).

[9] Z. Yoshida, J. Math. Phys. 50, 113101 (2009). [10] Z. Yoshida and S.M. Mahajan, Plasma Phys. Control. Fusion 54, 014003 (2012). [11] Z. Yoshida and E. Hameiri, J. Phys. A: Math. Theor. 46, 335502 (2013). [12] Y. Kaneko and Z. Yoshida, Plasma Fusion Res. 8, 1401057 (2013). [13] Y. Fukumoto, Topologica 1, 003 (2008). [14] D. Cordoba and C. Marliani, Commun. Pure Appl. Math. 53, 512 (2000). [15] R. Grauer, C. Marliani, Phys. Plasmas 5, 2544 (1998). [16] M. Janvier, Y. Kishimoto and J. Q. Li, Phys. Rev. Lett. 107, 195001 (2011). [17] M. Janvier, Y. Kishimoto and J. Li, Nucl. Fusion 51, 083016 (2011). [18] M. Ottaviani, F. Porcelli, Phys. Rev. Lett. 71, 3802 (1993). [19] T. J. Schep, F. Pegoraro and B. N. Kuvshinov, Phys. Plasmas 1, 2843 (1994). [20] B. N. Kuvshinov, F. Pegoraro and T.J. Schep, Phys. Lett. A 191, 296-300 (1994).

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . Preprint . 2014

Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

Kaneko, Yuta; Yoshida, Zensho;