Variational approach to multi-scale dynamical system; An Application to collisionless magnetic reconnection

Hirota, Makoto; Morrison, P. J.*

In mathematical models that describe multi-scale physics, a microscopic effect often acts as a singular perturbation of macroscopic governing equations; it brings a higher derivative term into the equations. Instead of directly solving such a multi-scale problem, it is mathematically convenient and physically informative to solve it with some approximation techniques such as the (renormalized) perturbation method and the asymptotic matching method. In this talk, we present another approach that utilizes the variational principle. This approach is basically applicable to multi-scale "Hamiltonian" systems in which the singular perturbation does not induce energy dissipation but modifies conservation laws. If successful, we can predict strongly nonlinear dynamics by this approach even when other perturbation techniques fail. As an application, we mainly argue the problem of magnetic reconnection in collisionless (i.e., dissipationless) plasma.