Modified plasma–fluid equations from nonstandard Lagrangians with applications to nuclear fusion

Abstract

Nonstandard Lagrangian dynamics have gained great interest recently, in particular within the theory of nonlinear differential equations and dissipative dynamical systems. In this paper, we address their implications in plasma–fluid dynamics. The mathematical settings are constructed starting from the modified Vlasov–Boltzmann transport equation, which is derived from modified Euler–Lagrange equations of motion. Far from giving a self-consistent nonstandard Lagrangian theory of plasma–fluid dynamics, in this paper we have just introduced the basic settings and discussed some illustrative examples that such a modified theory should have in plasma–fluid theory and nuclear fusion.