ABSTRACT
This chapter focuses on methods to treat noncartesian geometrical effects in curvilinear coordinates. It discusses generalized geometric treatments of plasmas. In plasma physics, geometry plays an essential role partly because the Coulombic interaction is long-ranged; the influence of boundaries and the shape of the plasma and device are directly related to the properties of the state of the plasma. In this sense, the behavior of plasmas can be said to be (often) essentially global. The chapter examines the techniques to handle geometry in magnetohydrodynamic (MHD), kinetic, and transport levels. It considers corrections that arise from the transition from cylindrical geometry to toroidal geometry. The chapter discusses applications of generalized coordinates and tensor analysis to the three dimensional particle and MHD codes. It also discusses the toroidal case in particular and also focuses on flux coordinates. The chapter presents a method for solving MHD and transport equations in an axisymmetric geometry in flux coordinates.
