Magnetic Fields of Equilibrium Plasmas

Abstract

In this chapter we describe the magnetic structure of equilibrium plasmas in tokamaks. First we briefly recall the Grad-Shafranov equation for the equilibrium magnetic configuration of plasmas. Then the magnetic configurations in the plasmas with the circular cross section will be considered. Particularly, the standard model of the magnetic field and the model of the equilibrium plasmas with the Shafranov shift will be presented. We describe also the analytical equilibria for the plasmas with the elongated shape, particularly, with the magnetic separatrix recently proposed in the literature. The generic properties of a magnetic field near the magnetic separatrix and the X-point will be studied. Finally, we consider also the so-called wire models of plasmas, which are often used to study the magnetic field of tokamak plasmas near the magnetic separatrix and the divertor. Particularly, we study the so-called magnetic field with the snowflake divertor configuration recently proposed to expand the heat load on the divertor plates.