Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction

112To first order in ɛ = r/R 0 ,whereR 0 is the radius of the magnetic axis, the fieldstrength at some point in the torus is (show this)B = B 0 (1 − ɛ cos θ) (4.92)where θ is the poloidal angle coordinate with respect to the magnetic axis and B 0is the magnetic field strength on axis. (See Fig. 4.16 for the coordinate systemused here).If we now follow an electron along a helical field line, then if it starts at theoutside of the torus and moves towards the torus axis (inside), the magnetic fieldincreases. As a result, some of the electrons will be reflected (at points P and QFigure 4.16: Diagram showing toridal magnetic geometryin Fig. 4.17) by the mirror effect. The projection of the guiding centre drift ontothe R–z plane shows a banana-shaped orbit. Between the reflection points thereis an upward drift due to curvature and ∇B. Typically, the banana width fora tokamak < ∼ 0.1a where a is the minor radius. Particles with sufficiently highparallel velocity will penetrate the magnetic well and complete a toroidal circuit.These are called passing particles.