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Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction

Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction

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106Figure <strong>4.1</strong>0: The grad B drift for a cylindrical field.Note that the two contributions add with similar magnitude because 〈v 2 ‖ 〉∼k B T/m and 1 2 〈v2 ⊥ 〉∼k BT/m.Magnetic mirrors — ∇B ‖ BWe have looked at particle drifts when ∇B is at an angle to B. What happenswhen the gradient is aligned with B? This situation is encountered in magneticmirrors where the magnetic field strength increases along the direction of thelines of force as shown in Fig. <strong>4.1</strong>1.Figure <strong>4.1</strong>1: Schematic diagram showing lines of force in a magnetic mirror device.We shall show that a charged particle inside such a magnetic topology canbe trapped under certain circumstances. Let’s describe mathematically the fieldstructure. The field must be divergence free (no sources or sinks): ∇.B =0. In

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