Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
108where the subscript 0 refers to the low field conditions and subscript m is forthe high field “mirror” region. Thus if B m >B 0 then v ⊥m >v ⊥0 . However, theB-field does no work so that the total particle kinetic energy remains unchanged:K = m(v‖ 2 0+ v⊥0 2 )/2 is constant. Therefore, we must have v ‖m
4.4 Inhomogeneous Fields 109Figure 4.12: Top:The flux linked by the particle orbit remains constant as theparticle moves into regions of higher field. The particle is reflected at the pointwhere v ‖ = 0. Bottom: Showing plasma confined by magnetic mirrorwhere the drift is up or down for electrons or ions (see Fig. 4.10). We thus obtainv Tv th∼ ±r LR c≡ κ. (4.90)For H-1NF, κ ≈ 1 × 10 −3 (drift angle to field line) so that the toroidal traveldistance for a particle to drift out of the magnetic volume is d T =0.1m/κ = 100m which is about 16 toroidal orbits.As already noted, the electrons and ions drift in opposite directions. Thisgenerates a vertical electric field as shown in Fig. 4.14. The resulting E×B driftpushes the plasma to the wall and the plasma is not confined.This problem can be remedied by twisting the field lines (by introducinga toroidal current). Particles moving freely along B will then short out the
- Page 9: 4.3 Time Varying Fields 95analogous
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- Page 15 and 16: 4.3 Time Varying Fields 101withD =
- Page 17 and 18: 4.4 Inhomogeneous Fields 103where
- Page 19 and 20: 4.4 Inhomogeneous Fields 105r^F cθ
- Page 21: 4.4 Inhomogeneous Fields 107cylindr
- Page 25 and 26: 4.4 Inhomogeneous Fields 111Figure
- Page 27 and 28: 4.4 Inhomogeneous Fields 113Passing
- Page 29 and 30: 4.4 Inhomogeneous Fields 115Compari
- Page 31 and 32: 4.4 Inhomogeneous Fields 117Problem
4.4 Inhomogeneous Fields 109Figure <strong>4.1</strong>2: Top:The flux linked by the particle orbit remains constant as theparticle moves into regions of higher field. The particle is reflected at the pointwhere v ‖ = 0. Bottom: Showing plasma confined by magnetic mirrorwhere the drift is up or down for electrons or ions (see Fig. <strong>4.1</strong>0). We thus obtainv Tv th∼ ±r LR c≡ κ. (4.90)For H-1NF, κ ≈ 1 × 10 −3 (drift angle to field line) so that the toroidal traveldistance for a particle to drift out of the magnetic volume is d T =0.1m/κ = 100m which is about 16 toroidal orbits.As already noted, the electrons and ions drift in opposite directions. Thisgenerates a vertical electric field as shown in Fig. <strong>4.1</strong>4. The resulting E×B driftpushes the plasma to the wall and the plasma is not confined.This problem can be remedied by twisting the field lines (by introducinga toroidal current). Particles moving freely along B will then short out the
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