Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
110θ mv zvv ⊥v yv xFigure 4.13: Particles having velocities in the loss cone are preferentially lostpotential difference. Another way of thinking of this is to note that at the top ofthe torus the particle is drifting out, while at the bottom, it is drifting inwards.These two drifts compensate. The helicity of the lines of force is called therotational transform and is shown in Fig. 4.154.4.3 Particle orbits in a tokamak fieldThe toroidal magnetic field in a tokamak varies inversely with major radius. Tosee this, let us apply Ampere’s law around a closed circular loop threading thetorus. We assume this imaginary loop encloses N toroidal field coils each carryingcurrent I in the same direction. We then have∮B.dl = 2πRB = µ 0 NI
4.4 Inhomogeneous Fields 111Figure 4.14: The grad B drift separates vertically the electrons and ions. Theresulting electric field and E/B drift pushes the plasma outwards.Figure 4.15: A helical twist (rotational transform) of the toroidal lines of forceis introduced with the induction of toroidal current in the tokamak. Electronsfollow the magnetic lines toroidally and short out the charge separation causedby the grad B drift.B = µ 0NI2πR . (4.91)
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110θ mv zvv ⊥v yv xFigure <strong>4.1</strong>3: Particles having velocities in the loss cone are preferentially lostpotential difference. Another way of thinking of this is to note that at the top ofthe torus the particle is drifting out, while at the bottom, it is drifting inwards.These two drifts compensate. The helicity of the lines of force is called therotational transform and is shown in Fig. <strong>4.1</strong>54.4.3 Particle orbits in a tokamak fieldThe toroidal magnetic field in a tokamak varies inversely with major radius. Tosee this, let us apply Ampere’s law around a closed circular loop threading thetorus. We assume this imaginary loop encloses N toroidal field coils each carryingcurrent I in the same direction. We then have∮B.dl = 2πRB = µ 0 NI
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