2 - Particle orbit theory  pp. 12-47

Particle orbit theory

By T. J. M. Boyd and J. J. Sanderson

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On the face of it, solving an equation of motion to determine the orbit of a single charged particle in prescribed electric and magnetic fields may not seem like the best way of going about developing the physics of plasmas. Given the central role of collective interactions hinted at in Chapter 1 and the subtle interplay of currents and fields that will be explored in the chapters on MHD that follow, it is at least worth asking “Why bother with orbit theory?”. One attraction is its relative simplicity. Beyond that, key concepts in orbit theory prove useful throughout plasma physics, sometimes shedding light on other plasma models.

Before developing particle orbit theory it is as well to be clear about conditions under which this description might be valid. Intuitively we expect orbit theory to be useful in describing the motion of high energy particles in low density plasmas where particle collisions are infrequent. More specifically, we need to make sure that the effect of self-consistent fields from neighbouring charges is small compared with applied fields. Then if we want to solve the equation of motion analytically the fields in question need to show a degree of symmetry. We shall find that scaling associated with an applied magnetic field is one reason – indeed the principal reason – for the success of orbit theory. Particle orbits in a magnetic field define both a natural length, rL, the particle Larmor radius, and frequency, ω, the cyclotron frequency.