Drift theory of charged particles in electric and magnetic fields

Abstract

In this paper we review the drift theory of charged particles in electric and magnetic fields. No new physical interpretations are added to this classical topic, but through an alternative, simplified derivation of the guiding centre velocity, several complexities are eliminated and possible misconceptions of the theory are clarified.

It is shown that:

  1. (i)

    The curvature/gradient drift velocity in the magnetic field, averaged over a particle distribution function is to lowest order in the direction of×B/B 2, while the average particle velocity is in the direction ofB×∇ P withP the scalar particle pressure.

  2. (ii)

    These drift directions are correct for first-order expansions of the particle distribution function, and only second-order or higher expansions change these directions.

  3. (iii)

    The∇×B/B 2 drift, which is the standard gradient plus curvature drift, and which is usually considered as a ‘single particle’ drift, need not be ‘reconciled’ with theB× P, or ‘macroscopic, collective’ drift, as is often asserted in the literature. They are in fact related per definition and we show how.

  4. (iv)

    When viewed in fixed momentum intervals (p,p+dp), the so-called Compton-Getting factor enters into the electric field (E×B)/B 2 drift term.

  5. (v)

    The results are independent of the scale length of variation ofE andB, in contrast to existing drift theory. We discuss the implications of this result for three important cases.

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Burger, R.A., Moraal, H. & Webb, G.M. Drift theory of charged particles in electric and magnetic fields. Astrophys Space Sci 116, 107–129 (1985). https://doi.org/10.1007/BF00649278

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Keywords

  • Magnetic Field
  • Charged Particle
  • Particle Velocity
  • Drift Velocity
  • Scalar Particle