Adiabaticity of Charged-Particle Trajectories in a Cusped Magnetic Field

Abstract

The region of adiabatic charged-particle motion for a spindle-cusp field is determined on the basis of confinement times both by numerical integration of the particle orbits and by an experiment utilizing electrons. If the critical flux line dividing the adiabatic and nonadiabatic regions is expressed in Grad's form, ψc = (aλ0)3, where λ0 is the cyclotron radius of the particle corresponding to its total velocity, the numerical analysis yields a value for the constant a of 3.5–4.2 and the experiment yields a = 4.36. It is further shown that the transition zone between the regions of adiabatic and nonadiabatic motion is about two-thirds of an electron cyclotron radius in width, and that the relative field variation encountered during one cyclotron period by an electron whose guiding center is located in this zone is between 11 and 19%. A random-walk model of particle motion, based on the near noncorrelation between fluctuations of the magnetic moment on successive traversals of the field, is used to calculate the effect on particle lifetime of the location of the first reflection point, and thereby explain the apparently excessive random scatter of the data.