Sattin, F.; Escande, D.F. Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields. Symmetry2021, 13, 1784.
Sattin, F.; Escande, D.F. Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields. Symmetry 2021, 13, 1784.
Sattin, F.; Escande, D.F. Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields. Symmetry2021, 13, 1784.
Sattin, F.; Escande, D.F. Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields. Symmetry 2021, 13, 1784.
Abstract
The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic–although possibly incommensurate–motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet–to our knowledge–such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle’ orbit without the need to pass through the hourly law of motion.
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