Quantify the required smallness of the adiabaticity coefficient

Determine how much smaller than unity the adiabaticity coefficient must be to guarantee the validity of the adiabatic approximation for the magnetic transport of electrons in non-uniform static guiding magnetic fields.

Background

The adiabatic approximation is commonly used to describe the motion of charged particles in slowly varying magnetic fields. A dimensionless adiabaticity coefficient is typically introduced to characterize the degree of slowness of the field variation relative to the particle’s motion, and adiabatic transport is asserted when this coefficient is much smaller than one.

However, the paper emphasizes that the precise quantitative bound on this coefficient remains unspecified. Establishing this threshold would clarify the regime of validity for the adiabatic approximation and delineate when non-adiabatic (Størmer/chaotic) effects must be taken into account for reliable predictions of charged-particle trajectories and confinement or loss.