Magnetic cavities, also known as magnetic holes, are ubiquitous in space plasmas
characterized by depressed magnetic strength and enhanced plasma pressure. Most of the observed
cavities are associated with anisotropic particle distributions with higher fluxes in the direction
perpendicular to the magnetic field. Recent observations of kinetic-scale magnetic cavities have
identified another type of electron distributions in the pitch angle spectrum, the so-called donut-shaped
distributions, although their formation mechanism remains unclear. Here, we present a simplistic
model of cavity shrinkage and deepening, in which electrons are traced backward in time to the initial,
equilibrium-state cavity. The resulting electron distributions, determined from Liouville's theorem, agree
with the observations in the presence of donut-shaped pitch angle structures. The model also enables a
quantitative evaluation on the roles of betatron cooling, radial transport, and pitch angle variations in the
formation of donut-shaped electron distributions within evolving magnetic cavities.

magnetic cavity