  We present a detailed description of the electromagnetic filter for the
PTOLEMY project to directly detect the Cosmic Neutrino Background (CNB).
Starting with an initial estimate for the orbital magnetic moment, the
higher-order drift process of ExB is configured to balance the gradient-B drift
motion of the electron in such a way as to guide the trajectory into the
standing voltage potential along the mid-plane of the filter. As a function of
drift distance along the length of the filter, the filter zooms in with
exponentially increasing precision on the transverse velocity component of the
electron kinetic energy. This yields a linear dimension for the total filter
length that is exceptionally compact compared to previous techniques for
electromagnetic filtering. The parallel velocity component of the electron
kinetic energy oscillates in an electrostatic harmonic trap as the electron
drifts along the length of the filter. An analysis of the phase-space volume
conservation validates the expected behavior of the filter from the adiabatic
invariance of the orbital magnetic moment and energy conservation following
Liouville's theorem for Hamiltonian systems.
