A theoretical analysis of nonlinear electrostatic waves using coupled equations for a magnetized plasma yields a generalized BGK-like equation for trapped-particle distributions that produce these structures in the guiding-center approximation. A conditional requirement is found for electron trapping, and the amount of trapping decreases as the angle of the electric field relative to the backgrounnd magnetic field increases, ceasing at a critical finite angle. The results are applied to broadband electrostatic waves (BEN) in the magnetail. For BEN, trapping can occur over larger angles in the near-Earth case because of the large magnetic field there, whereas trapping is confined to close alignment with the magnetic field further out (e.g., under 20¿ at distances out 13 RE and above), and strongly supports the conclusion that in cases further out into the magnetotail that solitary waves are highly field-aligned.