  The charged wave packets with non-Gaussian spatial profiles are shown to
possess intrinsic multipole moments. The magnetic dipole moment and the
electric quadrupole moment are found for a wide class of the packets, including
the vortex electrons with orbital angular momentum $\ell$, the Airy beams, the
so-called Schr\"odinger's cat states, and their generalizations. For the
packets with no phase vortices, the electric quadrupole moment is shown to grow
quadratically with the packet's width, $|Q_{\alpha\beta}| \sim e\cdot
\sigma_{\perp}^2$, while it is also $|\ell|$ times enhanced for the vortex
beams. For available beams of electron microscopes, these multipole moments are
relatively easily adjusted and can be quite large, which affects the packets'
electromagnetic fields and also allows one to develop new diagnostic tools for
materials science, atomic and molecular physics, nuclear physics, and so forth.
