Multipoles beyond the quadrupole can correct for spherical aberration and in particle accelerators the dipole bending magnets are really composed of a large number of elements with different superpositions of multipoles.
Usually the dependency is given for the kinetic energy itself depending on the power of the velocity.
So for an electrostatic lens the focal length varies with the second power of the kinetic energy,
while for a magnetostatic lens the focal length varies proportional to the kinetic energy.
And a combined quadrupole can be achromatic around a given energy.
If a distribution of particles with different kinetic energies is accelerated by a longitudinal electric field, the relative energy spread is reduced leading to less chromatic error. An example of this is in the electron microscope.