  Coulomb collisions in plasmas are typically modeled using the Boltzmann
collision operator, or its variants, which apply to weakly magnetized plasmas
in which the typical gyroradius of particles significantly exceeds the Debye
length. Conversely, O'Neil has developed a kinetic theory to treat plasmas that
are so strongly magnetized that the typical gyroradius of particles is much
smaller than the distance of closest approach in a binary collision. Here, we
develop a generalized collision operator that applies across the full range of
magnetization strength. To demonstrate novel physics associated with strong
magnetization, it is used to compute the friction force on a massive test
charge. In addition to the traditional stopping power component, this is found
to exhibit a transverse component that is perpendicular to both the velocity
and Lorentz force vectors in the strongly magnetized regime, as was predicted
recently using linear response theory. Good agreement is found between the
collision theory and linear response theory in the regime in which both apply,
but the new collision theory also applies to stronger magnetization strength
regimes than the linear response theory is expected to apply in.
