  Plasmas that are strongly magnetized in the sense that the gyrofrequency
exceeds the plasma frequency exhibit novel transport properties that are not
well understood. As a representative example, we compute the friction force
acting on a massive test charge moving through a strongly coupled and strongly
magnetized one-component plasma using a generalized Boltzmann kinetic theory.
Recent works studying the weakly coupled regime have shown that strong
magnetization leads to a transverse component of the friction force that is
perpendicular to both the Lorentz force and velocity of the test charge; in
addition to the stopping power component aligned antiparallel to the velocity.
Recent molecular dynamics simulations have also shown that strong Coulomb
coupling in addition to strong magnetization gives rise to a third component of
the friction force in the direction of the Lorentz force. Here, we show that
the generalized Boltzmann kinetic theory captures these effects, and generally
agrees well with the molecular dynamics simulations over a broad range of
Coulomb coupling and magnetization strength regimes. The theory is also used to
show that a "gyro" component of the friction in the direction of the Lorentz
force arises due to asymmetries associated with gyromotion during short-range
collisions. Computing the average motion of the test charge through the
background plasma, the transverse force is found to strongly influence the
trajectory by changing the gyroradius and the gyro friction force is found to
slightly change the gyrofrequency of the test charge resulting in a phase
shift.
