In the textbook 'Introduction to Plasma Physics and Controlled Fusion' (F. Chen) the Curvature Drift of a particle in a magnetic field with constant radius of curvature is derived like this:
A particle in the field experiences a centrifugal force $\vec{F}_{cf}$, pointing outwards from the center of curvature.
Then, because we know that a force applied to a particle in a magnetic field results in a drift, given by $\vec{v} = \frac{1}{q}\frac{\vec{F}\times\vec{B}}{B^2}$, it follows that the drift due to the curvature of the B field is $\vec{v}_R = \frac{1}{q}\frac{\vec{F}_{cf}\times\vec{B}}{B^2}$.
This argument doesn't seem convincing to me: The equation for the drift of a particle when experiencing a general force was derived in an inertial reference frame. Now we are substituting the centrifugal force, which only exists in the accelerating reference frame of the particle, for $\vec{F}$ to find the drift.
Why aren't we using the centripetal force to find the drift, and getting a drift velocity in the opposite direction instead as a result?
