Why Centrifugal Force in the Derivation of Curvature Drift

[RubinLicht]

Homework Statement

This is a question about a pretty basic plasma physics derivation. In the standard derivation of the Curvature Drift of a charged particle in a magnetic field with curvature, the force that they use is the "imaginary" centrifugal force (or the force the guiding center sees in its own frame. The derivation is shown below (it is not complete, only includes up to relevant parts).

My question: Why do they use the centrifugal force? why not the "real" average force acting on the particle, which is a force pointing towards the center of curvature, not away?

Homework Equations

the drift due to arbitrary force is shown in equation 2.40

The Attempt at a Solution

I tried following the derivation of 2.40 to see why they would use the force in the frame of the guiding center instead of the "actual" average force acting on the guiding center, but I couldn't figure out where that might come in.

 

[_coyote_]

I think it has something to do with the fact that the particle is moving in a curved path, but I'm not sure.