Curvature drift is a mode of motion of charged particles in a curved magnetic field. In contrast to the motion of charged particles in a uniform magnetic field, where the charged particles gyrate around the magnetic fields, in curvature drift the particles move mostly parallel to the magnetic field.

Consider a toroidal magnetic field of uniform intensity $ \mathbf{B} = B \hat{\varphi} $. A charge particle in such a field can also move in a helical trajectory, with constant speed. The equations of motion are

$ m \gamma \frac{d \mathbf{v}}{d t} = \frac{q}{c} \mathbf{v} \times \mathbf{B} $

The velocity is assumed to be of the form $ \mathbf{v} = v_z \hat{z} + v_{\varphi} \hat{\varphi} $, where $ v_z $ and $ v_{\varphi} $ are constants. Substituting into the equation of motion, keeping in mind that $ \frac{d \hat{\varphi} }{d t} = - \frac{v_{\varphi}}{r} \hat{r} $, where $ r $ is the distance from the axis, yields

$ v_z = \frac{\gamma m c}{q B r} v_{\varphi}^2 $

In contrast to the helical motion in a uniform magnetic field, where the two components of the velocity are independent.