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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.