Pulsars have typical magnetic field strengths between 108and 1012G. Therefore, even if the particles are produced with nonzero perpendicular component of velocity at the pole, they radiate out this component quickly due to synchrotron radiation. Therefore, the motion of a particle along a field line becomes one dimensional in regions where filed lines are straight. However, when they move along the curved magnetic field lines, they get accelerated due to the centrifugal force. They gain again

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... e perpendicular energy at the expense of parallel energy, but can not gyrate in the curved field lines and hence do not experience any curvature or gradient drifts.