Abstract The effect of magnetic field ripple on tokamak plasma without turbulence is studied numerically and augmented with a reduced analytical model that includes neoclassical processes in the presence of non-axisymmetric perturbation and stochastic transport. For this study, a magnetic field ripple perturbation has been implemented in the GYSELA gyrokinetic code. This implementation has been verified thanks to a test of toroidal angular momentum conservation. The GYSELA code was then successfully benchmarked against the NEO code, which solves the drift kinetic equation, and against the reduced model in the collisionality range ν ⋆ ∈ [0.05–0.5] for several amplitudes of the magnetic ripple. An observation, shared by the model, the NEO code and GYSELA simulations is that the thermal drive of the mean poloidal velocity—measured by the k V P coefficient—decreases sharply for large yet experimentally relevant magnetic ripple amplitudes, and may even change sign.