The AM Herculis binaries are an important class of cataclysmic variables in which the accreting white dwarf primary is observed to rotate synchronously with the orbit. The torque needed to spin the primary towards synchronism is believed to be generated by the interaction of the primary's magnetic field with the tidally synchronized secondary star. It is shown here that such a torque is generated by the interaction of the magnetosphere of an asynchronous primary with the turbulent secondary. The effects of magnetic diffusion, shearing and field advection are accounted for and the resulting magnetic torques are calculated for a range of degrees of asynchronism. Non-central magnetic forces enable the primary to exchange angular momentum with the orbit, while a torque acts on the star which spins it towards synchronism. This torque has the form of a resonance curve, with a maximum value at moderate asynchronism.
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