The interplay of chirality and magnetism is of fundamental physical interest. A free electron on a helix with periodic boundary conditions is possibly the simplest model exhibiting both chirality and orbital paramagnetism. In a previous report we have studied with this model the relation between natural circular, magnetic circular and magnetochiral dichroism. Here we extend our investigation to the second-order nonlinear optical phenomena designated as the inverse Faraday effect and as the inverse magnetochiral effect. Both effects manifest themselves as a radiation-induced time-independent magnetic field which lifts the magnetic degeneracy of the system. While the inverse Faraday effect is circular differential, the comparatively much weaker inverse magnetochiral effect is independent of the polarization of the incident radiation.