  We study how the shape of a periodic magnetic field affects the presence of
Majorana bound states (MBS) in a nanowire-superconductor system. Motivated by
the field configurations that can be produced by an array of nanomagnets, we
consider spiral fields with an elliptic cross-section and fields with two
sinusoidal components. We show that MBS are robust to imperfect helical
magnetic fields. In particular, if the amplitude of one component is tuned to
the value determined by the superconducting order parameter in the wire, the
MBS can exist even if the second component has a much smaller amplitude. We
also explore the effect of the chemical potential on the phase diagram. Our
analysis is both numerical and analytical, with good agreement between the two
methods.
