The most sensitive desktop-sized ionizer utilising electron bombardment is currently the solenoidal ion source. We present an alternate design for such an ion source whereby the solenoidal windings of the electromagnet are replaced by a shaped cylindrical permanent magnet in order to reduce the complexity and running costs of the instrument. Through finite element modelling of the magnetic field in COMSOL and experimental measurements on a small-scale prototype magnet stack, we demonstrate the required shape of the permanent magnet in order to generate the needed field, and the necessity of soft iron collars to smooth fluctuations along the central axis.