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We report results from calculations investigating stationary magnetic fieldconfigurations in accretion discs around magnetised neutron stars. Our strategyis to start with a very simple model and then progressively improve itproviding complementary insight into results obtained with large numericalsimulations. In our first model, presented here, we work in the kinematicapproximation and consider the stellar magnetic field as being a dipole alignedwith the stellar rotation axis and perpendicular to the disc plane, while theflow in the disc is taken to be steady and axisymmetric. The behaviour in theradial direction is then independent of that in the azimuthal direction. Weinvestigate the distortion of the field caused by interaction with the discmatter, solving the induction equation numerically in full 2D. The influence ofturbulent diffusivity and fluid velocity on the poloidal field configuration isanalysed, including discussion of outflows from the top and bottom of the disc.We find that the distortions increase with increasing magnetic Reynolds numberR_m (calculated using the radial velocity). However, a single global parameterdoes not give an adequate description in different parts of the disc and we useinstead a `magnetic distortion function' D_m(r,\theta) (a magnetic Reynoldsnumber defined locally). Where D_m<<1 (near to the inner edge of the disc)there is little distortion, but where D_m>1 (most of the rest of the disc),there is considerable distortion and the field becomes weaker than the dipolewould have been. Between these two regions, there is a transition zone wherethe field is amplified and can have a local minimum and maximum. The locationof this zone depends sensitively on the diffusivity. The results depend verylittle on the boundary conditions at the top of the disc.

An investigation of magnetic field distortions in accretion discs around neutron stars. I. Analysis of the poloidal field component