  We present calculations of magnetic potential associated with the
perturbation of Saturn's magnetic field by a rotating, equatorially-situated
disc of plasma. Such structures are central to the dynamics of the rapidly
rotating magnetospheres of Saturn and Jupiter. They are `fed' internally by
sources of plasma from moons such as Enceladus (Saturn) and Io (Jupiter). We
use a scaled form of Euler potentials for the Jovian magnetodisc field (Caudal,
1986). In this formalism, the magnetic field is assumed to be azimuthally
symmetric about the planet's axis of rotation, and plasma temperature is
constant along a field line. We perturb the dipole potential by using
simplified distributions of plasma pressure and angular velocity for both
planets, based on observations by Cassini (Saturn) and Voyager (Jupiter). Our
results quantify the degree of radial `stretching' exerted on the dipolar field
lines through the plasma's rotational motion and pressure. A simplified version
of the field model, the `homogeneous disc', can be used to easily estimate the
distance of transition in the outer magnetosphere between pressure-dominated
and centrifugally-dominated disc structure. We comment on the degree of
equatorial confinement as represented by the scale height associated with disc
ions of varying mass and temperature. For Saturn, we identify the principal
forces which contribute to the magnetodisc current and make comparisons between
the field structure predicted by the model and magnetic field measurements from
Cassini. For Jupiter, we reproduce Caudal's original calculation in order to
validate our model implementation. We also show that compared to Saturn, where
plasma pressure gradient is, on average, weaker than centrifugal force, the
outer plasmadisc of Jupiter is clearly a pressure-dominated structure.
