  Spherical shell dynamo models based on rotating convection show that the flow
within the tangent cylinder is dominated by an off-axis plume that extends from
the inner core boundary to high latitudes and drifts westward. Earlier studies
explained the formation of such a plume in terms of the effect of a uniform
axial magnetic field that significantly increases the lengthscale of convection
in a rotating plane layer. However, rapidly rotating dynamo simulations show
that the magnetic field within the tangent cylinder has severe lateral
inhomogeneities that may influence the onset of an isolated plume. Increasing
the rotation rate in our dynamo simulations (by decreasing the Ekman number
$E$) produces progressively thinner plumes that appear to seek out the location
where the field is strongest. Motivated by this result, we examine the linear
onset of convection in a rapidly rotating fluid layer subject to a laterally
varying axial magnetic field. A cartesian geometry is chosen where the finite
dimensions $(x,z)$ mimic $(\phi,z)$ in cylindrical coordinates. The lateral
inhomogeneity of the field gives rise to a unique mode of instability where
convection is entirely confined to the peak-field region. The localization of
the flow by the magnetic field occurs even when the field strength (measured by
the Elsasser number $\varLambda$) is small and viscosity controls the smallest
lengthscale of convection. The lowest Rayleigh number at which an isolated
plume appears within the tangent cylinder in spherical shell dynamo simulations
agrees closely with the viscous-mode Rayleigh number in the plane layer linear
magnetoconvection model. The localized excitation of viscous-mode convection by
a laterally varying magnetic field provides a mechanism for the formation of
isolated plumes within Earth's tangent cylinder.
