  Jupiter's magnetic field is generated by the convection of liquid metallic
hydrogen in its interior. The transition from molecular hydrogen to metallic
hydrogen as temperature and pressure increase is believed to be a smooth one.
As a result, the electrical conductivity in Jupiter varies continuously from
being negligible at the surface to a large value in the deeper region. Thus,
unlike the Earth where the upper boundary of the dynamo---the dynamo
radius---is definitively located at the core-mantle boundary, it is not clear
at what depth dynamo action becomes significant in Jupiter. In this paper,
using a numerical model of the Jovian dynamo, we examine the magnetic energy
spectrum at different depth and identify a dynamo radius below which (and away
from the deep inner core) the shape of the magnetic energy spectrum becomes
invariant. We find that this shift in the behaviour of the magnetic energy
spectrum signifies a change in the dynamics of the system as electric current
becomes important. Traditionally, a characteristic radius derived from the
Lowes--Mauersberger spectrum---the Lowes radius---gives a good estimate to the
Earth's core-mantle boundary. We argue that in our model, the Lowes radius
provides a lower bound to the dynamo radius. We also compare the
Lowes--Mauersberger spectrum in our model to that obtained from recent Juno
observations. The Lowes radius derived from the Juno data is significantly
lower than that obtained from our models. The existence of a stably stratified
region in the neighbourhood of the transition zone might provide an explanation
of this result.
