As a step towards a physically realistic model of a fast dynamo, we st
udy numerically a kinematic dynamo driven by convection in a rapidly r
otating cylindrical annulus. Convection maintains the quasi-geostrophi
c balance whilst developing more complicated time-dependence as the Ra
yleigh number is increased. We incorporate the effect ol Ekman suction
and investigate dynamo action resulting from a chaotic pow obtained i
n this manner. We examine the growth rate as a function of magnetic Pr
andtl number Pm, which is proportional to the magnetic Reynolds number
. Even for the largest value of Pm considered a clearly identifiable a
symptotic behaviour is not established. Nevertheless the available evi
dence strongly suggests a fast dynamo process.