  We consider the generation of magnetic activity --- dynamo waves --- in the
astrophysical limit of very large magnetic Reynolds number. We consider
kinematic dynamo action for a system consisting of helical flow and large-scale
shear. We demonstrate that large-scale dynamo waves persist at high $Rm$ if the
helical flow is characterised by a narrow band of spatial scales and the shear
is large enough. However for a wide band of scales the dynamo becomes
small-scale with a further increase of $Rm$, with dynamo waves re-emerging only
if the shear is then increased. We show that at high $Rm$ the key effect of the
shear is to suppress small-scale dynamo action, allowing large-scale dynamo
action to be observed. We conjecture that this supports a general "suppression
principle" --- large-scale dynamo action can only be observed if there is a
mechanism that suppresses the small-scale fluctuations.
