  The kinematic regime of the magnetic dynamo neglects the backreaction of the
magnetic field on the flow. For small magnetic diffusivity, in the early stage
of evolution, there is an ideal phase where dissipative effects can also be
neglected. We estimate the magnitude of the energy dissipation term (Ohmic
heating), taking into account differential constraints on chaotic flows. We
find that the period of ideal evolution is roughly doubled over an estimate
without constraints. The helicity generation terms are exponentially smaller
than the energy dissipation, so that large quantities of energy are dissipated
before any helicity can be created. Helicity flow is exponentially larger than
net helicity generation. The constraints also lead to the existence of a
singular initial condition for the magnetic field for which sizable amounts of
helicity can potentially be created.
