  In helical hydromagnetic turbulence with an imposed magnetic field (which is
constant in space and time) the magnetic helicity of the field within a
periodic domain is no longer an invariant of the ideal equations.
Alternatively, there is a generalized magnetic helicity that is an invariant of
the ideal equations. It is shown that this quantity is not gauge invariant and
that it can therefore not be used in practice. Instead, the evolution equation
of the magnetic helicity of the field describing the deviation from the imposed
field is shown to be a useful tool. It is demonstrated that this tool can
determine steady state quenching of the alpha-effect. A simple three-scale
model is derived to describe the evolution of the magnetic helicity and to
predict its sign as a function of the imposed field strength. The results of
the model agree favorably with simulations.
