  Models of large scale (magnetohydrodynamic) dynamos (LSD) which couple large
scale field growth to total magnetic helicity evolution best predict the
saturation of LSDs seen in simulations. For the simplest so called "{\alpha}2"
LSDs in periodic boxes, the electromotive force driving LSD growth depends on
the difference between the time-integrated kinetic and current helicity
associated with fluctuations. When the system is helically kinetically forced
(KF), the growth of the large scale helical field is accompanied by growth of
small scale magnetic (and current) helicity which ultimately quench the LSD.
Here, using both simulations and theory, we study the complementary
magnetically forced(MF) case in which the system is forced with an electric
field that supplies magnetic helicity. For this MF case, the kinetic helicity
becomes the back-reactor that saturates the LSD. Simulations of both MF and KF
cases can be approximately modeled with the same equations of magnetic helicity
evolution, but with complementary initial conditions. A key difference between
KF and MF cases is that the helical large scale field in the MF case grows with
the same sign of injected magnetic helicity, whereas the large and small scale
magnetic helicities grow with opposite sign for the KF case. The MF case can
arise even when the thermal pressure is approximately smaller than the magnetic
pressure, and requires only that helical small scale magnetic fluctuations
dominate helical velocity fluctuations in LSD driving. We suggest that LSDs in
accretion discs and Babcock models of the solar dynamo are actually MF LSDs.
