  A non-linear, time-dependent, magnetically driven dynamo theory which shows
how magnetically dominated configurations can relax to become helical on the
largest scale available is presented. Coupled time-dependent differential
equations for large scale magnetic helicity, small scale magnetic helicity,
velocity, and the electromotive force are solved. The magnetic helicity on
small scales relaxes to drive significant large scale helical field growth on
dynamical (Alfv\'en crossing) time scales, independent of the magnitude of
finite microphysical transport coefficients, after which the growing kinetic
helicity slows the growth to a viscously limited pace. This magnetically driven
dynamo complements the nonlinear kinetic helicity driven dynamo; for the
latter, the growing magnetic helicity fluctuations suppress, rather than drive,
large scale magnetic helicity growth. A unified set of equations accommodates
both types of dynamos.
