  We have studied the large scale dynamo process forced with helical magnetic
energy. The magnetically driven dynamo is not so well studied as kinetically
forced dynamo. It has been thought to represent the amplification of magnetic
field in the stellar corona, accretion disk, or plasma lab. However, the
interaction between the helical magnetic field and plasma is a more fundamental
phenomenon that can be extended to the early Universe. The scale-invariant
helical magnetic field not only explains the currently observed large scale
astrophysical magnetic fields but also has information on the horizon scale in
the early Universe.
  The interaction between magnetic field and plasma is inherently non-linear,
making its mechanism difficult to understand. But, if the plasma system is
driven with helical field, the process can be linearized with alpha&betaand
large scale magnetic field. Conventionally, alpha effect is thought to transfer
magnetic field to the large scale regime, and betaeffect diffuses magnetic
field. However, these conclusions are based on the incompletely derived
alpha&beta. To get the exact profiles of evolving alpha&\b{eta}, we solved a
coupled semi-analytic equation set and applied the result to simulation data
for the large scale magnetic helicity and magnetic energy.
  Our result shows that the averaged alpha effect decreases before making a
significant contribution to the amplification of large scale B field. Rather,
betaeffect, which keeps negative, de facto plays a key role in the
amplification of large scale B field with Laplacian. And, this negative
diffusivity accounts for the attenuation of plasma kinetic energy
