  Magnetohydrodynamic (MHD) turbulence is of key importance in many high-energy
astrophysical systems, where MHD instabilities can amplify local magnetic field
over very short time scales. Specifically, the magnetorotational instability
(MRI) and dynamo action have been suggested as a mechanism to grow
magnetar-strength magnetic field ($\ge10^{15} G$) and magnetorotationally power
the explosion of a rotating massive star. Such stars are progenitor candidates
for type Ic-bl hypernova explosions and make up all supernovae connected to
long gamma-ray bursts (GRBs). The MRI has been studied with local
high-resolution shearing box simulations in 3D or with global 2D simulations,
but it is an open question whether MRI-driven turbulence can result in the
creation of a large-scale ordered and dynamically relevant field. Here we
report results from global 3D general-relativistic magnetohydrodynamic (GRMHD)
turbulence simulations and show that MRI-driven MHD turbulence in rapidly
rotating protoneutron stars produces an inverse cascade of energy. We find a
large-scale ordered toroidal field that is consistent with the formation of
bipolar magnetorotationally driven outflows. Our results demonstrate that
rapidly rotating massive stars are plausible progenitors for both type Ic-bl
supernovae and long GRBs, present a viable formation scenario for magnetars,
and may account for potentially magnetar-powered superluminous supernovae.
