  We develop an approach to chiral kinetic theories for electrons close to
equilibrium and neutrinos away from equilibrium based on a systematic power
counting scheme for different timescales of electromagnetic and weak
interactions. Under this framework, we derive electric and energy currents
along magnetic fields induced by neutrino radiation in general nonequilibrium
states. This may be regarded as an effective chiral magnetic effect (CME),
which is present without a chiral chemical potential, unlike the conventional
CME. We also consider the so-called gain region of core-collapse supernovae as
an example and find that the effective CME enhanced by persistent neutrino
emission in time is sufficiently large to lead to the inverse cascade of
magnetic and fluid kinetic energies and observed magnitudes of pulsar kicks.
Our framework may also be applicable to other dense-matter systems involving
nonequilibrium neutrinos.
