  Fermi-LAT reveals two huge gamma-ray bubbles existing in the Galactic Center,
called 'Fermi Bubbles'. The existence of two microwave bubbles at the same
region are also reported by the observation by WMAP, dubbed 'WMAP haze'. In
order to explain these components, It has been argued that the gamma-rays arise
from Inverse-Compton scattering of relativistic electrons accelerated by plasma
turbulence, and the microwaves are radiated by synchrotron radiation. But no
previous research reproduces both the Fermi Bubbles and WMAP haze under typical
magnetic fields in the galaxy. We assume that shocks present in the bubbles and
the efficiency of the acceleration by plasma turbulence, 'stochastic
acceleration', changes with the distance from the shock front. The distance
from the shock front increases with time, accordingly the efficiency of the
acceleration changes with time. We also consider the time development of the
electrons escape from the turbulence by diffusive loss. Our model succeed to
reproduce both the observed characteristics of the Fermi Bubbles and WMAP haze
under typical magnetic fields.
