The Fermi Large Area Telescope has recently discovered two giant gamma-ray bubbles which extend north and south of the Galactic center with diameters and heights of the order of H \sim 10 kpc .
We suggest that the periodic star capture processes by the Galactic supermassive black hole Sgr A ^ { * } , with a capture rate of \tau _ { cap } ^ { -1 } \sim 3 \times 10 ^ { -5 } yr ^ { -1 } and an energy release of W \sim 3 \times 10 ^ { 52 } erg per capture , can result in hot plasma injecting into the Galactic halo at a wind velocity of u \sim 10 ^ { 8 } cm s ^ { -1 } .
The periodic injection of hot plasma can produce a series of shocks .
Energetic protons in the bubble are re-accelerated when they interact with these shocks .
We show that for energy larger than E > 10 ^ { 15 } eV , the acceleration process can be better described by the stochastic second-order Fermi acceleration .

We propose that hadronic cosmic rays ( CRs ) within the “ knee ” of the observed CR spectrum are produced by Galactic supernova remnants distributed in the Galactic disk .
Re-acceleration of these particles in the Fermi Bubble produces CRs beyond the knee .
With a mean CR diffusion coefficient in this energy range in the bubble D _ { B } \sim 3 \times 10 ^ { 30 } cm ^ { 2 } s ^ { -1 } , we can reproduce the spectral index of the spectrum beyond the knee and within .
The conversion efficiency from shock energy of the bubble into CR energy is about 10 % .
This model provides a natural explanation of the observed CR flux , spectral indices , and matching of spectra at the knee .