The envelope instability of high intensity beams in circular accelerators is studied via multiparticle simulations. The space charge kicks are derived from a Gaussian potential model for an efficient tracking. The evolution of the envelope phase space coordinates are derived from the bunch distribution. We found that the envelope stop band played an important role in emittance growth. Correction schemes of the envelope stop bands are studied. Because the space charge force pushes the envelope tunes downward, harmonics less than twice the betatron tunes are also important on emittance growth. Our code is efficient and fast, it can be used to study the effect of space charge force on high power accelerators.
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