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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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At DESY the Synchrotron Light Source PETRA III offers scientists outstanding opportunities for experiments with hard X-rays of exceptionally high brilliance since 2009. Research activities have been started to upgrade PETRA III to the ultra-low emittance source PETRA IV, which will be diffraction limited up to the hard X-ray range. Therefore the future light source PETRA IV will be ideal for 3D X-ray microscopy of biological, chemical, and physical processes under realistic conditions at length scales from atomic dimensions to millimeters. The lattice design is aiming for a horizontal emittance in the range between 10 pm rad and 30 pm rad at a beam energy of 6 GeV. Presently, two different approaches are considered for the lattice design: a design based on a hybrid multibend achromat with an interleaved sextupole configuration based on the ESRF-EBS design, and a lattice with a double non-interleaved sextupole configuration. The current status of the design activities is reported including the injector and several technical aspects.

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