Lawrence Berkeley National Laboratory is designing a new electron synchrotron for scientific research using synchrotron radiation. An upgrade of the Advanced Light Source (ALS) would position the nation to retain its international competitiveness in the soft X-ray sciences. The ALS is a 1.9 GeV storage ring operating at 500 mA of beam current. It is optimized to produce intense beams of soft X-rays, which offer spectroscopic contrast, nanometer-scale resolution, and broad temporal sensitivity. Upgrading the ALS storage ring from a triple-bend-achromat to a multibend-achromat (MBA) lattice design will provide a soft X-ray source that is up to 100–1,000 times brighter than today’s ALS and will provide a significantly higher fraction of coherent light in the soft X-ray region than is currently available at the ALS. The upgraded ALS will offer the highest coherent flux of any existing or planned storage-ring facility, worldwide, up to a photon energy of 3.5 keV. The addition of an accumulator ring that enables on-axis, swap-out, recovery, and exchange of bunch trains is required to achieve this coherence and brightness. Analysis of the radiation generated and shielding required by the addition of this new accelerator is presented in this paper.