Accelerator physics issues for future electron-ion colliders

Interest continues to grow in the physics of collisions between electrons and heavy ions, and between polarized electrons and polarized protons. We compare the parameters of some machines under discussion. DESY has begun to explore the possibility of upgrading the existing HERA-p ring to store heavy ions, in order to collide them with electrons (or positrons) in the HERA-e ring, or from TESLA. An upgrade to store polarized protons in the HERA-p ring is also under discussion. BNL is considering adding polarized electrons to the RHIC repertoire, which already includes heavy and light ions, and polarized protons. The authors of this paper have made a first pass analysis of this "eRHIC" possibility. MIT-BATES is also considering electron ion collider designs.