Centroid Theory of Transverse Electron-proton Two-stream Instability in a Long Proton Bunch Revisited

We have identified a few technical errors in our recent paper on the electron-proton instability [1]. Although the overall qualitative results in the original paper are still correct, an error in Eq. (42) does cause some minor changes in the quantitative results including three figures and alternations in several equations. The most significant change is the required frequency spread for stability given in Eq. (68), which is now found to be twice that given in the original paper. This revision and related changes have been published in a recent Erratum [2]. This note summarizes the main results of the original paper and the highlight of the main changes made in the Erratum.