Incoherent Effects Driven by the Electron Cloud∗

As a result of the synchrotron radiation from a positivelycharged beam, an electron cloud is expected to develop in the vacuum chamber from the combined effects of the photoelectric and secondary emission processes [1–3]. We provide here a first estimate of the electron-cloud effect on individual particles of the beam. We focus on the spacecharge tune spread, the distortion of the beta function and the dispersion, and synchro-betatron coupling. We illustrate the effects with numerical applications to the PEP-II positron ring [4]. We conclude that the magnitude of the effect is not negligible, although it is not large either. However, the present calculations can only be considered as a first estimate, since they do not include details of the electron cloud formation in different regions of the ring. 1 METHOD AND APPROXIMATIONS We assume that an electron cloud has been established in the vacuum chamber of a positively-charged beam of closely spaced bunches. Although our analysis can be applied to any case with similar conditions, we will choose as an example the PEP-II low-energy ring (LER), which contains the positron beam. Numerical simulations for the pumping straight chambers in the arcs of the PEP-II LER for a photon reflectivity R ' 1, photoelectric yield Y ′ = 1 and secondary electron yield corresponding to TiN, show that the electron cloud density is approximately uniform near the center of the chamber [3]. Indeed, the density on axis is d ' 6.5 × 10 electrons/cm, while its average value is d̄ ' 4.1 × 10 electrons/cm. For the purposes of this article we will make the approximation that the electron cloud density is uniform throughout the chamber and we will focus on the details of the electron cloud within a positron bunch as it traverses this uniform cloud. For vacuum chamber regions within a dipole magnetic field, the uniform-density approximation is not a good one, and a more detailed calculation is required. For the PEP-II LER, however, the pumping straight chambers account for ∼ 93% of the arc length and ∼ 62% of the ring circumference; hence our results, though incomplete, are meaningful. When a bunch travels through the cloud, its head sees a density d̄; trailing positrons within the bunch sample different values of the density as the electrons are pulled in. The local electron density d is characterized by a dimensionless function ρ(z) of the longitudinal coordinate z such ∗Work supported by the US Department of Energy under contract no. DE-AC03-76SF00098. Presented at the PAC99, New York City, March 29-April 2nd, 1999. † E-mail: [email protected]. 1.5