Electron - Cloud Build - Up : Theory and Data ∗

We present a broad-brush survey of the phenomenology, history and importance of the electron-cloud effect (ECE). We briefly discuss the simulation techniques used to quantify the electron-cloud (EC) dynamics. Finally, we present in more detail an effective theory to describe the EC density build-up in terms of a few effective parameters. For further details, the reader is encouraged to refer to the proceedings of many prior workshops, either dedicated to EC or with significant EC contents, including the entire “ECLOUD” series [1–22]. In addition, the proceedings of the various flavors of Particle Accelerator Conferences [23] contain a large number of EC-related publications. The ICFA Beam Dynamics Newsletter series [24] contains one dedicated issue, and several occasional articles, on EC. An extensive reference database is the LHC website on EC [25]. THE BASIC OVERALL PICTURE The qualitative picture of the development of an electron cloud for a bunched beam is as follows: 1. Upon being injected into an empty chamber, a beam generates electrons by one or more mechanisms, usually referred to as “primary,” or “seed,” electrons. 2. These primary electrons get rattled around the chamber from the passage of successive bunches. 3. As these electrons hit the chamber surface they yield secondary electrons, which are, in turn, added to the existing electron population. This process repeats with the passage of successive bunches. The EC density ne grows until a saturation level is reached. The density gradually decays following beam extraction, or during the passage of a gap in the beam. In many cases of interest, the net electron motion in the longitudinal direction, i.e. along the beam direction, is not significant, hence the electron cloud is sensibly localized. For this reason, in first approximation, it makes sense to study it at various locations around the ring independently of the others. In addition, given that the essential dynamics of the electrons is in the transverse plane, i.e. perpendicular to the beam direction, two-dimensional simulations ∗Work supported by the US DOE under contract DE-AC0205CH11231 and by the CesrTA program. Invited talk presented at the ECLOUD10 Workshop (Cornell University, Oct. 8-12, 2010). †[email protected] are also a good first approximation to describe the build-up and decay. In some cases, such as the PSR, electron generation, trapping and ejection from quadrupole magnets is now known to be significant, and these electrons act as seeds for the EC buildup in nearby drift regions [26]. The main sources of primary electrons are: photoemission from synchrotron-radiated photons striking the chamber walls; ionization of residual gas; and electron generation from stray beam particles striking the walls of the chamber. Depending on the type of machine, one of these three processes is typically dominant. For example, in positron or electron storage rings, upon traversing the bending magnets, the beam usually emits copious synchrotron radiation with a ∼keV critical energy, yielding photoelectrons upon striking the vacuum chamber. In proton rings, the process is typically initiated by ionization of residual gas, or from electron generation when stray beam particles strike the chamber. The above-mentioned primary mechanisms are usually insufficient to lead to a significant EC density. However, the average electron-wall impact energy is typically∼100– 200 eV, at which secondary electron emission is significant. As implied by the above description, secondary emission readily exponentiates in time, which can lead to a large amplification factor, typically a few orders of magnitude, over the primary electron density, and to strong temporal and spatial fluctuations in the electron distribution [27]. This compounding effect of secondary emission is usually the main determinant of the strength of the ECEs, and is particularly strong in positively-charged bunched beams (in negatively-charged beams, the electrons born at the walls are pushed back into the wall with relatively low energy, typically resulting in relatively inefficient secondary emission). The ECE combines many parameters of a storage ring such as bunch intensity, size and spacing, beam energy [28], vacuum chamber geometry, vacuum pressure, and electronic properties of the chamber surface material such as photon reflectivity Rγ , effective photoelectric yield (or quantum efficiency) Yeff , secondary electron yield (SEY), characterized by the function δ(E) (E =electron-wall impact energy), secondary emission spectrum [29, 30], etc. The function δ(E) has a peak δmax typically ranging in 1−4 at an energyE = Emax typically ranging in 200−400 eV. A convenient phenomenological parameter is the effective SEY, δeff , defined to be the average of δ(E) over all electron-wall collisions during a relevant time window. Unfortunately, there is no simple a-priori way to determine δeff , because it depends in a complicated way on a combination of many of the above-mentioned beam and chamber parameters. If δeff < 1, the chamber walls act as net absorbers of electrons and ne grows linearly in time following beam injection into an empty chamber. The growth saturates when the net number of electrons generated by primary mechanisms balances the net number of electrons absorbed by the walls. If δeff > 1, the EC grows exponentially. This exponential growth slows down as the space-charge fields from the electrons effectively neutralize the beam field, reducing the electron acceleration. Ultimately, the process stops when the EC space-charge fields are strong enough to repel the electrons back to the walls of the chamber upon being born, at which point δeff becomes = 1. At this point, the EC distribution reaches a dynamical equilibrium characterized by rapid temporal and spatial fluctuations, determined by the bunch size and other variables. For typical present-day storage rings, whether using positron or proton beams, the spatio-temporal average ne reaches a level ∼ 1010−12 m−3, the energy spectrum of the electrons typically peaks at an energy below ∼ 100 eV, and has a high-energy tail reaching out to keV’s. Figure 1 illustrates the build-up of the electron cloud in the LHC. If there is a gap in the beam, or if the beam is extracted, the cloud dissipates with a falltime that is controlled by the low-energy value of δ(E) [31]. In general, there is no simple, direct correlation between the risetime and the falltime. In regions of the storage ring with an external magnetic field, such as dipole bending magnets, quadrupoles, etc., the EC distribution develops characteristic geometrical patterns. For typical fields in the range B = 0.01 − 5 T and typical EC energies < 100 eV, the electrons move in tightly-wound spiral trajectories about the field lines. In practice, in a bending dipole, the electrons are free to move in the vertical (y) direction, but are essentially frozen in the horizontal (x). As a result, the y-kick imparted by the beam on a given electron has an x dependence that is remembered by the electron for many bunch passages. It often happens that the electron-wall impact energy equals Emax at an x-location less than the horizontal chamber radius. At this location δ(E) = δmax, hence ne is maximum, leading to characteristic high-density vertical stripes symmetrically located about x = 0 [32]. For quadrupole magnets, the EC distribution develops a characteristic four-fold pattern, with characteristic four-fold stripes [33]. In summary, the electron-cloud formation and dissipation: • Is characterized by rich physics, involving many ingredients pertaining to the beam and its environment. • Involves a broad range of energy and time scales. • Is always undesirable in particle accelerators. • Is often a performance-limiting problem, especially in present and future high-intensity storage rings. • Is challenging to accurately quantify, predict and extrapolate. The main goals of current research in electron-cloud physics are, in no particular order of importance or relevance: • Identify the relevant variables in each case. • Estimate the electron density, time dependence, incident flux at the walls of the chamber walls, etc. • Compare predictions against measurements as thoroughly as possible; iterate the process and pin down the values of the relevant variables. • Predict the magnitude of the effect in other cases; if possible, minimize the effect at the design stages of new machines. • Define a relatively simple set of rules of thumb, or a simple effective theory, to approximately determine the severity of the effect. • Design and implement mitigation or suppression mechanisms. These latter mechanisms can be classified into passive and active. Passive mechanisms that have been employed at various machines include: • Coating the chamber with low-emission substances such as TiN [34, 35], TiZrV [19, 36–42] and amorphous carbon (a-C) [43, 44]. • Etching grooves on the chamber surface in order to make it effectively rougher, thereby decreasing the effective quantum efficiency via transverse grooves [45] or the effective SEY via longitudinal grooves [46, 47]. • Implementing weak solenoidal fields (∼10–20 G) to trap the electrons close to the chamber walls, thus minimizing their detrimental effects on the beam [48, 49] In terms of active mechanisms, clearing electrodes [50, 51] show significant promise in controlling the electron cloud development. If an electron cloud is unavoidable and problematic, active mechanisms that have been employed to control the stability of the beam include tailoring the bunch fill pattern [52] and increasing the storage ring chromaticity [27]. Fast, single-bunch, feedback systems are under active investigation as an effective mechanism to stabilize electron-cloud induced coherent instabilities [53, 54]. BRIEF HISTORY: BCE AND CE The year 1995 is a dividing mark in the history of the ECE. That year, a report was published describing a fast and peculiar transverse coupled-bunch instability at the Photon Factory (PF) at KEK [55] that arose only when the machine was operated with a positron beam. Unlike the Figure 1: Cartoon illustrating the build-up of the electron cloud in the LHC for the case of 25-ns bunch spacing. The process starts with photoelectrons and is amplified by the secondary emission process. This cartoon was generated by F. Ruggiero. ion-induced instability observed when the PF was operated with an electron beam, the positron beam instability persisted even with a substantial gap in the bunch train. The observed coupled-bunch mode spectrum for the positron beam was qualitatively different from that for an electron beam under otherwise similar conditions. The phenomenon disappeared when the bunch spacing was sufficiently large, and it could not be attributed to known machine impedances. The amplitude of the unstable motion reached saturation and was accompanied by the excitation of vertical coupled-bunch oscillations, and possibly of vertical emittance growth. Experimental analysis [55], simulations [56] and analytical work [57] showed that the cause of the instability is an electron cloud (EC) that developed inside the vacuum chamber generated by photoelectron emission by synchrotron radiation from the beam striking the walls of the chamber. This photoelectron instability (PEI) [56] is one of many ECEs investigated in positron storage rings since then. The phenomenon was subsequently studied in dedicated experiments at BEPC [58] and the APS [59]. The ECE led to serious performance limitations at PEP-II and KEKB [60]. A closely related coupled-bunch instability was previously observed at CESR, although in this case the photoelectrons were trapped and localized in a section of the ring rather than spread out over most of the circumference [61]. A comprehensive program dedicated to measurements and analysis of ECE’s for e+e− storage rings is now ongoing at CESR [62]. The above-mentioned ECE’s are related to previously observed electron-proton dynamical effects such as beaminduced multipacting (BIM), first observed at the CERN proton storage ring ISR [63] when operated with bunched beams. Closely related to BIM is trailing-edge multipacting observed at the LANL spallation neutron source PSR [64], where electron detectors register a large signal during the passage of the tail of the bunch even for stable beams. All ECEs in e+e− as well as in hadron storage rings have precursors in the e-p instabilities for bunched and unbunched beams first seen at BINP in the mid-60s [65]. For the above reasons, 1995 marks the beginning1 of the Common Era (CE) of the ECE (i.e., common to lepton and hadron rings). Before the Common Era (BCE), the only beam dynamics phenomena that were understood to be caused by electrons pertained to proton beams. As far as I know, 1997 was the first year in which ECEs from both positron and proton storage rings were discussed at the same meeting [2, 3].