Electron-Cloud Build-Up: Theory and Data

CBP-872/LBNL-xxxx (Mar. 25, 2011) Electron-Cloud Build-Up: Theory and Data M. A. Furman, † Center for Beam Physics, LBNL, Berkeley, CA 94720, and CLASSE, Cornell University, Ithaca, NY 14853 Abstract 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 quan- tify 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 en- tire “ECLOUD” series [1–22]. In addition, the proceed- ings of the various ﬂavors of Particle Accelerator Confer- ences [23] contain a large number of EC-related publica- tions. The ICFA Beam Dynamics Newsletter series [24] contains one dedicated issue, and several occasional arti- cles, 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, usu- ally referred to as “primary,” or “seed,” electrons. 2. These primary electrons get rattled around the cham- ber 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 n e 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 lon- gitudinal 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 dynam- ics of the electrons is in the transverse plane, i.e. perpen- dicular to the beam direction, two-dimensional simulations ∗ Work supported by the US DOE under contract DE-AC02- 05CH11231 and by the CesrTA program. Invited talk presented at the ECLOUD10 Workshop (Cornell University, Oct. 8-12, 2010). † mafurman@lbl.gov are also a good ﬁrst approximation to describe the build-up and decay. In some cases, such as the PSR, electron genera- tion, 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: photoemis- sion from synchrotron-radiated photons striking the cham- ber walls; ionization of residual gas; and electron gener- ation 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 bend- ing magnets, the beam usually emits copious synchrotron radiation with a ∼keV critical energy, yielding photoelec- trons 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 am- pliﬁcation 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 par- ticularly 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 emis- sion). 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 R γ , effective photoelectric yield (or quantum efﬁciency) Y eﬀ , secondary electron yield (SEY), characterized by the function δ(E) (E =electron-wall im- pact energy), secondary emission spectrum [29, 30], etc. The function δ(E) has a peak δ max typically ranging in 1−4 at an energy E = E max typically ranging in 200−400 eV. A convenient phenomenological parameter is the effec- tive SEY, δ eﬀ , deﬁned to be the average of δ(E) over all electron-wall collisions during a relevant time window. Un- fortunately, there is no simple a-priori way to determine