Electron Cloud Studies for KEKB and ATF KEK, May 17 May 30, 2003

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2 Electron Cloud Studies for KEKB and ATF KEK, May 17 May 3, 23 F. Zimmermann April 12, 23 Abstract I describe a few recent electron-cloud simulations for KEKB and the ATF. For KEKB the dependence of the electron build up on the peak solenoid field is studied, for the ATF the minimum bunch population required to build up an electron cloud in a possible future positron operation. 1 ATF The injection of a positron beam from the KEKB injector into the ATF damping ring has been proposed, in order to study electron-cloud effects in linear-collider damping rings. One concern is the rather low bunch charge that the present injector can deliver, about.4 nc, or positrons. We have performed a series of simulations to assess, under which conditions a significant electron cloud builds up, and under which it potentially exceeds the threshold density for the single-bunch head-tail instability. The three main parameters we vary in these simulations are the bunch charge, the rate of primary electron production, due to synchrotron radiation and photoemission, and the maximum secondary emission yield. In a two-particle model, the average electron density corresponding to the instability threshold is [1] Q s γ2 ρ e,thr = πr e C < β >, (1) which, for Q s.6 and < β > 2.2 m, amounts to about 1 13 m 3. This estimate assumes that the electron cloud exists all around the ring. Below the single-bunch threshold, there can still be significant electron densities, which may possibly induce a coupled-bunch instability. A critical parameter in the ATF simulation is the primary rate of photoelectrons. For a bending field of.75 T and 1.28 GeV energy, the bending radius ρ is about 5.74 m. Then without interception by an antechamber the rate of photoelectrons emitted from the chamber wall per unit length behind a dipole bend is of the order dλ e ds Y 5α 2 γ 3 ρ, (2) where α denotes the fine-structure constant, and Y the photo-emission yield per absorbed photon. For Y.1, the photo-emisison rate behind the bend is.46 m 1. Much larger values are possible behind a wiggler section; smaller values are found a farther distance downstream or if some photons are absorbed by the antechamber. In the ATF, about 7% of the emitted synchrotron radiation photons are estimated to enter into an antechamber, while the other 3% impact on the chamber wall [2]. The electron cloud which builds up in these latter regions can induce a beam instability. Table 1 lists parameters assumed in the ATF simulations. Figure 1 shows the simulated build up of electrons in a bending magnet during the passage of 37 bunches, with varying charges and varying primary electron production rates. We note that for primary photo-electron fluxes of dλ e /ds.46 m 1 or 4.6 m 1, the electron line density exceeds the threshold density even for a bunch population as low as The estimated average density for the instability threshold according to Eq. (1), is λ e,thr ρ e,thr πb m 1. Figure 2 depicts analogous results for a field-free region. The 1

3 Table 1: Parameters assumed for the ATF electron-cloud simulations. variable symbol value bunch population N b rms bunch length σ z 5 mm rms horizontal beam size σ x 47 µm rms vertical beam size σ y 6 µm max. sec. em. yield δ max 1.5 energy at max. sec. em. yield ɛ max 2 ev chamber hor. half aperture h x 12 mm chamber vert. half aperture h y 12 mm bunch spacing L sep.84 m bending field B.75 T ( T) primary electron rate dλ e /ds 4.6/e + /m photon reflectivity R 3% saturated electron densities are comparable to the case of the dipole field, only the build-up times are a little shorter. Figure 3 compares the build up for maximum secondary emission yields δ max of 1.5 and 1.7, considering a constant low bunch population of N b = and three different values of the primary photoelectron generation rate. The difference between the two values of δ max is much smaller than that obtained by varying the primary flux of photo-electrons. On the other hand increasing the secondary emission yield further, to δ max = 1.9, yields an avalanche-like increase in the number of electrons over very few bunches (not shown), which suggests that for δ max 1.8 beam-induced multipacting becomes the dominant process. 2

4 6e+1 5e+1 4e+1 3e+1 2e+1 1e+1 1e-8 2e-8 3e-8 4e-8 5e-8 6e-8 7e-8 8e-8 9e-8 1e-7 1e-8 2e-8 3e-8 4e-8 5e-8 6e-8 7e-8 8e-8 9e-8 1e-7 1.4e+1 1.2e+1 1e+1 8e+9 6e+9 4e+9 2e+9 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 2.5e+9 2e+9 1.5e+9 1e+9 5e+8 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 Figure 1: Electron cloud line density in units of m 1 (left) and central volume density in units of m 3 during the passage of a positron bunch trin through an ATF bending magnet of.75 T, assuming the parameters of Table 1. The primary electron emission rate varies from row to row: dλ e /ds = 4.6 m 1 (top), dλ e /ds =.46 m 1 (center), dλ e /ds =.46 m 1 (bottom). 3

5 6e+1 5e+1 4e+1 3e+1 2e+1 1e+1 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 1.4e+1 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 1.2e+1 1e+1 8e+9 6e+9 4e+9 2e+9 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 4e+9 3.5e+9 3e+9 2.5e+9 2e+9 1.5e+9 1e+9 5e+8 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 Figure 2: Electron cloud line density in units of m 1 (left) and central volume density in units of m 3 during the passage of a positron bunch train through an ATF drift space, assuming the parameters of Table 1. The primary electron emission rate varies from row to row: dλ e /ds = 4.6 m 1 (top), dλe /ds =.46 m 1 (center), dλe /ds =.46 m 1 (bottom). 4

6 3e+1 dλ/ds=.46/m dλ/ds=.46/m 3.5e+1 dλ/ds=.46/m dλ/ds=.46/m dλ/ds=4.6/m dλ/ds=4.6/m 2.5e+1 3e+1 2.5e+1 2e+1 2e+1 1.5e+1 1.5e+1 1e+1 1e+1 5e+9 5e+9 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 2e-8 4e-8 6e-8 8e-8 1e-7 1.2e-7 Figure 3: Electron cloud line density in units of m 1 during the passage of a positron bunch train through an ATF bend, considering two different maximum secondary emission yields and three rates of primary photoelectron emission, and otherwise assuming the parameters of Table 1 and N b = The left picture is for δ max = 1.5, the right for δ max =

7 Table 2: Parameters assumed for the KEKB LER electron-cloud simulations. variable symbol value bunch population N b rms bunch length σ z 4 mm rms horizontal beam size σ x 6 µm rms vertical beam size σ y 6 µm max. sec. em. yield δ max 1.5 energy at max. sec. em. yield ɛ max 2 ev chamber hor. half aperture h x 47 mm chamber vert. half aperture h y 47 mm bunch spacing L sep 2.4 m solenoid peak field B 1 11 G primary electron rate dλ e /ds.15/e + /m photon reflectivity R 3% 2 KEKB Table 2 lists simulation parameters for the KEKB LER. Figure 4 shows the simulated build up of an electron line density for three different solenoid configurations and 6 different field strengths. Figure 5 displays the corresponding central volume density of electrons in the immediate vicinity of the beam. The periodic symmetric and asymmetric configurations considered in these two figures are supposed to represent the cases where adjacent solenoids have either equal ot opposite sign, respectively. The periodic solenoid field was modelled using the parametrization of E. Perevedentsev [3, 4], and truncating his series after the 5th term. The solenoid radius was chosen as 7 cm, sufficiently larger than the chamber radius of 4.7 cm (otherwise we would have needed to retain additional terms in the expansion). The simulations were performed for a distance between adjacent solenoids of 15 cm, and for a solenoid length of 6 cm. Figure 4 shows that the line density still decreases when the solenoid field is further increased from 5 G to 11 G. The asymmetric solenoid configuration is much less effective than the symmetric in suppressing the electron build up. Only for this configuration can electrons reach the center of the chamber for fields above 3 G, over the time scale considered, as is illustrated in Fig. 5. However, for the symmetric and uniform solenoid configurations in Fig. 4, the simulated electron line density exhibits a slow long-term growth at certain field strengths, 9 G and 11 G, respectively. Since this is not seen for the other fields, it may be due to a resonance between bunch passages and cyclotron frequency. 6

8 6e+1 sym, 1 G sym, 3 G sym, 5 G sym, 9 G 6e+1 asym, 1 G asym, 3 G asym, 5 G asym, 9 G sym, 11 G asym, 11 G 5e+1 5e+1 4e+1 4e+1 3e+1 3e+1 2e+1 2e+1 1e+1 1e+1 2e-7 4e-7 6e-7 8e-7 1e-6 1.2e-6 1.4e-6 1.6e-6 2e-7 4e-7 6e-7 8e-7 1e-6 1.2e-6 6e+1 unif, 1 G unif, 3 G unif, 5 G unif, 9 G unif, 11 G 5e+1 4e+1 3e+1 2e+1 1e+1 5e-8 1e-7 1.5e-7 2e-7 2.5e-7 3e-7 3.5e-7 4e-7 4.5e-7 5e-7 Figure 4: Electron cloud line density in units of m 1 during the passage of a positron bunch train through a weak solenoid in the KEKB LER, considering six different solenoid strength (the six curves in each picture). The top left picture shows a symmetric periodic solenoid (adjacent solenoids have the same sign), the top right picture an asymmetric configuration (opposite sign), and the bottom picture a uniform solenoid. sym, 1 G sym, 3 G sym, 5 G sym, 9 G asym, 1 G asym, 3 G asym, 5 G asym, 9 G sym, 11 G asym, 11 G 1e+1 5e-8 1e-7 1.5e-7 2e-7 2.5e-7 3e-7 3.5e-7 4e-7 4.5e-7 5e-7 1e+1 5e-8 1e-7 1.5e-7 2e-7 2.5e-7 3e-7 3.5e-7 4e-7 4.5e-7 5e-7 Figure 5: Electron-cloud center density in units of m 3 during the passage of a positron bunch train through a weak solenoid in the KEKB LER, considering five different solenoid strengths (the five curves in each picture). The left picture shows a symmetric periodic solenoid (adjacent solenoids have the same sign), the right picture an asymmetric configuration (opposite sign). The case for a uniform solenoid is not shown, as in the simulation no electron reaches the vicinity of the beam, even for the lowest field of 1 G, and the center density is always zero. 7

9 3 Conclusions Electron-cloud simulations for a positron beam in the ATF suggest that an electron-cloud build up and possibly an electron-induced head-tail instability can be observed, even if the number of positrons per bunch is only 2 1 9, which can be provided by the KEKB injector. The electron build up is dominated by photo-emission, and, therefore, a certain minimum flux of synchrotron radiation is required to raise the electron density above the instability threshold. This minimum flux is roughly the same as expected downstream of an ATF arc dipole. The (re-)installation of wiggler magnets could help in exceeding the critical value of electrons for the onset of instability. If necessary, the instability threshold may also be lowered by reducing the synchrotron tune. Nevertheless, the ATF conditions will not be exactly the same as those in a linear-collider damping ring. For the latter, the electron-cloud build up will likely be due to beam-induced multipacting and most photons are absorbed by antechambers (at the ATF only about 7% of the photons hit an antechamber). Indeed the verification of countermeasures to the electron cloud might be a more worthwhile research goal for the ATF. For example, simulations have shown that clearing electrodes at kv potentials can be an extremely efficient measure for removing electrons from the vacuum chamber [5]. However, the impedance of such electrodes is a big concern, and this question could be studied in the ATF also with the presently available electron beam. For KEKB, using the updated ECLOUD code we have reproduced earlier simulation results [4] showing that an asymmetric solenoid arrangement is much less efficient than the pattern in which adjacent solenoids are of the same polarity. Increasing the peak field from 5 G to 11 G further reduces the central density of electrons for the asymmetric solenoid configuration, and it lowers the average line density of electrons for all three configurations (adjacent solenoids of equal polarity, of opposite polarity, and a uniform solenoid). The simulations indicate that even for a field of 11 G the electron build up can still be decreased by increasing the field strength, especially for the asymmetric case. It is difficult to simulate the long-term evolution of the electron cloud in a solenoidal field and the possible slow diffusion of electrons towards the center of the chamber over µs or ms time scales. We expect that, if such a diffusion exists, its speed will strongly depend on the solenoid field strength. Possibly, Fig. 4 showed a first indication of such an effect. The single-bunch wake due to electrons trapped by a solenoid field (near the wall of the chamber) [6] is another question we should address in the near future. References [1] K. Oide, F. Zimmermann, Head-Tail Instability Caused by Electron Cloud in Positron Storage Rings, Phys. Rev. Letters 85, 3821 (2) [2] J. Urakawa, private communication (23). [3] E. Perevedentsev, Periodic Solenoid Field, unpublished note, KEK, November 2 (2). [4] F. Zimmermann, H. Fukuma, K. Ohmi, More Electron Cloud Studies for KEKB: Long-Term Evolution, Solenoid Patterns, and Fast Blow Up, CERN-SL-Note-2-61 (2). [5] F. Zimmermann, Beam Sizes in Collision and Electron-Cloud Suppression by Clearing Electrodes for KEKB, CERN-SL-Note (21). [6] K. Oide, private communication (23). 8