1. 4. Summary and outlook 4. Summary and outlook Electron cloud evolution can be modeled using polynomial maps whose coefficients are functions of beam and chamber parameters, derived from simulations codes like CSEC or ECLOUD. This has helped to optimize the RHIC bunch pattern, and enables investigation of the phase transition from “off”  ”on”. For R 0  1 the map coefficients at low bunch intensities appear to show long term memory, suggesting the presence of hysteresis. Abstract Bunch to bunch simulations of Electron Clouds at RHIC using a third order polynomial map successfully reproduce CSEC results for uneven bunch spacings. Maps enable the use of analytical expressions to find the best bunch pattern, that minimizing electron cloud formation. Recent map studies focused on the experimental observation of first order phase transitions in RHIC: how do electron clouds go from “on” to “off”? An overview of RHIC studies, and first results for LHC, are presented. Maps for electron clouds U. Iriso and S. Peggs C-A D, Brookhaven National Laboratory REFERENCES [1] U. Iriso and S. Peggs. Use of maps in the exploration of electron cloud parameter space. Proceedings of ECLOUD’04, Napa Valley, USA, 2004. [2] M. Blaskiewicz et al. Electron cloud instabilities in the PSR and SNS. PRST-AB 6, 014302. January 2003. [3] F. Zimmermann and G. Rumolo, Practical user guide for ECLOUD. CERN-SL-Note-2002-016 (AP). [4] M.A. Furman and M. Pivi, PRST-AB 5, 124404, Dec. 2002. [5] R. Cimino, I. Collins, et al. Can low Energy electrons affect high energy accelerators? Phys Rev Lett. 93, 014801 (2004). [6] U. Iriso and S. Peggs, Use of maps in the exploration of electron cloud parameter space. C-AD/AP/153, 2004 2. Transition “OFF”  “ON “ Only 2 nd order phase transitions are seen using detailed simulations codes (CSEC), despite observations at RHIC show both 1 st and 2 nd order phase transitions [6]. Can an exploration in parameter space reproduce 1 st order phase transitions? Can we get the coefficients below the EC thresholds? Launching 40 bunches with N grow > Nc, followed by 80 bunches with N decay < Nc, we can obtain the map coefficients below Nc. Looks like hysteresis is not present: the final value of the saturated e- density is the same. 3. Scan for RHIC… Values for Eq. 2 coefficients, scan in SEY max and N. RHIC results for a single beam pipe, 108 ns, R 0 =0.6, using parameterization in [4]. Saturated e- density from fit parameters: Values for Eq. 2 coefficients, scan in δ max and N. LHC results for a single beam pipe, 25 ns, R 0 =1, using parameterization in [5]. Hysteresis effect? …and LHC…, other expressions are possible as well: MEC In RHIC, successful reproduction of the EC evolution is obtained through a computer algorithm (MEC) which uses 4 three dimensional vectors with the cubic form: Polynomial maps have been successfully used to reproduce Electron Cloud (EC) bunch to bunch evolution in the Relativistic Heavy Ion Collider (RHIC) [1]. This way of tackling the EC effect still needs from the usual detailed (slow) codes (like CSEC [2] or ECLOUD [3]) to obtain the coefficients of the used expressions. 1.Introduction But the important factor is what this new way of tackling the EC can render. At RHIC, for example, a way to distribute the bunches along the bunch train is analytically obtained using the map formalism. An ECLOUD/CSEC simulation last ~1hour --> MEC simulation last ~ms. Agreement is not bad  (2).(1) N=2x10 10 ppb