Electron Cloud Modeling for the Main Injector Seth A. Veitzer 1 Paul L. G. Lebrun 2, J. Amundson 2, J. R. Cary 1, P. H. Stoltz 1 and P. Spentzouris 2 1 Tech-X Corporation 2 Fermi National Accelerator Laboratory Project X Collaboration Meeting FermiLab September 8-9, 2010 Part of this work is being performed under the auspices of the Department of Energy as part of the ComPASS SCiDAC project (DE-FC02-07ER41499) and through the Small Business Innovation Research program

New Simulation Models Help Us Understand Electron Cloud Effects Electron cloud effect may seriously limit future accelerator performance Simulations of electron cloud effects in the Main Injector will aid design for Project X Electron cloud growth rate depends on Secondary Electron Yield (SEY) parameters, bunch intensity, and magnetic field configuration Recent simulations using VORPAL have focused on modeling cloud buildup in different sections of the Main injector (field-free, dipole, quadrupole) over many bunch crossings We have also modeled the effect of different SEY models on long- timescale cloud buildup Microwave injection experiments may be able to diagnose cloud density and evolution. VORPAL simulations are able to connect side-band observations with electron cloud effects VORPAL is a 1-D, 2-D, and 3-D self-consistent plasma simulation code that runs on laptops up to leadership class high-performance clusters These electrodynamic simulations include embedded cut-cell geometry, self-consistent EM fields, kinetic particles, and secondary electron emission

VORPAL Simulation Parameters We have modeled electron clouds in the Main Injector with short and long beam pipe geometries Elliptical cross section with embedded cut-cell boudaries 2.34 cm minor axis & 5.88 cm major axis Short configuration:.25 m with 384 x 48 x 48 (885k) cells Long configuration: 16 m with 6144 x 48 x 48 (14.15M) cells 5 m dipole -> quadrupole -> field free -> dipole Typical Cell Size: 2.6 x 1.1 x 2.7 mm Proton bunch is Gaussian, about 0.3 m long and 3 mm radius, with 0.7x10 10 to 3x10 11 protons/bunch and a bunch spacing of 18.8 ns Simulation time was between hundreds of ns to about a microsecond Short configurations were run on a small Tech-X cluster (32 processes) Long configurations were run on Intrepid (512 processes)

Recent Ecloud Simulation Results In field free regions, clouds evolve to more uniform densities In dipole regions, electrons evolve into vertical striped patterns In quadrupole regions, electron density shows an X pattern Non-uniform cloud density has a significant feedback on theory Connection between rf side band amplitudes and phase shifts assume uniform density clouds N. Eddy, Project X Collab. Meeting 2009

Recent Ecloud Simulation Results Clouds are attracted to the positive potential of the beam, and are accelerated to beam pipe walls, where they may produce secondary electrons Cloud density saturates when the density averaged over a few bunch crossings is constant Here, the beam bunch intensity is 0.7x10 11 m -3, and the beam is offset by 5 mm, giving rise to an asymmetric cloud density P. Lebrun, IPAC10

Recent Ecloud Simulation Results At the beginning of the relaxation phase, just after a bunch has passed, the spatially averaged cloud density is at a maximum At the beginning of a bunch crossing, secondary electrons are just migrating away from the beam pipe walls, and average cloud density is at a minimum With 10x10 11 protons/bunch, the peak volume-averaged density is approximately 2.4x10 13 m -3 The linear cloud density over 1  of the bunch is about 75% of the average linear density of the proton bunch P. Lebrun, IPAC10 max min

Comparison of Secondary Electron Models Used in Simulations Cloud buildup depends intimately on the secondary electron model We have considered two models; The Vaughan model and the Furman-Pivi model. Both the shape of the SEY curve and the value of the maximum of the SEY contribute to the electron cloud growth rate In VORPAL, we can model the SEY as either Vaughan or Furman-Pivi, and rescale the maximum of the SEY Furman-Pivi (copper) Vaughan (stainless steel)

SEY Model Comparisons The cloud saturates quickly when the maximum SEY is large (red) FP model with SEY max = 2.0 (purple) V model with with SEY max = 3.6 Slower growth is seen when the maximum SEY is lower (blue) V model with SEY max = 1.8 (green) V model with SEY max = 1.0 Decay time is about 40 ns in the dipole case, not short enough to kill the electron cloud in between Main Injector bunch trains 300 ns ~ 1/4 MI revolution period P.H. Stoltz, SciDAC 2010

Current and Future Research Comparison between 2-D electrostatic and 3-D electromagnetic simulations Modeling electron clouds as a dielectric plasma instead of kinetic particles Detailed modeling of BPM and other diagnostic responses to traveling wave microwave signals Measure realistic beam pipe responses to traveling wave microwave diagnostics

Comparison between 2-D electrostatic and 3-D electromagnetic simulations Modeling electron clouds as a dielectric plasma instead of kinetic particles Detailed modeling of BPM and other diagnostic responses to traveling wave microwave signals Measure realistic beam pipe responses to traveling wave microwave diagnostics Current and Future Research

Comparison between 2-D electrostatic and 3-D electromagnetic simulations Modeling electron clouds as a dielectric plasma instead of as kinetic particles Detailed modeling of BPM and other diagnostic responses to traveling wave microwave signals Measure realistic beam pipe responses to traveling wave microwave diagnostics Current and Future Research - Provides significant speedup over kinetic PIC simulations, while maintaining accuracy in phase and frequency shifts due to the plasma - Allows for inclusion of magnetic fields in a natural way, through a dielectric tensor - Since the plasma dielectric depends on the plasma density (via the plasma frequency) it is straightforward and accurate to simulate non-uniform density clouds - Captures the frequency dependence of the plasma response to microwaves - The Courant condition remains unchanged, but no particle push! - Plasma dielectric model is only valid for cold plasmas, but it is possible to relax the conditions on collisionless plasmas

Comparison between 2-D electrostatic and 3-D electromagnetic simulations Modeling electron clouds as a dielectric plasma instead of as kinetic particles Detailed modeling of BPM and other diagnostic responses to traveling wave microwave signals Measure realistic beam pipe responses to traveling wave microwave diagnostics Current and Future Research - Currently we have modeled BPM response by measuring the voltage at the BPM location - An offset beam will exhibit an echo effect if the electron cloud density is comparible to the linear beam density - FFT response of BPM voltages showed that the electron cloud weakly resonated at the cutoff frequency of the beam pipe in a dipole section -Better modeling of BPMs, RFAs, and even optical detection of electron-wall interactions are needed

Comparison between 2-D electrostatic and 3-D electromagnetic simulations Modeling electron clouds as a dielectric plasma instead of as kinetic particles Detailed modeling of BPM and other diagnostic responses to traveling wave microwave signals Measure realistic beam pipe responses to traveling wave microwave diagnostics Current and Future Research - Microwaves injected into the beam pipe can measure the electron cloud density, which appears as side bands when the plasma modulates the rf wave - However, reflections and power dispersion in actual beam pipes (not smooth simulated cylinders) change the side band amplitudes, which can not be uncoupled from cloud density - Also, non-uniform clouds do not map so nicely to side band amplitudes - So we need an understanding of the rf transmission characteristics of beam pipes as well as non-uniformity issues in order to deduce cloud density from microwave experiments