253124263 4 2008 Tech X Modeling Breakdown in RF Cavities Using PIC Codes

MODELING BREAKDO WN IN RF CA VI TIES US ING P AR TICLE-IN-CELL (PIC) CODES ∗ S. Mahalingam † , J.R. Cary, P.H. Stoltz, S.A. Veitzer, Tech-X Corporation, Boulder, CO 80303, USA Abstract A main limitation on the design of future accelerators is breakdownof metallic struc tures. We have dev elope d computer models of the process of breakdown using Particle- In- Cel l (PIC) codes. We use the pla sma simulation pac kag e OOPIC Pro, a two dimensional electromagnetic code, to self-consistently model the breakdown. We describe here the results of our numerical experi ments , includ ing sensi- tivity of breakdown triggers on field emission parameters, and the potential to measure the onset of breakdo wn by ex- aminin g impurity radia tion. We also report our work on enhancing the parallel capabilities available in the OOPIC Pro code which allows plasma simulations to run on multi- ple processors with distributed memory. INTRODUCTION Future accelerator projects [1] desire to use large electric fields (> 50 MV/m) coupled with high magnetic fields (> 2.5 T) for generating high intensity muon beams re- quired for the produ ction of high-energ y neutrinos . These large fields will reduce the numbe r of costl y focus ing ele- ments needed for limiting the muon beam emittance. How- ever, metallic structures often break down when operating with such large field gradien ts. Break down pro cess es in RF cavities have been experimentally studied by many re- searchers, for instance, [2]-[4] have recently studied breakdown in 805 MHz and 200 MHz copper cav ities . Break - down limits in acclerating structures [4] are presently the main constraint on the electric field strength in muon cool- ing designs. We have developed computer models to study br ea kdown usi ng OOPIC Pro [5]. OOPI C Pro is a 2- Dimensional Particle-in-Cell (PIC) code that is being used by plasma physicists and engineers for modeling various plasma proble ms. OOPIC Pro self- consi stent ly solves the interactions of fields and particles and adopts a kinetic particles to model the plasma. BREAKDO WN MODEL A series of recent experiments [2]- [4] have resulted in a theory of breakdown processes involved in metallic structures like thos e used for muon coolin g. The theory pos - tulates that stresses induced by electric fields exceed the tensile strength of surface materials and this results in fragments of surface mate rial being pried loose . These metal fragments are then broken apart, excited and ionized by ∗ Work supported by US Department of Energy under Small Business Innovation Research Contract DE-FG02-07ER84833 † [email protected] field emitted electrons resulting in a high density plasma of impuri ties. This plasma radiate s away energy as photons, res ult ing in ads orption of RF power . Also the impurit y copper ions that impact cavity surfaces can cause secondary emission of electrons and physical sputtering of wall mate- rial. These processes lead to an avalanche of plasma impurity produc tion inside the cav ity . Event ually with RF power being taken away by radiation and coupled with the ero- sion processes of cavity surfaces, an arc may form, causing physical damage to the cavity structures. The main features in our computational model are field- emission of electrons, electron-impact ionization of neu- trals, ion-in duced secon dary emissio n of elect rons, ion- induced sputtering of neutral atoms, plasma radiation effects, and surface heating due to bombardment of charged partic les. Detai ls of these featur es are prese nted in Refer- ence [6]. Prior computa tional bre akdo wn models [7] using OOPIC Pro, did not consider the following physical processes: ion-induced sputtering, ion-induced secon dary emission and plasma radiation. We have enabled these features into the OOPIC Pro package by interfacing it with TxPhysics [8]. TxPhysics is a cross-platform numerical li- brary composed of various physical process modules. Breakdown is modeled by considering a conical asperity in the cavity surface with a surrounding background copper gas of near solid density. This is similar to the situation ima gined by Nor em et. al. [2]. Figu re 1 shows the 2-D breakdown simulation geometry and physical dimensions consi dered in OOPIC Pro. We used 0.2 µ m square com- putati onal cell s with a 0.01 ps time step. The time step is chosen to keep particles from crossing more than one computational cell per step. We use macro particles in our simulations, so each simulated particle represents 50 physical particles. Numer ically , the conic al defec t itsel f is stair-s teppe d into 5 segments to align the emitting surface with the computational grid. An electric field is appli ed through an externa l RF source wit h a frequ enc y of 805 MHz . The magnit ude of the electric fields are in the range 20 to 60 MV/m. We consider a field enhancement factor, β F N = 184, as estimated by Norem et. al [2], in our Fowl er-Nordheim field emission model. The Fowler -Nordh eim emiss ion depends on the net surface field, including contributions from both the applied RF signal and the space-charge fields of the plasma particles. RESULTS Simulation results for a background gas pressure of 35 torr and the effects of applied external magnetic fields can be found in [6]. We present here numer ical resu lts for a Proceedings of EP AC08, Genoa, Italy WEPP111 03 Linea r Collid ers, Lepto n Acce lera tors and New Acce lera tion Techni ques A09 Muon Acce lera tors and Neutr ino Fac tories 2767

253124263 4 2008 Tech X Modeling Breakdown in RF Cavities Using PIC Codes

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