Electron cloud build up studies for the CLIC positron damping ring

Electron cloud build up studies for the CLIC positron damping ring G. Iadarola, G. Rumolo, H. Bartosik Thanks to: F. Antoniou, E. Koukovini-Platia, Y. Papaphilippou CLIC Workshop 2014 CERN, 5 February 2014

Outline • Introduction • CLIC Damping Ring machine elements and beam scenarios • e-cloud buildup simulation with PyECLOUD • Peculiarities of simulations for low emittance rings • Features of the e-cloud buildup in the CLIC DR machine elements • Wigglers • Dipoles • Quadrupoles

Introduction • When the an accelerator is operated with close bunch spacing an Electron Cloud (EC) can develop in the beam chamber due to the Secondary Emission from the chamber’s wall. • Secondary Electron Yield (SEY) of the chamber’s surface: • ratio between emitted and impacting electrons • function of the energy of the primary electron • SEYmax

Introduction • When the an accelerator is operated with close bunch spacing an Electron Cloud (EC) can develop in the beam chamber due to the Secondary Emission from the chamber’s wall. • LHC Dipole chamber @ 7TeV • Strong impact on beam quality (EC induced instabilities, particle losses, emittance growth) • Dynamic pressure rise • Heat load (on cryogenic sections)

CLIC e+ damping ring Extracted (εx, εy) = (500 nm, 5 nm) Injected (εx, εy) = (63 μm, 1.5 μm)

CLIC e+ damping ring C = 427.5 m e-cloud formation has been investigated in three families of devices Wiggler a=40mm, b=6mm Ltot = 104 m Quadrupole a=9mm, b=9mm Ltot = 86 m Dipole a=40mm, b=9mm Ltot = 58 m

CLIC e+ damping ring • Studies performed with parameters of beam before extraction: • Beam energy: 2.86 GeV • Bunch population: 4x109 e+ • Transverse emittances (εx, εy): (500 nm, 5 nm) • Two bunch patterns: 156 b. 312b. 556 empty buckets 2538 empty buckets 156 b. 556 empty buckets • 0.5 ns bunch spacing – b.l. = 6.4 mm • 1.0 ns bunch spacing – b.l. = 7.2 mm Trev= 1.425 μs

PyECLOUD simulation recipe t=t+Δt Generate seed e- • PyECLOUD is a 2D macroparticle (MP) code for the simulation of the electron cloud build-up with: • Arbitrary shaped chamber • Ultra-relativistic beam • Arbitrary magnet configuration Evaluate the electric field of beam at each MP location Evaluate the e- space charge electric field Compute MP motion (t->t+Δt) Detect impacts and generate secondaries

PyECLOUD simulation recipe t=t+Δt Generate seed e- Evaluate the electric field of beam at each MP location • Evaluate the number of seed e-generated during the current time step and generate the corresponding MP: • Residual gas ionization and photoemission are implemented Evaluate the e- space charge electric field Compute MP motion (t->t+Δt) Detect impacts and generate secondaries

PyECLOUD simulation recipe t=t+Δt Generate seed e- Evaluate the electric field of beam at each MP location Evaluate the e- space charge electric field • The field map for the relevant chamber geometry and beam shape is pre-computed on a suitable rectangular grid or loaded from file in the initialization stage Compute MP motion (t->t+Δt) Detect impacts and generate secondaries

PyECLOUD simulation recipe t=t+Δt Generate seed e- Evaluate the electric field of beam at each MP location • Classical Particle In Cell (PIC) algorithm: • Electron charge density distribution ρ(x,y) computed on a rectangular grid • Poisson equation solved using finite difference (FD) method • Field at MP location evaluated through linear (4 points) interpolation Evaluate the e- space charge electric field Compute MP motion (t->t+Δt) Detect impacts and generate secondaries

PyECLOUD simulation recipe t=t+Δt Generate seed e- Evaluate the electric field of beam at each MP location • The dynamics equation is integrated in order to update MP position and momentum: Evaluate the e- space charge electric field Compute MP motion (t->t+Δt) Detect impacts and generate secondaries

PyECLOUD simulation recipe t=t+Δt Generate seed e- Evaluate the electric field of beam at each MP location • When a MP hits the wall theoretical/empirical models are employed to generate charge, energy and angle of the emitted charge Evaluate the e- space charge electric field Compute MP motion (t->t+Δt) Detect impacts and generate secondaries

PyECLOUD simulation recipe t=t+Δt • Simulations for the CLIC e+ Damping Ring • Bunch length ~20 ps Generate seed e- Evaluate the electric field of beam at each MP location • Δt = 0.5 ps necessary to resolve the e-pinch • ~3x109 steps for a full turn (~36 h CPU time) Evaluate the e- space charge electric field Compute MP motion (t->t+Δt) • Beam and electron distributions at the limit of present capabilities of the code Detect impacts and generate secondaries

Beam field • LHC: Aperture = 100 x σbeam • CLIC-DR: Aperture = 10000 x σbeam Finite Difference calculation unaffordable  resorted to analytical expression for Gaussian beam in elliptical chamber: Bassetti-Erskine formula Image terms (effect of bundary) + where: where: • For the CLIC wiggler chamber (a/b=6.6) • 150 terms needed for convergence with:

e-cloud space charge field • In the cases of wigglers and dipoles e- accumulate in a narrow stripe close to the beam • Fine grid needed for Finite Difference Poisson solver (Δh = 50 um, 1e5 nodes), run many times during the simulation • LU factorization of the FD (sparse) matrixpre-calculated in the initialization stage to speed-up the calculation* *As proposed in: O. Haas, “Electron Cloud Modeling and Coupling to Tracking Codes”, joined CERN/TU Darmstadt e-cloud meeting (16/12/2013)

e-cloud space charge field • In the cases of wigglers and dipoles e- accumulate in a narrow stripe close to the beam • Fine grid needed for Finite Difference Poisson solver (Δh = 50 um, 1e5 nodes), run many times during the simulation • LU factorization of the FD (sparse) matrixpre-calculated in the initialization stage to speed-up the calculation* • e- field map re-evaluated only every Δtsc=0.02ns (≈b.l.) Cut on chamber’s positive semiaxis • During the bunch passage electric field due to the e- is completely negligible *As proposed in: O. Haas, “Electron Cloud Modeling and Coupling to Tracking Codes”, joined CERN/TU Darmstadt e-cloud meeting (16/12/2013)

e-cloud in the wiggler magnets • Threshold lower for 0.5 ns (mainly due to faster risetime)

e-cloud in the wiggler magnets • Threshold lower for 0.5 ns (mainly due to faster risetime) • Large e- densities (>1e13) at the beam location (severe effects on beam quality/stability) • e- horizontally confined in a narrow region around the beam (local low SEY coating or clearing electrode for full e-cloud suppression)

e-cloud in the dipole magnets • Threshold lower for 0.5 ns (mainly due to faster risetime) • Large e- densities (>1e13) at the beam location (severe effects on beam quality/stability) • e- horizontally confined in a narrow region around the beam (local low SEY coating or clearing electrode for full e-cloud suppression)

e-cloud in the quadrupole magnets • In the case of the quadrupoles, we noticed that saturation was not achieved within a single turn, but due to e- trapping it can be reached in a multiturn regime (not investigated yet)

e-cloud in the quadrupole magnets • In the case of the quadrupoles, we noticed that saturation was not achieved within a single turn, but due to e- trapping it can be reached in a multiturn regime (not investigated yet) • To get a first idea, we simulated an artificially longer train

e-cloud in the quadrupole magnets • Threshold lower for 0.5 ns (mainly due to faster risetime) • Large e- densities (>1e13) at the beam location • e-move around the quadrupole field line. Multipacting concentrated around the magnet pole regions (local low SEY coating or clearing electrode for full e-cloud suppression)

Dependence on bunch population • In the framework of CLIC parameter optimization, different bunch intensities have been also investigated Dipole - 1 ns Dipole - 0.5 ns • The multipacting threshold shows a weak dependence on the bunch population • Heat load significantly stronger for intensities larger than nominal

Dependence on bunch population • In the framework of CLIC parameter optimization, different bunch intensities have been also investigated Wiggler - 1 ns Wiggler - 0.5 ns • The multipacting threshold shows a weak dependence on the bunch population • Heat load significantly stronger for intensities larger than nominal

Summary and conclusions • The e-cloud formation in the wigglers, dipoles and quadrupolesof the CLIC e+ damping ring has been investigated with PyECLOUD simulations • Quite challenging simulation scenario (very short bunches, extremely small beam size, electron density concentrated in a small region of the beam pipe) • Dipoles and wigglers show similar features: • e-horizontally confined in a narrow region around the beam (local low SEY coating or clearing electrode for full e-cloud suppression) • Weak dependence of SEY multipacting threshold on bunch population • In the quadrupolese-cloud buildup is slower: • most likely saturation is reached in more than one turn (still to be fully investigated) • multipactingconcentrated around the magnet pole regions • large e- densities (>1e13) at the beam location (which can have serious impact on beam quality  see talk by H. Bartosik)

Thanks for your attention!

Dipole • In the cases of wigglers and dipoles e- accumulate….

Electron cloud build up studies for the CLIC positron damping ring