2 February 8th - 10th, 2016 TWIICE 2 Workshop Instability studies in the CLIC Damping Rings including radiation damping A.Passarelli, H.Bartosik, O.Boine-Fankenheim, G.Rumolo

Outline February 8th - 10th, 2016 TWIICE 2 Workshop3 Introduction Theory cross check Synchrotron Radiation Transverse Instability Conclusion & Outlook

Outline February 8th - 10th, 2016 TWIICE 2 Workshop4 Introduction Theory cross check Synchrotron Radiation Transverse Instability Conclusion & Outlook

The CLIC Design February 8th - 10th, 2016 TWIICE 2 Workshop5 Compact LInear Collider Machine Configuration for 3TeV center of mass energy 1)Laser driven DC/RF gun to produce e + /e - 2)Two e + /e - injector linacs up to 2.86GeV 3)Two ~430m damping rings + two ~400m pre-damping rings to have Norm. trans. emitt. (x/y) = 500/5 [nm] 4)One booster linac up to 9GeV 5)Two ~21km main linacs with copper cavities and a Drive beam complex for RF power production 6)Single Beam Delivery System 7)IP at 3TeV and Luminosity of 2X10 34 cm -2 s -1

Luminosity Requirements February 8th - 10th, 2016 TWIICE 2 Workshop6 The principle parameter driver in a collider is the production of luminosity at the Interaction Point (IP) N : the number of particles per bunch σ x and σ y : the horizontal and vertical rms beam sizes at the IP f r : the linac repetition rate n b : the number of bunches per pulse H D : is a factor describing the increase of luminosity due to beam-beam interaction

Role of the Damping Rings February 8th - 10th, 2016 TWIICE 2 Workshop7 accept large emittances (i.e. beam size) reduce the transverse beam size by Synchrotron Radiation Damping produce ultra-low emittance beams for achieving high luminosity collisions at the Interaction Point (IP).

HEADTAIL → PyHEADTAIL February 8th - 10th, 2016 TWIICE 2 Workshop8 HEADTAIL is a macro-particle simulation code developed to study collective effects in circular accelerators Created in 2000 by G. Rumolo (CERN) Written in C Next generation HEADTAIL → PyHEADTAIL: HEADTAIL + Versatile Extendible Maintainable

PyHEADTAIL Workflow February 8th - 10th, 2016 TWIICE 2 Workshop9 Particle BeamAccelerator Particle number Charge Mass Phase Space Coordinates Maps Collective effects Track

Outline February 8th - 10th, 2016 TWIICE 2 Workshop10 Introduction Theory cross check Synchrotron Radiation Transverse Instability Conclusion & Outlook

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop11 Broad Band Resonator : R T : 0 to 30MΩ/m f r : 0 to 40GHz Q : 1 Short bunch region Long bunch region B. Zotter, CERN/ISR-TH/82-10 (1982)

Outline February 8th - 10th, 2016 TWIICE 2 Workshop12 Introduction Theory cross check Synchrotron Radiation Transverse Instability Conclusion & Outlook

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop13 Study of transverse Synchrotron Radiation damping: Equation of motion considering the effect of the transverse Synchrotron Radiation damping: Related to emittance exponential damping Related to the effect of Quantum Excitation

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop14 Study of transverse Synchrotron Radiation damping: Damping time : 2ms Equilibrium emittance : μm.rad

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop15 Study of longitudinal Synchrotron Radiation damping: Equation of motion considering the effect of the longitudinal Synchrotron Radiation damping: Related to emittance exponential damping Related to the effect of Quantum Excitation Related to the effect of Energy loss per turn

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop16 Study of longitudinal Synchrotron Radiation damping: Damping time : 1ms Equilibrium momentum spread : 1.07 X Energy loss per turn : 3.98[MeV]

Outline February 8th - 10th, 2016 TWIICE 2 Workshop17 Introduction Theory cross check Synchrotron Radiation Transverse Instability Conclusion & Outlook

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop18 Scan the transverse shunt impedance parameter. Check the growth rate value to evaluate the threshold instability. Compare the threshold without radiation damping and the one with radiation damping. Evaluate the effect of chromaticity. R T : 0 to 20 MΩ/m f r : 5 GHz Q : 1 Broad Band Resonator :

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop19 Scan the transverse shunt impedance with ξ x,y = 0 In the first figure the damping effect is taken into account at the end of iteration In the second one is taken into account step by step There is no remarkable difference

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop20 Scan the transverse shunt impedance with ξ x,y = In the first figure the damping effect is taken into account at the end of iteration In the second one is taken into account step by step There is no remarkable difference

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop21 Scan the transverse shunt impedance with ξ x,y = In the first figure the damping effect is taken into account at the end of iteration In the second one is taken into account step by step The more realistic model produces an interesting improvement

Outline February 8th - 10th, 2016 TWIICE 2 Workshop22 Introduction Theory cross check Synchrotron Radiation Transverse Instability Conclusion & Outlook

February 8th - 10th, 2016 TWIICE 2 Workshop23 Conclusions PyHEADTAIL simulation results varying the resonator frequency have been successfully compared with analytical formula. Synchrotron Radiation simulations give self-consistent results both in transverse and longitudinal plane. The study of Synchrotron Radiation effect on transverse instability thresholds was started, interesting results for positive chromaticity. Outlook Ongoing studies of longitudinal BBR (Bunch lengthening & Microwave instability threshold) Include other elements in the impedance model (Strip-line kickers, RF- cavities) Analytical studies: Study the diffraction theory and short range limit. (Collaboration with Prof. Vaccaro)

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Backup slides

Synchrotron Radiation When a particle emits radiation, we have to take into account: the change in momentum of the particle (because of the momentum carried by the radiation). (For horizontal and vertical emittance) the change in coordinate x and momentum p x resulting from the change in energy deviation δ. (Only for horizontal, considering zero vertical dispersion). February 8th - 10th, 2016 TWIICE 2 Workshop26 For ultra-relativistic particle (E ≈ pc) the evolution of emittance is: Where the damping times are defined like: T 0 : the revolution period U 0 : the energy loss per period j x : hor. damping partition number

Synchrotron Radiation If radiation were a purely classical process, the emittances would damp to nearly zero. However radiation is emitted in discrete units (photons), which induces some “noise” on the beam. The effect of the noise is to increase the emittance. February 8th - 10th, 2016 TWIICE 2 Workshop27 The beam eventually reaches an equilibrium determined by a balance between the radiation damping and the quantum excitation. Cq : the “quantum constant” j x : hor. damping partition number I 2 I 5 : Synch. Rad. integrals The horizontal equilibrium emittance is:

Synchrotron Radiation When a particle emits radiation, we have to take into account: the change in energy deviation δ and longitudinal coordinate z (because of the energy lost by the particle through synchrotron radiation) February 8th - 10th, 2016 TWIICE 2 Workshop28 For ultra-relativistic particle (E ≈ pc) the evolution of emittance is: Where the damping time is defined like: T 0 : the revolution period U 0 : the energy loss per period j z : long. damping partition number

Synchrotron Radiation Quantum effects excite longitudinal emittance as well as transverse emittance. Consider a particle with longitudinal coordinate z and energy deviation δ, which emits a photon. February 8th - 10th, 2016 TWIICE 2 Workshop29 The equilibrium energy spread is determined essentially by the beam energy and by the bending radii of the dipoles. Note that the equilibrium energy spread does not depend on the RF parameters (either voltage or frequency). Cq : the “quantum constant” j z : hor. damping partition number I 2 I 3 : Synch. Rad. integrals The equilibrium energy spread is:

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop30 Study of transverse Synchrotron Radiation damping: Damping time : 2ms Equilibrium emittance : μm.rad

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop31 Study of longitudinal Synchrotron Radiation damping: Damping time : 1ms Equilibrium momentum spread : 1.07 x Energy loss per turn : 3.98MeV

PyHEADTAIL Simulations February 8th - 10th, 2016 TWIICE 2 Workshop32 Broad Band Resonator (BBR): R s : the shunt resistance is scanned between 0 and 40MΩ/m f r : the cut-off frequency is scanned between 0 and 40GHz Q : the quality factor is set to 1 if