Lecture HT14 Beam-Beam II ACCELERATOR PHYSICS HT14 2012 E. J. N. Wilson

Summary of last lectures – Beam Beam Effect I The Beam-beam effect Examples of the limit Field around a moving cylinder of charge Elliptical beam section Force on test particle Beam Beam Force Remember Q-shift from quadrupole Beam beam Q – shift Choosing lattice parameters

Beam-Beam Tune Shift II Coherent Beam-Beam limit Fourth integer resonance Satellite stop bands Phase space for fourth order resonance Example of tracking Importance of tune modulation

Need for higher luminosity

The Beam-beam effect - E. Wilson Luminosity f = the rev frequency k = number of bunches s = rms beam width or height Beam beam tune shift (linear effect on Q) Dependence of one upon the other

Estimating field tolerances for growth at a resonance Deflection in a dipole Total ring Reduced by 42 turns = 1ms exit time

Coherent Beam-Beam limit So far we have considered the force on an individual test particle. It sees a different force on each encounter. The linear force it sees will cause a constant shift in tune The non linear force will excite resonances. We could also take the average of the Q shift over a distribution of test particles an it turns out to be 1/2 of the incoherent effect Now we should look at how the two bunches interact, deflecting each other depending on their relative position when they clash One can imagine that they relate by a four by four matrix. There are two main coupled dipole modes

More about Coherent Beam Beam . CAS - CERN Accelerator School : 5th Advanced Accelerator Physics Course   20 Sep - 1 Oct 1993  - Rhodes, Greece  / Turner, Stuart (ed.) Geneva : CERN, 1995 - 2 v. CERN-95-06

Fourth integer resonance Substituting Incidentally Excites resonances making islands Amplitude Q dependence brings chains close

Phase space for fourth order resonance Island of stability

Satellite stop bands Fourier analysis of octupole pattern Ripple or rf modulation of Q Makes sidebands at Resonance when: EACH SIDEBAND MAKES NEW CHAIN Resonance when

Effect of satellites in phase space

Experimental results of satellites

Example of tracking Below the beam-beam limit and without tune modulation we see the many archipelagos of islands due to different multipole components in the beam-beam potential. Increasing the beam-beam interaction will enlarge the islands so that they overlap in stochastic regions where particle may diffuse out in 4 dimensional phase space. Increasing amplitude tune slope will merge them too Hadron collider luminosity limitations Author(s) Evans, Lyndon R In: 4th US-CERN School on Particle Accelerators, Hilton Head Island, South CA, USA, 7 - 14 Nov 1990, pp.592-599 TED0.PCT

Crossing the stochastic limit Increasing Q shift causes islands to merge in a stochastic sea of chaos

Importance of tune modulation Above is with – below is without modulation

Other details for linear colliders Luminosity enhancement (pinch) where D is “disruption” Beamstrahlung Make bunch length as large as possible but must be less than Courant’s b which is the length of the waist (hourglass effect)

History of colliders

Summary Beam-Beam Tune Shift The Beam-beam effect Examples of the limit Field around a moving cylinder of charge Elliptical beam section Force on test particle Beam Beam Force Remember Q-shift from quadrupole Beam beam Q – shift Choosing lattice parameters Coherent Beam-Beam limit Fourth integer resonance Satellite stop bands Phase space for fourth order resonance Example of tracking Importance of tune modulation