Simulations of LHC LongRange BeamBeam Compensation with DC

Simulations of LHC Long-Range Beam-Beam Compensation with DC and Pulsed Wires U. Dorda F. Zimmermann CERN – AB/ABP

Long range beam – beam interaction (LR) LHC: Nominal bunch: 120 LR encounter Extreme Pacman bunch: 60 LR encounter The nonlinear beam-beam force causes an amplitude dependent tune-shift which leads to beam-blow up and reduces the lifetime and limits the luminosity of LHC

The forces of the LR-interaction and the wire LR force caused by the strong beam Center of weak (studied) beam wire Within limits the force originating from the wire is very similar to the LR’s one. In the weak-strong simulation model the strong beam is assumed to stay unchanged while its presence influences the weak (studied) beam

Location of the compensation wires around the IP Strong beam wire IP wire weak beam 104. 93 m Ip 1 & Ip 5: The wires are positioned on both sides 104. 93 m from the IPs in a region where the two beams are separated βw=1760 m, σw=0. 9 mm

The compensation cannot work perfectly due to: • Phase advance between LR-IP and wire-position • Force is similar but not the same (especially close to the wire) • The wire cannot be positioned in the perfect position (9. 5 sigma) but behind the collimators (11 σ) • Assumption: round Gaussian beam • Not all LR-IPs are at the same distance wire The average phase-advance from LR-IP to wire is 2. 6º The beam-beam separation d varies from 7 to 13 σ

Weak-strong simulated footprints for LHC Long range Wire Nominal tune The linear tune shift scales with the inverse square of the beam-separation Long range & Head On Initial particles are launched on a square grid (0 -10 σ)

Long range & Head On & Wire Ideal wire current: The wires compensate for the long range interaction nearly completely

What about adding other nonlinearities ? Example: Adding one weak sextupole The wire proves to be still effective Corresponding x-x’-phasespace Sextupole only Stable up to 25 σ LR & HO Stable up to 7. 5 σ LR & HO & sextupole Stable up to 2. 5 σ

Pacman bunches The tune spread of the extreme PACMAN bunch is half that of the nominal one, because the former experiences only half the number of long-range collisions. Pacman (extreme case) & Head On

Compensation for Pacman bunches Pacman (extreme case) & HO & nominal wire & adjusted wire The wire is overcompensating The adjusted wire reduces the tune spread almost to the one of HO only. The wire’s current needs to be adjusted to the specific bunches in order to compensate each one perfectly.

Individual compensation requires pulsing of the wire current If pulsing is not exact it causes more trouble than it solves: e. g: Jitter causes an emittance growth A jitter of 4 m. A causes a 10 % emittance growth within 20 h.

Demands on the current supply Maximum current 120 A (l=1 m) or 60 A (l=2 m) Total ramp up/down time from/to zero 374. 25 ns Length of maximum excitation 1422. 15 ns Length of minimal excitation 573. 85 ns Average pulse rate 439 k. Hz Turn-to-turn amplitude stability (rel. ) 0. 5*10 -4 Turn-to-turn timing stability 0. 02 ns

Wire compensation experiment in SPS Experiment: Excite the beam with wire 1 and compensate for it with another one further downstream (phase advance: 1º) No excitation Both wires on Only wire 1 on Within a certain tune range the 2 nd wire is able to compensate nearly completely for the first one.

Parameter scans for the SPS Simulated sensitivity to positioning Optimal position Sensitivity to the current of wire nr. 2 Experiment Simulation

Regions of stability y [mm] Stable regions are in blue, unstable ones in red One wire only Both wires y [mm] 20 0 25 0 x [mm] 0 25 x [mm] Liaponov stability-criterion : Inspect the increase of the phasedifference between two initially close particles with time. Small amplitude large amplitude Δφ 0. 014 Δφ 0. 02 time Δφ 3. 2 Δφ 0. 7 time Linear Detuning with amplitude, stable time Exponential growth, unstable time

Summary • The simulated wire compensation shows promising behavior • The experiments in the SPS confirm this idea • The simulation tends to exaggerate the effects and further improvement modeling the other nonlinearities is needed but they reproduce the experimental results qualitatively. • A pulsed wire option is strongly recommended but the demands on the hardware challenging.