1. Principle of Wire Compensation Theory and Simulations Simulations and Experiments The Tevatron operates with 36 proton bunches and 36 anti-proton bunches. All particles share the same beam- pipe. The much more intense proton bunches affect the anti-proton bunches every time they pass each other. This happens 72 times each turn for every bunch, and only 2 of them are head-on, which are the desirable ones for physics. All others are called long-range or parasitic, which produce beam loss and degrade the lifetime. These are the subject of wire compensation. Collision Scheme Radial Separations at Parasitics Correction Principle The electric field of a round Gaussian proton beam at large distances is exactly of the same form as the magnetic field of a current carrying wire. By appropriate placement of the wire w.r.t the anti-protons the two effects cancel each other. Beam-Beam Kick Wire Kick Can be neglected at large distances Equal for appropriate wire parameters Theory Correction of One Round Beam-Beam by One Wire K bb KwKw KwKw M Condition on M to leave the system unchanged is:  Phase advance in both planes multiples of p  Ratio of beta function at location of wire the same as at the beam- beam interaction  Current*length of wire = ecN b ; N b is the strong beam intensity  Transverse position: x PA =+/-x WA and y PA =+/-y WA Correction of Almost Round Beam-Beam The far-kick region coincides with the round beam case, and the near-kick region has the same falloff with the radial amplitude as the round beam case. Therefore, the wire compensation should be robust against small errors in optics and/or wire placement/current. Correction of Several (Possibly) Non-Round Beam-Beams No exact cancellation is possible by a single wire in this case. However, it is possible to cancel the kick that is felt on average by an anti-proton bunch. The average kick is the kick felt by the bunch centroid, with the strong beam’s size replaced by the r.m.s. size of the proton and anti- proton beams. Example: phase calculation in case of 2 arbitrary beam-beam interactions Simulations at Injection Energy Limit maximum number of wires at 4; fix length to 1 m; longitudinally place them at warm locations, in drift spaces; transversely at reasonable distance both from beams and beam pipes Realistic model of the wire, including fringe fields and positioning errors such as pitch and yaw; include measured multipoles in all magnets Use COSY for transfer map computation and optimization (map minimization), and Sixtrack for tracking (dynamic aperture) WireI [A]X [mm]Y [mm] WA175016.823-1.033 WC07512.993-11.028 WE0-2521.23214.282 WF023214.004-9.134 DA [s]Number of turns 10 4 10 5 10 6 Beam-beam on, no wires ~6.0~4.03.7 Beam-beam on, best case wires ~7.0~6.05.5 DA improves by almost 2  Simulations at Collision Energy Diffusion Coefficients Due to Each Parasitic InjectionCollision Average change in the action of particles with initial amplitudes of 5  over 10 6 turns due to each beam-beam interaction Effect of the Nearest Parasitics at Collision Compensation of the 4 nearest parasitics would significantly reduce diffusion at amplitudes below ~5  Work in progress to find the optimum wire parameters to achieve correction Wire Experiments at SPS Next Steps Wire compensator prototype built at CERN, used in SPS for tests of wire compensation of the LHC long-range beam-beam interactions. 60 cm wire with 267 A is equivalent to 60 long-range beam-beam interactions. Diffusive aperture in experiment and simulation roughly the same Corresponds to 9.5  Continue the average kick approach testing and pursue new ideas, especially for beams with aspect ratios significantly different than 1 Check whether it is possible to compensate several bunches with the same setup Consider the different operational phases Consider placement of wires outside the beam pipes Study additional flexibility introduced by several wires at the same longitudinal position Continue experiments at SPS and use data to benchmark simulation codes