October 4-5, Electron Lens Beam Physics Overview Yun Luo for RHIC e-lens team October 4-5, 2010 Electron Lens

October 4-5, Outline Motivation of E-lens Project Layout and Parameters Scope of Beam Physics Studies Simulation Results Requirements for Engineering Beam Experiments Luminosity Gain Summary

October 4-5, Luminosity Upgrade 1. Figure of Merit for experiments in the polarized proton run F=L P 2 B P 2 Y 2. Limits to the Luminosity beam-beam effect nonlinear magnetic fields parameter modulations 3. Luminosity increase at 250 GeV p-p reduce β * from current 0.7 m to 0.5 m increase bunch intensity to 2.0×10 11 or even beyond 4. Polarized source upgrade is under way high intensity, high polarization and low emittance

October 4-5, Beam-beam Limit Current working point is constrained between 2/3 and 7/10 for better lifetime and polarization. When proton bunch intensity is above 2.0×10 11, there is not enough tune space between 2/3 and 7/10 to hold the large beam- beam tune spread (no other tune region available to accommodate the increased spread) No BB With BB No BB With BB

October 4-5, Head-on Beam-beam Compensation Introduce electron beam into ring to collide head-on with the proton beam. Two electron lenses will be installed near IP10 where β function is 10 m. Each e-lens is about 2.5 meters long. The effective interaction region is 2.0 m. e-lens for Blue (Yellow) beam allows bunch intensity increase in Yellow (Blue) beam.

October 4-5, Schematic Layout of E-lens Installation IP10 Top View Side View The two proton beams are separated vertically by 10 mm in the e-lenses. The electron beams are injected in the horizontal plane. The two e-lenses are vertically shifted +/- 5 mm from the axis of the proton beam pipe. X Y [Vertical displacement exaggerated compared to e-lens magnet size.]

October 4-5, Lattice and Beam Parameters β* at IP6 and IP8 is 0.5 m. The β* at IP10 is 10 m. Electron and proton beam have same transverse profile and size (0.3 mm RMS). The e-lenses are working in a DC mode (I e = 0.6 A for N b = 2x10 11 ).

October 4-5, Scope of Beam Physics Studies 1.Principle of head-on beam-beam compensation 2.Lattice design and phase adjustment 3. Simulation studies - Single particle tracking: tune diffusion, amplitude diffusion, dynamic aperture, etc. - Multi-particle tracking : proton lifetime and emittance growth 4.Effects of E-lens on proton optics - Betatron coupling, polarization, orbit change 5. Requirements for engineering 6.Beam experiments at RHIC and Tevatron 7.Benchmark simulation code with operation

October 4-5, Frequency Map Analysis Simulation condition: bunch intensity 2.0×10 11, with half beam-beam compensation (HBBC) and full beam-beam compensation (FBBC). Head-on beam-beam compensation reduces the size of tune footprint and stabilizes the particles in the bunch core.

October 4-5, Dynamic Aperture Calculation (I) Dynamic aperture (DA) is defined as the maximum amplitude below which particles are not lost. Simulation condition: bunch intensity from 1.0×10 11 to 3.0×10 11 without compensation and with half beam-beam compensation. Simulation shows that HBBC increases the proton DA for N p > 2.0×10 11.

October 4-5, Dynamic Aperture Calculation (II) DA as function of compensation strength (= N e / (2N p )). For half and full compensation, compensation strength is 0.5 and 1.0 respectively. Compensation with strength larger > 0.7 reduces proton DA (tune footprint folding).

October 4-5, Particle Loss Rate Simulation (I) Multi-particle tracking is used to calculate the proton beam decay and emittance growth over 2×10 6 turns. Half compensation increases the proton beam lifetime for N p > 2.0×10 11.

October 4-5, Particle Loss Rate Calculation (II) In principle, the electron beam should have same transverse profile and size as the proton beam. Plot shows the proton particle loss in a scan of electron beam size. Proton bunch intensity is 2.5× Simulation shows that electron beam size should not be smaller than the proton’s beam size. In addition, the electron beam size with a 20%-40% larger electron beam size benefits the proton lifetime.

October 4-5, Requirement for E-lens Engineering 1.Electron beam size in the e-lenses RMS beam size: 0.3 mm mm 2. Gaussian shape of electron beam good fit to 3 σ 3. Straightness of magnetic field in main solenoid target of ± 50  m after correction 4 Steering electron beam in e-lens maximum shifting : ± 5 mm in X and Y planes maximum tilting : 0.1 mrad 3.Stability in electron current power supplies stability better than 1000 ppm 4. Overlap of electron and proton beams robust real-time measurement with resolution better than 100  m

October 4-5, Beam Experiments (I) 1.Beam experiments were carried out in RHIC and Tevatron to investigate aspects of head-on beam-beam compensation scheme, and to determine the tolerances of beam parameters. 2.Beam experiments in RHIC - Resolution of betatron phase control between IP8 and IP10 - Effect of truncated Gaussian beam 3.Beam experiments in Tevatron with Gaussian e-lens - Tune shift measurement - Beam spectrum measurement - Proton tune scan with/without e-lens - Scan transverse offset between electron and proton beams

October 4-5, Beam Experiments (II) Courtesy of C. Montag and A. Valishev Plot shows the proton bunch intensity with and w/o e-lens interaction in Tevatron. Proton bunch with e-lens has better lifetime than bunch without e-lens. Electron current in lens Proton vertical tune Proton intensity without e-lens. Proton intensity with e-lens.

October 4-5, Luminosity Gain with e-lenses (I) Wolfram Fischer Plot shows the measured proton beam lifetime with 1 and 2 collisions in RHIC. If 1 of 2 collisions can be compensated, gain up to ~50% in integrated luminosity under current conditions. Bunches with 1 collision Bunches with 2 collisions Beam lifetime with 1 and 2 collision in RHIC (pp at 100 GeV beam energy) Cogging

October 4-5, More luminosity can be gained with an increase in the bunch intensity: 2. Increase of proton bunch intensity requires: - Upgrade of the polarized proton source - Upgrades in RHIC [In progress: updating Safety Assessment Document, instrumentation, dump, collimation] - If 1 of 2 collisions can be compensated, then N p can be doubled while total beam-beam  N p  is maintained. - This would yield theoretically a factor of 4, expect in practice up to a factor of 2. Luminosity Gain with e-lenses (II)

October 4-5, A single electron lens yields half of the luminosity gain of two electron lenses. An increase in the Blue (Yellow) bunch intensity, leads to an increase in the Yellow (Blue) beam-beam parameter, which can be compensated by a Yellow (Blue) electron lens Luminosity is proportional to both Blue and Yellow bunch intensity [Two lenses are operationally easier since Blue and Yellow sc solenoids compensate each other for x-y coupling and spin rotations.] Luminosity gain with single e-lens

October 4-5, Summary 1.Simulations shows that half head-on beam-beam compensation –reduces proton beam-beam tune spread –reduces diffusion in the beam core –increases the DA and beam lifetime for N p > 2.0× Benchmarking of simulation code with RHIC pp observations ongoing ( We see smaller losses in simulation than in observations) 3. Tevatron experience with electron lenses has demonstrated basic properties and established tolerances for alignment and e-beam current ripple 4. Expect increase in average proton luminosity of up to a factor 2