Beam Loss Simulation in the Main Injector at Slip-Stacking Injection A.I. Drozhdin, B.C. Brown, D.E. Johnson, I. Kourbanis, K. Seiya June 30, 2006 A.Drozhdin

RF frequency of main, first and second stations during slip-stacking injection at simulations. June 30, 2006 A.Drozhdin Beam parameters at simulations: σ dP/P =0.0004, σ φ =0.667rad, ε 95% =12π mm-mrad

RF phase of beam 1 and 2 at slip-stacking injection. Second beam is injected at turn No when RF phase of main RF station is close to zero. At this time RF phase of the second beam is taken equal to 90 X 2π to get the same phase for both beams at beginning of capture to common separatrix. This phase can be chosen equal to any integer number of 2π, but for comparison of two beams position on a phase plane at beginning of capture to common 1 MV separatrix this is more convenient. June 30, 2006 A.Drozhdin

Longitudinal phase plane for the first (left) and second (right) beam at step 3 - second beam injection during 2000 turns (turn 6000), at turn start capture to common separatrix (middle), and at turn (bottom) for both beams. June 30, 2006 A.Drozhdin

Calculated bunch populations after slip-stacking injection June 30, 2006 A.Drozhdin

Particle population (top) and distribution (bottom) in the arc preceding MI10 at turn No.1 and turn No.500 (beam displacement by 1300 Hz). Beam emittance at 95% level is 12π mm-mrad. June 30, 2006 A.Drozhdin

RF voltage, synchronous phase and particle loss diagram (left), and particles lost at beam pipe at capture both beams to common separatrix. Beam losses are calculated without nonlinear fields in the main dipole and quadrupole magnets. 3.6% of the beam is lost. 0.9% of the beam is lost from the main and 2.66% from parasitic separatrix. 0.1% of lost particles - at LAM60, 0.02% - at LAM40 and 0.04% - at LAM52A. June 30, 2006 A.Drozhdin

Particle loss distribution along the ring without collimators. 1 mm thick scattering target is placed in the middle of each quadrupole of accelerator for simulation of particle interaction with accelerator beam pipe. Aperture of the target is decreased by 1 mm with respect to quadrupole aperture. Beam loss in 1 mm steel scattering element is distributed along 1 m region of the quadrupole to eliminate peaks in the distribution. June 30, 2006 A.Drozhdin

Measured distribution of nonlinear fields in 155 accelerator magnets of the Main Injector. b1, b2, b3 (top), b4 (middle) and b5, b6 (bottom) are shown. June 30, 2006 A.Drozhdin

Average value and sigma of Gaussian distribution of nonlinear field harmonics in the IDA and IDB (L=6.096 m) Main Injector dipoles. According to rules for transformation of MTF measurements to the Main Injector reference frame normal harmonic strengths of IDA and IDC magnets should be multiplied by (-1) n+1, skew harmonics - by (-1) n. Normal and skew harmonics of IDB and IDD magnets - by -1. June 30, 2006 A.Drozhdin

Average value and sigma of Gaussian distribution of nonlinear field harmonics in the IQB (L= m) Main Injector quadrupoles. Focusing quadrupoles are installed and powered in the Main Injector with the conditions used at the magnets measurements. They do not need measurement data transformation to the accelerator frame. Defocusing quadrupoles are installed in the Main Injector the same way as at measurements, but powered with different sign of current. So, to transform harmonics one has to multiply them by -1. June 30, 2006 A.Drozhdin

Gaussian distributions of multipole harmonics around the average value at nonlinear field simulations in the dipole and quadrupole magnets of the Main Injector. Total number of magnets in the accelerator is 552. Random number for each harmonic at each magnet is generated at the first turn, and then it is not changed during the tracking. June 30, 2006 A.Drozhdin

Betatron tune plane at injection for Main Injector. June 30, 2006 A.Drozhdin

Main injector closed orbits are shown for different momentum. The chromati- city correction sextupoles located in the arcs produce quadrupole kick depending on particle momentum. This excites half integral resonance in horizontal and vertical plane. Depending on the accelerator chroma- ticity the particle, lost from separatrix, may reach horizontal or vertical resonance and may be lost on the aperture restriction. June 30, 2006 A.Drozhdin

Horizontal (left) and vertical (right) phase plane for different momentum. Chromaticity is ζx=-1, ζy=-8. Maximum amplitude is 3σ xy. Without nonlinear fields in magnets. June 30, 2006 A.Drozhdin dP/P= dP/P= dP/P= vert. resonance dP/P= dP/P=+0.024

June 30, 2006 A.Drozhdin Horizontal (left) and vertical (right) phase plane for different momentum. Chromaticity is close to zero in both planes. Amplitude is 1σ xy. With nonlinear fields in magnets. Pc=8.756 GeV Pc=8.800 GeV Betatron tune Pc=9.067 GeV Pc=8.889 GeV

RF voltage, synchronous phase and particle loss diagram (left), and particles lost at beam pipe at capture both beams to common separatrix (right). Beam losses are calculated without nonlinear fields in the main dipole and quadrupole magnets. 3.6% of the beam is lost. 0.9% of the beam is lost from the main and 2.66% from parasitic separatrix. 0.1% of lost particles - at LAM60, 0.02% - at LAM40 and 0.04% - at LAM52A. June 30, 2006 A.Drozhdin

Particle loss diagram and particles lost at beam pipe aperture during capture to main separatrix with all nonlinear field harmonics in the main dipole and quadrupole magnets. 21.4% of the beam is lost. 18.5% of the beam is lost from the main and 2.9% from parasitic separatrix. 87% of lost particles - at LAM60 and 10% - at LAM52A. Skew quadrupole harmonics are excluded from simulations. June 30, 2006 A.Drozhdin

Particle loss distribution along the ring without collimators without nonlinear fields in the main dipole and quadrupole magnets (top, loss 3.6%) and with all harmonics (bottom, loss 21.4%). Simulated closed orbit #1. June 30, 2006 A.Drozhdin

Particle loss diagram and particles, lost at the Lambertson magnets LAM60, LAM52 and beam pipe aperture during capture to main separatrix with nonlinear fields in the main dipole and quadrupole magnets including skew harmonics without 4-pole and 6-pole harmonics. 3.9% of the beam is lost. 1.2% of the beam is lost from the main and 2.7% from parasitic separatrix. 29% of lost particles - at LAM60, 3.5% - at LAM40 and 1.5% - at LAM52A. Simulated closed orbit #1. June 30, 2006 A.Drozhdin

Main Injector Lambertson magnet aperture and beam position at slip-stacking injection before capture to main separatrix. Closed orbit was simulated according to measurements in the accelerator (orbit #2). June 30, 2006 A.Drozhdin

Particle loss distributions along the ring without collimators with nonlinear fields in the main dipole and quadrupole magnets without 6-pole and 4-pole harmonics. Simulated closed orbit #1 (top) and #2 (bottom) are presented. Beam loss in the Lambert- son magnets with orbit #2 better correspond to real measurements. June 30, 2006 A.Drozhdin

Particle distributions at the beginning of capture to 1MV separatrix at ordinary (red) and slip-stacking injection (blue and green) are diffe- rent. This effects different losses at capture and acceleration. With sexupole harmonics of nonlinear fields in the main dipole and quadrupole magnets, but without 4-pole harmonics, 6.6% of the beam is lost from the main separatrix at slip-stacking injection and 0.2% at ordinary injection. June 30, 2006 A.Drozhdin

Beam loss at slip-stacking injection with different content of nonlinear fields in the dipole and quadrupole magnets (simulated closed orbit #1). June 30, 2006 A.Drozhdin

Beam loss at normal and slip-stacking injection from 1 MV main separatrix (simulated closed orbit #1). June 30, 2006 A.Drozhdin

Beam loss at slip-stacking injection for different random distributions of nonlinear fields along the accelerator (simulated closed orbit #2). June 30, 2006 A.Drozhdin