lattice element example in the Recycler Ring octupole 14 0.00000 - PDF document

Crystal Extraction from the Recycler Ring ∗ A.I. Drozhdin Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 May 31, 2012 1 Recycler Ring Lattice The choices to install the crystal in the Recycler Ring would be between straight section MI52 and MI62. The prefered location currently would be MI62. The reason that MI52 looked good was because that is where there would be a Lambertson magnet to try to attempt to extract beam using VR. However, MI52 has many more elements there and it may be hard to get it installed. ( from Dean Still) Protvino crystal: Pc=8.88889 GeV crystal length=1mm, R=2m, bend=-0.5mrad, crystal thickness = 1mm RPmis= 0.00mrad, critical angle = 0.071mr volume reflection angle = +0.140mr Dechanneling length = 8.8mm Impact at the crystal at first interaction is 50 µ m Secondary collimators are at 5 sigma + 0.5mm Simulation during 200 turns ∗ Work supported by Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Depart- ment of Energy. 1

lattice element example in the Recycler Ring octupole 14 0.00000 0.33083E-01 0.0000E+00 MP610BN quadrupole 2 0.00000 0.54000E-04 0.0000E+00 MP610BS sextupole 15 0.00000 -0.47400E-03 0.0000E+00 MP610BS octupole 14 0.00000 -0.99249E-01 0.0000E+00 MP610BS grad.magnet 19 1.54940 0.22538E-01 0.1330E+01 G610B sextupole 15 0.00000 -0.43383E-04 0.0000E+00 G610B grad.magnet 19 1.54940 0.22538E-01 0.1330E+01 G610B octupole 14 0.00000 0.33083E-01 0.0000E+00 MP610BN quadrupole 2 0.00000 0.54000E-04 0.0000E+00 MP610BS sextupole 15 0.00000 -0.47400E-03 0.0000E+00 MP610BS octupole 14 0.00000 -0.99249E-01 0.0000E+00 MP610BS lattice element example in the Recycler Ring octupole 14 0.00000 -0.16414E+00 0.0000E+00 MP333BN quadrupole 3 0.00000 0.14000E-03 0.0000E+00 MP333BS sextupole 15 0.00000 -0.14220E-02 0.0000E+00 MP333BS octupole 14 0.00000 0.11833E+00 0.0000E+00 MP333BS quadrupole 3 0.00000 0.50472E-03 0.0000E+00 MPS333BU sextupole 15 0.00000 0.38914E-01 0.0000E+00 MPS333BU octupole 14 0.00000 0.21377E+00 0.0000E+00 MPS333BU grad.magnet 17 2.24790 0.10920E-01 0.1375E+01 G333B sextupole 15 0.00000 -0.11008E+00 0.0000E+00 G333B grad.magnet 17 2.24790 0.10920E-01 0.1375E+01 G333B quadrupole 2 0.00000 0.13743E-04 0.0000E+00 MPS333BD sextupole 15 0.00000 0.11960E-02 0.0000E+00 MPS333BD octupole 14 0.00000 0.13742E+00 0.0000E+00 MPS333BD octupole 14 0.00000 -0.16414E+00 0.0000E+00 MP333BN quadrupole 3 0.00000 0.14000E-03 0.0000E+00 MP333BS sextupole 15 0.00000 -0.14220E-02 0.0000E+00 MP333BS octupole 14 0.00000 0.11833E+00 0.0000E+00 MP333BS 2

80 MAD, horizontal 70 STRUCT, horizontal Beam line Horizontal beta functions, m 60 50 40 30 20 10 0 -10 0 500 1000 1500 2000 2500 3000 Path Length, m 80 MAD, vertical 70 STRUCT, vertical Beam line Vertical beta functions, m 60 50 40 30 20 10 0 -10 0 500 1000 1500 2000 2500 3000 Path Length, m Figure 1: Horizontal (top) and vertical (bottom) beta-functions in the Recycler Ring. 3

80 80 MAD, horizontal MAD, horizontal 70 MAD, vertical 70 MAD, vertical STRUCT, horizontal STRUCT, horizontal 60 60 STRUCT, vertical STRUCT, vertical Beam line Beam line Beta functions, m Beta functions, m 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 0 100 200 300 400 500 500 600 700 800 900 1000 Path Length, m Path Length, m 80 80 MAD, horizontal MAD, horizontal 70 MAD, vertical 70 MAD, vertical STRUCT, horizontal STRUCT, horizontal 60 STRUCT, vertical 60 STRUCT, vertical Beam line Beam line Beta functions, m Beta functions, m 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 1000 1100 1200 1300 1400 1500 1500 1600 1700 1800 1900 2000 Path Length, m Path Length, m 80 80 MAD, horizontal MAD, horizontal 70 MAD, vertical 70 MAD, vertical STRUCT, horizontal STRUCT, horizontal 60 60 STRUCT, vertical STRUCT, vertical Beam line Beam line Beta functions, m Beta functions, m 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 2000 2100 2200 2300 2400 2500 2500 2600 2700 2800 2900 3000 Path Length, m Path Length, m 80 80 MAD, horizontal MAD, horizontal 70 MAD, vertical 70 MAD, vertical STRUCT, horizontal STRUCT, horizontal 60 60 STRUCT, vertical STRUCT, vertical Beam line Beam line Beta functions, m Beta functions, m 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 3000 3100 3200 3300 3400 3500 3000 3100 3200 3300 3400 3500 Path Length, m Path Length, m Figure 2: Beta-functions along the Recycler Ring. 4

70 70 Recycler Ring, horizontal Recycler Ring, horizontal 60 MI60 Main Injector, horizontal 60 MI62 Main Injector, horizontal Recycler Ring, vertical Recycler Ring, vertical 50 Main Injector, vertical 50 Main Injector, vertical RR Beam line RR Beam line Beta functions, m Beta functions, m 40 40 MI Beam line MI Beam line MI Beam line MI Beam line 30 30 20 20 10 10 0 0 -10 -10 -20 -20 0 20 40 60 80 100 120 140 240 260 280 300 320 340 360 Path Length, m Path Length, m 80 60 Recycler Ring, horizontal Recycler Ring, horizontal 70 Main Injector, horizontal Main Injector, horizontal 50 MI22 Recycler Ring, vertical Recycler Ring, vertical 60 MI10 Main Injector, vertical Main Injector, vertical 40 RR Beam line RR Beam line 50 Beta functions, m Beta functions, m MI Beam line MI Beam line 30 40 MI Beam line MI Beam line 30 20 20 10 10 0 0 -10 -10 -20 -20 550 600 650 700 750 1420 1440 1460 1480 1500 1520 1540 Path Length, m Path Length, m 70 70 Recycler Ring, horizontal Recycler Ring, horizontal 60 MI30 Main Injector, horizontal 60 MI32 Main Injector, horizontal Recycler Ring, vertical Recycler Ring, vertical 50 50 Main Injector, vertical Main Injector, vertical RR Beam line RR Beam line Beta functions, m Beta functions, m 40 40 MI Beam line MI Beam line MI Beam line MI Beam line 30 30 20 20 10 10 0 0 -10 -10 -20 -20 1600 1650 1700 1750 1800 1850 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 Path Length, m Path Length, m 70 70 Recycler Ring, horizontal Recycler Ring, horizontal 60 MI40 Main Injector, horizontal 60 MI52 Main Injector, horizontal Recycler Ring, vertical Recycler Ring, vertical 50 Main Injector, vertical 50 Main Injector, vertical RR Beam line RR Beam line Beta functions, m Beta functions, m 40 40 MI Beam line MI Beam line MI Beam line MI Beam line 30 30 20 20 10 10 0 0 -10 -10 -20 -20 2280 2300 2320 2340 2360 2380 3100 3120 3140 3160 3180 3200 Path Length, m Path Length, m Figure 3: Comparison of beta-functions in the straight sections of the Main Injector and Recycler Ring. 5

1 sigma, horizontal 1 sigma, vertical Horizontal beam half-size, mm 15 5 sigma, horizontal 5 sigma, vertical Beam line 10 5 sigma at crystal: 5 sigma at collimator: X=10.553mm, X’=-0.987mrad X=10.995mm, X’=-1.169mrad 5 Y=+13.758mm, Y’=+1.235mrad Y=-12.386mm, Y’=-0.952mrad collimator 0 crystal collimator dPSI(cry/coll)=150 degree 240 260 280 300 320 340 360 Path Length, m Figure 4: Beam size in the MI62 cristal and collimator of the Recycler Ring. 20 Kick at crystal = -0.5 mrad Kick at crystal = +0.5 mrad 15 beam line 10 5 X, mm SM 0 crystal dump -5 -10 -15 -20 260 280 300 320 340 360 Path Length, m Figure 5: Horizontal trajectory in the MI62 section from the kick at crystal of ± 0 . 5 mrad . 6

Bending kick of particles at first interaction with crystal depends on miscut angle, X=0.0mm, ψ =0.0 alignment and bending angle of crystal. ψ X’(plane)=-miscut+ =-1.6mrad Halo particles at ψ first interaction alignment=-bend+ =+0.41mrad ψ X=bend*L/2- *L=-0.001025mm X ψ X’(plane)=-bend-miscut+ =-1.19mrad X=0.0 impact ~0.001mm X’(plane)=-miscut+alignment=0.12mrad X S S beam beam Negative miscut=-0.12mrad Positive miscut=+1.6mrad L=0.005m, bend=-0.36 mrad L=0.005m, bend=-0.41 mrad alignment=0.0 ψ =0.0 ψ =-0.36 mrad At negative miscut all incomming particles are parallel to the crystal plane and are channeled. middle of crystal: This particles get an angular kick from zero to ψ some angle which is less or equal to crystal X=bend*L/8- *L/2=-0.000256mm bending angle. ψ X’(plane)=-bend/2-miscut+ =-1.395mrad alignment is angle of side surface at crystal At positive miscut angle only small number of particles are entrance w/r to accelerator central line. channeled because the critical channeling angle (7 microrad) ψ is angle of side surface at crystal exit is much less compared to range of crystal plane orientation w/r to accelerator central line in the region of particles interaction with crystal (~400 microrad). Figure 6: Particle channeling at crystal located inside or bottom of the circulating beam. Bending angle of crystal is negative. Miscut angle is positive if crystal side surface is at positive angle with respect to channeling planes. This shows that the sign of crystal miscut must be the same as the sign of crystal bending to achieve an efficient channeling. 7