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 50µm 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

• ctupole

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

• ctupole

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

• ctupole

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

• ctupole

14 0.00000

• 0.99249E-01

0.0000E+00 MP610BS lattice element example in the Recycler Ring

• ctupole

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

• ctupole

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

• ctupole

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

• ctupole

14 0.00000 0.13742E+00 0.0000E+00 MPS333BD

• ctupole

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

• ctupole

14 0.00000 0.11833E+00 0.0000E+00 MP333BS 2

• 10

10 20 30 40 50 60 70 80 500 1000 1500 2000 2500 3000 Horizontal beta functions, m Path Length, m MAD, horizontal STRUCT, horizontal Beam line

• 10

10 20 30 40 50 60 70 80 500 1000 1500 2000 2500 3000 Vertical beta functions, m Path Length, m MAD, vertical STRUCT, vertical Beam line

Figure 1: Horizontal (top) and vertical (bottom) beta-functions in the Recycler Ring. 3

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10 20 30 40 50 60 70 80 100 200 300 400 500 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 1000 1100 1200 1300 1400 1500 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 2000 2100 2200 2300 2400 2500 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 3000 3100 3200 3300 3400 3500 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 500 600 700 800 900 1000 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 1500 1600 1700 1800 1900 2000 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 2500 2600 2700 2800 2900 3000 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

• 10

10 20 30 40 50 60 70 80 3000 3100 3200 3300 3400 3500 Beta functions, m Path Length, m MAD, horizontal MAD, vertical STRUCT, horizontal STRUCT, vertical Beam line

Figure 2: Beta-functions along the Recycler Ring. 4

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10 20 30 40 50 60 70 20 40 60 80 100 120 140 Beta functions, m Path Length, m MI60 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 70 80 550 600 650 700 750 Beta functions, m Path Length, m MI10 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 70 1600 1650 1700 1750 1800 1850 Beta functions, m Path Length, m MI30 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 70 2280 2300 2320 2340 2360 2380 Beta functions, m Path Length, m MI40 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 70 240 260 280 300 320 340 360 Beta functions, m Path Length, m MI62 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 1420 1440 1460 1480 1500 1520 1540 Beta functions, m Path Length, m MI22 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 70 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 Beta functions, m Path Length, m MI32 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

• 20
• 10

10 20 30 40 50 60 70 3100 3120 3140 3160 3180 3200 Beta functions, m Path Length, m MI52 Recycler Ring, horizontal Main Injector, horizontal Recycler Ring, vertical Main Injector, vertical RR Beam line MI Beam line MI Beam line

Figure 3: Comparison of beta-functions in the straight sections of the Main Injector and Recycler Ring. 5

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

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• 5

5 10 15 20 260 280 300 320 340 360 X, mm Path Length, m crystal SM dump Kick at crystal = -0.5 mrad Kick at crystal = +0.5 mrad beam line Figure 5: Horizontal trajectory in the MI62 section from the kick at crystal of ±0.5mrad. 6

middle of crystal:

At positive miscut angle only small number of particles are channeled because the critical channeling angle (7 microrad) in the region of particles interaction with crystal (~400 microrad).

Halo particles at first interaction X’(plane)=-miscut+alignment=0.12mrad X=0.0 Bending kick of particles at first interaction with crystal depends on miscut angle, alignment and bending angle of crystal. Negative miscut=-0.12mrad L=0.005m, bend=-0.36 mrad

is much less compared to range of crystal plane orientation

X X=bend*L/2- *L=-0.001025mm X=bend*L/8- *L/2=-0.000256mm Positive miscut=+1.6mrad L=0.005m, bend=-0.41 mrad =0.0 alignment=0.0 impact ~0.001mm X’(plane)=-bend-miscut+ =-1.19mrad X’(plane)=-bend/2-miscut+ =-1.395mrad S X beam beam S

At negative miscut all incomming particles are parallel to the crystal plane and are channeled. This particles get an angular kick from zero to some angle which is less or equal to crystal bending angle.

alignment is angle of side surface at crystal is angle of side surface at crystal exit

ψ ψ ψ ψ ψ ψ

=-0.36 mrad X’(plane)=-miscut+ =-1.6mrad alignment=-bend+ =+0.41mrad X=0.0mm, ψ =0.0

ψ ψ ψ

w/r to accelerator central line w/r to accelerator central line. entrance

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

• f crystal bending to achieve an efficient channeling.

7

• 1
• 0.5

0.5 1 1.5 2

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• 5

5 10 15 X’, mrad X, mm crystal H_cryst_5sigma ellipse particles at crystal particles at crystal

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5

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• 15
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• 5

5 10 Y’, mrad Y, mm collimator for channeling H1-coll_5sigma ellipse particles from crystal

• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5

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• 5

5 10 15 20 Y’, mrad Y, mm collimator for volum reflection H2-coll_5sigma ellipse particles from crystal

Figure 7: Position of particles at crystal entrance (top) and collimators H1-coll and H2-coll entrance (middle and bottom) in a phase plane during the first turn after interaction with crystal. 8

0.8 0.82 0.84 0.86 0.88 0.9 0.92

• 12.92 -12.91
• 12.9
• 12.89 -12.88 -12.87 -12.86 -12.85 -12.84 -12.83

X’, mrad X, mm crystal H_cryst_5sigma ellipse particles at crystal particles at crystal 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

• 12.92 -12.91
• 12.9
• 12.89 -12.88 -12.87 -12.86 -12.85 -12.84 -12.83

dN/dX X, mm crystal particles at crystal 200 400 600 800 1000 1200 1400 1600 1800

• 8
• 6
• 4
• 2

2 4 6 8 dN/dY Y, mm crystal particles at crystal

Figure 8: Initial particle population and distributions at the crystal entrance at multi-turn simula- tions. 9

500 1000 1500 2000 2500 3000 3500

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dN/dX X, mm "hist_sept3_Recycler_Hor_0.5mr_miscut_0.0_m128373_p0.860"

Figure 9: Particle distribution in the collimator H1-coll with crystal alignment at 0.860 mrad w/r to accelerator central line. 10

500 1000 1500 2000 2500 3000 3500 4000

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dN/dX X, mm 5-sigma circulating beam adge is at X=-8.86mm H1-septum entrance septa entrance septa exit 200 400 600 800 1000 1200 1400 1600 1800

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dN/dX X, mm Beam Dump

Figure 10: Particle distribution in the Septum-magnet H1-sept (top), and beam Dump with crystal alignment at 0.860 mrad w/r to accelerator central line. Particle loss distribution: extracted to beam Dump - 89.9%, lost at 2-mm thick septa - 9.9%, lost in the ring - 0.2%. Septum-magnet parameters: L=0.3m, B=3 kGauss, Vert. aperture - 40mm, septa thickness - 2mm. 11

500 1000 1500 2000 2500 3000 3500 4000

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dN/dX X, mm 5-sigma circulating beam adge is at X=-8.86mm H1-septum entrance septa entrance septa exit 200 400 600 800 1000 1200 1400 1600 1800

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dN/dX X, mm Beam Dump

Figure 11: Particle distribution in the Septum-magnet H1-sept (top), and beam Dump with crystal alignment at 0.860 mrad w/r to accelerator central line. Particle loss distribution: extracted to beam Dump - 98.6%, lost at 0.2-mm thick septa - 1.1%, lost in the ring - 0.2%. 12

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0.7 0.75 0.8 0.85 0.9 0.95 1 Loss at beam Dump and septa Alignment, mrad loss at beam Dump loss at septa of septum-magnet 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.7 0.75 0.8 0.85 0.9 0.95 1 Loss at crystal and accel. aperture Alignment, mrad loss at crystal loss at accel. aperture

Figure 12: Particle loss at beam Dump and 2-mm thick septum-magnet septa (top), and at crystal and accelerator aperture (bottom) as a function of crystal alignment w/r to accelerator central line. 13