NonScaling Linear FFAGs for e RHIC D Trbojevic

Non-Scaling Linear FFAG’s for e. RHIC D. Trbojevic FFAG workshop 2013 at TRIUMF, Vancouver September 21, 2013 10/30/2020 Dejan Trbojevic – FFAG-1013 1

The Pillars of the e. RHIC Physics program s p t h r s H f E 3 y o p a i l D s n i d e e i g n r l I c c o d m t s c P n s a r o h i g o o l y s i Wide physics program with high on detector and machine performance f requirements o s a W r Dejan Trbojevici – FFAG-1013 n 10/30/2020 t 2

Most Compelling Physics Questions imaging spin physics what is the polarization of gluons at what is the spatial distribution of small x where they are most abundant quarks and gluons in nucleons/nuclei what is the flavor decomposition of understand deep aspects of gauge the polarized sea depending on x theories revealed by k. T dep. distr’n determine quark and gluon contributions possible window to to the proton spin at last orbital angular momentum physics of strong color fields quantitatively probe the universality of strong color fields in AA, p. A, and e. A understand in detail the transition to the non-linear regime of strong gluon fields and the physics of saturation how do hard probes in e. A interact with the medium 10/30/2020 Dejan Trbojevic – FFAG-1013 3

The Probe: Deep Inelastic Scattering Kinematics: Measure of resolution power Measure of inelasticity Measure of momentum fraction of struck quark Gluon splits into quarks Quark splits into gluon splits into quarks … 10 -16 m 10 -19 m 10/30/2020 Dejan Trbojevic – FFAG-1013 higher √s increases resolution 4

How many gluons have space in A proton? q current theory (DGLAP) has a built in energy catastrophe G rapid raise violates unitary bound small x / higher energy x = Pparton/Pnucleon q BK/JIMWLK non-linear evolution includes recombination effects saturation Ø Dynamically generated scale Saturation Scale: Q 2 s(x) § Increases with energy or decreasing x Ø Scale with Q 2/Q 2 s(x) instead of x and Q 2 a nit g o nc I a rr e T as~1 10/30/2020 Bremsstrahlung ~ asln(1/x) as << 1 Recombination ~ asr Saturation must set in at low x high occupancy space becomes crowded gluons start to overlap recombination Dejan Trbojevic – FFAG-1013 5

Layout of the e. RHIC inside the RHIC tunnel V Ge 0 0. 1 2. 8 her Co V Dejan Trbojevic – FFAG-1013 Ge Ge. V Ge. V 0. 1 10/30/2020 #1 2. 8 #2 - 3. 7 #3 4. 6 #4 5. 5 #5 6. 4 #6 7. 3 #7 8. 2 #8 9. 1 #8 10. 0 9 -1. 1. 0 AG e. V -FF 9 G NS ac 0. Lin ent coo Elec ling tron Passes through the #1 FFAG 6

SOLUTIONS: VFFAG and Non-Scaling FFAG 10/30/2020 Dejan Trbojevic – FFAG-1013 7

NS-FFAG with sextupoles 1. 51 – 10 Ge. V 2. 51 m 0. 17 0. 4 m 1. 2 m 10. 00 Ge. V 9. 2 mm 6. 3 mm 3. 2 mm 8. 585 Ge. V 7. 170 Ge. V 5. 755 Ge. V 4. 344 Ge. V 2. 925 Ge. V 1. 510 Ge. V -2. 9 mm -7. 5 mm 10/30/2020 8 cm 0. 4 m 0. 17 Dejan Trbojevic – FFAG-1013 8

TUNES VS. ENERGY with sextupoles 10/30/2020 Dejan Trbojevic – FFAG-1013 9

Dynamical Aperture 142*6 cells @ 10 Ge. V LINEAR WITH SEXTUPOLES y(m) 1 y(mm) 0. 5 2. 5 1 0. 0 1 m 0. 0 -0. 5 -1 -2. 5 -0. 5 0. 0 0. 5 x(m) 1. 2 -5 -2. 5 0. 0 2. 5 5 x 10/30/2020 Dejan Trbojevic – FFAG-1013 10

Two Non-Scaling FFAG’s The central momentum pc in the NS-FFAG creates the circular orbit for the reference particle. 1. Large Ring 2. 8 10 Ge. V: pc =pmax The circular orbit is at the top energy of 10 Ge. V while the minimum energy entering FFAG is 4. 5 Ge. V. The energy gain: Etop/Ein= 10/2. 8 =3. 57 δp/p=(pmin- pmax)/pmax=(pmin/pmax-1)= 0. 357 - 1 = -0. 72 2. Small Ring (two passes) 1. 0 & 1. 9 Ge. V The energy gain: Etop/Ein= 1. 9/1. 0 =1. 9 10/30/2020 Dejan Trbojevic – FFAG-1013 11

Two passes 1. 0 and 1. 9 Ge. V with small ring and nine in the RHIC tunnel 2. 8 -10 Ge. V NS-FFAG 3 9 0. 9 90 Dump Low energy 1. 00 Ge. V 1. 90 Ge. V 2. 80 Ge. V 10/30/2020 E-injector Gain 1 -ffag #N 1 -ffag E top-ffag 0. 1 2. 8 3. 5714 2 9 10. 0 TOTAL NUMBER OF PASSES THROUGH THE LINAC = 12 3 passes to get to 1. 9 Ge. V and 9 additional passes to get to 10 Ge. V V Me m ~9 e. V M 90 h ug e. V o r G s th 1. 9 e s & s pa c 1. 0 o Tw lina the E-linac V n Me gu 10 ctron Ele 1. 9 1. 0 ro #N linac Dejan Trbojevic – FFAG-1013 Passes through large NS-FFAG in RHIC #1 2. 8 Ge. V pass# 3 #2 3. 7 Ge. V pass# 4 #3 4. 6 Ge. V pass# 5 #4 5. 5 Ge. V pass# 6 #5 6. 4 Ge. V pass# 7 #6 7. 3 Ge. V pass# 8 #7 8. 2 Ge. V pass# 9 #8 9. 1 Ge. V pass#10 #9 10. 0 Ge. V pass#11 12

Two passes 1. 0 and 1. 9 Ge. V with the second ring in the RHIC tunnel 2. 8 - 10 Ge. V NS-FFAG 0. 9 Ge. V ~90 m Ro~ 9 m or 30 m Regular transport ~9 m 90 Me. V Dump Two passes: #1 1. 0 Ge. V #2 1. 9 Ge. V 17’ – 10” 10/30/2020 Dejan Trbojevic – FFAG-1013 20’ – 8” 6. 8 m 13

Number of magnets for NS-FFAG: One arc has 132 cells: each cell has a combined function defocussing magnet QD and two QF quads One arc has 132 cells 356. 3 m = 132 BD, 264 QF Total number of magnets in the six arcs : BD comb. Def. : 132 x 6 = 792, QF’s=132 x 6 = 1584 TOTAL: Combined Defocusing: Combined Focusing: 10/30/2020 792 1584 To be compared with previous design of the six arcs: Dipoles arc total = 2520 quad arc total = 3240 Without spreaders Dejan Trbojevic – FFAG-1013 14

NS-FFAG matching to Linac 0. 9 Ge. V ~90 m Regular transport ~9 m 90 Me. V Dump Two passes: #1 1. 0 Ge. V #2 1. 9 Ge. V r≈9 m or r≈30 m 10/30/2020 Dejan Trbojevic – FFAG-1013 15

1 – 1. 9 Ge. V NS-FFAG ring two options 10/30/2020 Dejan Trbojevic – FFAG-1013 16

Possible place 10/30/2020 Dejan Trbojevic – FFAG-1013 17

Possible place @ 10 o’clock 10/30/2020 Dejan Trbojevic – FFAG-1013 18

VERSION # 1 average radius = 9. 93 m 1. 20 m 1. 0 Ge. V -4. 71 cm 0. 22 m θF=0. 030208 BYF=0. 87 T GF=+34. 964 0. 60 m θD=0. 030207622 BYD=0. 638 T GD=-20. 89 T/m RD=9. 931 m 10/30/2020 Dejan Trbojevic – FFAG-1013 1. 9 Ge. V 0. 22 m θF=0. 030208 BYF=0. 87 T GF=+34. 964 RF=7. 283 m 19

VERSION # 2 average radius = 30. 0 m 1. 545 m 1. 0 Ge. V -1. 79 cm 1. 9 Ge. V 0. 33 m θF=-0. 00644 0. 725 m θD=0. 06438 BYF=-0. 124 T BYD=0. 563 T GF=19. 4 T/m GD=-14. 25 T/m RD=11. 26 m 10/30/2020 Dejan Trbojevic – FFAG-1013 0. 33 m θF=-0. 00644 BYF=-0. 124 T GF=19. 40 RF=-51. 26 m 20

Large 2. 8 – 10 Ge. V ring 10/30/2020 Dejan Trbojevic – FFAG-1013 21

SPREADERS for the large ring ~80 m 10/30/2020 Dejan Trbojevic – FFAG-1013 22

Basic Cell: 2. 8 - 10 Ge. V -72%< Δp/p >100% 2. 699245758 m x(mm) Bf=0. 10 T, Gf= 23. 67 T/m BD=0. 10 T, Gd= -17. 9 T/m Bf=0. 10 T, Gf= 23. 67 T/m 0. 0 10 Ge. V -4. 6 9. 1 Ge. V 2. 8 Ge. V -8. 6 -16. 7 -17. 5 -18. 1 3. 7 Ge. V 8. 2 Ge. V 4. 6 Ge. V 7. 3 Ge. V -11. 9 -14. 7 -17. 8 6. 4 Ge. V 2. 8 Ge. V 5. 5 Ge. V 4. 6 Ge. V 3. 7 Ge. V 0. 145 m 0. 5 m θF=1. 57 mrad ρF=318. 529 m 10/30/2020 1. 25 m θD=3. 9243 mrad ρD=318. 529 m Dejan Trbojevic – FFAG-1013 0. 5 m 0. 145 m θF=1. 57 mrad ρF=318. 529 m 23

Tunes per cell 10/30/2020 Dejan Trbojevic – FFAG-1013 24

Orbit Offsets per cell 10/30/2020 Dejan Trbojevic – FFAG-1013 25

Path Length for 2. 8 – 10 Ge. V lattice 10/30/2020 Dejan Trbojevic – FFAG-1013 26

Path Length for 2. 8 – 10 Ge. V lattice 10/30/2020 Dejan Trbojevic – FFAG-1013 27

Betatron Functions for 2. 8 – 10 Ge. V lattice (m) βx and βy 5 4 3 2 4. 12 βy E=2. 8 G e. V E=3. 7 Ge. V E= 2. 8 E=3. 7 Ge. V E=5. 5 E=4. 6 E=10 Ge. V βx E=2. 8 Ge. V E=10 Ge. V 1 10/30/2020 Dejan Trbojevic – FFAG-1013 28

Dispersion for 2. 8 – 10 Ge. V lattice D(m) 0. 07 0. 06 0. 05 0. 04 0. 03 0. 02 0. 01 E=10 Ge. V E=9. 1 Ge. V E=8. 2 Ge. V E=7. 3 Ge. V E=6. 4 Ge. V E=5. 5 Ge. V E=4. 6 Ge. V E=3. 7 Ge. V E=2. 8 Ge. V -0. 01 -0. 02 -0. 03 10/30/2020 Dejan Trbojevic – FFAG-1013 29

Delays for the large ring Dipole magnet B=1. 2 T L=1 m Δs 10 Ge. V= 2. 59 cm Δs 9. 1 Ge. V= 3. 13 cm Δs 8. 2 Ge. V= 3. 85 cm Δs 7. 3 Ge. V= 4. 86 cm Δs 6. 4 Ge. V= 6. 33 cm Δs 5. 5 Ge. V= 8. 57 cm Δs 4. 6 Ge. V=12. 26 cm Δs 3. 7 Ge. V=18. 98 cm Δs 2. 8 Ge. V=33. 24 cm 20 m ~40 m 10/30/2020 Dejan Trbojevic – FFAG-1013 30

WUZHENG MENG: Combined Function (D): Gradient = - 17. 9 T/m [September 12, 2013] Bo = 0. 10472 T, B = Bo + Gd x = 0. 10472 + (-17. 9) (-17. 1 mm)=0. 41 T Xmin ~ - 17 mm: (By = 0. 3680 T) Xmax ~ 0 mm: (By = 0. 10472 T) 10/30/2020 Dejan Trbojevic – FFAG-1013 31

Large Arc Quads Requirements : 10/30/2020 Dejan Trbojevic – FFAG-1013 WUZHENG MENG: 32

Large Arc Quads Requirements : WUZHENG MENG: Gradient = 23. 671 T/m September 12, 2013 Bo = 0. 10472 T Aperture R > 10 mm (design R = 13. 5 mm) Bmax = Bo + Gf xmax = 0. 10472 + (23. 671) (-17. 1 mm)= - 0. 3 T 10/30/2020 Dejan Trbojevic – FFAG-1013 33

Large Arc Quads Requirements : WUZHENG MENG: Gradient = 23. 671 T/m September 12, 2013 Bo = 0. 10472 T Aperture R > 10 mm (design R = 13. 5 mm) Bmax = Bo + Gf xmax = 0. 10472 + (23. 671) (-17. 1 mm)= - 0. 3 T 10/30/2020 Dejan Trbojevic – FFAG-1013 34

Test RADIA Simulations for e-RHIC FFAG Magnet: Hybrid PM “Wiggler Type” Geometry–Oleg Tchoubar 3 D Model B vs X in Center d(∫B dz)/dx vs X in Cen y y ∫Bydz vs X in Center. By vs Z at x = -12 mm, y = 0 PM Iron Min. Gap: 15 mm Iron Length: 0. 49 m PM Material: Sm 2 Co 17, Br = 1. 05 T PM Volume: 0. 002 m 3 10/30/2020 Dejan Trbojevic – FFAG-1013 35

Bypasses around Detectors and straight section 10/30/2020 Dejan Trbojevic – FFAG-1013 36

THREE possible solutions for matching NS-FFAG to Linac: 1. With the special straight section 2. With few special arc cells at the end of NS-FFAG arc 3. The simplest is by the spreaders and combiners 10/30/2020 Dejan Trbojevic – FFAG-1013 37

Jefferson Lab patent: Gantry Patent: 10/30/2020 Dejan Trbojevic – FFAG-1013 38

Misalignment • • • E 1=0. 0001; !Simple MAs (DX, DY, DS) E 2=0. 00005; !Lengthwise Rotation MAs (about Y and X axis) scaled to the Elements' lengths E 3=0. 00005; !Twist Rotation about S axis (rad) 1 degree=. 01745 rad • use, period=ARC; • • • select, flag=error, clear; select, flag=error, class=rbend; EOPTION, SEED=101; EALIGN, DX: =tgauss(2. 5)*E 1, DY: =tgauss(2. 5)*E 1, DS: =tgauss(2. 5)*E 1, DPHI: =tgauss(2. 5)*E 2, DTHETA: =tgauss(2. 5)*E 2, DPSI: =tgauss(2. 5)*E 3; • !EPRINT, full=true; • PTC_ALIGN; 10/30/2020 Dejan Trbojevic – FFAG-1013 39

E 1=50 μm 10/30/2020 Dejan Trbojevic – FFAG-1013 40

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E 1=150μm 10/30/2020 Dejan Trbojevic – FFAG-1013 46

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Lattice work for OC • Define lattice for a whole pass, instead of repeating one arc by 6 times • Separate a lattice file (lattice. ffag) from the main input file • Add monitors and correctors 10/30/2020 Dejan Trbojevic – FFAG-1013 52