Jun'15 eRHIC Baseline Arc Cells

June 24, 2015 Stephen Brooks, eRHIC meeting 1

Design for 4+12 turn FFAGs

High-Energy Cell Rationale

• The 5-turn FFAG1 is perceived to be risky– Tunes are near the limits in both directions– Proximity to half-integer tends to give strong

chromatic effects

• Want a 4+12 turn configuration, as published, to work on, do correction studies etc.

• Based on previous lattices collected by Dejan• Not “the best possible”, just “no major issues”

June 24, 2015 Stephen Brooks, eRHIC meeting 2

High-Energy Cell (6.6-21.2GeV)Element Length (m) Angle (mrad) Gradient (T/m) Offset (mm)

QF2 1.847 5.418061 -20.60 7.87

BD2 1.1293 3.312967 28.87 -5.61

Both drifts 0.18 0

June 24, 2015 Stephen Brooks, eRHIC meeting 3

• Both equivalent dipoles equal: Gx = -0.1620T– This means “central energy” with same radius of

curvature in both magnets exists (Rmag=340.88m)

• Watch out for signs: Muon1 uses negative electrons going anticlockwise…

High-Energy Cell Performance

June 24, 2015 Stephen Brooks, eRHIC meeting 4

Parameter Jan’14 (50T/m FODO) Oct’14 (30T/m doublet) Jun’15

Energy range 7.944 – 21.164 GeV 7.944 – 21.164 GeV 6.622 – 21.164 GeV

Energy ratio 2.66× 2.66× 3.20×

Turns (1.322GeV linac)

11 11 12

Synchrotron power (* L=2138m arcs)

9.8MW @ 21.1GeV, 18mA10.2MW @ 15.8GeV, 50mA3.2MW @ 10.5GeV, 50mA

9.9MW @ 21.1GeV, 20mA9.5MW @ 15.8GeV, 50mA3.0MW @ 10.5GeV, 50mA

10.1MW @ 21.1GeV, 16mA10.0MW @ 15.8GeV, 44mA4.6MW @ 10.5GeV, 50mA

TOF range 22.4ppm (5cm) 38.0ppm (9cm) 56.9ppm (12cm)

Drift space 28.8cm 45.0cm (and 6.0cm) 18.0cm

Tune range 0.035 – 0.369 0.033 – 0.410 0.024 – 0.346

Orbit range (quads) 12.6mm (rmax = 9.1mm) 21.6mm (rmax = 15.8mm) 30.5mm (rmax = 21.7mm)

Max |B| on orbit 0.451 T 0.416 T 0.467 T

Max quad strength 49.515 T/m 29.256 T/m 28.870 T/m

High-Energy Cell Orbits

June 24, 2015 Stephen Brooks, eRHIC meeting 5

Cell in Vladimir’s Coordinates• = 0.012470287 m

– NB: this is a total "offset" of 13.48 mm in Muon1! Not the same.

• h = 0.001176114 m• R(1-cos ) = 0.003641082 m• R = 382.1117394 m• = 0.004365514 radians =

0.250125528 degrees– Not ¼° due to length rounding

• We also tried optimising for minimal SR at 21.2GeV

• Won 2% at expense of 6% higher B field and 19% more SR at 15.9GeV, so decided to leave as is

June 24, 2015 Stephen Brooks, eRHIC meeting 6

R(1-cos )

Low-Energy Cell Rationale

• Make a reasonable 4-turn FFAG1• Yue was using a cell with same length as

FFAG2 but this resulted in large orbit offsets• This made time-of-flight variation very large– Causes problems in longitudinal dynamics, R56

• Scale the cell down to 2/3 the length of FFAG2– While retaining most of the properties– Approximately based on next slide

June 24, 2015 Stephen Brooks, eRHIC meeting 7

Scaling type(by factor a) Length Angle Dipole Gradient Quad offset (=dipole/grad)

& orbit excursion

Momentum (~energy) 1 1 a a 1

Machine radius a 1 a-1 a-2 a

FFAG beta length (fixed bend radius, fixed cell tune)

a a 1 a-2 a2

FFAGarc-to-straight(=row 3/row 2)

1 a a 1 a

FFAG radius with fixed orbit excursion and field (row 2*row 1/sqrt(row 3))

a1/2 a-1/2 1 1 1

FFAG scaling* laws* not scaling FFAG laws

June 24, 2015 Stephen Brooks, eRHIC meeting 8

I’m going to use this one to reduce the length of the FFAG1 cell to 2/3 (offsets to 4/9)

Low-Energy Cell (1.3-5.3GeV)Element Length (m) Angle (mrad) Gradient (T/m) Offset (mm)

QF1 0.8121 2.910342 -10.6 5.6

BD1 0.8121 2.910342 10.6 -5.6

Both drifts 0.3 0

June 24, 2015 Stephen Brooks, eRHIC meeting 9

• Equal-length, equal-gradient FODO lattice• Both equivalent dipoles equal: Gx = -0.0594T– This means “central energy” with same radius of

curvature in both magnets exists (Rmag=279.04m)

• Gradient increased 3.5 10.6 T/m

Low-Energy Cell Performance

June 24, 2015 Stephen Brooks, eRHIC meeting 10

Parameter Jan’14 Oct’14 Jun’15

Energy range 1.334 – 6.622 GeV 1.334 – 6.622 GeV 1.334 – 5.300 GeV

Energy ratio 4.96× 4.96× 3.97×

Turns (1.322GeV linac) 5 5 4

Synchrotron power 0.26MW @ 50mA 0.34MW @ 50mA 0.11MW @ 50mA

TOF range 54.7ppm (12cm) 31.0ppm (7cm) 42.7ppm (9cm)

Drift space 28.8cm 45.0cm 30.0cm

Tune range 0.036 – 0.424 0.033 – 0.408 0.062 – 0.277

Orbit range (quads) 31.3mm (rmax = 23.6mm)

16.9mm (rmax = 11.1mm)

28.1mm (rmax = 23.3mm)

Max |B| on orbit 0.227 T 0.266 T 0.238 T

Max quad strength 9.986 T/m 25 T/m 10.6 T/m

Low-Energy Cell Orbits

June 24, 2015 Stephen Brooks, eRHIC meeting 11