1. The Optics of the Low Energy FFAG cell of the eRHIC collider, using realistic field maps
N. Tsoupas, S. Brooks, A. Jain, G. Mahler, F. Meot, V. Ptitsyn, D. Trbojevic, BNL
M. Severance, SBU
ERL2015

2. Schematic diagram of the eRHIC accelerator
ERL2015

3. FFAG Cell structure of the eRHIC
Energy of e-bunches circulating in Low Energy ring 1.32, 2.64, 3.96, 5.28, 6.6 GeV
212 cells per sextant
Interaction points
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4. FFAG Cell of the eRHIC x(mm) =0.283o 2.7 mm 2.7 mm 6 cm ERL2015
Bf= T,
Gf= 30 T/m
xFoffset= -2.7 mm
BD = T,
Gd = -30 T/m
xDoffset=+2.7 mm
x(mm)
N=212 cells per arc, m o
8.1 mm
=0.283o
GeV
2.7 mm
5.3 GeV
2.7 mm
3.978 GeV
GeV
GeV
-8.8 mm
6 cm
0.48 m
0.44 m
70 cm
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5. ERL2015
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6. Perm. Magnet Material SmCO
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7. Perm. Magnet Material SmCO
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8. Perm. Magnet Material SmCO
Perm. Magnet Material NdFeB
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9. 2D Design establishes the magnet’s cross section
Perm. Magnet Material SmCO
Perm. Magnet Material NdFeB
2D Design establishes the magnet’s cross section
-The 12pole multipole=0 for R=1 cm
-NdFeB-N45 allows for larger inner radius
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10. Schematic diagram of 3 consecutive FFAG cells
55 mm Displ.
54 mm QF QD
54 mm QF QD
54 mm QF QD
Reference orbit
cell
cell
cell
=0.283o
=0.283o
=0.283o
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11. 3D Magnetic field calculations for the FFAG cellsQF QD
=0.283o
cell
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12. 3D Magnetic field calculations for the FFAG cells
3Dimensional Field map is
obtained over the volume of
a single cell where beam exists.
ERL2015

13. Long coil measurement of the magnetic multipoles at R=1 cm
[Gauss]
Q_Diff/Qmeas
[Gauss.cm-4]
12p_diff/Qmeas
SmCo R26HS Temp.=20o
Calculations
337.4
Magnet#1
Measurement
4.3x10-3
350.6
7x10-4
Magnet#2
20x10-3
371.5
17x10-4
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14. Theory
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15. The Optics of the Low Energy FFAG cell*
3D Field Maps were obtained from the 3D EM Calculations
Calculate the closed orbits in the range 1.3 GeV to 6.6 GeV
Calculations of tunes Qx,Qy and chromaticities x, y per cell.
Calculations of the maximum beam emittances x, y transported in the low energy arc for each of the five orbits.
Calculation of the dynamic aperture of the transport ring.
Calculation of the beta functions.
* The zgoubi computer code was used in the calculations.
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16. Closed orbits in the range 1.3 GeV to 6.6 GeVQF QD
Y tranverse [m]
x-along beam [m]
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17. Tunes Qx,Qy and chromaticities x, y; Range: 1.3 GeV to 6.6 GeV
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18. Calculations of the maximum beam emittance x transported in all six arcs for each of the five orbits.
5.28 GeV
6.60 GeV
3.96 GeV
2.64 GeV
1.32 GeV
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19. Calculations of the maximum beam emittance x transported in all six arcs for each of the five orbits.
Max_N-rms=0.02 m.rad
Required_N-rms to be transported=30x10-6 m.rad
5.28 GeV
6.60 GeV
3.96 GeV
2.64 GeV
1.32 GeV
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20. Calculations of the maximum beam emittance y transported in all six arcs for each of the five orbits.
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21. Calculations of the maximum beam emittance y transported in all six arcs for each of the five orbits.
Max_N-rms=0.02 m.rad
Required _N-rms to be transported=30x10-6 m.rad
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22. The dynamic aperture at the exit of 1000 cells
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23. Beta functions of 3 different energiesQF QD x
1.3 GeV y
2.6 GeV
6.6 GeV
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24. Conclusions
The results from the calculations on the beam optics of the low energy cell meet well the requirements.
The calculated 3D magnetic fields of a single magnet are in good agreement with the measurements.

25. Thank you for your attention
The End
Thank you for your attention
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26. How can we correct for the multipoles?
Method II
Change the direction of wedge’s-easy-axis by
Easy-axis for Sext 
Easy-axis for Quad

27. How can we correct for the multipoles?
Method II
Change the direction of wedge’s-easy-axis by 
-1.5o
-0.8o
-0.6o
+0.6o
+0.8o
+1.5o
Easy-axis for Sext 
Easy-axis for Quad

28. How can we correct for the multipoles?
Method ΙΙ
Change the direction of Rod’s-easy-axis by
Either method can “easily”
reproduce the measure sextupole
The rest of the multipole including
the quad remain practically unchanged
Easy-axis for Quad
Easy-axis for Sext 

29. How can we correct for the multipoles?
Method ΙΙ
Change the direction of Rod’s-easy-axis by
Either method can “easily”
reproduce the measure sextupole
The rest of the multipole including
the quad remain practically unchanged 
-20o
-11o
-8o
+8o
+11o
+20o
Easy-axis for Quad
Easy-axis for Sext 

30. How can we correct for the multipoles?
Method ΙΙΙ
Use surface-current coils