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

Schematic diagram of the eRHIC accelerator ERL2015

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 ERL2015

FFAG Cell of the eRHIC x(mm) =0.283o 2.7 mm 2.7 mm 6 cm ERL2015 Bf= 0.0813 T, Gf= 30 T/m xFoffset= -2.7 mm BD = 0.0813 T, Gd = -30 T/m xDoffset=+2.7 mm x(mm) N=212 cells per arc, 1.680 m o 8.1 mm =0.283o 6.622 GeV 2.7 mm 5.3 GeV 2.7 mm 3.978 GeV 1.334 GeV 2.656 GeV -8.8 mm 6 cm 0.48 m 0.44 m 70 cm 4/18 ERL2015

ERL2015 5/18

Perm. Magnet Material SmCO ERL2015 6/18

Perm. Magnet Material SmCO ERL2015 7/18

Perm. Magnet Material SmCO Perm. Magnet Material NdFeB ERL2015 8/18

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 ERL2015 9/18

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 ERL2015

3D Magnetic field calculations for the FFAG cells QF QD =0.283o cell ERL2015

3D Magnetic field calculations for the FFAG cells 3Dimensional Field map is obtained over the volume of a single cell where beam exists. ERL2015

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 18730.5 337.4 Magnet#1 Measurement 18650.0 4.3x10-3 350.6 7x10-4 Magnet#2 19096.0 20x10-3 371.5 17x10-4 ERL2015

Theory 180.1 ERL2015

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. ERL2015 15/18

Closed orbits in the range 1.3 GeV to 6.6 GeV QF QD Y tranverse [m] x-along beam [m] ERL2015 16/18

Tunes Qx,Qy and chromaticities x, y; Range: 1.3 GeV to 6.6 GeV ERL2015 17/18

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 ERL2015 18/18

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 ERL2015 19/18

Calculations of the maximum beam emittance y transported in all six arcs for each of the five orbits. ERL2015 20/18

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 ERL2015 21/18

The dynamic aperture at the exit of 1000 cells ERL2015 22/18

Beta functions of 3 different energies QF QD x 1.3 GeV y 2.6 GeV 6.6 GeV ERL2015 23/18

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.

Thank you for your attention The End Thank you for your attention ERL2015 25

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

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

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 

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 

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