2D-SIMULATION OF COMBINED FUNCTION QUADRUPOLE/SEXTUPOLE MAGNET FOR EXISTING BOOSTER SYNCHROTRON Vanshree Thakur, R.K.Mishra, G.Singh, Raja Ramanna Centre for Advanced Technology, Indore 452 013, India Abstract Table 2: Sextupole Specifications The booster synchrotron used as the injector for Indus 1 Sextup Integrated gradient (T/m) : G'L = (d 2B/ dx 2)L & Indus 2 synchrotron radiation sources does not have oles sextupole magnets for chromaticity correction. Sufficient 20 MeV 700 MeV space is also not available to accommodate independent Sf 0.039 3.2 sextupole magnets. Therefore, it is proposed to replace Sd 0.051 4.3 the quadrupole magnets with the combined function quadrupole/sextupole magnets. We have adopted a DESIGN OPTIMIZATION standard quadrupole design to produce quadrupole field and additional auxiliary coils are mounted on the pole 1. Quadrupole Magnet faces to produce a sextupole field. These auxiliary coils The standard quadrupole magnet design has been produce the required sextupole field and also a dipole followed with hyperbolic pole tip profile to fulfill the field [1]. One more coil is mounted on each pole to annul beam dynamical requirement. Magnetic field simulation this dipole field. In this paper, we report a 2 D design has been carried out using 2D static code POISSON [3]. simulation of the quadrupole/sextupole magnet carried In order to suppress the field gradient error and enlarge out using POISSON software. The effect of combined the good field region, the optimization of the pole shim excitation of the quadrupole and sextupole field strength design has been made. The magnet geometry is simulated and also higher order harmonics is also presented. to produce minimum field gradient of 0.268 T/m at 20 MeV and ramping up to maximum field gradient of 9.32 INTRODUCTION T/m. Yoke and core thickness of 50 mm has been chosen The existing Booster Synchrotron has been designed to to avoid the saturation. The ampere turn of 9600AT per accelerate an electron beam from 20 MeV to 700 MeV . It pole is required for the maximum field gradient of 9.32 consists of six superperiods, each having a dipole magnet T/m. The conductor of 15mm x15mm cross section with and a pair of a focussing and a defocusing quadrupole hollow diameter of 10 mm has been chosen. The turn magnets for tuning [2]. All the quadrupoles are required number is determined to be 12 per pole and maximum current of 800A considering the maximum current density to be combined function in which sextupole field will be 2 superimposed due to constraint of space. The beam of 5.46 A/mm . The magnet parameters are listed in Table dynamical requirement is to produce a quadrupole 3. integrated gradient of 0.067 T at injection energy of 20 As a result of the optimization by the tangential shim, we have obtained the field uniformity better than the MeV and ramped up to 2.33 T at nominal beam energy of 4 700 MeV in the required useful aperture of 40 mm radius required field uniformity of ±1X10 throughout the with the field uniformity of ±2X10 4. All the quadrupoles ramping range from injection energy to maximum beam (Qf & Qd) require the same strength whereas the required energy. Figure 1 illustrates the gradient error (∆G/G 0) at strengths for focussing and defocusing sextupoles are the mid plane at injection and maximum energy levels. different and varies from 0.039T/m to 3.2T/m for The systematic multipole components n=6 and n=10 are focussing sextupole magnets (SF) and from 0.051T/m to very small (< 0.001%). The multipole components for maximum 4.3T/m for defocusing sextupoles (SD). Design only quadrupole full excitation are listed in Table 4. specifications for the quadrupole magnet and sextupole magnet are given in table 1 and table 2 respectively. 3.E 04 700MeV 3.E 04 20MeV 2.E 04 Table 1: Quadrupole Specifications 2.E 04 Integrated gradient (T) 1.E 04
(dG)/G0 5.E 05 GL = (dB/ dx)L Strength 0.E+00 Quadrupoles 2 (m ) 5.E 05 20 MeV 700 MeV 1.E 04 Qf 4 0.067 2.33 1 1.5 2 2.5 3 3.5 4 Qd 4 0.067 2.33 R (cm) Figure 1 : Field uniformity at mid plane of quadrupole The overall saturation of core shows 1.1 % at the highest coefficients for combined full excitation of Quadrupole excitation level of only quadrupole field. and sextupole are listed in table 6. The overall saturation of core shows 2.2 % at the highest excitation level of Table 3 : Main parameters of Quadrupole magnet combined quadrupole/sextupole field.
1. Aperture diameter 100 (mm) Quadrupole coil 2. Effective length (mm) 250 3. Gradient (T/m) Dipole coil at 700 MeV 9.32 at 20 MeV 0.268 4. Good field region (mm) ± 40 5. Field uniformity ∆G/G <± 1E 04 6. Ampere turns per pole 9600 7. Number of turns/coil 12 8. Peak current ( A) 800 9. Conductor size 15 x 15 x 10 mm Table 4 : Multipole components of Quadrupole magnet at the full excitation level at normalization radius = 40mm Sextupole coil Figure 1: Field contour and configuration of coils n Relative field error bnl (B n/B 2) . at the R=4 cm Table 5: Main parameters for combined 2 1 0.9640 Quadrupole.Sextupole magnet 6 9.66 E 06 3.6375 1 Sextupole coil ampere turns 644 per coil 10 5.38 E 06 792431 2 Dipole correction coil 310 ampere turns per coil 3 Maximum Quadrupole field 9.43T/m 2 Where normal components for 2n pole fields defined as 4 Maximum Sextupole field 17.41 T/m n 1 n 1 bn = (d By/dx )/(Bρ.(n 1)!) Table 6 : Multipole components of combined 2. Combined Quadrupole /Sextupole Magnet Quadrupole/Sextupole excitation at normalization radius After finalising the basic quadrupole magnet design = 40mm parameters and the shape of pole tip, additional auxiliary coils are mounted on the quadrupole faces to produce the Relative field required maximum sextupole field (G=17.41T/m 2). The n b l error (B /B ) n auxiliary coils are producing sextupole field gradient n 2 without modifying the quadrupole pole profile. This 1 5.43E 05 2.09099E 07 design is having flexibility to vary the sextupole field 2 1.00E+00 0.9632 gradient independently irrespective of quadrupole field gradient. These auxiliary coils are producing the required 4 3.61E 04 0.2174 sextupole field and also an additional dipole field 5 3.38E 03 50.92 (83gauss) as an error field. One more coil (Dipole correction coil) is mounted on each pole to annul this 6 1.04E 04 39.03 dipole field. The layout of the core and coils of combined Quadrupole/Sextupole magnet has been shown in Fig.1. 7 9.13E 03 85890 The field simulation has been done for the maximum 8 5.83E 05 13705 sextupole field gradient of 17.41 T/m 2 along with maximum quadrupole field gradient of 9.32 T/m. The 9 5.02E 03 29533843 2 maximum field gradient of 17.41 T/m is required 644 AT 10 5.36E 05 7883427 per pole. The design parameters for combined Quadrupole/Sextupole for maximum sextupole and quadrupole strengths are listed in Table 5. Field CONCLUSION The Booster quadrupole magnet has been designed by means of 2 D calculation. For two dimensional calculation (POISSON), the pole width and the yoke size are determined to be 50mm , for the bore radius of 50 mm. For the design of the pole shim, the tangential line of the hyperbola was adopted. As a result, the good field region within the field gradient error (∆G/G 0 )of 0.01% can be achieved in the region of ± 40mm. In case of full excitation of bothe quadrupole and sextupole fields, the multipole components n=5 and n=7 and n=9 are >0.1% of the main quadrupole field at the radius of r=4cm.
REFERENCES [1] S.P Mhaskar, R.K.Mishra and V.Tomar, “Compound Multipole Magnets for Indus 1”, Internal conference Synchrotron radiation sources, CAT,Indore, India, February 1992, , p. 210. [2] Singh, G., Sahoo, G. K., Angal Deepa, Singh, B., Ghodke, A. D. and Ramamurthi, S. S., CAT Report No. 88/CAT/EAP/30000/0001/D, 1988. [3] Poisson is a two dimensional code at the Los Alamos National Laboratory, LA UR 87 126(1987)