Accelerators 2.6 Magnet System 2.6.1 Introduction According to the BEPCII double ring design scheme, a new storage ring will be added in the existing BEPC tunnel. The tasks of the magnet system can be divided into two parts: (a) design and fabrication of new magnets and (b) modification and replacement of coils of some old magnets. A design of the new magnets is described in the following. 2.6.2 Main Requirements 2.6.2.1 Bending Magnet Table 2.6-1 Bending magnet Magnet type 70B142 70B105 Number of magnets 42+2 * (reference + spare) 2 Beam energy E (GeV) 2.0 Bending angle (rad) 0.154685 0.114537 Effective length (mm) 1421.7 1052.7 Gap (mm) 70 Central field B 0 (Gs) 7251.4 Good filed region (H V) (mm mm) 100 46 Good field uniformity BL/BL 5 10-4 Adjustment capability of the trim coil ±1% 2.6.2.2 Quadrupole Magnet Table 2.6-2 Quadrupole magnet Number of magnets 52+1 (spare) Effective length (mm) 400 Inscribed radius (mm) 55 Magnetic field gradient (Gs/cm) 1118 Good field radius (mm) r 50 BL/B 2 L 5 10-4 Good field quality b 3 3 10-4 b 4 1 10-4 b 5 1 10-4 119
Magnet System 2.6.2.3 Sextupole Magnet with Vertical Correction Dipole Coils Table 2.6-3 Sextupole magnet with vertical correction dipole coils Number of magnets 72+1 (Spare) Effective length (mm) 200 Inscribed radius (mm) 70 Sextupole field strength B (Gs/cm 2 ) 150 Good filed radius (mm) r 50 BL/B 3 L 5 10-3 Good filed quality b 4 1 10-3 b 5 4 10-3 Vertical correction dipole field B (Gs) 350 2.6.3 Conventional Magnet Design Based on the technical requirements and the existing boundary condition, there are some basic regulations in the magnet design. (1) The optimized energy for BEPCII is 1.89 GeV, but the magnets still can work normally under 2.0 GeV. (2) Due to the space limitation of the existing BEPC tunnel, the outline dimension of the inner ring magnets should be as compact as possible. (3) According to the design requirements, the main parameters of the new magnets should be the same as the old ones except the new bending magnet. (4) Because an antechamber type is adopted for the vacuum chamber in the positron ring, all the new magnets should be designed with an enough room given for the antechamber at the horizontal plane. (5) The pressure drop of the cooling water on all designed magnets must be kept under 6kg/cm 2, as in the BEPC machine. 2.6.3.1 Bending Magnet (1) Design of the pole contour and core structure The H-type design configuration has been selected for the new bending magnet. The core consists of an upper and a lower half fastened with bolts and positioned with dowel pins. In order to simplify the magnet construction and magnetic measurement, the magnet core is designed as a straight one. The pole width is determined by the width of the good field region with required field quality and sagitta of the curved beam orbit. 120
Accelerators Considering a gap height of 70 mm, sagitta of 27.5 mm and a good field region of 100mm,we choose a pole root of 290 mm and the pole width of 270 mm. Two 0.8mm thick shims are taken at two pole corners in order to optimize the field. There are two tilted angles 10mm 15mm at the two corners of the pole face to weaken the local magnetic saturation. The magnet core is of a laminated structure made of ultra-low carbon, low silicon steel sheets, which will be rolled by Wuhan Iron & Steel Company (DW540G-50, C 0.002%, thickness 0.5 mm, with semi-organic or inorganic insulation coating). The lamination is fabricated with a tolerance of 25 µm. There are two solid end-plates on each side of the laminated core. The end plates are made of low carbon steel plate. After precise stacking, they will be compressed axially and welded with side plates outside. The side plates are made of 30 mm thick structural steel plates. The tolerance of the core stacking should be better than 50 µm. The structure of the magnet is shown in Figure 2.6-2 and Figure 2.6-3. Figure 2.6-2 The lamination core of H-type dipole Figure 2.6-3 The three-dimensional picture of the dipole magnet 121
Magnet System (2) Excitation Ampere-turns and coil construction The bending magnet requires 40595.33 excitation Ampere-turns at 2.0 GeV and 7251.4 Gs field strength. The excitation coils having N=48 turns (total) and I=845.74 A, j=3.8a/mm 2, are water-cooled. Two flat pancakes on each pole are made of 20.4 13.4 mm 2 rectangular copper conductor with an 8.0 mm diameter cooling channel. Each pancake is composed of 2-layers, 12 turns in total and is wound without any joint. Each individual conductor is insulated with half-lapped Dacron tape (0.13 mm thick and 20 mm wide). Each coil pancake is ground insulated with a half-lapped fiber glass tape (0.25 mm thick and 20 mm wide) and then epoxy impregnated. The coils will be hipotted at a voltage 100% higher than the string voltage plus 1kV. Each coil will be water leak checked at 12 kg/cm 2 and must pass a water flow test. (3) Trim coils The trim coils are wound with a 2.0 3.55 mm 2 solid copper conductor. The field can be trimmed by±1% of the operating excitation, with N=72 turns (total), I 5.64 A and j 0.84 A/mm 2. (4) The magnetic field computer simulation The magnetic field simulation is computed with both OPERA 2D and POISSON programs. Calculations of the field distribution and transfer function (Figure 2.6-4 and Figure 2.6-5) shows that the current design satisfied the field quality requirements. The non-uniformity of the integrated field distribution caused by the end effect will be improved by pole chamfering. Figure 2.6-4 Lamination contour and flux lines of storage ring bending magnet 122
Accelerators (5) Bending magnet parameters Table 2.6-4 Design parameters of the storage ring bending magnet Magnet type 70B142 70B105 Beam energy (GeV) 2.0 Effective length (mm) 1421.7 1052.7 Gap height (mm) 70 Central field B (Gs) 7251.4 Excitation ampere-turns (A-turn) 40595.33 Ampere factor 1.005 Magnetic efficiency 0.995 Number of turns (2 poles) 48 Current (A) 845.74 Conductor size (mm 2 ) 20.4 13.4, 8.0, R1 Current density (A/mm 2 ) 3.80 Average turn length (m) 4.0 3.2 Resistance per magnet (Ω) 0.0164 0.013 Voltage drop per magnet (V) 13.87 11.0 Power loss per magnet (kw) 11.73 9.30 Stored energy per magnet (kj) 7.15 5.36 Inductance per magnet (H) 0.02 0.015 Core size (L W H) (mm) 1344.7 700 600 975.7 700 600 Core weight (kg) ~4200 ~2900 Copper weight (kg) 357.12 285.7 Number of water parallel circuits 2 Water pressure drop (kg/cm 2 ) 6.0 Water speed (m/s) 1.87 2.1 Water flow (kg/hr) 680 770 Temperature rise of coil ( C) 14.9 10.5 Trim coil parameters Number of turns (2 poles) 72 Current (A) 5.64 Conductor size (mm 2 ) 2.0 3.55 R 0.65 Current density (A/mm 2 ) 0.84 Resistance per magnet (Ω) 0.54 0.43 Voltage drop per magnet (V) 3.05 2.43 Power loss per magnet (kw) 0.017 0.014 Copper weight (kg) 2.0 1.65 123
Magnet System Transfer Function B/I(Gs/A) 8.6 8.55 8.5 0 200 400 600 800 1000 I(A) Figure 2.6-5 B/B curve and the transfer function of the bending magnet 2.6.3.2 Quadrupole Magnet New quadrupole magnets will be installed in the positron ring, where the vacuum chamber is an antechamber type. Therefore all the new quadrupole magnets should be built to accommodate the shape and dimensions of the antechamber. (1) Design of the pole contour and core structure The magnet core consists of a symmetrical upper and lower part (Figures 2.6-6 and 2.6-7). The basic part of the poleface has a hyperbolic curve. At the two corners, there are shims to improve the 2-D field quality. The pole body is designed as a wedged form to avoid over-saturation in the pole body and at the root. The material used for the quadrupole magnet core is the same as that for the dipole magnet. The principle of the 2-D magnetic field design is to reduce high order multipole components as small as possible. The end effect will be reduced by the end chamfering. (2) Excitation ampere-turns and coil construction The quadrupole magnet requires 13585.5 excitation ampere-turns at 1118 Gs/cm magnetic field gradient. On each pole of the quadrupole magnet, there are two coils. Both the inner coil and the outer coil have 45 turns each. The conductor used is 6.5 6.5, 4 mm copper tube. No joint is allowed inside a coil. (3) The magnetic field computer simulation The magnetic field simulation is computed with both the OPERA 2D and POISSON computer codes. The G/G curve and the transfer function of the quadrupole magnet (Figure 2.6-8 and Figure 2.6-9) show that the design satisfied the field quality require- 124
Accelerators ments. At the magnetic field gradient G=1118 Gs/cm, we have I=150.95 A, j=5.12 A/mm 2. Figure 2.6-6 The lamination of the quadrupole Figure 2.6-7 The three-dimensional picture of the quadrupole magnet Figure 2.6-8 Lamination contour and flux lines of the storage ring quadrupole 125
Magnet System G/I(Gs/cm/A) 7.5 7.4 7.3 7.2 7.1 Transfer Function 0 100 200 I(A) Figure 2.6-9 G/G curve and the transfer function of the quadrupole magnet (4) Main parameters of the quadrupole magnet Table 2.6-5 Design parameters of storage ring quadrupole Effective length (mm) 400 Inscribed radius (mm) 55 Magnetic field gradient (Gs/cm) 1118 Excitation ampere-turns per pole (A-turn) 13550.5 Ampere factor 1.007 Magnetic efficiency 0.993 Number of turns (per pole) 90 Current (A) 150.56 Conductor size (mm 2 ) 6.5 6.5, 4.0, R 0.5 Current density (A/mm 2 ) 5.11 Average turn length (m) 1.4 Resistance per magnet (Ω) 0.324 Voltage drop per magnet (V) 48.78 Power loss per magnet (kw) 7.345 Stored energy per magnet (kj) 1.02 Inductance per magnet (H) 0.09 Core size (L W H) (mm) 356 800 900 Core weight (kg) ~1683 Copper weight (kg) 131.04 Number of water parallel circuits 8 Water pressure drop (kg/cm 2 ) 6.0 Water speed (m/s) 1.45 Water flow (kg/hr) 530 Temperature rise of coil ( C) 12.2 126
Accelerators 2.6.3.3 Sextupole Magnet (1) Design of the pole contour and core structure The magnet core consists of three identical parts. The two matching surfaces are positioned with dowel pins and fastened with bolts and nuts (Figure 2.6-10 and Figure 2.6-11). The basic part of the pole face is a cubic equation curve. In determining the pole width, it should be considered first to have a good field quality within a good field region; second to leave enough room between two neighboring pole edges for coil mounting, and third to accommodate the profile of the vacuum chamber (antechamber type). The steel sheet used in the sextupole magnet core is the same as that for the dipole and quadrupole magnet. Figure 2.6-10 Three-dimensional picture of the sextupole and vertical correction coil Figure 2.6-11 1/3 Lamination of core of the sextupole 127
Magnet System (2) Excitation Ampere-turns and coil construction The sextupole magnet requires 6779.73 excitation Ampere-turns at 150 Gs/ cm 2 sextupole field strength. On each pole of the magnet, there is a sextupole field coil wound with 6.5 6.5, 4 mm copper conductor. No joint is allowed inside a coil. (3) Magnetic field computer simulation The magnetic field simulation is computed with both the OPERA 2D and POISSON codes. B y =f(x) curve and transfer function of the sextupole magnet are shown in Figure 2.6-12 and Figure 2.6-13. At sextupole field B =150.368 Gs/ cm 2, we need I=141.24 A and j=4.79 A/mm 2. Fig.2.6-12 The lamination contour and flux lines of the sextupole Transfer Function B"/I(Gs/cm2/A) 1.075 1.07 1.065 1.06 0 100 200 I(A) Fig.2.6-13 B y =f(x) curve and the transfer function of the sextupole magnet 128
Accelerators (4) Vertical correction coil design Magnetic field simulation is computed with both OPERA 2D and POISSON program. At dipole field B=360 Gs, it is needed NI=1984.5 A-turn. Four coils are installed on the four horizontal poles (Figure 2.6-14). B/B curve of the vertical correction field is shown in Figure 2.6-15. Each coil has 55 turns with I=36 A and j=1.30 A/mm 2. A 4.0 7.1 mm 2 solid copper conductor is used. Figure 2.6-14 The distribution of the flux lines of the vertical correction dipole field Figure 2.6-15 B x distribution curve of the vertical correction dipole field (5) Main parameters of the sextupole magnet 129
Magnet System Table 2.6-6 Design parameters of the storage ring sextupole Effective length (mm) 200 Inscribed radius (mm) 70 Sextupole field strength B (Gs/cm 2 ) 150 Excitation ampere-turns per pole (A-turn) 6779.73 Ampere factor ~1.0 Magnetic efficiency ~1.0 Number of turns (per pole) 48 Current (A) 141.24 Conductor size (mm) 6.5 6.5, φ4.0, R0.5 Current density (A/mm 2 ) 4.79 Average turn length (m) 0.55 Resistance per magnet (Ω) 0.102 Voltage drop per magnet (V) 14.4 Power loss per magnet (kw) 2.035 Stored energy per magnet (kj) 0.639 Inductance per magnet (H) 0.064 Core size (L W H) (mm) 176 800 800 Core weight (kg) ~600 Copper weight (kg) 41.2 Number of water parallel circuits 3 Water pressure drop (kg/cm 2 ) 6.0 Water speed (m/s) 1.60 Water flow (kg/hr) 220 Temperature rise of coil ( C) 8.1 Design parameters of vertical correction coil Horizontal dipole field strength B (Gs) 360 Excitation ampere-turns per pole (A-turn) 1984.5 Number of turns per pole 55 Current (A) 36.0 Conductor size (mm) 4.0 7.1, R0.65 Current density (A/mm 2 ) 1.30 Average length per turn (m) 0.60 Resistance per magnet (Ω) 0.082 Voltage drop per magnet (V) 2.95 Power loss per magnet (kw) 0.106 Stored energy per magnet (kj) 0.0162 Inductance per magnet (H) 0.025 Copper weight (kg) 3.4 130