INDICO-FNAL (Indico) · Web viewBhabha Atomic Research Centre Trombay, Mumbai-400085 Project...

Government of IndiaBhabha Atomic Research Centre

Trombay, Mumbai-400085

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Project LB-HB650MHz Linac

System Quadrupoles Doublet and Dipole Correctors for 650 MHz section of Linac

Description Design Report

Document Number

LB-HB650MHz/ SANGAM Document No. DAE/

Pages 33Rev 0

Revision History

Rev No

Date of release

Author Reviewed By Approved By Modifications Implications

0 September 15, 2017

Vikas Teotia Vishnu Verma R S ShindeSanjay Malhotra

P. Singh Initial Release

None

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Table of Contents

SN Particulars Page

1. Introduction 5

2.

Electromagnetic Design

Section 1 : Quadrupole Magnet Standalone design

Section 2 : Dipole Corrector Standalone design

Section 3 : Quadrupole Doublet with Dipole Corrector

Para 1 : Only Upstream Quadrupole powered

Para 2 : Only Dipole Corrector powered (both coil pairs)

Para 3 : Only Dipole Corrector powered (Vertical coil)

Para 4 : All magnets powered

7

7

11

15

16

17

19

20

3.

Thermal Design

Section 1 : Quadrupole Magnet

Section 2 : Dipole Corrector Magnet

22

22

25

4. Conformance with TRS 27

5. Summary & Conclusion of LB650/HB650 Magnets design 30

6. References 31

7. Interface details 32

8.Annexure A : Magnetic Properties of Material of Construction of Magnetic Yokes of

Quadrupole and Dipole Magnet33

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Abbreviations

1 A Ampere

2 ACnD Accelerator Control Division

3 AMTD Accelerator Magnet Technology Division

4 AT Ampere Turn

5 ∫B.dl Integral of Magnetic field (B) along the longitudinal axis. The range depends from physical length of magnet.

6 BARC Bhabha Atomic Research Centre

7 DAE Department of Atomic Energy

8 DM De-mineralized

9 EM Electromagnetic

10 EMAS Electromagnetic Application Section

11 FNAL Fermi National Accelerator Laboratory

12 FRS Functional Requirement Specification

13 ʃG.dl Integral of Magnetic field gradient (G) along the longitudinal axis. The range depends from physical length of magnet.

14 GFR Good Field Region

15 HB High Beta

16 I Symbol used for current

17 LB Low Beta

18 MMF Magneto Motive Force

19 NA Not Applicable

20 PIP Proton Improvement Plan

21 R Radius

22 RRCAT Raja Rammana Centre for Advanced Technology

23 RSD Reactor Safety Division

24 SN Serial Number

25 TRS Technical Requirement Specification

26 V Volts

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Introduction

The optical design of PIP-II [1] envisages warm quadrupoles for focusing the 2 mA H - beam, in the

energy range of 160 - 800 MeV corresponding to the LB650 and HB650 sections of the

superconducting linac. The design requires dipole correctors for the beam orbit correction and

optics measurements. The parameters of both the magnets are identical in both LB650 and HB650

sections. This document describes the design of quadrupole and dipole corrector magnets.

1. Functional Requirement Specifications (FRS) and Technical Requirement Specifications (TRS)

FRS and TRS of these magnets were jointly drafted approved by BARC and FNAL. The magnetic

design of the magnets has been carried out to meet the optics requirements elucidated in the

Functional Requirement Specifications. The engineering design has been done to meet the technical

requirements detailed in the TRS. Approved TRS and FRS are placed in Fermilab Team centre as

document number ED0003403 and ED0003441 respectively.

2. Design

Based on FRS, Electromagnetic and Thermal design of these Magnets was carried out in

compliance with TRS. This design is carried out at BARC, DAE. The design covers the

electromagnetic design for meeting the beam optics requirements. The design of standalone

magnets (Quadrupole & Dipole Corrector) were carried out followed by integrated design of the

Quadrupole Doublet Assembly which consist of one focusing Quadrupole, one de-focusing

quadrupole and one combined function dipole corrector magnets. For reducing the β-function

Dipole corrector is placed between the two Quadrupoles. When placed as Doublet, these magnets

show degradation in the integral field uniformity which is still within the physics requirements. The

strength (Transfer function) and uniformity of these magnets remains stable in complete range of

input current. The Electromagnetic design fulfils all the requirements of FRS and TRS.

As required by TRS, the Quadrupole magnets are water cooled using hollow water carrying

electrical conductors while Dipole correctors are cooled by natural convection. For each

Quadrupole Magnet one input header and output header will enable hydraulic connection to

services in the Linac cavern. The thermal design is done by closed form expressions and is

conservative. The thermal design meets the specifications. This report paves way for prototype

production and qualification. The full scale prototype, as specified in TRS will consist of features

related to magnetic axis referencing using laser nests and magnet alignment with each other and

with cryomodule in the beam line.

The acceptance measurements on these magnets will be as specified in TRS. Acceptance criteria

include electrical, thermal, hydraulic and magnetic testing.

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3. Organization of the report

The report is organized as follows

Part I : Electromagnetic Design

Section 1 : Quadrupole Magnet Standalone design

Section 2 : Dipole Corrector Standalone design

Section 3 : Quadrupole Doublet with Dipole Corrector



Para 3 : Only Dipole Corrector powered (Vertical coils only)

Para 4 : All three magnets powered

Part II : Thermal Design

Section 1 : Quadrupole Magnet

Section 2 : Dipole Corrector Magnet

Part III : Conformance of design with FRS and TRS

Part IV : Summary & Conclusion of LB650/HB650 Magnets design

4. Definitions and assumptionsa) Evaluation of integral Uniformity

Quadrupole Magnet

%Uniformity=√∑3

8

an2+∑

3

8

bn2

100

Dipole Magnet

%Uniformity=√∑2

8

an2+∑

2

8

bn2

100

Where anand bn are coefficient of Fourier expansion of integral fields at reference radius of 13 mm which is 50% of GFR. Though TRS specifies 12 mm as the reference radius, evaluating at higher radius is conservative. These coefficients are normalized with respect to Quadrupole component (n=2) and Dipole component (n=1) for evaluation of uniformity of Quadrupole magnet and dipole magnet respectively such that these components are equal to 10,000 units. This definition of uniformity is consistent throughout the report.

b) Range of integration for evaluation of ʃG.dl and ∫B.dl.The integration along the longitudinal axis is carried out from -1500 mm to 1500 mm. Z=0 coincides with mid transverse plane of the dipole corrector magnet. The layout of quadrupole doublet is given in figure 36.

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c) When all magnets are powered, uniformity of ∫B.dl is evaluated as quadrupole field gets cancelled die to focusing and defocusing action of two quadrupole magnets.

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Part I: Electromagnetic Design

The 3-D Model of the Quadrupole Magnet is shown in the Figure 1. Pole contouring is optimized

for obtaining the required ʃG.dl (Integral magnetic field gradient) uniformity in the Good Field

Region (GFR). This section summarizes the EM design of the Quadrupole magnet singlet. TOSCA

module from OPERA is used for magnetostatic analysis.

Figure 1: 3D Model of the Quadrupole Magnet

Section 1: Quadrupole Magnet Standalone design

The required specifications of the Quadrupole Magnet are tabulated in Table 1.

Table 1: Technical Specifications of Quadrupole MagnetS.N. Parameters Value Unit

1. Integral magnetic field gradient (ʃG.dl) 3.0 Tesla

2. Magnetic field gradient 13.5 T/m

3. Aperture 52 mm

4. Good field region aperture 26 mm

5. Uniformity of ʃG.dz in GFR 0.1 %

6. Separation between Quad centre 600 mm

7. Physical length 200 mm

8. Maximum transverse dimensions 600 mm

9. Maximum longitudinal dimensions (including coils) 300 mm

10. Power supply preferences (Current) <15 A

11. Power supply preferences (Voltage) <30 V

Electrical design of Quadrupole Magnet is tabulated in Table 2.

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Table 2: Electrical design of the Quadrupole Magnet (per coil)S.N. Parameter per coil Value Unit

1. MMF 3600 AT2. Number of turns 240 -3. Cross section of conductor 3 X 3.5 mm X mm4. Area of current carrying section 10.5 mm2

5. Total length of copper conductor 192 m6. Nominal current 15 A7. Current density 1.43 A/mm2

8. Resistance 325 mΩ9. Voltage 4.9 V10. Power dissipation 75 Watts

Figure 2: Physical dimensions of Quadrupole Magnet

Magnetic parameters of the Quadrupole at varying currents are tabulated in Table 3.

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Table 3: Magnetic Design parameters of the Quadrupole Magnet

SN I (A) ∫G.dl (T)

Transfer Function (T/kA)

Uniformity of ∫G.dl (%)

Magnetic Field Gradient(T/m)

Average magnetic field of yoke (T)

Magnetic Field at Tip(T)

1. 38.33 1.0261 26.765 0.008 4.47 0.308 0.113

2. 76.66 2.0518 26.765 0.008 8.94 0.618 0.226

3. 115.00 3.0675 26.674 0.008 13.36 0.930 0.339

Current required for ∫G.dl = 3 T: 112.5 A (Nominal Current)

Figure 3: Magnetic Field (|B|) in Quad at I=115A at X=13mm (from Z= -1500 to +1500 mm)

Figure 4: BØ and Harmonics at I=38.33 A; R=13 mm (Quadrupole Magnet; standalone)

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Integrated Magnetic Field (T)

Figure 5: BØ and Harmonics at I=76.66.33 A ; R=13 mm (Quadrupole Magnet; standalone)

Figure 6: BØ and Harmonics at I=115 A; R=13 mm (Quadrupole Magnet; standalone)

Magnetic flux density distribution in the Yoke

Figure 7: Magnetic Field in the Yoke at I=115 A (Quadrupole Magnet; standalone)

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Integrated Magnetic Field (T.mm)


Section 2: Dipole Corrector Standalone design

The 3-D Model of the Dipole Corrector Magnet is shown in Figure 8. The magnet design is

optimized to obtain the required ʃB.dl and its uniformity in the Good Field Region (GFR). This

section summarizes the EM design of the Dipole Corrector magnet in standalone mode, i.e. when no

other magnet is in proximity.

Figure 8: 3D Model of Dipole Corrector Magnet

The required specifications of the Dipole Corrector Magnet are tabulated in Table 4.

Table 4: Technical Specifications of the Dipole Corrector MagnetS.N. Parameter Value Unit1. Integral magnetic field 10 mT.m2. Pole tip to pole tip gap (Minimum) 52 mm3. Good field region aperture 26 mm4. Uniformity in GFR 1 %5. Desired yoke thickness 100 mm6. Maximum transverse dimensions 600 mm7. Maximum longitudinal dimensions (including coils) 180 mm8. Power supply preference (Current) <15 A9. Power supply preference (Voltage) <30 V

Electrical design of Dipole Corrector Magnet is tabulated in Table 5.

Table 5: Electrical and magnetic Design of Dipole Corrector MagnetS.N. Parameter per coil Value Unit1. MMF 7020 AT2. Number of turns 702 -3. Wire Cross section Rectangular4. Cross section dimension 4 X 2 mm x mm5. Area of current carrying section 8 mm2

6. Total length of copper conductor 312 m7. Nominal current 9.25 A8. Resistance 650 m Ohms9. Voltage 6 V10. Power 55 Watts

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Figure 9: Physical Dimensions of Dipole Corrector

The magnetic field of the Dipole Corrector magnet at different currents is tabulated in Table 6.

Figure 10: Magnetic Field in the aperture plotted along axis at 10A with both coils powered

Table 6: Magnetic design parameters of Dipole Corrector MagnetSN I (A) ∫B.dl

(mT.m)Transfer Function (T.m/kA)

Uniformity of ∫B.dl

(%)

B-Field at Magnet centre(Tesla)

Average Magnetic Field in Yoke (Tesla)

1. 2 3.3023 1.6512 0.3944 0.0097 0.214

2. 4 6.6060 1.6515 0.3862 0.0194 0.428

3. 6 9.9036 1.6506 0.3867 0.0291 0.644

4. 8 13.173 1.6466 0.3887 0.0387 0.861

5. 10 16.357 1.6357 0.4027 0.0481 1.074

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Figure 11: BØ and Harmonics at I=2 A; R=13 mm (Dipole Corrector Magnet; standalone)



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Magnetic flux density distribution in the Yoke

Figure 14: Magnetic flux density distribution in the Yoke of Dipole Corrector

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Section 3: Quadrupole Doublet with Dipole Corrector

Each Quadrupole Doublet consists of two Quadrupole magnets and one dipole corrector magnet as

shown in Figure 15. Behaviour of each of these magnets when placed in proximity of other magnets

is different from standalone configuration. This occurs because the ferrous material of the nearby

magnet modifies the spatial magnetic reluctance. Since the magnets are used in vicinity of magnets

as describes above, it is important to analyse the magnetic parameters of theses magnets when

placed as doublet. Main influence of the proximity of magnets is on strength and integral magnetic

field uniformity.

This section describes combined magnetic parameters of the Quadrupole Doublet along with Dipole

Corrector.

The relative position of three magnets of the LB650/HB650 magnets is as per TRS and is shown in

figure. The analysis for this set-up is done as four cases are given below.



Para 3 : Only Dipole Corrector powered (Vertical coils only)

Para 4 : All three magnets powered

Figure 15: 3D model of Quadrupole Doublet with Dipole Corrector Magnet

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Upstream Quadrupole

Dipole Corrector Downstream

QuadrupoleMagnet

Para 1: Only Upstream Quadrupole Magnet PoweredTable 7: Magnetic parameters of Upstream Quadrupole in vicinity of Dipole Corrector and downstream Quadrupole Magnet

SN I (A)∫G.dl (T)

Transfer Function(T/kA)

Uniformity of ∫G.dl (T) (%)

B-field Gradient(T/m)

Average B-field of yoke

B-Field at Tip

1. 37.2 0.9967 26.793 0.039 4.3364 0.302 0.10972. 74.4 1.9931 26.789 0.039 8.6711 0.606 0.21933. 111.6 2.9806 26.708 0.039 12.968 0.912 0.32804. 124.0 3.3039 26.644 0.039 14.375 1.013 0.3625Upstream Quadrupole Magnet and Dipole Corrector switched ON1. 111.6 2.9798 26.700 0.181 12.921 0.913 0.3266

Figure 16: BØ and Harmonics at I=37.2 A ; R=13 mm (Quadrupole Magnet; in Doublet)

Figure 17: BØ and Harmonics at I=74.4 A; R=13 mm (Quadrupole Magnet; in Doublet)

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Figure 18: BØ and Harmonics at I=111.6 A; R=13 mm (Quadrupole Magnet; in Doublet)

Figure 19: BØ and Harmonics at I=124 A; R=13 mm (Quadrupole Magnet; in Doublet)

Para 2: Only Dipole Powered (Both Coils)Table 8: Magnetic Parameters when Dipole Corrector (both coils) powered on vicinity of other magnetsSN I (A) ∫B.dl

(mT.m)Transfer Function (T.m/kA)

Uniformity of ∫B.dl (%)

B-Field at (0,0,0)(Tesla)

Average B-field in Yoke (Tesla)

1. 3 3.4585 1.1528 0.7615 0.01436 0.3462. 6 6.9096 1.1516 0.7630 0.02868 0.6943. 9 10.279 1.1421 0.7733 0.04266 1.039

Figure 20: Dipole Corrector powered when placed in Doublet

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Figure 21: BØ and Harmonics at I=3 A ; R=13 mm (Dipole Corrector Magnet (Both Coils); in Doublet)

Figure 22: BØ and Harmonics at I=6 A; R=13 mm (Dipole Corrector Magnet (Both Coils); in Doublet)

Figure 23: BØ and Harmonics at I = 9 A; R=13 mm (Dipole Corrector Magnet (Both Coils); in Doublet)

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Para 3: Only Dipole Powered (Single Coils)Table 9: Magnetic Parameters when Dipole Corrector (vertical coils) powered on vicinity of other magnetsSN I (A) ∫B.dl

(mT.m)

Transfer

Function

(T/kA)

Uniformity

of ∫B.dl (%)

Magnetic

Field at

(0,0,0)(Tesla)

Average Magnetic

Field in Yoke

(Tesla)

1. 3.0 2.4460 0.8153 0.5373 0.01015 0.231

2. 6.0 4.8909 0.8152 0.5373 0.02030 0.463

3. 9.0 7.3163 0.8129 0.5375 0.03037 0.696

4. 12.5 10.018 0.8014 0.5342 0.04139 0.914

Figure 24: BØ and Harmonics at I=3 A; R=13 mm (Dipole Corrector Magnet (Only Vertical Coils; in Doublet)


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Para 4: All magnets powered

Table 10: Magnetic Parameters when all Magnets are powered ON

SNCurrent (A)

∫B.dl (mT.m)Uniformity of ∫B.dl (%)

Quadrupole Magnet

Dipole Corrector

Including harmonics from n=2 to n=6

Including harmonics from n=3 to n=6

1. 37.2 3 3.4679 1.1174 0.8627

2. 74.4 6 6.9377 1.1403 0.8919

3. 111.6 9 10.463 1.3779 1.1799

4. 124.0 10 11.635 1.5504 1.3760

Figure 27: BØ and Harmonics at R=13 mm (As Doublet; All magnets powered ON; I_Quad=37.2; I_DC=3; Dipole Corrector: both Coils powered)

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Figure 30: BØ and Harmonics at R=13 mm (As Doublet; All magnets powered ON; I_Quad=124; I_DC=10; Dipole Corrector: both Coils powered)

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Part II: Thermal Design

Section I: Thermal design of Quadrupole Magnets

Electromagnetic Coils of Quadrupoles are cooled by passive Hydraulic circuit. Solid current

carrying conductors are used as current carrying element and are called active coils. This solid

conductor is jacketed by hollow water carrying conductor. The heat generated in the solid

conductor is conducted to water carrying conductor and removed by forced convective heat transfer

using Demineralized water. As per the civil design of the accelerator cavern, these quadrupoles

shall not dissipate heat to the ambient. More than 95% heat shall be removed from the Magnets by

circulating water.

Figure 31 shows the cross section of the Quadrupole magnets along with EM Coil. Figure 32 shows

details of EM coils.

Figure 31: Arrangement of EM Coil in Quadrupole Yoke

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Figure 32: EM Coil

In Hydraulic circuit four Passive coils of a given Quadrupole magnet will be connected in parallel

to a common inlet and outlet header. The header will be made out of 12.7 mm diameter SS tubing.

Each magnet will have one inlet hydraulic connection and one outlet hydraulic connection. The

maximum permissible pressure available across inlet and outlet header is 3.45 bars.

Table 11: Key parameters of the thermal design (Ambient temperature = 28°C)SN Parameter Value Unit1. Current Carrying Conductor (per Coil) Active Coil1.a Cross section of conductor 3.5 X 3 mm X mm1.b Layers 8 -1.c Turns per layer 30 -1.d Total number of turns 240 -1.e Resistance at 25° C 0.325 Ω1.f Nominal current 15 A1.g Voltage at 25° C 4.9 V1.h Weight 18 Kg1.i MMF 3600 AT1.j Current density 1.42 A/mm21.k Power (assuming negligible temperature rise in coils) ~75 Watts2. Water Carrying Conductor (Passive Coil)2.a Cross section Square mm2.b Width 8 mm

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2.c Outer chamfer radius 1 mm2.d Inner diameter 5 mm2.f Weight of Copper per meter 0.38 Kg2.g Area of copper 41 mm sq2.h Weight of Passive Coil 11.5 Kg4. Pressure drop 4.a Water velocity (as designed) 1.5 m/sec

4.bTotal pressure drop in coil including bends and inlet/outlet headers

3.3 bar

5. Cooling fluid details

5.a FluidDM water

-

5.b Bulk temperature of water (input) 28 °C5.c Velocity 1.5 m/s5.g Mass flow rate 1.8 LPM6. Key thermal parameters6.a Rise in water temperature <1 °C6.b Bulk temperature of Copper <29 °C

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Section 2: Thermal design of Dipole Correctors

Electromagnetic Coils of the dipole correctors are cooled by natural air convection. To

accommodate more number of turns per coil and also to minimize the air gap, electromagnetic coils

are designed as graded coils. The 3D view of EM coil of Dipole Corrector is as shown in Figure 33.

Figure 34 shows overall arrangement of yokes and EM coils in dipole corrector. Dimension of the

graded coils are shown in Figure 35.

Figure 33: EM Coils in Dipole Corrector

Figure 34: Dimensions of Dipole Corrector

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Figure 35: Details of EM Coils2.2 Key parameters of the thermal design are tabulated in Table 12. 1 set of coil winding (per leg)

Table 12: Key design parameters of the thermal design (1 set of coil winding per leg)SN Parameters Value Unit

1.Power dissipation per coil 55 Watts

2.Current density 1.5 A/mm2

3.Initial Resistance 0.6 Ω

4.Ambient Temperature 25 °C

5.Equivalent Convective Heat transfer coefficient 5.6 W/m2/° C

6.Total surface area for each coil 0.177 m2

7.Emissivity (for enamel) 0.9 -

8.Steven Boltzmann Constant 5.67e-8 W/m2.K4

9.Temperature rise at steady state 27 °C

10.Temperature coefficient of copper 0.004 %/˚C

11.Resistance at steady state 0.68 Ω

12.Power dissipation at steady state 55 W

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13.Average temperature of the coils 52 °C

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Part III: Conformance of design with Technical Requirement Specifications

1. Physical dimensions and placement of magnets in Doublet configuration

Two Quadrupole magnets and one combined function dipole corrector magnet are arranged as

specified in TRS. Same from Figure 3 of TRS is reproduced below with modifications necessitated

in the design phase.

Figure 36: Layout of Magnets in Doublet ConfigurationThe suggested longitudinal dimension of Dipole Corrector is changed from 180 mm to 200 mm in

actual design. The spacing between Quadrupole magnet and Dipole Magnet is therefore reduced

from 35 mm to 25 mm. The overall relative placement of magnets is in conformance with the TRS.

2. Electromagnetic Design

a. Quadrupole Magnet

Table 13: Conformance of EM design of Quadrupole magnet with TRS

S.N. ParameterDesired as per TRS

Obtained in Design

Unit Conformance with TRS

1. Integral Magnetic field gradient 3.0 3.0 Tesla Complied

2. Magnetic field gradient 13.5 13.06 T/m Complied

3. Pole tip to pole tip gap 52 52 mm Complied

4. Good Field region aperture 26 26 mm Complied

5. Uniformity of ʃG.dz in GFR ≤ 0.1 0.008 % Complied

6. Separation between Quad centre 600 600 mm Complied

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7. Advised physical length 200 200 mm Complied

8. Maximum transverse dimension 600 520 mm Complied

9. Maximum longitudinal dimension (including coils)

300 300 mm Complied

10. Power supply preferences (Current)

<15 15 AComplied

11. Power supply preferences (Voltage)

<30 20 V

b. Dipole Corrector Magnet

Table 14: Conformance of EM design of Dipole Corrector magnet with TRSS.N. Parameter Value as

required in TRS

Obtained in Design

Unit Conformance

1. Integral Magnetic field 10 10 mT.m Complied

2. Pole tip to pole tip gap

(Minimum)

52 52 mm Complied

3. Good Field region aperture 26 26 mm Complied

4. Uniformity in GFR 1 0.4 % Complied

5. Advised physical length 100 100 mm Complied

6. Maximum transverse dimensions 600 mm Complied

7. Maximum longitudinal

dimensions (including coils)

180 200 mm Slight deviation

8. Power supply preferences

(Current)

<15 9.25 A Complied

9. Power supply preferences

(Voltage)

<30 24 V Complied

3. Thermal Designa. Quadrupole Magnet

Table 15: Conformance of Thermal design of Quadrupole magnet with TRSSN Parameter Maximum

Allowed

Achieved in

Design

Unit Conformance

1. Cooling type - Passive Water cooling

- Complied

2. Heat Dissipation Not mentioned 75 W Acceptable

3. Pressure drop 3.45 3.3 bar Complied

4. Permissible heat loss to

ambient

3.75 <1 W Achieved

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5. Water velocity 2 1.5 m/s Complied

6. Water temperature rise 5 <1 °C Complied

b. Dipole Corrector Magnet

Table 16: Conformance of Thermal design of Dipole Corrector magnet with TRSSN Parameter Maximum

AllowedAchieved in Design

Unit Conformance

1. Cooling type Natural air Convection

Natural air Convection

- Complied

2. Heat Dissipation Not mentioned 55 W Acceptable3. Coil temperature rise

when mechanical barrier are not used

25 NA °C Complied(Decision of using mechanical barrier will be based on measured temperature of the magnets)

4. Coil temperature rise when mechanical barrier are used

>25 28 °C

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Part IV: Summary & Conclusion of LB650/HB650 Magnets design

Section 1: Summary and Conclusion of the Electromagnetic Design

1. The required integral field strength (3 Tesla) for Quadrupoles is achieved at 3600 Ampere

Turns per coil with uniformity of 0.008%. When placed in Doublet configuration (without

powering Dipole Magnet), the strength remains practically unchanged, however the

uniformity reduces to 0.039%. The field uniformity is within specifications.

2. The Dipole Corrector in standalone configuration has integral strength uniformity of 0.4%

when both coils are powered. When placed in Doublet with two Quadrupole Magnets, this

reduces to 0.77%. In Doublet configuration, when one vertical coil pair was powered ON,

integral uniformity is 0.54%. The integral field uniformity is within specifications.

3. The integral strength of Dipole Corrector in standalone configuration with both coils

switched ON is 1.6357 T/kA. This gets reduced to 1.1421 T/kA when Dipole corrector is

placed in Doublet. For single coil powered ON and placed in doublet, the transfer function is

0.8060 T/kA. The current is increased accordingly to achieve the required integral strength.

Section 2: Summary & Conclusion of the Thermal Design

1. Quadrupole Magnet: The thermal design meets the engineering and design requirements

specified in the TRS. Table 16 summarizes the desired requirements and the design values.

During fabrication of the EM coils following additional requirements will be taken into

consideration.

a) The cooling circuit will be designed for a maximum allowable working pressure

(MAWP) of 100 psi

b) The circuit will be hydrostatically tested to 1.5 x MAWP for 30 minutes.

2. Dipole Correctors: The temperature rise in the Dipole Correctors at full power is 27 °C.

Based on past experience, temperature rise measured on built magnets is lower than the

design estimate. TRS suggests putting mechanical barriers when surface temperature

exceeds 50 °C. A decision on using thermal barrier will depend on measured temperature on

built prototypes.

Section 3: Summary & Conclusion to the overall design

1. The design meets the optical, magnetic and engineering requirements stated in the technical

requirement specifications (TRS).

2. Based on the above design, fabrication of engineering prototypes of the quadrupole magnet and

the dipole corrector can be initiated.

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References

1. PIP-II Functional Requirements Specification: Document #: ED0001222

2. PIP-II Quadrupoles and Dipole Correctors Functional Requirement Specification

Document #: ED0003403

3. PIP-II Warm Magnets: Technical Requirement Specification: Document #: ED0003441

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Interface details

The section aims at bringing out the interface of the Quadrupole Doublet Magnets with PIP-II

Linac. Exact details of these interfaces will be worked subsequently.

1. Power Supply: The EM coils of the Magnets will be terminated on terminal blocks of 20 A

rating. Connection from terminal blocks to the power supply is in FNAL scope.

2. Hydraulic connection: Each Quadrupole will have one inlet connection and one outlet

connection. The details of adapters shall be provided by FNAL.

3. Mounting of BPM: Like P2IT MEBT Quadrupoles, the BPM which is part of vacuum

chamber will be mounted on the poles of Quadrupole magnets. FNAL shall provide details

of the mounting arrangements.

4. Assembly of the base frame to the Linac: The details of mounting holes of the base frame

(all three magnets will be mounted on this frame) will be provided by BARC to FNAL. This

information will be used by FNAL for mounting the base frame (along with the magnets) to

the Beam Line.

1.

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Annexure AMagnetic Properties of Material of Fabrication of Magnetic Yokes of Quadrupole and Dipole

Magnets

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5000

10000

15000

20000

25000

B-H Curve of Soft Magnetic Matreial Used

Magnetic Field Intensity (Oe)

Mag

netic

Fie

ld In

duct

ion

(Gau

ss)

SN H (Oe) B(Gauss)1 0 02 2.09 57573 2.5 68004 3.02 79185 3.63 89496 4.365 99217 5.248 108218 6.31 116409 7.586 12373

10 9.12 1302111 10.96 1358612 13.18 1407413 15.85 1449414 22.91 1517115 27.54 1545116 39.8 1595517 57.54 1645518 83.18 1701919 120.23 1767920 144.5 1804521 173.8 1843222 208.9 1883123 251.2 1923624 301.99 1963625 363.08 20022

****End of document****

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