3-Axis Vector Magnet: Construction and Characterisation of Split Coils at RT. Semester Project Petar Jurcevic

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1 3-Axis Vecto Magnet: Constuction and Chaacteisation of Split Coils at RT Semeste Poject Peta Jucevic

2 Outline Field Calculation and Simulation Constuction Details Field Calculations Chaacteization at RT Summay

3 A shot epetition Maxwell s equations (SI units Right-hand ule 3

conducto at position : Point whee the field is computed ' ' 3

4 Magnetic field of a cicula loop Biot-Savat Law db( μ π 4 Idl( ' μ : Pemeability I: Cuent in Ampee dl( : infinitesimal length of the conducto at position : Point whee the field is computed ' ' 3 Paametization of the loop x ' y z B( P I μ Q Q N cos( φ φ Q 3 ( + Q P N: Numbe of windings 4

5 5 Cuved cicula loop: Paametization I θ cos( cos( θ θ z x y cos( cos sin z x y θ y x z y φ z y x y

6 6 Cuved cicula loop: Paametization II cos( cos sin ( m m

7 Cuved cicula loop: Paametization III Thee ae a lot of othe possible paametizations like: ρ ( ρ cos( n a cos ( with n,, ρ: adius of the loop in x-y plane a: diffeence between the highest and the lowest point of the loop Advantage Calculations can be simplified The tem cos n a ( can be substituted fo any symmetic and peiodic function Disadvantage The field is not calculated in the cente of the IVC, but in the cente of the cuved loop -> need of a additional paamete 7

8 8 Field Calculations cos( cos sin ( How to poceed: (φ has to be nomalized To get the infinitesimal length dl of the conducto take the deivative of (φ: dl(φ d(φ/dφ Calculate only the x-component of the coss-poduct Remembe: Bio-Savat Law 3 ' ' ' ( 4 ( Idl db π μ ( cos + ( 3 ( cos sin cos ( cos 4 π μ I db x + +

9 9 Field Simulation I Integation of db x not easy Numeical appoach Real coils have a cetain thickness Sepaation of the cuvatue fom distance in x-diection Intoduction of a new paamete ξ which descibes the distance in x-diection 3 ( cos sin cos sin cos ( cos ξ π μ I db x

10 Field Simulation I x y ( -3 m 5 y ( -3 m 5 5 B (T / A y ( -3 m 5.. length ( m x ( -3 m x ( -3 m x ( -3 m Gid 5mm x 5mm windings B-field at Ampee:.3 T; B-field at 5 Ampee:,6 T Estimated wie length: 5.5 m

11 The Coil

12 Winding

13 3

14 Foce Calculations I Loentz Foce F I dl B Right Hand Rule x z y B y z x I Integation ove the π no net foce Integation ove the semi cicle (-π/, π/ F x NIB 33.6 kn 34* 3 chocolate bas B 9T; I 5A;.7m; N 4

15 Foce Calculations II Fo the cuved cicula loop: F x NIB sin 3.4 kn I 5A; B 9T; N ;.7m.m The foce ove the whole cicle is zeo, but points in opposit diection ove the two semi cicles Emegence of a toque We just conside the flat case v M μ B μ AI A πn M y 44Nm 7 Nm 5

16 Measuement setup 6

17 Measuements I Spools & Spools 3 & 4.53 ma (&.38 ma (3&4 Compaison with simulation (B z (3 mt: Accuacy 3.4% - 8.9% 7

18 Measuements II x y z B z ma 8

19 Measuements III B z ma B z ma 9

20 Measuements IV Coil Coil Coil 3 Coil 4 Numbe of windings ma.9mt.6mt.6mt.5mt Resistance R DC 69.4Ω 63.4Ω 6.Ω 63.6Ω Resistance Hz 84.Ω 74.Ω 75.5Ω 76.9Ω Resistance khz 338.7Ω 3.8Ω 35.4Ω 38.6Ω Inductance Hz 7.8mH.9mH 4.6mH 4.6mH Inductance khz 6.mH 59.8mH 6.6mH 59.9mH Inductance khz 4.5mH 4.5mH 4.mH 4.5mH Phase Hz Phase khz Phase khz

21 Next Steps Install the coils into the cage Inset and install the -axis split pai system into the solenoid Chaacteize the system at liquid helium tempeatue

22 Summay High foces and a high toque can act on the system The calculated magnetic field is compaable with the measued field In the dimension of the device the magnetic field is almost homogeneous

23 Basel Cyolab, :45pm, incedible 9 Tesla......and the look fits 3 Wette Taft 3

Magnetic Fields Due to Currents

Magnetic Fields Due to Currents PH -C Fall 1 Magnetic Fields Due to Cuents Lectue 14 Chapte 9 (Halliday/esnick/Walke, Fundamentals of Physics 8 th edition) 1 Chapte 9 Magnetic Fields Due to Cuents In this chapte we will exploe the elationship