Measurement of magnetic permeability of steel laminations of - PowerPoint PPT Presentation

Measurement of magnetic permeability of steel laminations of Booster gradient magnets Yury Tokpanov supervisors: Valery Lebedev, Bill Pellico 1

Problem � Calculation of impedance of Booster gradient magnets � Unknown magnetic permeability of the steel 2

Idea of measurement Electromagnetic wave propagation in strip lines depends upon properties of materials, including magnetic permeability Microstrip line Network analyzer Strip line 3

1D transmission line Basic element of transmission line: Telegrapher’s equations: ∂ ∂ U I  = − − IR L  ∂ ∂ x t   ∂ ∂ I U = − C  ∂ ∂ x t   Harmonic solutions: = ω − + ω + U A i t ikz B i ikz exp( ) exp( ) γ γ A B = ω − − ω + I i t ikz i t ikz exp( ) exp( ) + ω + ω R i L R i L + ω U R i L = − ω + ω k i C R i L 2 ρ = = ( ) Wave impedance: ω I i C 4

Microstrip line parameters The simplest formulae (valid if W>>H) for parameters per unit length: W H + ωµ ωµ i (1 ) = εε = µ   C L =   +   R sqrt sqrt H   0 W σ σ 0 W       2 2     strip ground   More complicated formulae exist, which take into account edge effects. ε = ε − ε i ' '' µ ω = µ ω − µ ω i ( ) '( ) ''( ) ε '' δ = tan Loss tangent: ε ' If resistive losses are negligible (for example, in the case of copper), then i δ δ L ≈ ω ≈ ωτ  −  kl l LC ρ ≈ ≈ ρ  +  i 1 0 1   C   2 2     5

S-parameters Definition: S-parametes are measured by network analyzer Our case (symmetric): κ + i kl 2 ( 1) tan ω − U i t ikz = S 2 exp( ) ω − ω − ɶ U i t ikz ɶ U i t ikz 4 exp( ) 0 exp( ) κ + κ + i kl 11 2 2 ( 1) tan κ 2 ω + U i t ikz ɶ ω + = U i t ikz 1 exp( ) S 3 exp( ) κ + κ + kl i kl 21 2 2 cos ( 1)sin ρ κ = Z 0 6

Experimental setup Tapering Copper microstrip line Copper strip line Steel microstrip line Network analyzer 7

Copper microstrip line 1 180 150 0.9 120 0.8 90 0.7 60 0.6 30 e itud S11m ase n S11m fit ag h 0.5 0 S11 p 11 m S11p S11p fit -30 S 0.4 -60 0.3 -90 = = W mm H mm 0.2 1.4 12 -120 0.1 -150 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 frequency, Hz 1 180 150 0.9 ρ = ρ = Ω Ω 120 17.4 17.4 0.8 0 0 90 0.7 60 0.6 30 S21 magnitude S21m 9 sec S21 phase − τ = ⋅ S21m fit 1.91 10 0.5 0 S21p rad S21p fit -30 0.4 -60 0.3 δ = 0.02 -90 0.2 -120 0.1 -150 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 8 frequency, Hz

Tapered copper microstrip line 1 180 150 0.9 120 0.8 90 0.7 60 0.6 de 30 S11m itu ase S11m fit n h ag 0.5 0 S11 p S11p 11 m S11p fit -30 S 0.4 -60 0.3 -90 0.2 -120 0.1 -150 = = W mm H mm 1.4 12 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 frequency, Hz 1 180 150 0.9 ρ = Ω 120 17.3 0.8 0 90 0.7 60 0.6 30 e itud S21m ase 9 sec − τ = ⋅ n S21m fit h ag 0.5 0 1.84 10 21 p S21p 21 m rad S S21p fit S -30 0.4 -60 0.3 δ = -90 0.02 0.2 -120 0.1 -150 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 9 frequency, Hz

Strip transmission line 1 180 150 0.9 120 0.8 90 0.7 60 0.6 30 S11 magnitude S11m S11 phase S11m fit 0.5 0 S11p S11p fit -30 0.4 -60 0.3 -90 = = W mm H mm 0.2 12 1.4 -120 0.1 -150 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 frequency, Hz 1 180 150 0.9 ρ = Ω 120 10.1 0.8 90 0 0.7 60 0.6 30 S21 magnitude S21m S21 phase 9 sec − τ = ⋅ S21m fit 0.5 0 2 10 S21p rad S21p fit -30 0.4 -60 0.3 δ = -90 0.02 0.2 -120 0.1 -150 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 10 frequency, Hz

Weakly-linked resonator 1.00E+00 180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 150 = W mm 12 1.00E-01 120 = H mm 90 0.8 1.00E-02 60 30 S21 magnitude S21 phase S21m 1.00E-03 0 S21p -30 1.00E-04 -60 -90 1.00E-05 -120 -150 1.00E-06 -180 frequency, Hz 9 sec 9 sec − − τ = ⋅ τ = ⋅ 1.88 10 1.85 10 instead of rad rad 11

Steel How to take into account resistive losses: 1 180 R 150 0.9 τ = τ + 1 120 0.8 s c ω i L 90 0.7 60 0.6 S11 magnitude 30 S11m copper R S11 phase S11m steel 0.5 0 ρ = ρ + S11p copper 1 S11p steel -30 s c ω 0.4 i L -60 0.3 -90 0.2 ρ τ ⋅ + ωµµ i -120 (1 )   = L = c c R sqrt 0 0.1 -150  σ  l W 2 0 -180 s   S 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 frequency, Hz σ = ⋅ 6 2.3 10 s 1 180 m 150 0.9 120 Landau-Lifshitz ferromagnetic 0.8 90 resonance model: 0.7 60 µ 0.6 S21 magnitude 30 S21m copper µ = + S21 phase s 1 S21m steel 0.5 0 S21p copper 2 f f S21p steel -30   0.4 + −  i f 1 -60  f 0.3 -90 a r   0.2 -120 0.1 -150 0 -180 1.00E+05 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 12 frequency, Hz

Results � Technique for determining necessary parameters is developed � Experimental investigation of the problem is carried out � Rough estimation of magnetic permeability is obtained Plans � Solve problem of additional phase shift � Carry out experiments in strong dc magnetic field (~1-2 T) 13

Thank you! 14