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Tests on the Mode Matching Method. Webmeeting 24-10-2011 N.Biancacci, B.Salvant, V.G.Vaccaro. Outline: . Motivation Comparisons with: > Thick wall formula > CST Thin inserts models. Conclusion and Outlook.

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  1. Tests on the Mode Matching Method Webmeeting 24-10-2011N.Biancacci, B.Salvant, V.G.Vaccaro Outline: • Motivation • Comparisons with: • > Thick wall formula • > CST • Thin inserts models Conclusion and Outlook Acknowledgement: A.Burov, F.Caspers, H.Day, E.Métral, N.Mounet, C.Zannini, M.Migliorati, A.Mostacci

  2. Motivation • We developed a Finite Length code to study the effect of finite length on simple geometries in order to investigate the effect for real devices. • A list of benchmark has been done in order to validate the Mode Matching Method applied to simple geometries: Filling material (ε’,ε’’,σ,μ) Comparison with the classical Thick wall impedance formula for different conductivities. Comparison with CST for different conductivities of the filling material and length of the device. Length dependence of impedance. Application of the theory for thin insertion impedance and comparison with Shobuda-Chin-Takata model. length

  3. 1-Thick Wall Formula: Test for high conductivity σ (1/1) Varying conductivity Thick wall formula: Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=8 F/m σ variable

  4. 2-CST: Varying σ (1/4) • For high onductivity we can compare the impedance from the thick wall formula and CST. • The model is a simple cavity in PEC. • The wakefield is too low, this leads to numerical problem on the impedance. σ=103 Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=1 F/m σ = 103 S/m σ=103

  5. 2-CST: Varying σ (2/4) σ=1 σ=1 Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=1 F/m σ = 1 S/m

  6. 2-CST: Varying σ (3/4) σ=10-3 σ=10-3 Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=1 F/m σ = 10-3 S/m

  7. 2-CST: Varying σ (4/4) σ=10-4 σ=10-4 Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=1 F/m σ = 10-4 S/m

  8. 2-CST: Varying Length (1/3) Varying length L=20 cm cut off L=20 cm Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=1 F/m σ = 10-2 S/m

  9. 2-CST: Varying Length (2/3) L=60 cm L=60 cm Parameters:Inner radius=5cm Outer radius=30cm Length=60cmεr=1 F/m σ = 10-2 S/m

  10. 2-CST: Varying Length (3/3) L=100 cm L=100 cm Parameters:Inner radius=5cm Outer radius=30cm Length=100cmεr=1 F/m σ = 10-2 S/m

  11. 3- Length dependence of impedance (1/2) Longitudinal impedance for Alumina 96%. For Length >inner radius, longitudinal modes are well visible in case of low conductivity. Parameters:Inner radius=7.7cm Outer radius=9.2cm Length=variableεr=9.4 F/m σ = 10-12 S/m

  12. 3- Length dependence of impedance (2/2) We also studied the dependence of length for the case of ReWall impedance for multilayer beam pipes1. In this case conductivity is high and the length does not play significant rule (all curves are overimposed). Discrepancy at low frequency is under investigation. Parameters:Inner radius=2mm Outer radius=25mm Length=variableεr=1 F/m σ = 105 S/m 1.N.mounet, E.Metral, “Impedances of an Infinitely Long and Axisymmetric Multilayer Beam Pipe: Matrix Formalism and Multimode Analysis”

  13. 4-Thin insertions • Small isolating insertions between beam pipe flanges in SPS could present impedance peaks at enough low frequency to overlap with the bunch spectrum. • But.... insertion • Geometry is difficult to study with e.m. Simulators like CST. The thickness of the insertion is on the order of 200 um, the radius of the beam pipe 15 cm . But.... • ModeMatching Method (MMM) and Shobuda-Chin-Takata’s 2 (SCT) model could help. Courtesy of B.Salvant 2. COUPLING IMPEDANCES OF A SHORT INSERT IN THE VACUUM CHAMBER

  14. Mode-Matching Method and Shobuda-Chin-Takata’s model for thin inserts Quick comparison..: MMM SCT’s model • Provides a numerical-analytical way to compute the e.m. Fields excited inside cavity-like discontinuities in circular beam pipes. • Based on cavity eigenmodes decomposition + field matching on the boundary and separation surfaces. • The cavity can be filled with whatever material provided an analytical description (e’,e’’,σ). • Provides an analytical way to compute the e.m. Fields excited inside thick discontinuities in circular beam pipes. • Fields are decomposed in sum of scatterd waves along the pipe, the insert, and outside in vacuum, no longitudinal variation is taken into account, no PEC boundary over the insert (radiation). S3 S2 S1

  15. CST – MMM comparisons (1/4) Thin insertion with MMM Insert properties: Thickness = 15 mm Gap width = 800 μm Pipe radius = 7.5 cm PEC bounded on the top Material properties: Beam parameters:

  16. CST – MMM comparisons (2/4)

  17. CST – MMM comparisons (3/4) 1.67 GHz 4.8 GHz 8.0 GHz wakefield 20m

  18. CST – MMM comparisons (4/4) 1.67 GHz 4.8 GHz 8.0 GHz 30% discrepancy in magnitude... But CST peaks are still not satu- rated as my CPU memory. Wake length= 20.000 mmBunch length=15 mm TotalNumberOfMesh=105

  19. CST – SCT comparisons (1/4) Thin insertion with SCT’s model Insert properties: Thickness = 15 mm Gap width = 800 μm Pipe radius = 7.5 cm No boundary on the top, free space. Material properties: Beam parameters:

  20. CST – SCT comparisons (2/4)

  21. CST – SCT comparisons (3/4) The wake is shifted down.

  22. CST – SCT comparisons (4/4) • 0 frequency peak: Thin insertion has very low conductivity, image current finds an open and accumulate charges on the insert extremities building up a static electric field. It is an effect of this simplified model. In reality currents finds closed loops that move this peack to low frequency. • In SCTs model there is a restriction to pure transverse modes (the scattered field is always supposed constant longitudinally) here is a good approximation: the first longitudinal mode goes over hundreds of GHz.

  23. Conclusion and outlook • CONCLUSIONS • The Mode Matching Method has been succesfully applied to benchmark the Thick wall impedance formula, and different geometries simulated in CST particle Studio with different conductivity and length. • Having a Finite-Length method is important in order to correctly model low conductivity/ high permeability materials, where, if the length is greater than the transverse dimension, longitudinal modes start to be relevant in comparison to 2D models. • Thin inserts models of MMM and SCT have been succesfully benchmarked with CST showing the differences between the two methods in modelizing thin insert impedances. • Little discepancies in magnitude of renonance peak have been shown when a complete convergence cannot be reached in the emsimulator CST. • OUTLOOK • These results show us the importance of having 3D simple models for impedance extimation. Further extension to the transverse impedance, quadrupolar and dipolar, is foreseen as well as further analysis and comparisons on 2D/3D difference and limitatons.

  24. Thanks for your attention!

  25. Backup slides Notes:

  26. CST: Varying σ σ=104 Parameters:Inner radius=5cm Outer radius=30cm Length=20cmεr=1 F/m σ = 104 S/m σ=104

  27. 2-CST: Varying Length (2/5) Parameters:Inner radius=5cm Outer radius=30cm Length=40cmεr=1 F/m σ = 10-2 S/m

  28. 2-CST: Varying Length (4/5) Parameters:Inner radius=5cm Outer radius=30cm Length=80cmεr=1 F/m σ = 10-2 S/m

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