Skin Depth Investigation Lei Zang The University of Sheffield 1
Introduction: CST STUDIO • CST STUDIO is a package of tools for designing, simulating and optimizing electromagnetic systems. • CST: Computer Simulation Technology • It includes various modules dedicated to specific application areas: • Microwave studio, EM Studio, Particle Studio, MPHYSICS Studio, Design Studio, PCB Studio, CABLE Studio • CST is based on “MAFIA” --- “solving MAxwell’s equations using the Finite Integration Algorithm*” * T. Weiland, "A Discretization Method for the Solution of Maxwell’s Equations for Six -Component Fields", Electronics and Communication, (AEÜ), Vol. 31, p.116, 1977 2
Some Accelerator Related Example with CST • CST Microwave Studio: RF Cavity design • CST EM Studio: Magnet design • CST Particle Studio: particle and Wakefield 3
CST Work Demonstration measurement data at low current (1.36 kA) FLUX Concentrator 0.5 • Bz Pulsed current flows to the 0.4 FC2 data Bz primary coil. CST Bz • The induced current flow into 0.3 the inner core through the slit. Bz [T] • Duo to the skin effect, current 0.2 has a path near inner surface 0.1 Field measurement and simulation 0.0 -20 0 20 40 60 80 100 results agreed very well!! Longitudinal Position [mm] 0.010 Primary Coil Bx 0.005 Slit Central Core 0.000 Bx [T] -0.005 Bore -0.010 FC2 data Bx CST Bx -0.015 Primary Current -0.020 -20 0 20 40 60 80 100 Induced Current 4 Longitudinal Position [mm]
LBNE Horn Inner Conductor For the first step: What is the skin depth in the horn neck section? 5
Simulation Results Validation • The penetration of current in a good conductor is characterized by the skin depth. At this depth, the current density is 1/e~0.37 of that at the conductor surface. 𝜀 = 2 𝜕𝜈𝜏 [ 𝑛 ] • Software: CST Studio • Where ω is the angular frequency of current, μ is the • Purpose: compare the simulation results with the theoretical calculation permeability and σ is the conductivity. • Geometry: Cylinder, R=15mm • Material: Aluminium and Aluminium alloy (6061-T6) Aluminium Material Al, Al alloy and Al Current Path alloy at 75 o C AC Current Frequency 625Hz Calculate the current density in the middle position z=100mm 6
CST Simulation Results Aluminium Skin Depth= 3.46mm Theoretical prediction=3.28mm 6061-T6 Skin Depth=4.17mm Theoretical prediction=4.02mm 7
CST and theory agrees well for a simple cylinder geometry. We proved that the software is 6061-T6 at 75 degree capable of doing this calculation. Now, how about a HORN? At 75 degree, 6061- T6’s resistivity=4.7 e-8 ohm-m Skin depth = 4.45mm Theoretical prediction=4.36mm 8
Horn Neck Skin Depth Approximate Evaluation 9
• Same thickness as Horn neck • Material 6061-T6 at 75 degree A Tube • Inner radius is 9mm • Outer radius is 13.5mm Max=2.3e+11 Min=1.8e+11 Current density will not drop to 1/e 10
Conclusions • CST Studio could simulate skin effect to get fair accurate results. (Tested with different frequency, material and resistivity) • Skin depth theoretical equation can only apply to the simple geometry such as a cylinder. In which case, CST agrees well with it. • A tube geometry has been used as an approximation. The results indicated a current density degradation of 22%. • Therefore, we can conclude that the current flow in horn neck should be relatively uniform. 11
Future Plan • After obtaining the the skin depth with some approximation, I would like to see the results again with the realistic geometry. I expect they are the same. • Investigate the magnetic field distortion, which is caused by the input power. • Generate 3D horn field map to implement it to G4LBNE simulation. A realistic 3D field should return a more accurate neutrino yield. 12
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