Skin Depth Investigation
Lei Zang
The University of Sheffield
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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
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Some Accelerator Related Example with CST
• CST Microwave Studio: RF Cavity design
• CST EM Studio: Magnet design
• CST Particle Studio: particle and Wakefield
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-20 0 20 40 60 80 1000.0
0.1
0.2
0.3
0.4
0.5
FC2 data Bz
CST Bz
Bz [T
]
Longitudinal Position [mm]
measurement data at low current (1.36 kA)
-20 0 20 40 60 80 100-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
FC2 data Bx
CST Bx
Bx [T
]
Longitudinal Position [mm]
Bz
Bx
CST Work Demonstration
Bore
Central Core
Slit
Primary Coil
Primary CurrentInduced Current
FLUX Concentrator
• Pulsed current flows to the
primary coil.
• The induced current flow into
the inner core through the slit.
• Duo to the skin effect, current
has a path near inner surface
Field measurement and simulation results agreed very well!!
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LBNE Horn Inner Conductor
For the first step:
What is the skin depth in the horn neck section?
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Simulation Results Validation
• Software: CST Studio
• Purpose: compare the simulation results with the theoretical calculation
• Geometry: Cylinder, R=15mm
• Material: Aluminium and Aluminium alloy (6061-T6)
Aluminium MaterialAl, Al alloy and Al alloy at 75oC
Current PathAC CurrentFrequency 625Hz
Calculate the current density in the middle position z=100mm
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• 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.
• Where ω is the angular frequency of current, μ is the permeability and σ is the conductivity.
𝛿 = 2
𝜔𝜇𝜎 [𝑚]
CST Simulation Results
Aluminium Skin Depth= 3.46mmTheoretical prediction=3.28mm
6061-T6 Skin Depth=4.17mmTheoretical prediction=4.02mm
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6061-T6 at 75 degree
At 75 degree, 6061-T6’s resistivity=4.7 e-8 ohm-mSkin depth = 4.45mmTheoretical prediction=4.36mm
CST and theory agrees well for a simple cylinder geometry. We proved that the software is capable of doing this calculation.
Now, how about a HORN?
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Horn Neck Skin Depth Approximate Evaluation
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A Tube• Same thickness as Horn neck
• Material 6061-T6 at 75 degree
• Inner radius is 9mm
• Outer radius is 13.5mm
Max=2.3e+11Min=1.8e+11Current density will not drop to 1/e
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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.
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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.
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