Analysis of Eddy Currents in Gradient Coils

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Analysis of Eddy Currents in Gradient Coils
Napoli, 23-09-2003
J.M.B. Kroot TU/e Eindhoven
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Contents

• Introduction
• Model
• Analysis
• Results
• axisymmetric Rings
• Non-axisymmetric Rings and islands
• Conclusions
• Further research

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Introduction

• Use of a coil Apply a varying current to the
  conductors on the coil to create a magnetic field
  with a certain gradient.
• Goal of the PhD-project Optimize the magnetic
  field such that the gradient is as straight as
  possible.
• Optimization by adding/removing conductors, or
  changing the shape.

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Goal

• Consider the coil as strips of thin conductors
  on a cylinder, to which a low frequency current
  (kHz) is applied.
• Goal for this presentation Determine the
  current distribution in the conductors

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Model

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Assumptions

• Source time harmonic electric field
• Quasi static approach
• ? D / ? t ? 0
• ? ? / ? t ? 0
• Strips are negligibly thin
• J J (f,z)

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Analysis

• ( K ie I ) J f
• K is integral operator, with Greens kernel
• K Ksing Kreg
• Ksing has logarithmic kernel with respect to z
• J Sn an Bn
• Bn Bn (f,z) consist of Legendre polynomials
  and trigonometric functions

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Results f-independent
j
j
z
z
j
j
z
z
? 200
? 1000
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Results f-dependent
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Conclusions

• Current distribution defined by Fredholm integral
  equation of second kind
• Legendre polynomials for fast convergence
• Eddy currents occur due to coupling

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Further research

• Eigen modes
• Model reduction
• Characteristics of the system
• Optimize magnetic field