| Paper | Title | Page |
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| TUPSM053 | Analytical Method for Determining Errors in Current Measurements with a Rogowski Coil | 274 |
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We have derived algebraic expressions for the open-circuit voltage that is induced on a Rogowski coil, having imperfectly spaced turns, by a time-dependent current which passes through the aperture of the coil. The derivation of these expressions requires that the layer of the winding is thin, the number of turns is large, and the cross-section of the winding is uninform and rectangular. Examples are given in which these expressions are applied to determine the effects of the gap between the ends of the coil, as well as other irregularities in the spacing of the turns, on the position sensitivity–defined as the dependence of the induced voltage on the coordinates of the current. The results in these examples agree with those that others have obtained by numerical methods or measurements with Rogowski coils. This technique may be used to quickly define the design specifications which are required to satisfy a specific upper limit for the positional sensitivity. |
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| TUPSM054 | Monitoring Transverse Beam Profile with Nonuniformly-Wound Toroidal Coils | 278 |
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Others have shown that the voltages induced on one uniformly-wound toroidal coil and two sinusoidally-wound toroidal coils may be used to determine the current in a single filament and its coordinates. We have extended this technique to show that the voltages measured on a group of sinusoidally-wound toroidal coils may be used to approximate the distribution of current within their common aperture. This is possible because each measured voltage is proportional to the product of unique functions of the radial and azimuthal coordinates of each increment of the current [1,2]. We have developed matrix methods to determine the transverse distribution of the current and determined the sensitivity of these calculations to measurement errors. Shielded sinusoidally-wound coils with a precision of 0.02 cm have been prepared using rapid prototyping, and methods have been defined to prepare the next generation of these coils, which will have a precision of 0.001 cm, by using an engraving tool with the 4th axis of a vertical milling machine. |