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Extra resources for Case Studies in Superconducting Magnets: Design and Operational Issues (Selected Topics in Superconductivity)

Example text

E = ∞ , obviously do not dissipate power, your < P > vs ρ e plot should start with < P > = 0 and < P > → 0 as ρ e → ∞. < P > given by Eq. 57 indeed indicates this behavior. i) The behavior of the < P > vs ρ e plot described above suggests the existence of a critical resistivity, ρec , at which < P > is maximum. 5-mm wall thickness (d), and ρ e = 2 × 10 –10 Ω m. This resistivity corresponds roughly to copper’s resistivity at liquid helium temperatures. 6—Part 2 e) In the sinusoidal case, the time-averaged total power (per unit length), < p >, is given by , where is the complex current density (Eq.

9 shows a plot of < P > vS ρe . 15) Solving Eq. 59 is important in induction heating. A uniform, sinusoidally timevarying magnetic field is applied to a conducting sample to heat it by eddy currents. For a given material resistivity and sample dimensions, the critical frequency, derivable from Eq. 59 and identical to f sk , is selected to maximize the heating. 53) Another way of interpreting ƒs k is, as discussed earlier, that the induced magnetic is negligible compared with for ƒ << ƒ sk . field Fig.

As discussed in the next problem where a superconducting cylinder is considered, a discontinuity in the θ component of the fields at r = R requires a surface current (confined within a thin layer). Because this current, once set up, must flow persistently, it implies that the sphere’s electrical conductivity, like the superconductor’s, must be infinite. As discussed in Chapter 1, a perfectly diamagnetic material must at the same time be a perfect conductor; that is, such a material is automatically a superconductor.

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