Superconductive energy storage

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Superconducting magnetic energy storage (SMES) has a specific energy limit of 1-10 W·h/kg, as noted in Wikipedia. Larger SMES rings may mitigate issues related to Lorentz forces, but practical challenges arise in maintaining structural integrity and cooling for larger configurations. The energy density for a thin ring encircling the Earth would depend on its dimensions and material properties, particularly if a hypothetical superconductor with perfect conductivity were used. Voltage in SMES systems is influenced by current and magnetic fields, with both factors crucial for energy storage. The discussion highlights the complexities of designing effective SMES systems, particularly regarding size, material properties, and operational parameters.
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Article in Wikipedia states that specific energy of Superconducting magnetic energy storage is limited to 1 - 10 W·h/kg.
http://en.wikipedia.org/wiki/Superconducting_magnetic_energy_storage
Do I understand it correct that the larger will be radius of SMES ring the less problem with Laurence law we will have? And what would be energy density per kg if we have relatively thin ring such as couple of cm in diameter which circles entire Earth? And in addition to that, what if we would have a hypothetical superconductor in which absolutely all electrons contribute to conductivity? And how voltage of SMES is defined?
 
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Laurence law? Lorentz force? This is given by current*magnetic field, and both are important for the stored energy, so you don't want to reduce them.

For small rings, you can make the whole ring stiff enough - that won't work for larger rings, where you need some way to keep the coil in place with external connections. Those connections could be an issue for cooling.

And in addition to that, what if we would have a hypothetical superconductor in which absolutely all electrons contribute to conductivity?
How would such a superconductor look like?

And how voltage of SMES is defined?
Which voltage?
 
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