4 research outputs found
Adequate mathematical tools for superconductivity
This paper has for essential objective to point out the existence of,
at least, two original mathematical techniques, particularly well adapted
to the problems arised from the superconductors ; taking the interest and
the complexity of the latter into account, it is really urgent to investigate
a concrete cooperation between the concerned communities (Mathematicians,
Physicists, Engineers) in order to improve their respective competences
Practical criteria for the thermal stability of a unidimensional superconductor
The criterion of "equal area" [4, 5] is known as a necessary and sufficient
condition in order that a unidimensional superconductor of infinite length,
submitted to fixed current density and magnetic field, could not evolve
towards a resistive state after an accidental local overheating ;
this criterion relates only to the normalized source term of heating
(competition between the heat power generated by joule effect and
the one which is absorbed by the cryogenic bath). We give here an
optimal criterion, valid for any length (case of an uncooled region
situated between two well cooled ones) ; it allows the engineers to
play upon a non dimensional grouping of parameters (characterizing
the intensity of the source term), related to the conductor, in order
to extend the field of its superconducting properties. We give also
some intermediate complementary criteria which are only sufficient
but much more easy to check