Quench Simulation of Superconducting Strand

Thermal stability and quench propagation have long been a major concern of the superconducting magnet technology. Analytical solutions for mono-filament conductors can be found in every text book of superconductivity. However, the real situation of the strand has much more complicated geometry. A true multi-filament situation has been difficult to handle even in numerical solutions. However, the progress of computer technplogy made it possible to do the complete FEM analysis of realistic superconductors.
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Thermal stability of superconducting strand can be simulated using FEM. This kind of simulation has been around for a single filament conductors or a simple one-dimensional model. This simulation works on a real multi filament strand. The propagation of quench in a strand was simulated as shown in this movie. Once the quench propagation is successfully simulated in a model, various characteristics of the quench can be studied using this model. To see the geometry effect in the stability and quench propagation, two kinds of models are introduced. (A) Model has copper in the outer layer of the strand. This is for the bronze method Nb3Sn, Nb3Al and DT method Nb3Sn. Superconductors are surrounded by bronze. (B) Model has copper in between filaments/filament bundles. This is for NbTi, RRP Nb3Sn and PIT Nb3Sn. Superconductors (bundles) are in the copper stabilizer. To compensate the heat capacity of bronze, additional bronze layer is attached to the copper. By this, amount of materials are exactly the same for both models.
(A) model (PIT)
propagation
(B) model (DT)
propagation
By the difference of geometry, quench propagations of these models are different. It is interesting that the Heat generation happens in the copper rather than the superconductor. Therefore, the quench wave front is in the copper part of the strand.
quench propagation
propagation velocity
The simulation requires large CPU time. The first result is the quench propagation as a function of time. It looks linear enough to define the "quench propagations velocity". It becomes faster when the current is increased. 3mm of normal zone was sustained for initial 0.03 msec to start quench. The quench velocity taken from above calculation is summarized in the figure. Velocity increased with current but a tendency of saturation is seen. Probably this is due to the mesh size.
The quench propagation velocity in compound conductors have been often reported very slow compared to NbTi conductors. It is found that the quench propagation velocity largely depends on the conductor structures even if they have the same copper ratio and the same superconductor characteristics. (B) model has much slower quench propagation than (A) model, common Nb3Sn structure using bronze method. This is because the heating happens in the copper close to the surface.
RRR=100 and I=105A
The stability of a strand can be evaluated by the MPZ. A series of program runs to find the MPZ determined the MPZ of the strand. If the initial normal zone (INZ)is smaller than the MPZ, the normal zone shrinks and entire conductor recovers to the superconducting state. If the INZ is larger than the MPZ, the normal zone increases and a quench is initiated.
Summarizing the above analysis, The Current dependence of MPZ is obtained as shown in the graph. The RRR=100 conductor becomes cryostable at 63A. The dotted line is for the case RRR=50. The RRR dependence of MPZ is clearly seen.