Multiplicities and thermal runaway of current leads for superconducting magnets

Krikkis, Rizos N.

doi:10.1016/j.cryogenics.2017.01.009

Cited by 3 publications

(6 citation statements)

References 49 publications

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“…The numerical methods and the computer code developed in [26] were applied to the solution of the two-point boundary value problem described by Equations ( 17)- (19). The same algorithms were also utilized for the numerical continuation and the stability analysis (eigenvalues and eigenfunctions).…”

Section: Resultsmentioning

confidence: 99%

“…Because of the nonlinearities involved in Equation ( 25), the corresponding bifurcation diagram Θ L versus u consists of multivalued curves, which are depicted in Figure 2 for a filling ratio of η = 0.1 and different current densities. More specifically, for a given value of the conduction-convection parameter, up to three solutions exist bounded by two limit points, shown as (•) and denoted with different colors for clarity, which are the roots of the equation du/dΘ L j = 0 (26) and denoted as u u LP , (Θ L ) u LP for the upper one and u l LP , (Θ L ) l LP for the lower one, where…”

Section: Resultsmentioning

confidence: 99%

“…m is used to cool the conductor along the longitudinal direction X. Assuming that the conductor is thermally thin (i.e., the Biot number is much less than unity), the transverse temperature gradients may be neglected and the energy balance for the lead and the cooling gas stream takes the form (Krikkis [26]):…”

Section: Discussionmentioning

confidence: 99%

“…J 2023, 6 303 both experimentally and theoretically [23][24][25][26]. Two steady states exist, one stable and one unstable, separated by a limit point.…”

Section: Introductionmentioning

confidence: 97%

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Analysis of High-Temperature Superconducting Current Leads: Multiple Solutions, Thermal Runaway, and Protection

Krikkis¹

2023

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The multiple steady states of Ag/Bi2212-composite high-Tc superconducting leads modeling current delivery to a superconducting magnet have been numerically calculated. The model is based on longitudinal conduction combined with convective heat dissipation from a helium gas stream along the conductor. Because of the nonlinearities introduced by the voltage–current relationship and the temperature-dependent material properties, up to three solutions have been identified within the range of parameters considered. Linear stability analysis reveals that two of them are stable, i.e., the superconducting and the normal branches, while the remaining one is unstable. The limit points separating the stable from the unstable steady states form the blow-up threshold, beyond which any further increase in the operating current results in a thermal runway. Interesting findings are that for low filling ratios no bounded solution exists when the length of the lead exceeds the lower limit point, while very high maximum temperatures may be encountered along the normal solution branch. The effect of various parameters such as the conduction–convection parameter, the applied current, and the reduction in coolant flow (LOFA) on the bifurcation structure and their stabilization effect on the blow-up threshold are also evaluated. Apart from the steady and unsteady operating modes, the multiplicity analysis is also used to identify the range of the design and operating variables where safe operation, with a sufficient margin from the onset of instabilities, may beestablished, thus facilitating the protection of the leads and the device connected to it.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…J 2023, 6 303 both experimentally and theoretically [23][24][25][26]. Two steady states exist, one stable and one unstable, separated by a limit point.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Analysis of High-Temperature Superconducting Current Leads: Multiple Solutions, Thermal Runaway, and Protection

Krikkis¹

2023

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“…This phenomenon has been discussed qualitatively by Gurevich and Mints [7] and rigorously by Bandle and Brunner [37]. An engineering application for current leads for superconducting magnets has been presented by Krikkis [38]. In that case, however, the solution structure is much simpler, since only two solutions exist.…”

Section: Quench the Destruction Of Bistability And Thermal Runawaymentioning

confidence: 97%

On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

Krikkis¹

2021

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In the present study, a numerical bifurcation analysis is carried out in order to investigate the multiplicity and the thermal runaway features of metallic and superconducting wires in a unified framework. The analysis reveals that the electrical resistance, combined with the boiling curve, are the dominant factors shaping the conditions of bistability—which result in a quenching process—and the conditions of multistability—which may lead to a temperature blowup in the wire. An interesting finding of the theoretical analysis is that, for the case of multistability, there are two ways that a thermal runaway may be triggered. One is associated with a high current value (“normal” runaway) whereas the other one is associated with a lower current value (“premature” runaway), as has been experimentally observed with certain types of superconducting magnets. Moreover, the results of the bifurcation analysis suggest that a static criterion of a warm or a cold thermal wave propagation may be established based on the limit points obtained.

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Effect of Defects on the Quench Properties of Stacked REBCO Tapes

Shi

Yang

et al. 2021

IEEE Trans. Appl. Supercond.

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Multiplicities and thermal runaway of current leads for superconducting magnets

Cited by 3 publications

References 49 publications

Analysis of High-Temperature Superconducting Current Leads: Multiple Solutions, Thermal Runaway, and Protection

Analysis of High-Temperature Superconducting Current Leads: Multiple Solutions, Thermal Runaway, and Protection

On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

Effect of Defects on the Quench Properties of Stacked REBCO Tapes

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