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

Round 1

Reviewer 1 Report

The manuscript by Krikkis presents a detailed numerical study of the thermal runaway of the quenching of superconducting wires. The topic is relevant for technological applications and this well written theoretical study reflects properly on experiments. 

A minor quibble: the boundary conditions for partial differential equations are of 'von Neumann' type, not "Newmann".

I wonder if the findings of this study are also relevant for the recently discovered electric field-effect in superconductors: 

Large enhancement of critical current in superconducting devices by gate voltage
Rocci et al, Nano Letters V21 pp216 (2020)

Gate-Controlled Suspended Titanium Nanobridge Supercurrent Transistor
Rocci et al, ACS Nano 2020, 14, 10, 12621–12628

Author Response

The author is indebted to the reviewer for taking the time to read the manuscript and suggest improvements.

1. The typographical error for Neumann boundary conditions has been corrected.
2. Despite the difference in scale the very interesting findings in the superconducting transistors suggested by the reviewer and especially the non-linear and non-monotonic temperature-resistance relationship as source of a more complex bifurcation structure has been reflected in the revised manuscript.

Reviewer 2 Report

 The author reports the theoretical analyses of thermal dynamics of metallic and superconducting wires. The numerical simulations have revealed that the multistability is composed of normal runway and premature one. The latter corresponds to the low current case.

 The thermal stability and the temperature distribution in a superconducting magnet are essential issues. The author’s approach would be original and be helpful for the practical use of superconducting magnets. The paper is interesting and valuable for publication. I recommend the minor revision. Please address the minor issues listed below.

1. The references cited in the introduction are typically old papers. Please cite several new papers, which report recent progress of theoretical models and are published after 2016.
2. In p.10, please mention the work [22] in more detail.
3. In p.11, line 18, the author mentions the green arrow. However, I cannot catch the green arrow in Figure 10.
4. In p.13, line 10, the period is missing after “two solutions exist”.

Author Response

The author is indebted to the reviewer for taking the time to read the manuscript and suggest improvements.

1.  Additional references have been introduced in to the revised manuscript.
2. The work of Zhukov and Barelko has been described in amore detailed manner in the revised manuscript.
3. Although for the discussion of Fig 10 the reader is referred back to Fig 5, the green arrows have been included in Fig 10 as well for reasons of clarity and completeness.
4. The missing period has been corrected in the revised manuscript.