Download Intermediate state of a superconducting wire

Departement Physik und Astronomie, Universität Basel
Prof. C. Bruder (4.2, Tel.: 73692)
Theorie der Supraleitung
Blatt 3 (Abgabe: 28. April 12 Uhr Tutor: Audrey Cottet Zimmer 4.16
10 Punkte)
Intermediate state of a superconducting wire
Consider a metallic wire with radius a λ and superconducting critical field Hc , carrying a
total current Itot .
1. What is the critical current Ic above which the wire cannot be entirely superconducting?
We are going to discuss how the normal state appears in this wire for Itot > Ic (we will consider
a stationnary state).
2. Explain why having a superconducting core for r ≤ a0 < a is not possible (plot H(r))
3. Explain why having the whole wire in the normal state is not possible either (plot H(r))
We will assume that for r ≥ r1 , the wire is in the normal state and for r ≤ r1 , it is in an
intermediate state with H(r) = Hc and a fraction of the conduction path r/r1 in the normal
state (see Figure)
4. Give the current density J(r) =
R r+dr →
→
− −
j · dS/2πrdr as a function of Hc
r
5. Why can the longitudinal electric field E be considered as independent of r?
6. Use Omh’s law to express J(r) as a function of E, r, r1 and the resistivity ρ of the metal
in the normal state.
7. Express r1 as a function of Hc .
8. Express the total current I1 flowing at r < r1 as a function of E
9. Use Ohm’s law to express the total current I2 flowing at r ≥ r1 as a function of E
10. Express E as a function of Itot
We will call R the resistance of the wire and Rn the resistance of the wire in a fully normal
state.
11. Express and plot R/Rn as a function of Itot /Ic
12. Assuming Hc ∝ Tc − T , express and plot R/Rn as a function of T .