2. Superconductors as Energy Materials

Question 1

Give the definition of superconductivity. What are the three main criteria (boundary conditions) for the material to demonstrate superconductive properties?

Answer 1

Superconductivity is the phenomenon which occurs when materials exhibit zero measured electrical resistance to direct current.

The three main criteria is that it needs to be below a critical temperature, be subjected to a magnetic field below a critical field strength and must carry a current less than the critical current.

Question 2

Describe the phenomenology of the Meissner effect and isotope effect in superconducting materials. Why are these two effects contributed to the understanding of superconductivity?

Answer 2

Meissner effect: magnetic field is expelled from the superconducting magnet under the critical temperature. Electric currents near the surface of a superconductor induce the magnetic field which cancels the applied magnet fields within the bulk of the superconductor. Shows that superconductor is a perfect diamagnet.

Isotope effect: Superconductive transition temperature varied with the isotope atomic weight. Showed evidence for interaction between the electrons and the lattice; that phonons play an important role in superconductivity.

Question 3

Explain the mechanism of superconductivity using Bardeen-Cooper-Schrieffer (BCS) theory.

Answer 3

Superconductivity can be explained through electrons which can be attracted to one another through interactions with the crystalline lattice and form Cooper pairs. Cooper pair is a quantum effect, that can be represented as a pair of electrons bound together due to electron-phonon interactions. These electrons can be far apart. Cooper pairs behave as bosons, which mean that several Cooper pairs can occupy the same quantum state.

This theory leads to the relation T_c = A exp(-1/B), where A is the Debye temperature and B is the BSC bond constant. This gives that T_c is at 30-40K for most materials.

Question 4

Name the most important class of high temperature superconductors. Does BSC theory explain the mechanism of superconductivity in these materials (and why)?

Answer 4

The most important class of high temperature superconductors are the cuprates (Copper Oxides). They show superconductivity at temperatures up to 164K.

BSC theory does not explain the superconducting behavior in these high temperature superconductors. According to BSC, cupartes should most likely not exhibit this effect, as it is a relatively poor conductor at RT.

No satisfactory theory exists, but it is hypothesized that phonon-electron interactions are not the only that are responsible for the superconducting properties.

Question 5

Name state of the art superconducting materials for energy provision. What are basic concepts to use high and low temperature superconductors for this application? Analyze pros and cons.

Answer 5

State of the art high temperature superconducting material for this use is yttrium barium copper oxides (YBCO), using liquid N2 for cooling. Among the low temperature superconducting materials, niobium-tin (Nb3Sn) using liquid He as coolant or magnesium diboride (MgB2) using liquid hydrogen as a coolant.

Long Range DC Transmission lines:
It is constructed in a way with a central cryogenic channel, with several layers providing insulation and shielding.

Pros:

• long-range DC power transmission without losses.
• Already DC, so no need for a AC/DC-conversion when entering households.
• Can be designed to exclude outer electric fields, and will have a lesser environmental impact than today’s power lines as it can be placed underground, and will also have no degradation due to weather.
• High current densities (20-100 times better than Cu).

Cons: hard to fix if there is a problem. Still expensive technology. Need for constant cooling. Subject to critical temperature, magnetic field strength and current.

Question 6

Name state of the art superconducting materials for energy storage. What are basic concepts to use high and low temperature superconductors for this application? Analyze pros and cons.

Answer 6

State of the art material: Nb-Ti. Niobium-Titanium alloys

SMES - superconducting magnetic energy storage:
Makes use of a cooled superconducting coil and a power condition system. The current will ideally not decay when the coil is charged, which can be seen from the equation of the time constant in a coil, tau = L/R. When R goes to 0, tau goes to ∞.

It has a short time between charging and discharging, the energy loss is very low in the charging and discharging process and the absence of moving parts in the system main components reduce wear effects. It is good for buffering the output variations of wind and solar.

It is pricey, and the use of HTS is hard since they are brittle (hard to form a coil). To store energies at the scale of GW, one needs very large loop. This means that it is not viable as a energy storage like a battery.

Question 7

Where was superconductivity first observed?

Answer 7

In 1908 in the lab of H.K. Onnes in Leiden, Nederland.

Question 8

How does propulsion of a Maglev-train work?

Answer 8

It has an array of magnets (with varying N S N S) on the side of the track which pushes magnets on the train forward. These (either onboard or on the track) needs to be alternated so that it can continue to be pushed forward.

These trains use the effect of magnetic levitation (so-called maglev technology).

Question 9

Analyze pros and cons of superconductors in Transmission lines:

Answer 9

Transmission lines:
Long-distance DC transmission lines, using high T superconductors

Pros:

• Saving metals
• Saving space and installation costs
• looks prettier than overhead lines
• not influenced by weather since they are underground.

Cons:

• Maintenance issues, difficult to repair a cable damage
• high cost: High T superconductors material, and expensive cooling system (liquid N2)
• thermal leakes (between cold liquid N2 and warm sourroundings)
• limited strength in current that can be used in the cables, at some high currents, above I_critical the superconductivity is lost?

Question 10

Analyse pros and cons for using superconductors in Energy Storage Systems E.g. SMES (Superconducting Magnets Energy Storage)

Answer 10

• Superconducting magnetic energy storage (SMES)
  Consept: SMES systems store energy within the magnetic field created by the flow of direct current in a superconducting coil with near-zero loss of energy. A typical SMES consists of two parts: a cooled superconducting coil (e.g. Nb/Ti) and a power conditioning system. Ideally, once the superconducting coil is charged, the current will not decay and the magnetic energy can be stored indefinitely (because the magnetic field holds the energy?. The energy will be stored until the coil is again connected to the grid to be discharged.

Pros:
- the short time between the charging and discharging (almost instantaneous)
- the very low energy loss in the charging and discharging process
- the absence of moving parts in the system main components
Cons:
- Large price
- materials in the HTS are brittle and hard to shape into a coil shape
- to achive a energy storage on a commercial level, would need a loop of around 160km (very large area)

Question 11

Analyse pros and cons for superconductors in Transport

Answer 11

Maglev
Consept: These trains use the effect of magnetic levitation (so-called maglev technology). There is an approximately 10 mm gap between the maglev transport mean and the track minimizing losses due to friction. The superconducting magnet material is normally placed on board, while the role of the track is to be a guideway.
Pros:
- High speed trains
- Lower CO2 effision with Maglev than airplain, 3 times less CO2

Cons:
- High Cost compared to normal railways