HTS vs LTS Comparative Analysis
The difference: operating temperature
Overview
For a superconducting magnet I'm torn between classic NbTi and HTS REBCO tape. What should I compare?
Three main things: the power to cool it, the margin to the critical temperature, and behaviour in a quench (loss of superconductivity back to the normal state). NbTi is cheap, easy to handle and proven in MRI, but works only at liquid-helium temperature with a margin of a few kelvin. REBCO tolerates high fields even around 20 K and eases cooling, but the conductor is expensive and its tape form makes stresses and quench protection harder. Numbers make the contrast clear.
Main conductors
| Conductor | Class | Critical temperature | Typical operation | Example uses |
|---|---|---|---|---|
| NbTi | LTS | ~9 K | 4.2 K / 1.9 K | MRI, accelerators |
| Nb₃Sn | LTS | ~18 K | 4.2 K | Fusion, high-field magnets |
| MgB₂ | Intermediate | ~39 K | 10–20 K | Low-field MRI, power transmission |
| Bi-based | HTS | ~85–110 K | 20–77 K | Current leads, cables |
| REBCO | HTS | ~90 K | 20 K / 77 K | High-field magnets, fusion |
Cooling power
The ratio of input power $W$ to heat removed $Q$ for an ideal (Carnot) refrigerator rejecting heat from $T_c$ to room temperature $T_h$. It rises steeply at low temperature.
Critical temperature and field
The critical temperature of NbTi falls as the field rises; $T_{c0} = 9.2$ K and $B_{c20} = 14.5$ T are common approximations. Carrying current lowers the temperature at which superconductivity survives even further.
The 1986 “high-temperature” shock
For 75 years after superconductivity was discovered in mercury in 1911, no material exceeded 30 K. In 1986 two researchers at a Swiss laboratory reported superconductivity near 35 K in a copper-oxide ceramic, and the next year materials above 90 K were found. The world was electrified by superconductors that work in liquid nitrogen (77 K), and the discoverers received the Nobel Prize the following year. Turning brittle ceramics into long conductors took more than 20 years, and practical REBCO tape reached volume production only in the 2010s.
Worked examples
Example 1: cooling power
| Operating temperature | Ideal input per 1 W removed | Relative to 4.2 K |
|---|---|---|
| 4.2 K | 70.4 W | 1 |
| 20 K | 14.0 W | 1/5 |
| 65 K | 3.6 W | 1/20 |
| 77 K | 2.9 W | 1/24 |
These are ideal values; real refrigerators achieve a smaller fraction of Carnot efficiency the colder they run — often only a few percent at 4.2 K — so the real gap is larger still. Reducing heat leaks through current leads and supports is especially important for LTS magnets.
Example 2: NbTi temperature margin
| Field | Critical temperature (no current) | Margin from 4.2 K |
|---|---|---|
| 3 T | 8.0 K | 3.8 K |
| 5 T | 7.2 K | 3.0 K |
| 7 T | 6.2 K | 2.0 K |
| 9 T | 5.2 K | 1.0 K |
NbTi's upper critical field at 4.2 K is about 10.7 T, with practical use up to about 9 T. Beyond that, magnets are cooled with 1.9 K superfluid helium (raising the upper critical field to about 13.5 T) or use Nb₃Sn or HTS. Carrying current shrinks the margin further, and real magnets are often designed with about 1–2 K.
Example 3: heat needed to raise temperature
| Temperature range | Heat per kg of copper | Relative to 4.2→7.2 K |
|---|---|---|
| 4.2 → 7.2 K | 0.64 J | 1 |
| 20 → 23 K | about 30 J | about 50× |
| 20 → 30 K | about 170 J | about 270× |
| 20 → 50 K | about 1,400 J | about 2,200× |
Near 4 K a tiny amount of heat raises the temperature.
Specific heats are tiny at cryogenic temperatures. Friction heat from a conductor shifting slightly under magnetic force, or a small crack in the resin, is enough to raise the temperature a few kelvin and quench an LTS magnet. That is the origin of “training”, where a magnet reaches its design current only after repeated quenches. An HTS magnet at 20 K needs hundreds of times more heat to exceed a comparable margin, so it is very robust against such disturbances.
Analysis and design cautions
Differences in quench protection
- LTS: normal zones spread at metres to tens of metres per second, spreading heat over the magnet. Voltage detects them early, and protection heaters drive the whole magnet normal to discharge the current.
- HTS: normal zones spread only centimetres per second. Local temperature can rise while the voltage stays small, and burnout may occur before detection. Sensitive detection and approaches such as no-insulation windings that let current bypass are being studied.
What the analysis must capture
- Include the dependence of critical current on field, temperature and field angle; REBCO tape varies strongly with field direction.
- Give cryogenic specific heat and conductivity as functions of temperature; they change by orders of magnitude over a few kelvin.
- Evaluate electromagnetic stress; at high fields the forces on the winding govern conductor strength.
- For varying fields, estimate AC loss and add it to the cooling load.
Magnets cooled by refrigerators alone
Liquid helium has become expensive and its supply unreliable. Increasingly common are conduction-cooled magnets cooled directly by small cryocoolers without any liquid. With no liquid bath there is less capacity to absorb local heating, which makes NbTi design demanding. MgB₂ and HTS, usable around 20 K, have more refrigerator capacity and larger temperature margins, so they suit this approach well — an example of material choice shaping cooling method and ease of operation.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Comparing conductor price only | Cooling cost overlooked | Include refrigerator power and equipment |
| Critical temperature at zero field | Margin overestimated | Evaluate at operating field and current |
| Using LTS quench protection for HTS | Late detection, burnout | Design for slow propagation |
| Constant specific heat | Temperature rise badly wrong | Use temperature-dependent values |
| Ignoring REBCO field angle | Critical current overestimated | Use angle-dependent data |
I'd like to explore field calculations and related topics myself.
Try the solenoid field simulator for coil fields, the magnetic levitation simulator for levitation and the MRI coil SNR tool for MRI coils. For details see quench simulation, critical current density, MRI magnet design and AC loss in superconductors.