MAGNET COOLING Superconductor Critical Temperature

The superconducting state exists only at temperatures below the so-called critical temperature TC. For NbTi, TC can be esti­mated as a function of applied magnetic flux density B using

/ B 17

TC(B) = Tco (1 — n—j (22)

BC20 /

where TC0 is the critical temperature at zero field (about 9.2 K) and BC20 is the upper critical magnetic flux density at zero temperature (about 14.5 T).

Boiling and Supercritical Helium Cooling. To achieve low temperatures and ensure stable operations against thermal disturbances, the accelerator magnet coils are immersed in liquid helium (70). Helium is a cryogenic fluid whose pres — sure-temperature phase diagram is presented in Fig. 12. Its boiling temperature is 4.22 K at 1 atm (1 atm « 0.1 MPa).

Small superconducting magnet systems usually rely on boiling helium at 1 atm (71). Boiling helium offers the advan­tage that, as long as the two phases are present, the tempera­ture is well determined. However, in large-scale applications,
such as superconducting particle accelerators, the fluid is forced to flow through numerous magnet cryostats and long cryogenic lines, where heat leaks are unavoidable. The heat leaks result in increases in vapor contents and create a risk of gas pocket formation that may block circulation.

The aforementioned difficulty can be circumvented by tak­ing advantage of the fact that helium exhibits a critical point at a temperature of 5.2 K and a pressure of 0.226 MPa (see Fig. 12). For temperatures and pressures beyond the critical point, the liquid and vapor phases become indistinguishable. The single-phase fluid, which is called supercritical, can be handled in a large system without risk of forming gas pockets. However, its temperature, unlike that of boiling helium, is not constant and may fluctuate as the fluid circulates and is subjected to heat losses.

The cryogenic systems of the Tevatron, HERA, and RHIC, and that designed for the SSC, combine single-phase and two — phase helium (71). In the case of the Tevatron and HERA, the insides of the magnet cold masses are cooled by a forced flow of supercritical helium, while two-phase helium is circulated in a pipe running at the cold mass periphery (around the col — lared-coil assembly for Tevatron magnets, in a bypass hole in the iron yoke for HERA magnets). In the case of the SSC, it was planned to only circulate supercritical helium through the magnet cold masses, while recoolers, consisting of heat exchangers using two-phase helium as primary fluid, would have been implemented at regular intervals along the cryo­genic lines. The cryogenic system used for the RHIC is in­spired by that of the SSC. In all these schemes, the boiling liquid is used to limit temperature rises in the single-phase fluid.

Superfluid Helium Cooling

A peculiarity of helium is the occurrence of superfluidity (70). When boiling helium is cooled down at 1 atm, it stays liquid until a temperature of the order of 2.17 K, where a phase transition appears. For temperatures below 2.17 K (at 1 atm) helium loses its viscosity and becomes a superconductor of heat. This property, unique to helium, is called superfluidity. Superfluidity is very similar to superconductivity, except that, instead of electrical conductibility, it is the thermal conduct — ibility that becomes infinite. The transition temperature be­tween the liquid and superfluid phases depends on pressure. It is called the lambda temperature Tx.

Figure 12. Pressure-temperature phase diagram of helium (71).

Temperature (K)

The LHC magnets are cooled by superfluid helium, and their operating temperature is set at 1.9 K (72). Decreasing the temperature improves the current-carrying capability of NbTi dramatically and allows higher fields to be reached. (For NbTi, the curve of critical current density as a function of field is shifted by a about +3 T when lowering the tempera­ture from 4.2 K to 1.9 K.) The feasibility of a large-scale cryo­genic installation relying on superfluid helium has been dem­onstrated by Tore Supra, a superconducting tokamak built at Commissariat a l’Energie Atomique/Cadarache near Aix en Provence in the South of France and operating reliably since 1988 (73).

Magnet Cryostat

To maintain the magnet cold masses at low temperature, it is necessary to limit heat losses. There are three mechanisms of heat transfer (74): (1) convection, (2) radiation, and (3) con­duction. The convection losses are eliminated by mounting the cold masses into cryostats, which are evacuated (71,75). The radiation losses, which scale in proportion with the effec­tive emissivities of the surfaces facing each other and with the fourth power of their temperatures, are reduced by sur­rounding the cold masses with blankets of multilayer insula­tion and thermal shields at intermediate temperatures. The main sources of conduction losses are the support posts, the power leads, and the cryogenic feedthroughs, which are de­signed to offer large thermal resistances.

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