The most common way for cable cooling is by means of forced circulation (pumping) of sub-cooled liquid nitrogen. In order for the cable to remain in superconducting state it is extremely important that the cooling media has an homogeneous density and flow in order to dissipate heat from the cable (thermal losses and heat generated by the so called AC losses). Therefore the liquid nitrogen is not allowed to boil and create “bubbles”.

This is achieved by subcooling the liquid nitrogen that flows through the cable by bringing the liquid below its saturation temperature by increasing the pressure. The liquid nitrogen can now absorb the generated heat without boiling. Typically these systems operate in a temperature range of 66-72K (since this is the temperature range where the superconductor has it best characteristics). Sub-cooling pressures vary from 3-20 barg.

Stirling Forced Flow System
The Stirling Forced Flow Cooling systems are specifically designed for this type of use: liquid nitrogen is subcooled (by pressurizing) and forced flowed (pumped) through the power cable in a closed loop by means of a cryogenic pump. The heat of the cable increases the temperature of the liquid. This energy is dissipated either in a second bath of (boiling) liquid nitrogen on which the Stirling SPC cryogenerators cool away the released energy (1), or directly on the cold head of the Stirling SPC Cryogenerator. Option 1 is shown in below schematic (the heat exchanger on the left represents the power cable).
 

 
Although cooling of the cable may appears simple, in reality it is a rather complex system. First, an important number of components are not shown in the basic schematic (T & P transmitters, cryogenic valves, control units, safety valves etc). Since reliability is a major concern most of them require redundancy, what needs to be integrated cryogenically.

Additionally a “thermodynamic – economical” equilibrium must be determined. The number of coolers that can be connected to this system is unlimited in theory. Each component which will be integrated/added will come at a “thermal” cost: it adds to the total heat in-leak of the system. 
Last but not least, the temperature difference over the cable allowed by its designer (which determines the flow rate of the LN₂), in combination with the diameters of the piping and cable cryostat, can result in pump and friction losses forming an additional heat load for the system.