The cost of coolers for cooling superconducting devices at temperatures at 4.2 K, 20 K, 40 K and 77 K

Abstract

Abstract. This author and other authors have written papers concerning the cost of refrigeration as a function of the refrigeration delivered. These papers have included small coolers as well. The lowest temperature range from 3.8 K to 4.7 K (the liquid helium temperature range) is covered using coolers that have two stages. The use of magnets and power equipment that use MgB 2 conductors and HTS conductors have spurred the development of coolers that work well temperature ranges from 15 K to 30 K (hydrogen temperature applications), HTS conductors like BSSCO and YBCO for the range fro 35 to 50 K and HTS devices from 65 K to 80 K (applications in the liquid nitrogen temperature range). This paper will present some cost data for a number of commercial two-stage and single-stage coolers. This data will be fitted to allow one to estimate the cost of coolers as a function of refrigeration for temperatures of 4.2 K, 20 K, 40 K and 77 K. The efficiency of a large number of coolers over a range of temperatures is also discussed.

CMOS-based cryogenic control of silicon quantum circuits

“…A central challenge is that the power dissipation of the control electronics easily surpasses the typical cooling power of 10 μW available at 20 mK (refs. 20,21 ). Because silicon spin qubits can be operated and measured above 1 K (refs.…”

Josephson Junction Field-Effect Transistors for Boolean Logic Cryogenic Applications

“…For an overdamped and resistive JJ-FET, it means the transistor will become superconducting as soon as is increased such that > . However, a JJ or JJ-FET is overdamped only when the Stewart-McCumber parameter = 2 2 / 0 is small ( ≪ 4) [15,16], where and are the resistance and capacitance across the junction, and 0 is the magnetic flux quantum. On the other hand, a JJ becomes underdamped if is large, which means it remains in the resistive state even when the junction current is reduced below IC, leading to I-V hysteresis.…”

“…Assuming ( ) can be reduced at lower , by requiring that the total energy dissipated per switching operation, including the cooling cost, does not exceed the room temperature value, we arrive at the following energy balance equation: (1) The second term on the right-hand side of Eq. (1) represents the cooling cost at the ideal Carnot efficiency, corresponding to reservoir temperatures of 300 K and T. Equation (1) leads to the following simple scaling law for the operating voltage to break even in the ideal cooling limit: For example, a value of 0.7 V at room temperature will translate to a break-even value of 83 mV at 4.2 K (He boiling point), which is further reduced to ~26 mV if one factors in realistic cooling efficiencies of 5-10% [2]. As for the gate delay, while delay associated with load and parasitic capacitance being charged/discharged will scale with , the transit time delay of channel being switched may not scale down proportionally because of low Fermi velocity at low carrier concentration and reduced thermal excitation of carriers [3].…”

Mixed refrigerant cycle with neon, hydrogen, and helium for cooling sc power transmission lines

“…But it seems doubtful that these concepts are sufficient for a sc transmission line of several hundred kilometers length. The specific costs of a cryocooler referring to its cooling capacity are rather high and range between 0.8 to 4 $ kW −1 at an operating temperature of 20 K. At this temperature range the cooler efficiency ranges between 2 and 12 % of Carnot [9]. Furthermore, cryocoolers suffer from continuously wear, steadily decreasing the available cooling power [14].…”

“…Furthermore, cryocoolers suffer from continuously wear, steadily decreasing the available cooling power [14]. Cryocoolers are most suitable in the cooling power range between 10 and 100 W since there exists no cost efficient Claude cycle refrigerator [9]. In contradiction to this, Brayton or Claude cycles can provide cooling power of several kilowatts at higher efficiencies (around 17 % of Carnot).…”