Low Temperature Cooling by Thermal-Field Electron Emission in a Crossed-Field Gap

Summary form only given. A new method of refrigeration using thermal-field electron emission from nano-scale emitters of arbitrary work function in a vacuum crossed-field gap is proposed. With an external crossed magnetic field (parallel to the electrode surfaces), an additional potential barrier near the anode is created to restrict the tunneling of low energy electrons (below the Fermi energy) and thus providing a versatile cooling capability from room temperature down to less than 10 K. For one specific emitter, i.e., fixed work function (phi), characteristic radius (R), and gap spacing (L), the optimal voltage (V₀), magnetic field (B₀) are determined both numerically and analytically at various temperatures. It is found that the optimal local cooling power density (per emitter) is about 600 kW/cm² at 300 K, 2.7 kW/cm² at 50 K and 20 W/cm² ut 10 K. The typical ranges of the operation are R = 10s run, L = 100s mum, and B < 2 T. For a real cathode with an array of emitters, we consider some variations in the work function, radius of emitter and gap separation (phi, R, L), which are assumed to obey some distribution functions with peak values at (phi₀, R₀, L₀). Thus an average optimal cooling power density at a statistically optimal voltage (V_so) and magnetic field (B_so) is calculated. It is found that the degradation of cooling performance (due to the variations) depends mainly on the characteristics of the variations set by the assumed distribution functions. Compared to a bell-shaped distribution, an exponentially decay distribution function is found to perform better, which indicates that only positive deviation from desired optimal values (phi₀, R₀, L₀) is acceptable. In summary, this study suggests an interesting idea of using field-emitted electrons for cooling purposes by using nano-scale emitters with no restrict- ion on the work function of the emitters. Optimal conditions for maximum cooling are derived and calculated, which shows a much tetter cooling capability at low temperature (< 150 K) range that is not attainable by using other electron-emission based methods.