Production of a Square Temperature Wave in Filaments Operating at Low Temperatures

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Abstract
The problem of obtaining fast rising temperatures by resistance heating in a filament initially at low temperatures is examined. From a solution of the heat conduction equation the relationships, both steady state and transient, among temperature, heating current, and heating power are derived. These solutions are dependent on the initial temperature, the thermal properties of the filament, and its physical dimensions. For a typical filament the current‐temperature curves are of the form i = F + (B/T) where B is negative for 77°K boundary temperature, zero for approximately 50°K, and positive below this temperature. Experimental evidence taken with a 0.1‐mm diam tungsten filament 2.5 cm long confirms these predictions. A circuit capable of raising a filament from any temperature above 4.2°K to any desired temperature below 600°K in less than 0.3 sec is described.