A Simplified Theory of Current Leads
Closed form solutions for temperature, conducted heat and voltage drop are derived for a lead cooled with forced flow. The mass flow which will cause thermal runaway is expressed as a function of current. An optimal lead is defined as a lead where the conducted heat at the warm end is zero and where the total refrigerator load is minimal. Optimal mass flow and geometry at design current are derived under those two conditions. The margin between critical and optimal flow is too small: a 2% decrease in mass flow or a 10 % increase in current are sufficient to produce temperatures of 450 K. Therefore an operating mass flow is defined: it is the smallest flow for which the lead is always stable as long as the flow is proportional to the current. A curve giving the operating mass flow as a function of current is established. Mass flow, voltage drop and conducted heat under operating conditions can then be established. During operation, reading of voltage drop is the best way to monitor the leads since it is shown that voltage drop is a linear function of maximum temperature. Comparisons with leads cooled with boil-off and by conduction only are presented.
KeywordsMass Flow Voltage Drop Design Current Critical Flow Forced Flow
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