The equilibrium temperature distribution in an ideal metal rod, one end of which is subjected to an intense electric field, is studied. Particular attention is focused on the case where the emitting end cools down, and the necessary conditions for this effect are derived. Viewed as a ``heat pump,'' the maximum rate of heat flow as a function of emitter temperature is derived, and it is found that rates in excess of 0.1 cal/sec/cm2 are possible at room temperature if the emitter work function is less than an electron volt.
REFERENCES
1.
2.
3.
4.
A. Sommerfeld and H. Bethe, Handbuck der Physik (Verlag Julius Springer, Berlin, 1934), Vol. 24, part 2, p. 436.
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6.
7.
D. ter Haar, Elements of Statistical Mechanics (Rinehart and Company, Inc., New York, 1954), Chap. 10.
8.
A. H. Wilson, Theory of Metals (Cambridge University Press, New York, 1936), Chap. 9.
9.
Reference 4, p. 346.
10.
Since the critical field strength (and hence the optimum field as well) varies linearly with this would impose somewhat severe conditions on the attainability of maximal cooling in the laboratory. Namely, the field intensity must be within a percent or so of a predetermined value which changes with time as decreases, and must further be free from significant temporal and spatial fluctuations from this value. This latter requirement necessitates careful surface preparation to ensure freedom from patchiness as well as good regulation of the applied field.
11.
In particular, the Fowler‐Nordheim transmission coefficient [Eq. (32)] should be replaced by the more accurate expressions given, for example, by R. Good and E. Muller in Handbuch der Physik, edited by S. Flügge (Springer‐Verlag, Berlin, 1956), Vol. XXI, p. 189.
12.
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© 1962 The American Institute of Physics.
1962
The American Institute of Physics
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