Theory of space charge in vacuum diode tube. Part I. Hydrodynamic description

In this paper we describe a space charge theory developed on the basis of hydrodynamics, treating many thermal electrons in vacuum diode tube as fluid. We solve the problem under the two conditions. Under condition (1), as usual in hydrodynamics, the temperature changes adiabatically. Under condition (2) the temperature is nearly constant in the system. We call these conditions “adiabatic” and “constant temperature” approximations respectively. With constant temperature, the results under condition (2) are in good agreement with those of the space charge theories of Fry and Langmuir based on the assumption that electrons are emitted from a hot cathode with the Maxwllian velocity distribution. With the adiabatic approximation, the results are in poor agreement with experimental results for a weak electric current, because in this case the temperature may be constant due to the large thermal conductivity of the electron gas. This approximation is valid under the conditions which we discuss in more detail in part II.