Richardson Dushman Equation
The current density of electrons emitted from a hot cathode to an anode described by Richardson Dushman equation.
$$j= A\cdot T^2 e^{-\frac{W_a}{kT}}$$Here, $j$ is density of current of thermionic electrons. $T$ is temperature of hot cathode, $k$ is constant of the Boltzmann, $W_a$ is work needed to extract an electron from the metal, $A$ is Richardson's constant. For most materials $A \approx 120A/(m^2 \cdot K^2)$
