Methods of Electronic Optics Simulation Based on Numerical Solving the Vlasov-Poisson Equation

Two methods for simulation the motion of electron flows in vacuum, considering the thermal spread of velocities and space charge are presented. The first one is based on the numerical solution of the Vlasov-Poisson equations using the finite volume method, and the second is based on a particle-in-cell approach in phase space. Both methods were tested on a one-dimensional vacuum diode. The calculated current-voltage characteristics of the diode are in good agreement with each other, and with space-charge limited currents, predicted by Child-Langmuir law. These methods allowed us to study near-emitter region considering electrons thermal velocity spread, and space charge cloud, and to calculate the cut off voltage. The advantages and disadvantages of both methods are also discussed.