Some calculations of transients in an electronic valve
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The integro-differential equation for the non-steady behaviour of a beam of electrons injected into the space between two plane parallel electrodes at given potentials is obtained. When the anode and grid are kept at the same potential V0, the leading electrons reach the anode with energies greater than eV0. If the front of the beam is sharp and the injected beam current is then constant, then for the period until some electrons reach the anode and while the spatial order of electrons in the inter-electrode space remains the same as the time-order in which they passed through the grid, the integro-differential equation has an exact solution in terms of Airy functions. An example is given of results calculated from this solution, where applicable, and continued by numerical integration of the integrodifferential equation.
KeywordsCharge Distribution Potential Gradient Airy Function Integrodifferential Equation Electrode Plane
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