Abstract
The second order temporal differential equation, known to describe the space charge field in the high frequency region, is solved approximately in a closed analytical form. The condition for multiple resonances is found. The maxima and minima in the space charge field are shown to correspond to the roots of the zero and first order Bessel functions respectively. The analytical approximations for the space charge field are compared with numerical results for the complete range of frequencies, and it is shown that there is excellent agreement between the two for the high frequency region which includes all the resonances.
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