Improvement in the synthesis method of the Pierce electron gun

The iterative formulas in Vaughan’s iterative method are discussed and more logical ones are proposed. This improved iterative synthesis method will never be limited to the convergent Pierce electron guns with low convergence or the initial value of the convergence half angle. And 13 practical cases numerically show that, even if its initial value of convergence half angle arbitrarily varies in the range of 0°~70°, the proposed method would get reasonable results in the case of low, normal or high-convergence. The proposed method’s results of guns with normal and high-convergence agree well with that of Vaughan’s method, and the results of guns with extremely low convergence are well consistent with the corresponding actual values.