Improvement in non-iterative synthesis method of the Pierce gun

As far as the convergence half angles of Pierce electron guns vary in a wide range，some corresponding logical functions for Tiwary non-iterative method have been proposed. Using the improved approach, the results agree well with that of Vaughan iterative method and the difference of the convergence half angle between them can be below 1°. Furthermore, the function of the anode aperture radius of Tiwary method is also logically modified, and its anode-cathode spacing and gun shot are as good as that of Vaughan method. In particular, the accuracy of the new method is not influenced by the magnitude of the convergence half angle any longer. Thus, this proposed method extends the application range of the non-iterative method from small convergence half angle to large convergence half angle e