I wisch to know the difference in solution of Helmholz equation in cylindrical waveguide and cylindrical cavity resonator

Example (Ez)mnp for Cavity resonator

(Ez)mn for waveguide

$$d(x,y)\leq d(x,x_n)+d(x_n,y_n)+d(y_n,y).$$ The inequality in the second line comes from this inequality. ]]>