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18a    and b). r) \ to each other (see (116)). As rP1 this distance tends to zero. This means that all boundary lines A for P(4! (4! ) to , respectively (see Fig. 18a). Ya. Ender et al. / Physics Reports 328 (2000) 1}72 Now we address the boundary lines of another type, namely, those corresponding to the condition R /Rr"0. An example of such lines for s"0 is shown in Fig. 18b: they are the lines located between the points a and b and '0 and the points b and a at (0. In order to be   more de"nite we consider the lower ( , / ) half-plane.

In order to be   more de"nite we consider the lower ( , / ) half-plane. All conclusions will be valid for the upper  half-plane, too. The point a (r"1) is the intersection point of the lines 3, 5 and 6. In order to get the coordinates of the point b (r"0) we consider (114) at l"0. e. (<)'0. This means that s"0. 1 and both expressions contained in the braces have the same value and the opposite sign. From (29) with r"0 and <"0 we "nd the corresponding gap value: B  (0)"2  (0) . (117) Here the position of the "rst potential minimum (0) is given by (26) with r"0.

On the boundary of this region ( )"0 holds. Ya. Ender et al. / Physics Reports 328 (2000) 1}72 Fig. 5. The region of allowed values of the re#ection coe$cient r and the charge-nonneutrality parameter , represented by the nonhatched area. Fig. 6. The region of allowed values of " " (where nonhatched area. is the emitter electric "eld for "1) and of , represented by the The transformation of coordinates (75) and (78) can be supplemented by the transformation of the transit time. This transformation can be found by the ansatz ¹( )" \[¹(1)#S ] .

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