where n =integer /= frequency v = velocity Va=accelerating voltage Vr=reflecting voltage e=the fundamental charge m=electron mass d=grid separation 8=cathode to first grid distance e=second grid to reflector distance This equation contains two assumptions: (i) The rf field has negligible effect on the electron velocity on a single pass. (ii) No electron-electron interactions occur. From Eq. (1) we can gain some insight as to how the electrons can stay approximately in phase. As the electron velocity decreases so that the transit time between grids increases, the turnaround times decrease. Figure 5 represents a numerical solution of Eq. (1). We can see that for large v the curve becomes linear and the slope can be made small by careful choice of electrode separation distances and operating conditions. For example, a factor of two change in electron energy from 20 to 10 eV leads to less than a 20% phase shift between the rf field and the electron cycle. If we assume that the electrons derive all their velocity from the accelerating field, Eq. (1) predicts modes. Examples of these modes are shown in Fig. 6. Note the excellent qualitative agreement between the location of the predicted modes shown in Fig. 6 and the observed modes in Fig. 3. IV. SELF-OSCILLATION Our first tests to understand the operation of the photoklystron were in the biased 4 ______________ Fig. 5. Numerical solution to Eq. (1) at F=30 MHz. DI, D2 and D3 are parameters representing the grid, photocathode and reflector electrode spacing.
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