5.1 are limits imposed by mode competition as well as constraints on the beam voltage and current due to physical limits of the electron
5.1.1 Parametric Analysis
In this section, a parametric analysis based on the gyrotron model of Appendix C will be outlined. The figure of merit .for this
study was chosen to be the total efficiency, -iT. High efficiency is
- 115
-Wall Heat Flux P W
Cavity Radius
I
Wave EquationQoHm* QD of Cavity Cavity
Length -Mode v M
-n - QT QHM Mode Competition
- e [ 11+ (B,,81)2-1 Beam Energy U --- = P/lT
- n. From Nusinovich and Erm. n, is Function of all Parameters
--- -- Gun Constraints
Beam
Beam Radius
Fig. 5.1 Design Constraints of Gyrotron Frequency and Output Power Fixed
T __ _
important for gyrotrons for several reasons. First, it reduces the power supply requirements, which can significantly lower the cost of ECRH power. Second, it reduces the required beam power, which
prolongs the collector life and lowers the collector cooling needs.
Finally, it reduces the ohmic heating losses in the cavity and helps increase the cavity lifetime.
In order to better understand how the total efficiency of the gyrotron is related to the design parameters, nT has been plotted as a function of a variety of these parameters. These results are shown in Figs. 5.2 through 5.5. In all of these graphs, the length L is allowed to vary in order to find the highest overall efficiency
that can be achieved. Except where indicated, the following parameters have been assumed: v = 200 GHz, U = 70 kV, I = 4.lA, mode TE051' R = 2.07 mm (third radial maximum from cavity center), and / =
1.8.
Figure 5.2 shows the effect on nT of varying the operating frequency of the device. As the frequency is increased, the maximum efficiency will occur at.shorter lengths. This is consistent with the calculations of Nusinovich and Erm (Fig. C.l) in which both I and V, and therefore nV,,can be treated as functions of L/A, which can be rewritten as LW. If
QD
OHM, then nT virtually becomes a function of Lw. Fig. 5.2 illustrates that this dependence on Lwis approximately correct, although slightly higher total efficiencies can be obtained at lower frequencies. This dependence allows one to scale fl to other frequencies by keeping Lw constant.
In Fig. 5.3 the beam voltage is varied from 40 kV to 90 kV.
One can observe that operating at too high a voltage can cause a
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-reduction in total efficiency. This is due to the fact that as U is increased, the length must be increased to achieve the optimum j , but this causes f. and subsequently the maximum a to be reduced.
Calculations indicate that for = 1.8, the beam voltage should be between 40 and 60 kV to achieve the highest total efficiencies.
The effect of varying the beta ratio is shown in Fig. 5.4.
As one can see, the total efficiency is very sensitive to this ratio.
In order to achieve the highest n T the gyrotron should operate at as high a value of (3j/ ) as possible. However, as this ratio is increased, the velocity spread of the beam becomes more problematic [64] and can eventually cause a reduction in the efficiency of the device [see Eq. (C.28)]. Results in Fig. 5.4 do not include this decrease of a caused by the velocity spread. One should thus select a beta ratio that balances these two opposing influences.
Finally, Fig. 5.5 shows how the K factor in
QD
(see Eq. (C.9)) influences the total efficiency. This factor can be interpreted as a measure of RF field trapping by the resonator. The higher K is, the more effectively the cavity traps the field. The graph indicates that the optimum length, as well as the width of the curve, is strongly dependent on K. This suggests a possible procedure for optimizing a gyrotron design. Once the operating mode is selected, a length can be chosen that corresponds to a tolerable heat flux P . Then K canw
be varied until the peak of the efficiency curve occurs at this
length. This value of K can then be obtained by selecting the appro-priate cavity shape and output coupling.
The effect of the constraints imposed by the magnetron gun on the operating regime of the gyrotron will now be investigated. In
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Appendix C a model for the gun was described in which an upper limit was placed on the current (see Eq.(C.29) through Eq.(C.31)). This
limit on the beam current is illustrated in Figs. 5.6 and 5.7. Except where indicated, the following parameters have been assumed: V =
200 GHz, U = 70 kV, mode TE0 5 1' Re = 2.82 mm (fourth radial maximum from center), and I / = 1.8.
Fig. 5.6 shows the effect of changing the maximum velocity spread of the beam.- The characteristics of the operating regime are very sensitive to the choice of E when this variable becomes
max
sufficiently small. As E is decreased, the limit imposed by Eq.
(C.29) becomes more restrictive, forcing the gyrotron to operate at higher beam energies and lower currents. The increase in beam energy
is beneficial because this causes the velocity spread due to surface roughness and thermal effects to be reduced. .As m is increased, the maximum current becomes limited by the beam to cavity voltage drop restriction (Eq. (C.31)) rather than by the velocity spread criterion.
This can be seen for c = 12%.
max
In Fig. 5.7, the radial maximum of the RF field involved in the interaction with the electron beam is varied. The gyrotron is operating in the TE051 mode with E = 10%. This graph indicates that it is advantageous for the beam to be as close to the cavity wall as possible in order to increase the current limit. However, one must avoid operating with the beam too close to the wall in order
to prevent additional wall heating due to electron bombardment. As in the previous figure, two different limits on the current can be observed. For interactions involving the third and fourth maxima, the current is limited by the cavity-beam voltage, while for the
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