Answer / sreenesh shashidharan

In high-power gyrotrons it is desirable to combine an
optimal resonator length with the optimal value of the
resonator quality factor. In resonators with the constant
radius of the central part, the possibilities of this
combination are limited because the quality factor of the
resonator sharply increases with its length. Therefore the
attempts to increase the length for maximizing the
efficiency leads to such increase in the quality factor
which makes the optimal current too small. Resonators with
slightly uptapered profiles offer more flexibility in this
regard. In such resonators, one can separate optimization
of the interaction length from optimization of the quality
factor because the quality factor determined by diffractive
losses can be reduced by increasing the angle of
uptapering. In the present paper, these issues are analyzed
by studying as a typical high-power 17 GHz gyrotron which
is currently under development in Europe for ITER
(http://en.wikipedia.org/wiki/ITER). The effect of a slight
uptapering of the resonator wall on the efficiency
enhancement and the purity of the radiation spectrum in the
process of the gyrotron start-up and power modulation are
studied. Results show that optimal modification of the
shape of a slightly uptapered resonator may result in
increasing the gyrotron power from 1052 to 1360 kW

two independent random variables x and y are uniformly distributed in the interval [-1,1].the probability that max[x,y] is less than 1/2 is a) 3/4 b)9/16 c)1/4 d)2/3

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