0
\$\begingroup\$

All units are in the SI

I'm doing my task from vacuum electronics - for the given klystron with a toroidal resonator[ug]

Resonator:

enter image description here

I have to find the $h$ parameter, that will satisfy given conditions:

$$f=10GHz$$

$$U_{resonator}=250V$$

$$electrons\space stream\space diameter\space 2a=6 mm=0,006 m$$

that can be found from the given toroidal resonator eigenfrequency formula, considering, $$b=2a$$ and \$c\$, as far, as I understand equals \$0,73\$: $$f_{\text{res}}=\frac{c}{\pi a \sqrt{\frac{2 h}{d} \ln \frac{b}{a}}}$$

\$d\$ can be found from the next equation, considering \$\theta=0,75\pi\$

$$\theta_{i}=\omega \tau=2 \pi f\left(d / v_{0}\right) \quad v_{0}=5,93 \times 10^{5} \sqrt{U_{\text{res}}}=9376153,262\space mps$$


When I put all this stuff in one, I got

$$d=v_0\dfrac{0,75\pi}{2\pi f}=\dfrac{0,75*3,14*9376153,262 }{2*3,14*10000000000}=0,000351606\space m$$ that seems correct

$$h=\dfrac{\dfrac{d(\dfrac{c}{f\pi 0,003})^2}{ln2}}{2}=\dfrac{\dfrac{0,000351606(\dfrac{0,73}{10000000000*3,14*0,003})^2}{ln2}}{2}=1,5*10^{-20}\space m$$ that is obviously wrong

If I put \$d\$ and \$h\$ in $$f_{\text{res}}=\frac{c}{\pi a \sqrt{\frac{2 h}{d} \ln \frac{b}{a}}}$$, I get 10000000000, that means, that I've calculated everything correctly.

I've been checking all steps, all formulas, maybe I had missed something, but no, seems that the problem is in resonator frequency formula - it's wrong. I've tried to find it in the internet but get failed.

Please, provide a specified toroidal resonator frequency formula, or, if the formula, given in my task correct, point me, where am I wrong.

\$\endgroup\$
0
\$\begingroup\$

enter image description here I got the next solution of my issue

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.