Question

A linac klystron at the CLS outputs RF waves with a frequency frc = 2865 MHz. Estimate the minimum transverse dimensions for a waveguide to propagate a TE 10 RF wave in vacuum from the klystron. Other modes might also be able to propagate in the waveguide with the dimensions estimated, so calculate the cut-off frequency of the next two higher modes and evaluate if they will be supported by dimensions estimated earlier.

Answer 1

In a given question, we need to find the dimensions of the resonator cavity for TE₁₀ having the values of m=1 and n=0
Any + Fou a Wave to propagate along the wave guide the frequency must be greater then some critical value; here for this case the frequency of Wave quide (Jef=2865 MHz) * We have expression as we= c/mory' = maja For exiven Teo mode we have {m= 1) b/n=0 so *80f=/Wj+(0j2 => | x \x 2.865 x 10€ +2 ) Se a= 3x108-6 - > 0.0523 meter + 5.23cm. 2x2865 the value The value of bo will be same for Teo mode for next mode will vary accordingly.

pagate is Te, mode Let Now the next Mode that will be able to the values of Te, mode will vary. We a c/moje maje Now (men-1 Let [a=b * Wc-c Vulaj , 2nf = c plus => 3*= C17 () a-sinen H **** & Now butting the value of a we have to set the Bride masa 40.56x108 a 4056 MHz. 2x0.05237 & Tire ceatt off frequency for this mode is higher then giren; so it will not supported.