GATE 2021 PH – Question 57
A linear charged-particle accelerator is driven by an alternating voltage at 10 MHz and accelerates electrons. After a few drift tubes the electrons reach $2.9\times10^8$ m s⁻¹. Find the minimum length of each subsequent drift tube in m, rounded to one decimal place.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 14.0 to 15.0
Explanation
The accelerating field must reverse while an electron is shielded within the drift tube. The shortest suitable transit time is half a voltage period, $\Delta t=1/(2f)$. At the stated speed the length is $l=v/(2f)=2.9\times10^8/[2(10\times10^6)]=14.5$ m. Longer odd half-period transit times are possible, but the question asks for the minimum.