Reflex klystron – Transit-time condition (in RF cycles) for sustained oscillations Let n be any integer. For a reflex klystron oscillator, the electron transit time through the repeller space must satisfy what condition (expressed in number of RF cycles) to sustain oscillations?

Introduction:A reflex klystron is a single-cavity microwave oscillator that depends on electron bunches returning to the cavity gap in the proper phase to deliver energy to the RF field. The required timing is specified as a transit-time condition in terms of RF cycles.

Given Data / Assumptions:

• Single re-entrant cavity (gap) and a negatively biased repeller electrode.
• Anode voltage sets initial beam velocity; repeller voltage sets turnaround distance/time.
• Oscillation occurs in discrete “n + 3/4” modes, with integer n ≥ 0.

Concept / Approach:

The phase condition for sustained oscillation is commonly written in radians as ωT ≈ (2n + 3/2) * π. Dividing by 2π converts radians to cycles: T / T_rf ≈ (2n + 3/2) * π / (2π) = n + 3/4. This ensures returning electrons encounter a decelerating RF field, transferring kinetic energy to the cavity and reinforcing the oscillation.

Step-by-Step Solution:

Verification / Alternative check:

Tuning curves show distinct reflector-voltage bands corresponding to different n + 3/4 modes, confirming the timing condition.

Why Other Options Are Wrong:

Other linear expressions (2n − 1, 2(n − 1), n + 1/2, n + 1/4) do not meet the standard phase requirement and would not consistently yield positive power transfer.

Common Pitfalls:

Confusing radians and cycles; forgetting that increasing repeller magnitude changes the transit time and therefore the oscillation mode and frequency.

Final Answer:

n + 3/4.