Reflex klystron timing: if the magnitude of the repeller voltage is increased (i.e., made more negative), how does the electron transit time to return to the cavity gap change?

Introduction / Context:
A reflex klystron is a single-cavity microwave oscillator in which electrons are emitted, pass through the cavity gap, are turned back by a negatively biased repeller electrode, and return to the gap. The transit time determines the bunching phase and thus oscillation frequency. This item asks how making the repeller voltage more negative affects that transit time.

Given Data / Assumptions:

• Repeller electrode is biased negative relative to the cavity.
• Increasing repeller voltage means increasing its negative magnitude.
• Electron motion is ballistic between interactions, neglecting space-charge complications for first-order reasoning.

Concept / Approach:
A more negative repeller increases the retarding electric field. Electrons penetrate less deeply into the repeller space before being turned around, so their path length shortens. With a stronger retarding field, their turnaround occurs sooner, reducing the round-trip time to the gap. Therefore, the transit time decreases as the magnitude of the negative repeller bias is increased.

Step-by-Step Solution:

Verification / Alternative check:
Reflex klystron tuning curves show frequency increasing with more negative repeller voltage over particular regions, consistent with decreased transit time setting a different bunching condition.

Why Other Options Are Wrong:

• Increased: contradicts the physical effect of stronger repulsion.
• Same: ignores electric-field strength dependence.
• Either: not ambiguous for a fixed geometry; direction is deterministic.

Common Pitfalls:
Confusing sign conventions; forgetting that the relevant change is in the magnitude of negative bias, not toward zero.

Final Answer:
will be decreased