Klystron amplifier — gap transit-time requirement In a klystron amplifier cavity, the electron transit time across the gap should be:

Introduction / Context:
Klystron amplifiers rely on velocity modulation at the input cavity gap, followed by bunching and energy extraction at the output cavity. If electrons spend too long traversing the gap, the RF field changes phase significantly during transit, reducing effective modulation and gain. This is the classic “transit-time effect.”

Given Data / Assumptions:

• Single gap within an RF cavity.
• RF frequency f with period T = 1/f.
• Uniform field approximation across a small gap length compared to the electron path.

Concept / Approach:
Define the gap transit angle ψ = ω * τ, where τ is electron time in the gap. For efficient modulation, ψ should be sufficiently small, commonly taken as ≤ π/2 (i.e., τ ≤ T/2). This ensures electrons experience substantially uniform field polarity while crossing the gap. Tighter criteria (e.g., τ ≤ T/4) further reduce distortion but are not strictly necessary in many practical designs; the widely cited limit is “less than half a cycle.”

Step-by-Step Solution:

Verification / Alternative check:
Klystron theory shows gain decreasing as ψ grows; design texts specify small transit angles, often targeting ψ around 1 radian or less, which is below π/2.

Why Other Options Are Wrong:

• Less than one cycle: too loose; significant phase reversal can occur within one period.
• Less than quarter cycle: overly strict for general requirement; not mandatory in all designs.
• More than quarter cycle: can be acceptable in some cases, but beyond half cycle clearly degrades modulation; the accepted rule is “less than half cycle.”

Common Pitfalls:
Confusing gap transit time with drift region bunching time; ignoring relativistic effects at very high voltages.

Final Answer:
less than half cycle