In a traveling-wave tube (TWT) amplifier, how does the amplitude of the resultant RF wave along the helix vary under small-signal operation?

Introduction / Context:
Traveling-wave tubes (TWTs) are broadband linear amplifiers. An electron beam interacts continuously with an RF wave on a slow-wave structure (e.g., helix), transferring kinetic energy to the wave and producing gain.

Given Data / Assumptions:

• Small-signal regime (no saturation).
• Proper synchronism between electron beam and RF wave phase velocity.
• Neglecting distributed loss for the conceptual answer.

Concept / Approach:

In the linear region, the coupled-mode equations predict an exponential growth of the RF amplitude with distance along the helix, characterized by a spatial gain constant dependent on beam current, voltage, and circuit parameters.

Step-by-Step Solution:

Verification / Alternative check:

Measured TWT gain (in dB) scales with length in small-signal operation, consistent with exponential growth until saturation effects limit further increase.

Why Other Options Are Wrong:

• Linear increase: An oversimplification; the correct dependence is exponential in the small-signal model.
• Decrease constant: Contradicts amplification mechanism.
• Constant or oscillatory amplitude: Not true for an amplifying device in linear regime.

Common Pitfalls:

Confusing TWT amplifiers with oscillators; assuming uniform amplitude due to misinterpreting the helix as a passive line.

Final Answer:

It increases exponentially along the interaction region