In a backward-wave oscillator (BWO) using a slow-wave structure, which statement best describes the direction of propagation of the RF wave with respect to the electron beam and power flow?

Introduction / Context:
A backward-wave oscillator is a vacuum-electron device where a slow-wave circuit supports a dispersion relation with negative slope, allowing phase to travel opposite to the direction of energy transport.

Given Data / Assumptions:

• Slow-wave structure with a dispersion curve ω(β) of negative slope in the operating region.
• Electron beam provides energy for oscillation.

Concept / Approach:

In a BWO, group velocity (power flow) and phase velocity have opposite signs. The device exploits synchronism between the backward wave and the electron beam to sustain oscillation and enable electronic frequency tuning via beam voltage.

Step-by-Step Solution:

Verification / Alternative check:

Experimental field probes in slow-wave structures show phase advance toward the gun while power is extracted at the output end.

Why Other Options Are Wrong:

• Meanders back and forth: Not a correct physical description of propagating modes.
• Phase progresses only forward: Describes a forward-wave device, not a BWO.
• Either (a) or (c): Not contingent solely on beam voltage; it is set by dispersion.
• Both phase and power backward: Violates energy extraction at the output.

Common Pitfalls:

Confusing phase direction with power flow; assuming backward behavior depends purely on beam voltage rather than circuit dispersion.

Final Answer:

The RF phase progresses in the backward direction while power flows forward