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?
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AThe wave meanders back and forth along the line without a definite direction
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BThe RF phase progresses only in the forward direction (same as power flow)
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CThe RF phase progresses in the backward direction while power flows forward
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DEither (a) or (c), depending on beam voltage only
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EBoth phase and power propagate backward
Answer
Correct Answer: The RF phase progresses in the backward direction while power flows forward
Explanation
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:
1) Identify dispersion where dω/dβ < 0 ⇒ group velocity opposite to phase velocity.2) Power (group velocity) travels toward the RF output (forward).3) Phase fronts move toward the electron gun (backward), hence the name backward wave.4) Beam–wave interaction is maintained by choosing an operating point where the beam line intersects the backward portion of the dispersion curve.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