Eight-cavity magnetron – Total phase shift around the ring in π-mode For a magnetron with 8 identical cavity resonators, what is the total phase shift around the periphery in the π-mode (adjacent cavities 180° out of phase)?

Introduction:
Multi-cavity magnetrons support discrete phase modes around their circular cavity arrays. The π-mode is preferred for stable, efficient operation and places adjacent cavities 180° out of phase.

Given Data / Assumptions:

• Eight cavities equally spaced.
• π-mode: phase step of π between neighbors.
• Steady periodic boundary condition around the ring.

Concept / Approach:

With N cavities and a phase advance Δφ between adjacent cavities, the total phase shift around the periphery is N * Δφ. In π-mode, Δφ = π.

Step-by-Step Solution:

Verification / Alternative check:

Mode charts for magnetrons label the π-mode with alternating polarity across adjacent cavities and total 8π phase around an 8-cavity ring.

Why Other Options Are Wrong:

4π or 2π correspond to other fractional modes; 16π doubles the correct value; zero would mean all in phase (0-mode), not π-mode.

Common Pitfalls:

Confusing total phase around the ring with the phase relative to a fixed cavity; forgetting to multiply by the number of cavities.

Final Answer:

± 8π radians around the periphery.