Magnetron operation – Meaning of π-mode In an N-cavity cavity magnetron, what does the π-mode signify in terms of phase difference between adjacent anode cavities (poles)?

Introduction:
Magnetrons support discrete phase modes around their circular cavity array. The π-mode is the preferred operating mode because it provides strong, stable interaction with the rotating electron spokes and efficient RF extraction at the output coupler. Understanding the per-cavity phase step is fundamental to interpreting magnetron mode behavior.

Given Data / Assumptions:

• Cylindrical magnetron with multiple identical cavities equally spaced.
• Modal description by phase advance Δφ between adjacent cavities.
• Steady, synchronous operation desired in the intended mode.

Concept / Approach:

In a general k-mode, the phase advance between adjacent cavities is Δφ = 2πk/N. For the π-mode, Δφ = π, meaning neighboring cavities are 180 degrees out of phase. This alternation creates transverse electric fields that efficiently bunch electrons into spokes and sustain oscillations at the desired frequency while suppressing some competing modes.

Step-by-Step Solution:

Verification / Alternative check:

Mode charts and phase diagrams of practical magnetrons show the π-mode with alternating field signs across neighbors, confirming the 180° phase relation, whereas 0-mode would have all in phase and different total periphery phase accumulation.

Why Other Options Are Wrong:

“Multiple of π” is vague and includes zero; total periphery phase of π is incorrect because the aggregate phase around N cavities in π-mode sums to ±Nπ; “in phase” is the opposite of π-mode.

Common Pitfalls:

Confusing per-cavity phase advance with total phase around the ring, and mixing π/2-modes with π-mode when interpreting field sketches.

Final Answer:

The phase difference between adjacent anode poles is π radians.