Assertion (A): A magnetron is generally operated in the π-mode. Reason (R): In π-mode, its operating frequency is well separated from adjacent competing modes, enabling stable, efficient operation.

Introduction / Context:
A magnetron is a crossed-field microwave oscillator whose resonant cavities can support multiple modes. Selecting a specific mode with good separation from others ensures stable frequency and high efficiency.

Given Data / Assumptions:

• Resonant cavity chain supports several modes (e.g., 0, π/2, π, etc.).
• Design goal is to suppress mode jumping and enhance efficiency.

Concept / Approach:

The π-mode sets adjacent cavity RF fields 180 degrees apart, creating strong azimuthal RF fields that interact efficiently with the rotating electron spokes. This mode typically has better separation from neighboring modes, reducing the risk of mode competition.

Step-by-Step Solution:

Verification / Alternative check:

Magnetron design literature shows strapping techniques specifically to favor π-mode by shorting alternate cavities, raising unwanted mode frequencies, and ensuring stable π-mode oscillation.

Why Other Options Are Wrong:

• Both correct but not explanatory: R directly explains why π-mode is chosen.
• A correct, R wrong: R is consistent with design practice.
• A wrong but R correct / Both wrong: Contrary to standard magnetron operation where π-mode is preferred.

Common Pitfalls:

Confusing π-mode with other modes used in different devices (e.g., klystrons or BWOs); assuming adjacent modes are harmless to stability.

Final Answer:

Both A and R are correct and R is the correct explanation of A