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Trapezoidal Cavity – Fundamental Mode

Resonant cavity with trapezoidal cross‑section.

Approximate fundamental mode | f0 ≈ ...

Electric Field (E) – Cross‑section (z=0)

Ey component (vertical).

Magnetic Field (H) – Cross‑section (z=0)

Hx and Hz components.

E‑field in x‑z plane (y=0)

Ey along x and z.

H‑field in x‑z plane (y=0)

Arrows: (Hx, Hz).

📐 Approximate Field Model

Ey ∝ (1 - (x/(w(z)/2))²) * sin(πz/d) where w(z) = w1 + (w2-w1)*(z/d)
Hx ∝ ∂Ey/∂z, Hz ∝ -∂Ey/∂x

📝 Description & Applications

Trapezoidal cavities are used in special filters and particle accelerators where varying cross‑section is needed.

Advantages: Can provide mode suppression, mechanical stability.
Disadvantages: Complex analysis.

💡 Interview Questions

How does the field distribution change when the top width is reduced?
What are the challenges in designing non‑rectangular cavities?