Output coil placement along a repeating field pattern

Where along the tube should the output coil sit to get the strongest signal?

ε = N \pi f \cdot \frac{Φ}{2}\left(1 + \cos\left(\frac{2\pi x}{λ}\right)\right)

Method

1. Find how far the coil position is around one period of the pattern: 2π × (position ÷ period).
2. Take the cosine of that and add 1, so the result runs from 0 (a node) to 2 (an antinode) rather than from −1 to 1.
3. Multiply by half the peak flux amplitude — this is the flux amplitude the pattern presents at this specific position, before it starts pulsing in time.
4. Multiply by π times the pulse frequency: for a pattern that pulses smoothly between zero and full strength at frequency f, this is the fastest rate its amplitude changes.
5. Multiply by the turns count. The result is the coil's peak output voltage at this position.

Assumptions

• The field pattern's spatial shape (high/low intensity along the tube) is fixed, and the whole pattern rises and falls together in time at the pulse frequency — the two effects are modelled as separable, position sets the local amplitude and time sets how fast that amplitude changes.
• The pulsing is smooth (sinusoidal) rather than a sharp square pulse. A hard-edged pulse train reaches a much higher instantaneous dV/dt at its edges than this figure — this is the gentlest case, not the worst one.
• This is one generic model standing in for all five patterns Meyer's figure shows (vertical, horizontal and rotational deflection, balancing fields, compressional waves). The figure gives no equation distinguishing them, so this does not attempt to reproduce which one produces a stronger or weaker field at a given position — only the general fact that position along a periodic pattern matters at all.
• No coupling loss, coil self-resonance or loading is modelled — see the mutual inductance calculation for how much of this a real, imperfectly-aligned pickup coil actually catches.