Clarification about Θ′ definition and unit in X–Θ′ plot (TraceWin v2.25.1.8)

[Jiyoung Choi]

Hello Didier,

I would like to confirm the current definition and unit of Θ′ in the X–Θ′ phase-space plot in TraceWin (v2.25.1.8).

1. Expected formula
Based on numerical comparison with exported phase-space data, the TraceWin result seems to correspond to:
Θ′ = (x y′ − y x′) / r, where r = √(x² + y²)
I plotted this using the exported columns (x(mm), x'(mrad), y(mm), y'(mrad)) and obtained a perfectly identical shape to TraceWin’s Θ′ plot.
Could you please confirm whether this is indeed the current implemented definition of Θ′?

2. Unit question
If the above formula is correct, then the unit should be **mrad**, not **mrad/mm**, since x′ and y′ are given in mrad and the division by r (in mm) cancels one mm.
However, the TraceWin plot label currently shows “Θ′ (mrad/mm)”.

3. Plot scaling
The displayed range in TraceWin (e.g., Θ′ ≈ ±0.006) matches the mrad → rad conversion scale, suggesting that the internal computation might be done in radians, even though the label uses mrad/mm.

I would appreciate clarification on:
- The exact formula used internally for Θ′
- The correct intended unit
- Whether the current plot label might need an update

Thank you very much for your help

Best regards,
Jiyoung Choi

[Didier]

Dear Jiyoung Choi,

I completely agree with your remarks and indeed, I use this formula. So that's fixed, you can upgrade your software.

Regards,

Didier