RMS emittance calculation in PlotWin
Posted: Tue 28 Jul 2026 18:48
Dear all,
There is a non conventional formulation P.10 of last release dated March 27 2023.
In the formulation of unnormalized emittance, the second member under the square root,
the covariance term, appears raised to the power 4 instead of 2.
As a reminder, the 2 dimensional RMS emittance derived from standard Courant–Snyder
invariant expressed through second central moments is defined by the square root of the
determinant of the 2×2 covariance matrix of the phase space variables. The determinant
always contains the square of the off diagonal term (covariance).
This typo may be related with the earlier definition of the RMS correlation again in P.10.
RMS position and angle are squared but not RMS correlation. Only the diagonal terms are
squared because they are variances. The off diagonal term is a covariance, and covariances
are not squared when forming the determinant detE=sigmax²sigmax'² - sigmaxx'².
Thanks for feedback.
F.
There is a non conventional formulation P.10 of last release dated March 27 2023.
In the formulation of unnormalized emittance, the second member under the square root,
the covariance term, appears raised to the power 4 instead of 2.
As a reminder, the 2 dimensional RMS emittance derived from standard Courant–Snyder
invariant expressed through second central moments is defined by the square root of the
determinant of the 2×2 covariance matrix of the phase space variables. The determinant
always contains the square of the off diagonal term (covariance).
This typo may be related with the earlier definition of the RMS correlation again in P.10.
RMS position and angle are squared but not RMS correlation. Only the diagonal terms are
squared because they are variances. The off diagonal term is a covariance, and covariances
are not squared when forming the determinant detE=sigmax²sigmax'² - sigmaxx'².
Thanks for feedback.
F.