Units and conventions

Todo

Consistency between font size of normal text and math text. Not aesthetic when I have text and units side to side.

Todo

General units: MeV etc

Beam parameters

The beam parameters are defined in beam_parameters and stored in the BeamParameters object. We use the same units and conventions as TraceWin.

RMS emittances

In LightWin	In TraceWin	Units	Normalized?
eps_x	\(\epsilon_{xx'}\)	\(\mathrm{\pi.mm.mrad}\)	✅
eps_y	\(\epsilon_{yy'}\)	\(\mathrm{\pi.mm.mrad}\)	✅
eps_z	\(\epsilon_{zn}\)	\(\mathrm{\pi.mm.mrad}\)	✅
eps_zdelta	\(\epsilon_{z\delta}\)	\(\mathrm{\pi.mm.\%}\)	✅
eps_phiw	\(\epsilon_{\phi W}\)	\(\mathrm{\pi.deg.MeV}\)	✅

Warning

In TraceWin’s output files partran.out and tracewin.out, eps_zdelta is expressed in \(\mathrm{\pi.mm.mrad}\), not in \(\mathrm{\pi.mm.\%}\)! The conversion is: \(1\pi\mathrm{.mm.mrad} = 10\pi\mathrm{.mm.\%}\)

Twiss

In LightWin	In TraceWin	Units
alpha_z	\(\alpha_{zz'}\)	\(\mathrm{1}\)
alpha_zdelta	\(\alpha_{z\delta}\)	\(\mathrm{1}\)
alpha_phiw	\(\alpha_{\phi W}\)	\(\mathrm{1}\)
beta_z	\(\beta_{zz'}\)	\(\mathrm{mm/(\pi.mrad)}\)
beta_zdelta	\(\beta_{z\delta}\)	\(\mathrm{mm/(\pi.\%)}\)
beta_phiw	\(\beta_{\phi W}\)	\(\mathrm{deg/(\pi.MeV)}\)
gamma_z	\(\gamma_{zz'}\)	\(\mathrm{mrad/(\pi.mm)}\)
gamma_zdelta	\(\gamma_{z\delta}\)	\(\mathrm{\%/(\pi.mm)}\)
gamma_phiw	\(\gamma_{\phi W}\)	\(\mathrm{MeV/(\pi.deg)}\)

Note that beta_kin, gamma_kin are the Lorentz factors.

Envelopes

In LightWin	In TraceWin	Units
x.envelope_pos		\(\mathrm{mm}\)
x.envelope_energy		\(\mathrm{mrad}\)
y.envelope_pos		\(\mathrm{mm}\)
y.envelope_energy		\(\mathrm{mrad}\)
z.envelope_pos		\(\mathrm{mm}\)
z.envelope_energy		\(\mathrm{mrad}\)
zdelta.envelope_pos		\(\mathrm{mm}\)
zdelta.envelope_energy		\(\mathrm{\%}\)
phiw.envelope_pos		\(\mathrm{deg}\)
phiw.envelope_energy		\(\mathrm{MeV}\)

Note

Envelopes are at \(1\sigma\) in LightWin, while they are plotted at \(6\sigma\) by default in TraceWin.

Note

Envelopes are calculated with un-normalized emittances in the \([z-\delta]\) and \([z-z']\) planes, but they are calculated with normalized emittance in the \([\phi-W]\) plane.

\(\sigma\) beam matrix

We save this matrix in SI units, i.e. in \(\mathrm{m}\) and \(\mathrm{rad}\). When given in the .toml configuration file, it must also be in SI units.