Emittance Sources¶
Emittance sources provide 4 ways of sampling particles’ position (X and Y) and momentum direction (X’ and Y’) on a plane. Specify source type as:
s:So/MySource/Type = "emittance"
To sample particle position and momentum direction from “Gaussian” (bivariate 2D gaussian) per axis (see the Emittance_Gaussian.txt example):
s:So/MySource/Distribution = "BiGaussian" # distribution name
d:So/MySource/SigmaX = 0.2 mm # std of x positions
u:So/MySource/SigmaXprime = 0.032 # std of x’, note that it’s unitless. 1 equals to 1.0 rad.
u:So/MySource/CorrelationX = -0.9411 # correlation of x and x’
d:So/MySource/SigmaY = 0.2 mm # std of y positions
u:So/MySource/SigmaYPrime = 0.032 # std of y’
u:So/MySource/CorrelationY = 0.9411 # correlation of y and y’
Alternative distributions are TWISS Gaussian, TWISS Kapchinskij-Vladimirskij (KV), and TWISS Waterbag (based on the Courant-Snyder invariant ellipse in the following figure for X axis only):
Additional parameters specify the TWISS alpha, beta and gamma as shown in the following from Emittance_Twiss.txt:
s:So/MySource/Distribution = "twiss_gaussian" # "twiss_gaussian", "twiss_kv" or "twiss_waterbag"
u:So/MySource/AlphaX = 0.2
d:So/MySource/BetaX = 600.0 mm
d:So/MySource/EmittanceX = 0.01 mm # we don’t multiply pi intrinsically.
u:So/MySource/AlphaY = 2.5
d:So/MySource/BetaY = 1400.0 mm
d:So/MySource/EmittanceY = 0.02 mm
# below for twiss gaussian option only
#0.9 means that 90 % particles will be included in ellipse circle
u:So/MySource/ParticleFractionX = 0.90
u:So/MySource/ParticleFractionY = 0.90
The energies and species of the emitted particles can be specified using the same parameters available to the Beam Sources.
The following images based on the Emittance_Twiss.txt example show how particle position and momentum directions are sampled and the shape of the beam spots (purple). The blue solid lines in X (red dots) and Y (green dots) represent the Courant-Snyder invariant ellipse. For example, 90% of particles are sampled from the given emittance ellipse in (a).
