Rename sigma to lambda where not stddev (#552)

* Rename sigma to lambda where not stddev

This commit replaces (hopefully) all occurrences of sigma<...> as input to
particle distributions with lambda<...> since the parameter describes the
axis intercepts of the phase space ellipse and is only identical to the RMS
extents when there is no correlation between q (position) and p (momentum).

* Apply changes after rebase

Changed PyTorch 15-stage example needed sigma->lambda

docs/source/theory/intro.rst

@@ -74,12 +74,12 @@ The first option is to characterize the distribution via the intersections of th
 .. math::
 
    \begin{align}
-        \sigma_q &= \sqrt{\frac{\epsilon}{\gamma}} \\
-        \sigma_p &= \sqrt{\frac{\epsilon}{\beta}} \\
+        \lambda_q &= \sqrt{\frac{\epsilon}{\gamma}} \\
+        \lambda_p &= \sqrt{\frac{\epsilon}{\beta}} \\
         \mu_{qp} &= \frac{\alpha}{\sqrt{\beta \gamma}}
    \end{align}
 
-The units are :math:`[\sigma_q] = \mathrm{m}`, :math:`[\sigma_p] = \mathrm{rad}`, and :math:`[\mu_{qp}] = 1`.
+The units are :math:`[\lambda_q] = \mathrm{m}`, :math:`[\lambda_p] = \mathrm{rad}`, and :math:`[\mu_{qp}] = 1`.
 To convert between normalized and unnormalized emittance, use the relation :math:`\epsilon_\mathrm{n} = (\beta\gamma)_\mathrm{ref} \cdot \epsilon` which uses the momentum of the reference particle.
 **Attention**: Here, :math:`(\beta\gamma)_\mathrm{ref}` are the Lorentz variables for the reference particle momentum and not the Courant-Snyder parameters.
 

docs/source/usage/parameters.rst

@@ -148,12 +148,12 @@ Initial Beam Distributions
 
     * Parameters that describe the phase space ellipse and position-momentum correlations:
 
-        * ``beam.sigmaX`` (``float``, in meters) phase space ellipse intersection with X
-        * ``beam.sigmaY`` (``float``, in meters) phase space ellipse intersection with Y
-        * ``beam.sigmaT`` (``float``, in meters) phase space ellipse intersection with T, normalized by multiplying with the speed of light *c*
-        * ``beam.sigmaPx`` (``float``, in radians) phase space ellipse intersection with Px
-        * ``beam.sigmaPy`` (``float``, in radians) phase space ellipse intersection with Py
-        * ``beam.sigmaPt`` (``float``, in radians) phase space ellipse intersection with Pt
+        * ``beam.lambdaX`` (``float``, in meters) phase space ellipse intersection with X
+        * ``beam.lambdaY`` (``float``, in meters) phase space ellipse intersection with Y
+        * ``beam.lambdaT`` (``float``, in meters) phase space ellipse intersection with T, normalized by multiplying with the speed of light *c*
+        * ``beam.lambdaPx`` (``float``, in radians) phase space ellipse intersection with Px
+        * ``beam.lambdaPy`` (``float``, in radians) phase space ellipse intersection with Py
+        * ``beam.lambdaPt`` (``float``, in radians) phase space ellipse intersection with Pt
         * ``beam.muxpx`` (``float``, dimensionless, default: ``0``) correlation X-Px
         * ``beam.muypy`` (``float``, dimensionless, default: ``0``) correlation Y-Py
         * ``beam.mutpt`` (``float``, dimensionless, default: ``0``) correlation T-Pt

docs/source/usage/python.rst

@@ -379,33 +379,33 @@ This module provides particle beam distributions that can be used to initialize
 .. py:module:: impactx.distribution
    :synopsis: Particle beam distributions in ImpactX
 
-.. py:class:: impactx.distribution.Gaussian(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.Gaussian(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A 6D Gaussian distribution.
 
-   :param sigx: for zero correlation, these are the related RMS sizes (in meters)
-   :param sigy: see sigx
-   :param sigt: see sigx
-   :param sigpx: RMS momentum
-   :param sigpy: see sigpx
-   :param sigpt: see sigpx
+   :param lambdax: phase space position axis intercept; for zero correlation, these are the related RMS sizes (in meters)
+   :param lambday: see lambdax
+   :param lambdat: see lambdax
+   :param lambdapx: phase space momentum axis intercept; for zero correlation, these are the related normalized RMS momenta (in radians)
+   :param lambdapy: see lambdapx
+   :param lambdapt: see lambdapx
    :param muxpx: correlation length-momentum
    :param muypy: see muxpx
    :param mutpt: see muxpx
 
-.. py:class:: impactx.distribution.Kurth4D(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.Kurth4D(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A 4D Kurth distribution transversely + a uniform distribution
    in t + a Gaussian distribution in pt.
 
-.. py:class:: impactx.distribution.Kurth6D(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.Kurth6D(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A 6D Kurth distribution.
 
    R. Kurth, Quarterly of Applied Mathematics vol. 32, pp. 325-329 (1978)
    C. Mitchell, K. Hwang and R. D. Ryne, IPAC2021, WEPAB248 (2021)
 
-.. py:class:: impactx.distribution.KVdist(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.KVdist(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A K-V distribution transversely + a uniform distribution
    in t + a Gaussian distribution in pt.
@@ -414,18 +414,18 @@ This module provides particle beam distributions that can be used to initialize
 
    This distribution sets all values to zero.
 
-.. py:class:: impactx.distribution.Semigaussian(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.Semigaussian(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A 6D Semi-Gaussian distribution (uniform in position, Gaussian in momentum).
 
-.. py:class:: impactx.distribution.Triangle(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.Triangle(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A triangle distribution for laser-plasma acceleration related applications.
 
    A ramped, triangular current profile with a Gaussian energy spread (possibly correlated).
    The transverse distribution is a 4D waterbag.
 
-.. py:class:: impactx.distribution.Waterbag(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
+.. py:class:: impactx.distribution.Waterbag(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)
 
    A 6D Waterbag distribution.
 

examples/alignment/input_alignment.in

@@ -7,12 +7,12 @@ beam.kin_energy = 2.0e3
 beam.charge = 1.0e-9
 beam.particle = proton
 beam.distribution = waterbag
-beam.sigmaX = 1.16098260008648811e-3
-beam.sigmaY = 1.16098260008648811e-3
-beam.sigmaT = 1.0e-3
-beam.sigmaPx = 0.580491300043e-3
-beam.sigmaPy = 0.580491300043e-3
-beam.sigmaPt = 2.0e-3
+beam.lambdaX = 1.16098260008648811e-3
+beam.lambdaY = 1.16098260008648811e-3
+beam.lambdaT = 1.0e-3
+beam.lambdaPx = 0.580491300043e-3
+beam.lambdaPy = 0.580491300043e-3
+beam.lambdaPt = 2.0e-3
 beam.muxpx = 0.0
 beam.muypy = 0.0
 beam.mutpt = 0.0

examples/alignment/run_alignment.py

@@ -30,12 +30,12 @@
 
 #   particle bunch
 distr = distribution.Waterbag(
-    sigmaX=1.16098260008648811e-3,
-    sigmaY=1.16098260008648811e-3,
-    sigmaT=1.0e-3,
-    sigmaPx=0.580491300043e-3,
-    sigmaPy=0.580491300043e-3,
-    sigmaPt=2.0e-3,
+    lambdaX=1.16098260008648811e-3,
+    lambdaY=1.16098260008648811e-3,
+    lambdaT=1.0e-3,
+    lambdaPx=0.580491300043e-3,
+    lambdaPy=0.580491300043e-3,
+    lambdaPt=2.0e-3,
     muxpx=0.0,
     muypy=0.0,
     mutpt=0.0,

examples/aperture/input_aperture.in

@@ -7,12 +7,12 @@ beam.kin_energy = 250.0
 beam.charge = 1.0e-9
 beam.particle = proton
 beam.distribution = waterbag
-beam.sigmaX = 1.559531175539e-3
-beam.sigmaY = 2.205510139392e-3
-beam.sigmaT = 1.0e-3
-beam.sigmaPx = 6.41218345413e-4
-beam.sigmaPy = 9.06819680526e-4
-beam.sigmaPt = 1.0e-3
+beam.lambdaX = 1.559531175539e-3
+beam.lambdaY = 2.205510139392e-3
+beam.lambdaT = 1.0e-3
+beam.lambdaPx = 6.41218345413e-4
+beam.lambdaPy = 9.06819680526e-4
+beam.lambdaPt = 1.0e-3
 beam.muxpx = 0.0
 beam.muypy = 0.0
 beam.mutpt = 0.0

examples/aperture/run_aperture.py

@@ -38,12 +38,12 @@
 
 #   particle bunch
 distr = distribution.Waterbag(
-    sigmaX=1.559531175539e-3,
-    sigmaY=2.205510139392e-3,
-    sigmaT=1.0e-3,
-    sigmaPx=6.41218345413e-4,
-    sigmaPy=9.06819680526e-4,
-    sigmaPt=1.0e-3,
+    lambdaX=1.559531175539e-3,
+    lambdaY=2.205510139392e-3,
+    lambdaT=1.0e-3,
+    lambdaPx=6.41218345413e-4,
+    lambdaPy=9.06819680526e-4,
+    lambdaPt=1.0e-3,
 )
 sim.add_particles(bunch_charge_C, distr, npart)
 

examples/apochromatic/input_apochromatic.in

@@ -7,12 +7,12 @@ beam.kin_energy = 100.0e3  # 100 GeV nominal energy
 beam.charge = 1.0e-9
 beam.particle = electron
 beam.distribution = gaussian
-beam.sigmaX = 1.288697604e-6
-beam.sigmaY = 1.288697604e-6
-beam.sigmaT = 1.0e-6
-beam.sigmaPx = 3.965223396e-6
-beam.sigmaPy = 3.965223396e-6
-beam.sigmaPt = 0.01  #1% energy spread
+beam.lambdaX = 1.288697604e-6
+beam.lambdaY = 1.288697604e-6
+beam.lambdaT = 1.0e-6
+beam.lambdaPx = 3.965223396e-6
+beam.lambdaPy = 3.965223396e-6
+beam.lambdaPt = 0.01  #1% energy spread
 beam.muxpx = 0.0
 beam.muypy = 0.0
 beam.mutpt = 0.0

examples/apochromatic/input_apochromatic_pl.in

@@ -7,12 +7,12 @@ beam.kin_energy = 100.0e3  # 100 GeV nominal energy
 beam.charge = 1.0e-9
 beam.particle = electron
 beam.distribution = gaussian
-beam.sigmaX = 1.288697604e-6
-beam.sigmaY = 1.288697604e-6
-beam.sigmaT = 1.0e-6
-beam.sigmaPx = 3.965223396e-6
-beam.sigmaPy = 3.965223396e-6
-beam.sigmaPt = 0.01  #1% energy spread
+beam.lambdaX = 1.288697604e-6
+beam.lambdaY = 1.288697604e-6
+beam.lambdaT = 1.0e-6
+beam.lambdaPx = 3.965223396e-6
+beam.lambdaPy = 3.965223396e-6
+beam.lambdaPt = 0.01  #1% energy spread
 beam.muxpx = 0.0
 beam.muypy = 0.0
 beam.mutpt = 0.0

examples/apochromatic/run_apochromatic.py

@@ -31,12 +31,12 @@
 
 #   particle bunch
 distr = distribution.Gaussian(
-    sigmaX=1.288697604e-6,
-    sigmaY=1.288697604e-6,
-    sigmaT=1.0e-6,
-    sigmaPx=3.965223396e-6,
-    sigmaPy=3.965223396e-6,
-    sigmaPt=0.01,  # 1% energy spread
+    lambdaX=1.288697604e-6,
+    lambdaY=1.288697604e-6,
+    lambdaT=1.0e-6,
+    lambdaPx=3.965223396e-6,
+    lambdaPy=3.965223396e-6,
+    lambdaPt=0.01,  # 1% energy spread
     muxpx=0.0,
     muypy=0.0,
     mutpt=0.0,

examples/apochromatic/run_apochromatic_pl.py

@@ -31,12 +31,12 @@
 
 #   particle bunch
 distr = distribution.Gaussian(
-    sigmaX=1.288697604e-6,
-    sigmaY=1.288697604e-6,
-    sigmaT=1.0e-6,
-    sigmaPx=3.965223396e-6,
-    sigmaPy=3.965223396e-6,
-    sigmaPt=0.01,  # 1% energy spread
+    lambdaX=1.288697604e-6,
+    lambdaY=1.288697604e-6,
+    lambdaT=1.0e-6,
+    lambdaPx=3.965223396e-6,
+    lambdaPy=3.965223396e-6,
+    lambdaPt=0.01,  # 1% energy spread
     muxpx=0.0,
     muypy=0.0,
     mutpt=0.0,

examples/cfbend/README.rst

@@ -11,7 +11,7 @@ C. Steier et al, "Status of the Conceptual Design of ALS-U", IPAC2017, WEPAB104,
 
 A 2 GeV electron bunch with normalized transverse rms emittance of 50 pm undergoes a 3.76 deg bend.
 
-In this test, the initial and final values of :math:`\sigma_x`, :math:`\sigma_y`, :math:`\sigma_t`, :math:`\epsilon_x`, :math:`\epsilon_y`, and :math:`\epsilon_t` must agree with nominal values.
+In this test, the initial and final values of :math:`\lambda_x`, :math:`\lambda_y`, :math:`\lambda_t`, :math:`\epsilon_x`, :math:`\epsilon_y`, and :math:`\epsilon_t` must agree with nominal values.
 
 
 Run

examples/cfbend/input_cfbend.in

@@ -7,12 +7,12 @@ beam.kin_energy = 2.0e3  #2 GeV
 beam.charge = 1.0e-9
 beam.particle = electron
 beam.distribution = waterbag
-beam.sigmaX = 5.0e-6  #5 um
-beam.sigmaY = 8.0e-6  #8 um
-beam.sigmaT = 0.0599584916  #200 ps
-beam.sigmaPx = 2.5543422003e-9 #exn = 50 pm-rad
-beam.sigmaPy = 1.5964638752e-9 #eyn = 50 pm-rad
-beam.sigmaPt = 9.0e-4  #approximately dE/E
+beam.lambdaX = 5.0e-6  #5 um
+beam.lambdaY = 8.0e-6  #8 um
+beam.lambdaT = 0.0599584916  #200 ps
+beam.lambdaPx = 2.5543422003e-9 #exn = 50 pm-rad
+beam.lambdaPy = 1.5964638752e-9 #eyn = 50 pm-rad
+beam.lambdaPt = 9.0e-4  #approximately dE/E
 beam.muxpx = 0.0
 beam.muypy = 0.0
 beam.mutpt = 0.0

examples/cfbend/run_cfbend.py

@@ -31,12 +31,12 @@
 
 #   particle bunch
 distr = distribution.Waterbag(
-    sigmaX=5.0e-6,  # 5 um
-    sigmaY=8.0e-6,  # 8 um
-    sigmaT=0.0599584916,  # 200 ps
-    sigmaPx=2.5543422003e-9,  # exn = 50 pm-rad
-    sigmaPy=1.5964638752e-9,  # eyn = 50 pm-rad
-    sigmaPt=9.0e-4,  # approximately dE/E
+    lambdaX=5.0e-6,  # 5 um
+    lambdaY=8.0e-6,  # 8 um
+    lambdaT=0.0599584916,  # 200 ps
+    lambdaPx=2.5543422003e-9,  # exn = 50 pm-rad
+    lambdaPy=1.5964638752e-9,  # eyn = 50 pm-rad
+    lambdaPt=9.0e-4,  # approximately dE/E
     muxpx=0.0,
     muypy=0.0,
     mutpt=0.0,

examples/cfbend/run_cfbend_madx.py

@@ -30,12 +30,12 @@
 
 #   particle bunch
 distr = distribution.Waterbag(
-    sigmaX=2.2951017632e-5,
-    sigmaY=1.3084093142e-5,
-    sigmaT=5.5555553e-8,
-    sigmaPx=1.598353425e-6,
-    sigmaPy=2.803697378e-6,
-    sigmaPt=2.000000000e-6,
+    lambdaX=2.2951017632e-5,
+    lambdaY=1.3084093142e-5,
+    lambdaT=5.5555553e-8,
+    lambdaPx=1.598353425e-6,
+    lambdaPy=2.803697378e-6,
+    lambdaPt=2.000000000e-6,
     muxpx=0.933345606203060,
     muypy=0.933345606203060,
     mutpt=0.999999961419755,

examples/cfchannel/input_cfchannel.in

@@ -7,12 +7,12 @@ beam.kin_energy = 2.0e3
 beam.charge = 1.0e-9
 beam.particle = proton
 beam.distribution = waterbag
-beam.sigmaX = 1.0e-3
-beam.sigmaY = 1.0e-3
-beam.sigmaT = 3.369701494258956e-4
-beam.sigmaPx = 1.0e-3
-beam.sigmaPy = 1.0e-3
-beam.sigmaPt = 2.9676219145931020e-3
+beam.lambdaX = 1.0e-3
+beam.lambdaY = 1.0e-3
+beam.lambdaT = 3.369701494258956e-4
+beam.lambdaPx = 1.0e-3
+beam.lambdaPy = 1.0e-3
+beam.lambdaPt = 2.9676219145931020e-3
 beam.muxpx = 0.0
 beam.muypy = 0.0
 beam.mutpt = 0.0

examples/cfchannel/input_cfchannel_10nC.in

@@ -8,12 +8,12 @@ beam.kin_energy = 2.0e3
 beam.charge = 1.0e-8
 beam.particle = proton
 beam.distribution = waterbag
-beam.sigmaX = 1.2154443728379865788e-3
-beam.sigmaY = 1.2154443728379865788e-3
-beam.sigmaT = 4.0956844276541331005e-4
-beam.sigmaPx = 8.2274435782286157175e-4
-beam.sigmaPy = 8.2274435782286157175e-4
-beam.sigmaPt = 2.4415943602685364584e-3
+beam.lambdaX = 1.2154443728379865788e-3
+beam.lambdaY = 1.2154443728379865788e-3
+beam.lambdaT = 4.0956844276541331005e-4
+beam.lambdaPx = 8.2274435782286157175e-4
+beam.lambdaPy = 8.2274435782286157175e-4
+beam.lambdaPt = 2.4415943602685364584e-3
 
 
 ###############################################################################

examples/cfchannel/run_cfchannel.py

@@ -31,12 +31,12 @@
 
 #   particle bunch
 distr = distribution.Waterbag(
-    sigmaX=1.0e-3,
-    sigmaY=1.0e-3,
-    sigmaT=3.369701494258956e-4,
-    sigmaPx=1.0e-3,
-    sigmaPy=1.0e-3,
-    sigmaPt=2.9676219145931020e-3,
+    lambdaX=1.0e-3,
+    lambdaY=1.0e-3,
+    lambdaT=3.369701494258956e-4,
+    lambdaPx=1.0e-3,
+    lambdaPy=1.0e-3,
+    lambdaPt=2.9676219145931020e-3,
 )
 sim.add_particles(bunch_charge_C, distr, npart)
 

examples/cfchannel/run_cfchannel_10nC.py

@@ -33,12 +33,12 @@
 
 #   particle bunch
 distr = distribution.Waterbag(
-    sigmaX=1.2154443728379865788e-3,
-    sigmaY=1.2154443728379865788e-3,
-    sigmaT=4.0956844276541331005e-4,
-    sigmaPx=8.2274435782286157175e-4,
-    sigmaPy=8.2274435782286157175e-4,
-    sigmaPt=2.4415943602685364584e-3,
+    lambdaX=1.2154443728379865788e-3,
+    lambdaY=1.2154443728379865788e-3,
+    lambdaT=4.0956844276541331005e-4,
+    lambdaPx=8.2274435782286157175e-4,
+    lambdaPy=8.2274435782286157175e-4,
+    lambdaPt=2.4415943602685364584e-3,
 )
 sim.add_particles(bunch_charge_C, distr, npart)