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Minor tweaks.
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DavidSagan committed Jan 15, 2025
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Expand Up @@ -76,7 +76,7 @@ Most elements in a tracking branch have an "`entrance`" and an "`exit`" coordina
illustrated in the above figure.
These coordinate frames are attached to the element and are part of the `element body coordinates`.
`Fiducial` elements ([xxx](#s:fiducial)) are an excption.
`Fiducial` elements only have a single coordinate frame that is tied to global coordinates
`Fiducial` elements only have a single coordinate frame that is tied to floor coordinates
and construction of the branch coordinate system starts at this coordinate system.
See [xxx](#s:fiducial) for more details.
Note that `Girder` elements ([xxx](#s:girder)) also only have a single coordinate frame but they
Expand Down Expand Up @@ -109,8 +109,9 @@ will have a discontinuity.
A) The branch coordinates are constructed by
connecting the `downstream` reference frame of one element with the `upstream` reference frame
of the next element in the branch. Coordinates shown are for the mating of element `A` to element
`B`. B) Example with drift element `dft1` followed by a bend `bnd1`. Both elements are
unreversed. C) Similar to (B) but in this case element `bnd1` is reversed. D) Similar to (C) but
`B`. B) Example with drift element `dft1` followed by a bend `bnd1`. Both elements have normal
(unreversed) orientation.
C) Similar to (B) but in this case element `bnd1` is reversed. D) Similar to (C) but
in this case a reflection patch `P` has been added in between `dft1` and `bnd1`.
In (B), (C), and (D) the {math}`(x,z)` coordinates are drawn at the `entrance` end of the elements.
The {math}`y` coordinate is always out of the page for this example.
Expand Down Expand Up @@ -160,15 +161,15 @@ with the downstream frame of element `A` mated to the upstream frame of element
The {math}`(x,z)` coordinates are drawn at the entrance end of the elements and {math}`z` will
always point towards the element's exit end.
{numref}`f:patch.between`B shows a line
with an unreversed drift named `dft1` connected to an unreversed bend named
with an normal (unreversed) orientation drift named `dft1` connected to a normal (unreversed) bend named
`bnd1`. {numref}`f:patch.between`C shows the same line but with `bnd1` reversed.
This gives an unphysical situation since a
particle traveling through `dft1` will "fall off" when it gets to the drift's end.
{numref}`f:patch.between`D shows the same line as in {numref}`f:patch.between`C with the addition
of a [`reflection patch`](#s:reflect.patch) `P` between `dft1` and `bnd1` to give a plausible geometry.
In this case, the patch rotates the coordinate system around the {math}`y`-axis by 180{math}`^o`
(in this example leaving the {math}`y`-axis invariant). This illustrates why
a reflection patch is always needed between reversed and unreversed elements.
a reflection patch is always needed between normal and reversed elements.

Notes:
- Irrespective of whether elements are reversed or not, the branch {math}`(x,y,z)` coordinate system
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