Survey

The survey command provides a simple interface to the geometric tracking code. [1] The geometric tracking can be used to place the elements of a sequence in the global reference system in Fig. 14.

Listing 1 Synopsis of the survey command with default setup.

mtbl, mflw [, eidx] = survey {
    sequence=sequ,  -- sequence (required)
    range=nil,      -- range of tracking (or sequence.range)
    dir=1,          -- s-direction of tracking (1 or -1)
    s0=0,           -- initial s-position offset [m]
    X0=0,           -- initial coordinates x, y, z [m]
    A0=0,           -- initial angles theta, phi, psi [rad] or matrix W0
    nturn=1,        -- number of turns to track
    nstep=-1,       -- number of elements to track
    nslice=1,       -- number of slices (or weights) for each element
    implicit=false, -- slice implicit elements too (e.g. plots)
    misalign=false, -- consider misalignment
    save=true,      -- create mtable and save results
    title=nil,      -- title of mtable (default seq.name)
    observe=0,      -- save only in observed elements (every n turns)
    savesel=fnil,   -- save selector (predicate)
    savemap=false,  -- save the orientation matrix W in the column __map
    atentry=fnil,   -- action called when entering an element
    atslice=fnil,   -- action called after each element slices
    atexit=fnil,    -- action called when exiting an element
    atsave=fnil,    -- action called when saving in mtable
    atdebug=fnil,   -- action called when debugging the element maps
    info=nil,       -- information level (output on terminal)
    debug=nil,      -- debug information level (output on terminal)
    usrdef=nil,     -- user defined data attached to the mflow
    mflow=nil,      -- mflow, exclusive with other attributes except nstep
}

Command synopsis

The survey command format is summarized in Listing 1, including the default setup of the attributes. The survey command supports the following attributes:

sequence

The sequence to survey. (no default, required).

Example: sequence = lhcb1.

range

A range specifying the span of the sequence survey. If no range is provided, the command looks for a range attached to the sequence, i.e. the attribute . (default: nil).

Example: range = "S.DS.L8.B1/E.DS.R8.B1".

dir

The \(s\)-direction of the tracking: 1 forward, -1 backward. (default: 1).

Example: dir = -1.

s0

A number specifying the initial \(s\)-position offset. (default: 0 [m]).

Example: s0 = 5000.

X0

A mappable specifying the initial coordinates {x,y,z}. (default: 0 [m]).

Example: X0 = { x=100, y=-50 }

A0

A mappable specifying the initial angles theta, phi and psi or an orientation matrix W0. [2] (default: 0 [rad]).

Example: A0 = { theta=deg2rad(30) }

nturn

A number specifying the number of turn to track. (default: 1).

Example: nturn = 2.

nstep

A number specifying the number of element to track. A negative value will track all elements. (default: -1).

Example: nstep = 1.

nslice

A number specifying the number of slices or an iterable of increasing relative positions or a callable (elm, mflw, lw) returning one of the two previous kind of positions to track in the elements. The arguments of the callable are in order, the current element, the tracked map flow, and the length weight of the step. This attribute can be locally overridden by the element. (default: 1).

Example: nslice = 5.

implicit

A logical indicating that implicit elements must be sliced too, e.g. for smooth plotting. (default: false).

Example: implicit = true.

misalign

A logical indicating that misalignment must be considered. (default: false).

Example: implicit = true.

save

A logical specifying to create a mtable and record tracking information at the observation points. The save attribute can also be a string specifying saving positions in the observed elements: "atentry", "atslice", "atexit" (i.e. true), "atbound" (i.e. entry and exit), "atbody" (i.e. slices and exit) and "atall". (default: true).

Example: save = false.

title

A string specifying the title of the mtable. If no title is provided, the command looks for the name of the sequence, i.e. the attribute seq.name. (default: nil).

Example: title = "Survey around IP5".

observe

A number specifying the observation points to consider for recording the tracking information. A zero value will consider all elements, while a positive value will consider selected elements only, checked with method :is_observed, every observe \(>0\) turns. (default: 0).

Example: observe = 1.

savesel

A callable (elm, mflw, lw, islc) acting as a predicate on selected elements for observation, i.e. the element is discarded if the predicate returns false. The arguments are in order, the current element, the tracked map flow, the length weight of the slice and the slice index. (default: fnil)

Example: savesel = \e -> mylist[e.name] ~= nil.

savemap

A logical indicating to save the orientation matrix W in the column __map of the mtable. (default: false).

Example: savemap = true.

atentry

A callable (elm, mflw, 0, -1) invoked at element entry. The arguments are in order, the current element, the tracked map flow, zero length and the slice index -1. (default: fnil).

Example: atentry = myaction.

atslice

A callable (elm, mflw, lw, islc) invoked at element slice. The arguments are in order, the current element, the tracked map flow, the length weight of the slice and the slice index. (default: fnil).

Example: atslice = myaction.

atexit

A callable (elm, mflw, 0, -2) invoked at element exit. The arguments are in order, the current element, the tracked map flow, zero length and the slice index -2. (default: fnil).

Example: atexit = myaction.

atsave

A callable (elm, mflw, lw, islc) invoked at element saving steps, by default at exit. The arguments are in order, the current element, the tracked map flow, the length weight of the slice and the slice index. (default: fnil).

Example: atsave = myaction.

atdebug

A callable (elm, mflw, lw, [msg], [...]) invoked at the entry and exit of element maps during the integration steps, i.e. within the slices. The arguments are in order, the current element, the tracked map flow, the length weight of the integration step and a string specifying a debugging message, e.g. "map_name:0" for entry and ":1" for exit. If the level debug \(\geq 4\) and atdebug is not specified, the default function mdump is used. In some cases, extra arguments could be passed to the method. (default: fnil).

Example: atdebug = myaction .

info

A number specifying the information level to control the verbosity of the output on the console. (default: nil).

Example: info = 2.

debug

A number specifying the debug level to perform extra assertions and to control the verbosity of the output on the console. (default: nil).

Example: debug = 2.

usrdef

Any user defined data that will be attached to the tracked map flow, which is internally passed to the elements method :survey and to their underlying maps. (default: nil).

Example: usrdef = { myvar=somevalue }.

mflow

A mflow containing the current state of a survey command. If a map flow is provided, all attributes are discarded except nstep, info and debug, as the command was already set up upon its creation. (default: nil).

Example: mflow = mflow0.

The survey command returns the following objects in this order:

mtbl: A mtable corresponding to the TFS table of the survey command.
mflw: A mflow corresponding to the map flow of the survey command.
eidx: An optional number corresponding to the last surveyed element index in the sequence when nstep was specified and stopped the command before the end of the range.

Survey mtable

The survey command returns a mtable where the information described hereafter is the default list of fields written to the TFS files. [3]

The header of the mtable contains the fields in the default order:

name: The name of the command that created the mtable, e.g. "survey".
type: The type of the mtable, i.e. "survey".
title: The value of the command attribute title.
origin: The origin of the application that created the mtable, e.g. "MAD 1.0.0 OSX 64".
date: The date of the creation of the mtable, e.g. "27/05/20".
time: The time of the creation of the mtable, e.g. "19:18:36".
refcol: The reference column for the mtable dictionnary, e.g. "name".
direction: The value of the command attribute dir.
observe: The value of the command attribute observe.
implicit: The value of the command attribute implicit.
misalign: The value of the command attribute misalign.
range: The value of the command attribute range. [4]
__seq: The sequence from the command attribute sequence. [5]

The core of the mtable contains the columns in the default order:

name: The name of the element.
kind: The kind of the element.
s: The \(s\)-position at the end of the element slice.
l: The length from the start of the element to the end of the element slice.
angle: The angle from the start of the element to the end of the element slice.
tilt: The tilt of the element.
x: The global coordinate \(x\) at the \(s\)-position.
y: The global coordinate \(y\) at the \(s\)-position.
z: The global coordinate \(z\) at the \(s\)-position.
theta: The global angle \(\theta\) at the \(s\)-position.
phi: The global angle \(\phi\) at the \(s\)-position.
psi: The global angle \(\psi\) at the \(s\)-position.
slc: The slice number ranging from -2 to nslice.
turn: The turn number.
tdir: The \(t\)-direction of the tracking in the element.
eidx: The index of the element in the sequence.
__map: The orientation matrix at the \(s\)-position. [5]

Geometrical tracking

Fig. 8 presents the scheme of the geometrical tracking through an element sliced with nslice=3. The actions atentry (index -1), atslice (indexes 0..3), and atexit (index -2) are reversed between the forward tracking (dir=1 with increasing \(s\)-position) and the backward tracking (dir=-1 with decreasing \(s\)-position). By default, the action atsave is attached to the exit slice, and hence it is also reversed in the backward tracking.

_images/dyna-trck-slice-crop.png — Fig. 8 Geometrical tracking with slices.

Slicing

The slicing can take three different forms:

A number of the form nslice=\(N\) that specifies the number of slices with indexes 0..N. This defines a uniform slicing with slice length \(l_{\text{slice}} = l_{\text{elem}}/N\).

An iterable of the form nslice={lw_1,lw_2,..,lw_N} with \(\sum_i lw_i=1\) that specifies the fraction of length of each slice with indexes 0..N where \(N=\)#nslice. This defines a non-uniform slicing with a slice length of \(l_i = lw_i\times l_{\text{elem}}\).

A callable (elm, mflw, lw) returning one of the two previous forms of slicing. The arguments are in order, the current element, the tracked map flow, and the length weight of the step, which should allow to return a user-defined element-specific slicing.

The surrounding P and P\(^{-1}\) maps represent the patches applied around the body of the element to change the frames, after the atentry and before the atexit actions:

The misalignment of the element to move from the global frame to the element frame if the command attribute misalign is set to true.

The tilt of the element to move from the element frame to the titled frame if the element attribute tilt is non-zero. The atslice actions take place in this frame.

These patches do not change the global frame per se, but they may affect the way that other components change the global frame, e.g. the tilt combined with the angle of a bending element.

Sub-elements

The survey command takes sub-elements into account, mainly for compatibility with the track command. In this case, the slicing specification is taken between sub-elements, e.g. 3 slices with 2 sub-elements gives a final count of 9 slices. It is possible to adjust the number of slices between sub-elements with the third form of slicing specifier, i.e. by using a callable where the length weight argument is between the current (or the end of the element) and the last sub-elements (or the start of the element).

Examples

Footnotes