Twiss

The twiss command provides a simple interface to compute the optical functions around an orbit on top of the track command, and the cofind command if the search for closed orbits is requested.

Command synopsis

The twiss command format is summarized in Listing 4, including the default setup of the attributes. Most of these attributes are set to nil by default, meaning that twiss relies on the track and the cofind commands defaults.

Listing 4 Synopsis of the twiss command with default setup.

mtbl, mflw [, eidx] = twiss {
        sequence=sequ,  -- sequence (required)
        beam=nil,       -- beam (or sequence.beam, required)
        range=nil,      -- range of tracking (or sequence.range)
        dir=nil,        -- s-direction of tracking (1 or -1)
        s0=nil,         -- initial s-position offset [m]
        X0=nil,         -- initial coordinates (or damap(s), or beta block(s))
        O0=nil,         -- initial coordinates of reference orbit
        deltap=nil,     -- initial deltap(s)
        chrom=false,    -- compute chromatic functions by finite difference
        coupling=false, -- compute optical functions for non-diagonal modes
        nturn=nil,      -- number of turns to track
        nstep=nil,      -- number of elements to track
        nslice=nil,     -- number of slices (or weights) for each element
        mapdef=true,    -- setup for damap (or list of, true => {})
        method=nil,     -- method or order for integration (1 to 8)
        model=nil,      -- model for integration ('DKD' or 'TKT')
        ptcmodel=nil,   -- use strict PTC thick model (override option)
        implicit=nil,   -- slice implicit elements too (e.g. plots)
        misalign=nil,   -- consider misalignment
        fringe=nil,     -- enable fringe fields (see element.flags.fringe)
        radiate=nil,    -- radiate at slices
        totalpath=nil,  -- variable 't' is the totalpath
        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=nil,    -- save selector (predicate)
        savemap=nil,    -- save damap in the column __map
        atentry=nil,    -- action called when entering an element
        atslice=nil,    -- action called after each element slices
        atexit=nil,     -- action called when exiting an element
        ataper=nil,     -- action called when checking for aperture
        atsave=nil,     -- action called when saving in mtable
        atdebug=fnil,   -- action called when debugging the element maps
        codiff=nil,     -- finite differences step for jacobian
        coiter=nil,     -- maximum number of iterations
        cotol=nil,      -- closed orbit tolerance (i.e.|dX|)
        X1=nil,         -- optional final coordinates translation
        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
}

The twiss command supports the following attributes:

sequence

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

Example: sequence = lhcb1.

beam

The reference beam for the tracking. If no beam is provided, the command looks for a beam attached to the sequence, i.e. the attribute seq.beam . [1] (default: nil).

Example: beam = beam 'lhcbeam' { beam-attributes }.

range

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

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

dir

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

Example: dir = -1.

s0

A number specifying the initial \(s\)-position offset. (default: nil).

Example: s0 = 5000.

X0

A mappable (or a list of mappable) specifying initial coordinates {x,px,y,py, t,pt}, damap, or beta0 block for each tracked object, i.e. particle or damap. The beta0 blocks are converted to damaps, while the coordinates are converted to damaps only if mapdef is specified, but both will use mapdef to setup the damap constructor. A closed orbit will be automatically searched for damaps built from coordinates. Each tracked object may also contain a beam to override the reference beam, and a logical nosave to discard this object from being saved in the mtable. (default: 0).

Example: X0 = { x=1e-3, px=-1e-5 }.

O0

A mappable specifying initial coordinates {x,px,y,py,t,pt} of the reference orbit around which X0 definitions take place. If it has the attribute cofind == true, it will be used as an initial guess to search for the reference closed orbit. (default: 0).

Example: O0 = { x=1e-4, px=-2e-5, y=-2e-4, py=1e-5 }.

deltap

A number (or list of number) specifying the initial \(\delta_p\) to convert (using the beam) and add to the pt of each tracked particle or damap. (default: nil).

Example: s0 = 5000.

chrom

A logical specifying to calculate the chromatic functions by finite different using an extra \(\delta_p=\) 1e-6. (default: false).

Example: chrom = true.

coupling

A logical specifying to calculate the optical functions for coupling terms in the normalized forms. (default: false).

Example: chrom = true.

nturn

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

Example: nturn = 2.

nstep

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

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: nil).

Example: nslice = 5.

mapdef

A logical or a damap specification as defined by the DAmap module to track DA maps instead of particles coordinates. A value of true is equivalent to invoke the damap constructor with {} as argument. A value of false or nil will be internally forced to true for the tracking of the normalized forms. (default: true).

Example: mapdef = { xy=2, pt=5 }.

method

A number specifying the order of integration from 1 to 8, or a string specifying a special method of integration. Odd orders are rounded to the next even order to select the corresponding Yoshida or Boole integration schemes. The special methods are simple (equiv. to DKD order 2), collim (equiv. to MKM order 2), and teapot (Teapot splitting order 2). (default: nil).

Example: method = 'teapot'.

model

A string specifying the integration model, either 'DKD' for Drift-Kick-Drift thin lens integration or 'TKT' for Thick-Kick-Thick thick lens integration. [2] (default: nil)

Example: model = 'DKD'.

ptcmodel

A logical indicating to use strict PTC model. [3] (default: nil)

Example: ptcmodel = true.

implicit

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

Example: implicit = true.

misalign

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

Example: misalign = true.

fringe

A logical indicating that fringe fields must be considered or a number specifying a bit mask to apply to all elements fringe flags defined by the element module. The value true is equivalent to the bit mask , i.e. allow all elements (default) fringe fields. (default: nil).

Example: fringe = false.

radiate

A logical enabling or disabling the radiation or the string specifying the 'average' type of radiation during the closed orbit search. The value true is equivalent to 'average' and the value 'quantum' is converted to 'average'. (default: nil).

Example: radiate = 'average'.

totalpath

A logical indicating to use the totalpath for the fifth variable 't' instead of the local path. (default: nil).

Example: totalpath = 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: false).

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 = "track 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: nil).

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 damap in the column __map of the mtable. (default: nil).

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 . (default: fnil).

Example: atexit = myaction.

ataper

A callable (elm, mflw, lw, islc) invoked at element aperture checks, by default at last slice. The arguments are in order, the current element, the tracked map flow, the length weight of the slice and the slice index. If a particle or a damap hits the aperture, then its status="lost" and it is removed from the list of tracked items. (default: fnil).

Example: ataper = 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.

codiff

A number specifying the finite difference step to approximate the Jacobian when damaps are disabled. If codiff is larger than \(100\times\)cotol, it will be adjusted to cotol \(/100\) and a warning will be emitted. (default: 1e-8).

Example: codiff = 1e-10.

coiter

A number specifying the maximum number of iteration. If this threshold is reached, all the remaining tracked objects are tagged as "unstable". (default: 20).

Example: coiter = 5.

cotol

A number specifying the closed orbit tolerance. If all coordinates update of a particle or a damap are smaller than cotol, then it is tagged as "stable". (default: 1e-8).

Example: cotol = 1e-6.

X1

A mappable specifying the coordinates {x,px,y,py,t,pt} to subtract to the final coordinates of the particles or the damaps. (default: 0).

Example: X1 = { t=100, pt=10 }.

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 :track and to their underlying maps. (default: nil).

Example: usrdef = { myvar=somevalue }.

mflow

A mflow containing the current state of a track 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 twiss command returns the following objects in this order:

mtbl

A mtable corresponding to the augmented TFS table of the track command with the twiss command columns.

mflw

A mflow corresponding to the augmented map flow of the track command with the twiss command data.

eidx

An optional number corresponding to the last tracked element index in the sequence when nstep was specified and stopped the command before the end of the range.

Twiss mtable

The twiss command returns a mtable where the information described hereafter is the default list of fields written to the TFS files. [4]

The header of the mtable contains the fields in the default order: [5]

name

The name of the command that created the mtable, e.g. "track".

type

The type of the mtable, i.e. "track".

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.

deltap

The value of the command attribute deltap.

lost

The number of lost particle(s) or damap(s).

chrom

The value of the command attribute chrom.

coupling

The value of the command attribute coupling.

length

The \(s\)-length of the tracked design orbit.

q1

The tunes of mode 1.

q2

The tunes of mode 2.

q3

The tunes of mode 3.

alfap

The momentum compaction factor \(\alpha_p\).

etap

The phase slip factor \(\eta_p\).

gammatr

The energy gamma transition \(\gamma_{\text{tr}}\).

synch_1

The first synchroton radiation integral.

synch_2

The second synchroton radiation integral.

synch_3

The third synchroton radiation integral.

synch_4

The fourth synchroton radiation integral.

synch_5

The fifth synchroton radiation integral.

synch_6

The sixth synchroton radiation integral.

synch_8

The eighth synchroton radiation integral.

range

The value of the command attribute range. [6]

__seq

The sequence from the command attribute sequence. [7]

The core of the mtable contains the columns in the default order: [8]

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.

id

The index of the particle or damap as provided in X0.

x

The local coordinate \(x\) at the \(s\)-position .

px

The local coordinate \(p_x\) at the \(s\)-position.

y

The local coordinate \(y\) at the \(s\)-position.

py

The local coordinate \(p_y\) at the \(s\)-position.

t

The local coordinate \(t\) at the \(s\)-position.

pt

The local coordinate \(p_t\) at the \(s\)-position.

slc

The slice index 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.

status

The status of the particle or damap.

alfa11

The optical function \(\alpha\) of mode 1 at the \(s\)-position.

beta11

The optical function \(\beta\) of mode 1 at the \(s\)-position.

gama11

The optical function \(\gamma\) of mode 1 at the \(s\)-position.

mu1

The phase advance \(\mu\) of mode 1 at the \(s\)-position.

dx

The dispersion function of \(x\) at the \(s\)-position.

dpx

The dispersion function of \(p_x\) at the \(s\)-position.

alfa22

The optical function \(\alpha\) of mode 2 at the \(s\)-position.

beta22

The optical function \(\beta\) of mode 2 at the \(s\)-position.

gama22

The optical function \(\gamma\) of mode 2 at the \(s\)-position.

mu2

The phase advance \(\mu\) of mode 2 at the \(s\)-position.

dy

The dispersion function of \(y\) at the \(s\)-position.

dpy

The dispersion function of \(p_y\) at the \(s\)-position.

alfa33

The optical function \(\alpha\) of mode 3 at the \(s\)-position.

beta33

The optical function \(\beta\) of mode 3 at the \(s\)-position.

gama33

The optical function \(\gamma\) of mode 3 at the \(s\)-position.

mu3

The phase advance \(\mu\) of mode 3 at the \(s\)-position.

__map

The damap at the \(s\)-position. [7]

The chrom attribute will add the following fields to the mtable header:

dq1

The chromatic derivative of tunes of mode 1, i.e. chromaticities.

dq2

The chromatic derivative of tunes of mode 2, i.e. chromaticities.

dq3

The chromatic derivative of tunes of mode 3, i.e. chromaticities.

The chrom attribute will add the following columns to the mtable:

dmu1

The chromatic derivative of the phase advance of mode 1 at the \(s\)-position.

ddx

The chromatic derivative of the dispersion function of \(x\) at the \(s\)-position.

ddpx

The chromatic derivative of the dispersion function of \(p_x\) at the \(s\)-position.

wx

The chromatic amplitude function of mode 1 at the \(s\)-position.

phix

The chromatic phase function of mode 1 at the \(s\)-position.

dmu2

The chromatic derivative of the phase advance of mode 2 at the \(s\)-position.

ddy

The chromatic derivative of the dispersion function of \(y\) at the \(s\)-position.

ddpy

The chromatic derivative of the dispersion function of \(p_y\) at the \(s\)-position.

wy

The chromatic amplitude function of mode 2 at the \(s\)-position.

phiy

The chromatic phase function of mode 2 at the \(s\)-position.

The coupling attribute will add the following columns to the mtable:

alfa12

The optical function \(\alpha\) of coupling mode 1-2 at the \(s\)-position.

beta12

The optical function \(\beta\) of coupling mode 1-2 at the \(s\)-position.

gama12

The optical function \(\gamma\) of coupling mode 1-2 at the \(s\)-position.

alfa13

The optical function \(\alpha\) of coupling mode 1-3 at the \(s\)-position.

beta13

The optical function \(\beta\) of coupling mode 1-3 at the \(s\)-position.

gama13

The optical function \(\gamma\) of coupling mode 1-3 at the \(s\)-position.

alfa21

The optical function \(\alpha\) of coupling mode 2-1 at the \(s\)-position.

beta21

The optical function \(\beta\) of coupling mode 2-1 at the \(s\)-position.

gama21

The optical function \(\gamma\) of coupling mode 2-1 at the \(s\)-position.

alfa23

The optical function \(\alpha\) of coupling mode 2-3 at the \(s\)-position.

beta23

The optical function \(\beta\) of coupling mode 2-3 at the \(s\)-position.

gama23

The optical function \(\gamma\) of coupling mode 2-3 at the \(s\)-position.

alfa31

The optical function \(\alpha\) of coupling mode 3-1 at the \(s\)-position.

beta31

The optical function \(\beta\) of coupling mode 3-1 at the \(s\)-position.

gama31

The optical function \(\gamma\) of coupling mode 3-1 at the \(s\)-position.

alfa32

The optical function \(\alpha\) of coupling mode 3-2 at the \(s\)-position.

beta32

The optical function \(\beta\) of coupling mode 3-2 at the \(s\)-position.

gama32

The optical function \(\gamma\) of coupling mode 3-2 at the \(s\)-position.

Tracking linear normal form

TODO

Examples

TODO

Footnotes

[1]

Initial coordinates X0 may override it by providing a beam per particle or damap.

[2]

The TKT scheme (Yoshida) is automatically converted to the MKM scheme (Boole) when appropriate.

[3]

In all cases, MAD-NG uses PTC setup time=true, exact=true.

[4]

The output of mtable in TFS files can be fully customized by the user.

[5]

The fields from name to lost are set by the track command

[6]

This field is not saved in the TFS table by default.

[7] (1,2)

Fields and columns starting with two underscores are protected data and never saved to TFS files.

[8]

The column from name to status are set by the track command.