ParameterSummaryFunctions#

Summaries of lattice parameters

Functions

`RadIntegrals()`	calcuate the contribution to the radiation integrals of a Wiggler.
`atsummary()`	Print out various parameters of the current AT lattice
`atx()`	Computes and displays global information
`ringpara()`	Print out various parameters of the current AT lattice
`twissline()`	calculates linear optics functions for an UNCOUPLED transport line
`twissring()`	calculates linear optics functions for an UNCOUPLED ring

RadIntegrals()#: calcuate the contribution to the radiation integrals of a Wiggler.

Wigidx is index of insertion devices

A.Mash’al, Iranian Light Source Facility, 2018-07-30

atsummary()#: Print out various parameters of the current AT lattice

atsummary() Print parameters of the global variable THERING

atsummary(ring) Print parameters of RING. RING may be 4D or 6D

atsummary(…,’dp’,dp) Specify off-momentum. For off-momentum lattices,

the equilibrium emittance and energy spread will not be computed

because the quadrupole contribution is missing.

atsummary(…,’dct’,dct) Specify the path lengthening

atsummary(…,’df’,df) Specify the RF frequency deviation

ringparams=atsummary(…) Return the results in a structure instead of

printing them

ringparams=atsummary(…,’display’) Restore the printout of parameters

The parameters that come after the Synchrotron Integrals are

parameters that depend on the Integrals themselves. The equations to

calculate them were taken from [1].

[1] Alexander Wu Chao and Maury Tigner, Handbook of Accelerator Physics

and Engineering (World Scientific, Singapore, 1998), pp. 183-187. (or

187-190 in ed. 2)

See also atx(), ringpara()

atx(ring)#: Computes and displays global information

beamdata=atx(ring) Computes linear optics, equilibrium emittances and damping times

RING: Ring description. If RING is 6D, it is used in OHMIENVELOPE and

a 4D copy may be used for linear optics computation.

If RING is 4D, a 6D copy with default options is used for

OHMIENVELOPE

beamdata=atx(ring,dp,refpts)

beamdata=atx(ring,refpts)

Specify the points of interest (Default: 1:length(RING)+1)

beamdata=atx(ring,dp,…)

beamdata=atx(ring,…,’dp’,dpp)

Specify the momentum deviation (Default: 0)

beamdata=atx(ring,…,’dct’,dct)

Specify the path lengthening

beamdata=atx(ring,…,’df’,df)

Specify the RF frequency deviation from nominal

beamdata=atx(ring,…,’method’,opticsfun)

Specify the method for linear optics. Default: @atlinopt6

Allowed values are @atlinopt2, @atlinopt4, @atlinopt6

beamdata=atx(ring,…,’6d’)

By default, linear optics is computed with the 4d version of the lattice.

If method is @atlinopt6 (the default), when specifying ‘6d’ the optics

is computed from the 6d version of the lattice.

ELEMDATA is a MATLAB structure array as long as the numver of refpoints

with fields:

From atlinopt:

ElemIndex - ordinal position in the RING

SPos - longitudinal position [m]

ClosedOrbit - closed orbit column vector with

components x, px, y, py (momentums, NOT angles)

Dispersion - dispersion orbit position vector with

components eta_x, eta_prime_x, eta_y, eta_prime_y

calculated with respect to the closed orbit with

momentum deviation DP

M - 4x4 transfer matrix M from the beginning of RING

to the entrance of the element for specified DP [2]

mu - [ mux, muy] horizontal and vertical betatron phase

beta - [betax, betay] vector

alpha - [alphax, alphay] vector

Other fields depend on the selected optics method, @atlinopt4 or

@atlinopt6

From ohmienvelope:

beam66 - 6x6 equilibrium beam matrix

emit66 - 6x6 emittance projections on x-x’, y-y’ and energy spread

beam44 - intersection of beam66 with dpp=0 (monochromatic beam)

emit44 - emittances of the projections of beam44 on x and y

modemit - emittance of the 3 eigenmodes

[elemdata,ringdata]=atx(…) Returns also a structure RINGDATA

with fields:

ll - Circumference

alpha - momentum compaction factor

fractunes

fulltunes

nuh - Tunes

nuv

chromaticity

dampingtime

espread - Energy spread

blength - Bunch length

energy

fs - synchrotron frequency

eloss - energy loss/turn

synchrophase- synchronous phase

modemittance- Eigen emittances

momcompact - momentum compaction factor

The following options are kept for backwards compatibility but are

deprecated:

beamdata=atx(ring,dpp,refpts,radring,radindex,cavindex)

Radiation must be turned on for emittance computation. This is done by

default using the ATRADON function with default arguments. If this is not

desired, this syntax allows to explicitly enter the radiative lattice

beamdata=atx(ring,dpp,refpts,radfunction)

RADFUNCTION is substituted to ATRADON to provide the radiative lattice

and indices, in the form:

[RADRING,RADINDEX,CAVINDEX]=RADFUNCTION(RING)

See also atlinopt(), atradon(), ohmienvelope(), ringpara(), atsummary()

ringpara()#: Print out various parameters of the current AT lattice

ringpara() Print parameters of the global variable THERING

ringpara(ring) Print parameters of RING. RING may be 4D or 6D

ringpara(ring,u0,…) Supply the total radiation loss in MeV

ringpara(…,’dp’,dp) Specify off-momentum For off-momentum lattices,

the equilibrium emittance and energy spread will not be computed

because the quadrupole contribution is missing.

ringpara(…,’dct’,dct) Specify the path lengthening

ringpara(…,’df’,df) Specify the RF frequency deviation

ringparams=ringpara(…) Return the results in a structure instead of

printing them

See also atx(), atsummary()

twissline(lattice, dp, twissdatain)#: calculates linear optics functions for an UNCOUPLED transport line

twissdata = twissline(lattice,dp,twissdatain) propagates twiss

parameters and closed orbit coordinates from the LINE entrance

given by TWISSDATAIN assuming constant energy deviation DP.

TWISSDATAIN is a 1-by-1 structure with the same field names

as the return argument. (See below)

!!! IMPORTANT: Since twissline does not search for closed orbit

its value at the entrance must be supplied in the

ClosedOrbit field of TWISSDATAIN structure.

twissdata = twissline(lattice,dp,twissdatain,refpts) calculates Twiss parameters

and closed orbit coordinates at specified reference points REFPTS

Note: REFPTS is an array of increasing indexes that

select elements from range 1 to length(LATTICE)+1.

See further explanation of REFPTS in the ‘help’ for FINDSPOS

twissdata = twissline(…,’chrom’, ddp) also calculates

linear dispersion. Dispersion is returned as one

of the fields in TwissData.

!!! Last argument DDP is a momentum deviation on top

of DP (the second argument) used to calculate and normalize

dispersion. If not supplied

the default value of 1e-8 is used.

TwisData is a 1-by-REFPTS (1-by-1 if no REFPTS specified) structure array with fields:

ElemIndex - integer (element number) in the LINE

SPos - longitudinal position [m]

ClosedOrbit - closed orbit column vector with

components x, px, y, py (momentums, NOT angles)

Dispersion - dispersion orbit position 4-by-1 vector with

components [eta_x, eta_prime_x, eta_y, eta_prime_y]’

calculated with respect to the closed orbit with

momentum deviation DP

M44 - 4x4 transfer matrix M from the beginning of LINE

to the entrance of the element for specified DP [2]

beta - [betax, betay] horizontal and vertical Twiss parameter beta

alpha - [alphax, alphay] horizontal and vertical Twiss parameter alpha

mu - [mux, muy] horizontal and vertical betatron phase

!!! NOT 2*PI normalized

Use CAT to get the data from fields of TwissData into MATLAB arrays.

Example:

>> TD = twissring(THERING,0,1:length(THERING));

>> BETA = cat(1,TD.beta);

>> S = cat(1,TD.SPos);

>> plot(S,BETA(:,1))

See also twissring(), linopt(), tunechrom()

twissring(lattice, dp)#: calculates linear optics functions for an UNCOUPLED ring

[twissdata, tune] = twissring(lattice,dp) calculates twiss parameters

and closed orbit coordinates at the RING entrance assuming

constant energy deviation DP.

[twissdata, tune] = twissring(lattice,dp,refpts) calculates Twiss parameters

and closed orbit coordinates at specified reference points REFPTS.

Note: REFPTS is an array of increasing indexes that

select elements from range 1 to length(LATTICE)+1.

See further explanation of REFPTS in the ‘help’ for FINDSPOS

[twissdata, tune, chrom] = twissring(…,’chrom’, ddp) also calculates

linear dispersion and chromaticity. Dispersion is returned as one

of the fields in TwissData.

!!! Last argument DDP is a momentum deviation on top

of DP (the second argument) used to calculate and normalize

dispersion and chromaticity. If not supplied

the default value of 1e-8 is used.

Note: To resolve the integer part of the tune

and the uncertainty of acos(trace(M)/2) it is necessary to

supply sufficient number of REFPTS properly spaced in betatron phase.

TwisData is a 1-by-REFPTS (1-by-1) structure array with fields

(Some are the same as in the output of LINOPT)

ElemIndex - integer (element number) in the RING

SPos - longitudinal position [m]

ClosedOrbit - closed orbit column vector with

components x, px, y, py (momentums, NOT angles)

Dispersion - dispersion orbit position 4-by-1 vector with

components [eta_x, eta_prime_x, eta_y, eta_prime_y]’

calculated with respect to the closed orbit with

momentum deviation DP

M44 - 4x4 transfer matrix M from the beginning of RING

to the entrance of the element for specified DP [2]

beta - [betax, betay] horizontal and vertical Twiss parameter beta

alpha - [alphax, alphay] horizontal and vertical Twiss parameter alpha

mu - [mux, muy] horizontal and vertical betatron phase

!!! NOT 2*PI normalized

Use MATLAB function CAT to get the data from fields of TwissData into MATLAB arrays.

Example:

>> td = twissring(thering,0,1:length(thering));

>> BETA = cat(1,TD.beta);

>> S = cat(1,TD.SPos);

>> plot(S,BETA(:,1))

See also twissline(), linopt(), tunechrom()