element_creation#

Create lattice elements

Functions

`atM66()`	Create an element applying an arbitrary 6x6 transfer matrix
`atM66Tijk()`	ATM66(FAMNAME,M66,Tijk,PASSMETHOD)
`atQuantDiff()`	creates a quantum diffusion element.
`atSimpleQuantDiff()`	SimpleQuantDiff creates a simple quantum difusion element
`ataperture()`	Creates a aperture element
`atbaselem()`	Create an AT element structure + various checks
`atcorrector()`	Creates a drift space element with class ‘Corrector’
`atcrabcavity()`	Creates an crab cavity element with Class ‘CrabCavity’
`atdampMatElem()`	creates an element that applies the global damping matrix
`atdrift()`	Creates a drift space element with Class ‘Drift’
`atenergyloss()`	creates an energy loss element
`atidtable()`	Creates an ID element
`atinsertiondevicekickmap()`	creates an insertion device kick-map element
`atmarker()`	Creates a marker space element
`atmonitor()`	Creates a Beam Position Monitor element with Class ‘Monitor’
`atmultipole()`	Creates a multipole element
`atquadrupole()`	Creates a quadrupole element with Class ‘Quadrupole’
`atrbend()`	Creates a rectangular bending magnet element with class ‘Bend’
`atrbendtune()`	Set X0ref and RefDZ for rectangular bending magnets
`atrfcavity()`	Creates an rfcavity element with Class ‘RFCavity’
`atringparam()`	Creates a RingParameter Element which should go at the beginning of the ring
`atsbend()`	Creates a sector bending magnet element with class ‘Bend’
`atsextupole()`	Creates a sextupole element with class ‘Sextupole’
`atskewquad()`	Creates a skew quadrupole element with Class ‘Multipole’
`atsolenoid()`	Creates a new solenoid element with Class ‘Solenoid’
`atthinmultipole()`	Creates a thin multipole element
`atvariablemultipole()`	Creates a variable thin multipole element
`atwiggler()`	Creates a wiggler

atM66(famname, atstruct, passmethod)#: Create an element applying an arbitrary 6x6 transfer matrix

FAMNAME family name

M66 transfer matrix, defaults to Identity(6)]

PASSMETHOD tracking function, defaults to ‘Matrix66Pass’

atM66(famname,atstruct,passmethod)

atM66 will generate the matrix by calling FINDM66(ATSTRUCT)

ATSTRUCT AT structure

atM66Tijk()#: ATM66(FAMNAME,M66,Tijk,PASSMETHOD)

atM66 creates an element that applies an arbitrary matrix m66

FAMNAME family name

M66 transfer matrix, defaults to Identity(6)]

Tijk 2nd order transfer matrix, defaults to zeros(6,6,6)]

PASSMETHOD tracking function, defaults to ‘MatrixTijkPass’

ATM66(FAMNAME,ATSTRUCT,PASSMETHOD)

atM66 will generate the matrix by calling FINDM66(ATSTRUCT)

ATSTRUCT AT structure

atQuantDiff(famname, diffmat)#: creates a quantum diffusion element.

elem=atQuantDiff(famname,diffmat) uses the given diffusion matrix

FAMNAME: family name

DIFFMAT: Diffusion matrix

elem=atQuantDiff(famnane,ring) computes the diffusion matrix of the ring

FAMNAME: family name

RING: lattice with radiation on

elem=atQuantDiff(famnane,ring,’orbit0’,orbit) computes the diffusion

matrix of the ring without computing the closed orbit

ORBIT: closed orbit at beginning of the ring

(this option is useful for the islands)

The default pass method is ‘QuantDiffPass’ which uses a global

pseudo-random pcg32 stream inplemented in C. More details at:

atcollab/at#879

See also quantumDiff()

atSimpleQuantDiff(famname, ...)#: SimpleQuantDiff creates a simple quantum difusion element

elem=atSimpleQuantDiff(famname,…)

FAMNAME: family name

elem=atSimpleQuantDiff(famname,…,’betax’,betax,…)

BETAX: Horizontal beta function. Default: 1.0

elem=atSimpleQuantDiff(famname,…,’betay’,betay,…)

BETAY: Vertical beta function. Default: 1.0

elem=atSimpleQuantDiff(famname,…,’emitx’,emitx,…)

EMITX: Horizontal equilibrium emittance. Default: 0.0

elem=atSimpleQuantDiff(famname,…,’emity’,emity,…)

EMITY: Vertical equilibrium emittance. Default: 0.0

elem=atSimpleQuantDiff(famname,…,’espread’,espread,…)

ESPREAD: Equilibrium momentum spread. Default: 0.0

elem=atSimpleQuantDiff(famname,…,’taux’,tau_x,…)

TAU_X: Horizontal damping time. Default: 0.0

elem=atSimpleQuantDiff(famname,…,’tauy’,tau_y,…)

TAU_Y: Vertical damping time. Default: 0.0

elem=atSimpleQuantDiff(famname,…,’tauz’,tau_z,…)

TAU_Z: Longitudinal damping time. Default: 0.0

ataperture()#: Creates a aperture element

**ataperture**(FAMNAME,LIMITS,PASSMETHOD

define physical aperture element (collimator)

lim=[-x,+x,-y,+y];

lim={[-x,+x,-y,+y],[-x,+x,-y,+y],[-x,+x,-y,+y],…};

will generate various aperture elements (one for every set of errors)

See also SetPhysicalAperture()

atbaselem(famname, method, 'fieldname1', value1, ...)#: Create an AT element structure + various checks

elem=atbaselem(famname,method,’fieldname1’,value1,…) create AT element

Create an AT element structure and check the consistence of

PolynomA, PolynomB, MaxOrder and NumIntSteps

NOTES

1. length of PolynomA and PolynomB are equal (zero padding)

2. MaxOrder is always lenght(PolynomA) - 1

atcorrector(famname, length, kick, passmethod)#: Creates a drift space element with class ‘Corrector’

atcorrector(famname,length,kick,passmethod)

INPUTS

1. FAMNAME family name

2. LENGTH length [m]

3. KICK [hor. kick, vert. kick] [rad]

4. PASSMETHOD tracking function, defaults to ‘CorrectorPass’

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. Each pair {‘FIELDNAME’,VALUE} is added to the element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = CorrectorPass

where req are mandatory field and opt are optional fields

atmultipole, atthinmultipole, atmarker

See also atquadrupole(), atsextupole(), atsbend(), atrbend()

atcrabcavity(famname, length, voltages, frequency, harmonicnumber)#: Creates an crab cavity element with Class ‘CrabCavity’

atcrabcavity(famname,length,voltages,frequency,harmonicnumber)

INPUTS

1. FAMNAME Family name

2. LENGTH Length [m]

3. VOLTAGES Array [Horizontal, Vertical] Peak voltages [V]

4. FREQUENCY RF frequency [Hz]

5. HARMNUMBER Harmonic Number

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

atcrabcavity(famname,…,passmethod,’fieldname1’,value1,…)

Each pair {‘FIELDNAME’,VALUE} is added to the element

atmultipole, atthinmultipole, atmarker, atcorrector

See also atdrift(), atsextupole(), atsbend(), atrbend(), atskewquad(), atrfcavity()

atdampMatElem(famname, ring, cavipass, bendpass, quadpass)#: creates an element that applies the global damping matrix

elem=atdampMatElem(famname,ring,cavipass,bendpass,quadpass)

FAMNAME: family name

RING: initial AT structure, without radiation passmethods

CAVIPASS: pass method for cavities (default RFCavityPass)

BENDPASS: pass method for bending magnets. Special values:

‘’ makes no change,

‘auto’ wille substitute ‘Pass’ with ‘RadPass’ in any method

(default: ‘auto’)

QUADPASS: pass method for quadrupoles

‘’ makes no change,

‘auto’ wille substitute ‘Pass’ with ‘RadPass’ in any method

(default: ‘’)

atdrift(famname, length, passmethod)#: Creates a drift space element with Class ‘Drift’

atdrift(famname,length,passmethod)

INPUTS

1. FAMNAME - Family name

2. LENGTH - Length [m]

3. PASSMETHOD - Tracking function, defaults to ‘DriftPass’

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. atdrift(famname,length,passmethod,’fieldname1’,value1,…)

each pair {‘fieldname’,value} is added to the element

atenergyloss(famname, eloss, passmethod)#: creates an energy loss element

elem=atenergyloss(famname,eloss,passmethod)

FAMNAME: family name

ELOSS: Energy loss [eV]

PASSMETHOD: Tracking methods, defaults to ‘IdentityPass’

the “energy loss” element is taken into account in ATSUMMARY: it adds damping by

contributing to the I2 integral, thus reducing the equilibrium emittance.

But it does not generate any diffusion. This makes sense only if the losses

summarised in the element occur in non-dispersive locations.

atidtable()#: Creates an ID element

FamName family name

Nslice number of slices (1 means the wiggler is represented by a

single kick in the center of the device).

filename name of file with wiggler tracking tables.

Energy Energy of the machine, needed for scaling

method tracking function. Defaults to ‘IdTablePass’

The tracking table is described in

P. Elleaume, “A new approach to the electron beam dynamics in undulators

and wigglers”, EPAC92.

returns assigned structure with class ‘KickMap’

atinsertiondevicekickmap()#: creates an insertion device kick-map element

Elem = atinsetiondevicekickmap( fname, …

method, …

filename, …

Normalization_energy, …

Nslice, …

length, …

xkick, …

ykick, …

xkick1, …

ykick1, …

xtable, …

ytable …

)

fname family name

method ‘IdTablePass’

filename name of the file used to create the element

Normalization_energy energy to which the field table was scaled

Nslice number of slices (1 means the wiggler is represented by a

single kick in the center of the device).

length length of the element

NumX number of horizontal points

NumY number of vertical points

xkick list of x positions

ykick list of y positions

xkick1 —

ykick1 —

xtable horizontal plane table

ytable vertical plane table

The tracking method is described in

P. Elleaume, “A new approach to the electron beam dynamics in undulators

and wigglers”, EPAC92.

Returns an element with Class ‘InsertionDeviceKickMap’

atmarker(famname, passmethod)#: Creates a marker space element

atmarker(famname,passmethod)

INPUTS

1. FAMNAME - Family name

2. PASSMETHOD - Tracking function, defaults to ‘IdentityPass’

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. atmarker(famname,passmethod,’fieldname1’,value1,…)

each pair {‘fieldname’,value} is added to the element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = IdentityPass

where req are mandatory field and opt are optional fields

atthinmultipole, atcorrector

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atrbend(), atskewquad()

atmonitor(famname, 'fieldname1', value1, ...)#: Creates a Beam Position Monitor element with Class ‘Monitor’

INPUTS

1. fname - Family name

atmonitor(famname,’fieldname1’,value1,…)

Each pair {‘FIELDNAME’,VALUE} is added to the element

atmultipole, atthinmultipole, atmarker, atcorrector

See also atdrift(), atsextupole(), atsbend(), atrbend()

atmultipole(famname, length, polynoma, polynomb, passmethod)#: Creates a multipole element

atmultipole(famname,length,polynoma,polynomb,passmethod)

INPUTS

1. FNAME - Family name

2. LENGTH - Length[m]

3. POLYNOMA - Skew [dipole quad sext oct];

4. POLYNOMB - Normal [dipole quad sext oct];

5. PASSMETHOD - Tracking function. Defaults to ‘StrMPoleSymplectic4Pass’

OPTIONS (order does not matter)

R1 - 6 x 6 rotation matrix at the entrance

R2 - 6 x 6 rotation matrix at the entrance

T1 - 6 x 1 translation at entrance

T2 - 6 x 1 translation at exit

NumIntSteps - Number of integration steps

MaxOrder - Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. atmultipole(famname,length,polynoma,polynomb,passmethod,’fieldname1’,value1,…)

each pair {‘fieldname’,value} is added to the element

atthinmultipole, atmarker, atcorrector

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atrbend(), atskewquad()

atquadrupole(famname, length, k, passmethod)#: Creates a quadrupole element with Class ‘Quadrupole’

atquadrupole(famname,length,k,passmethod)

INPUTS

1. FAMNAME - Family name

2. LENGTH - Length [m]

3. K - Strength [m-2]

4. PASSMETHOD - Tracking function, defaults to ‘StrMPoleSymplectic4Pass’

OPTIONS (order does not matter)

R1 - 6 x 6 rotation matrix at the entrance

R2 - 6 x 6 rotation matrix at the entrance

T1 - 6 x 1 translation at entrance

T2 - 6 x 1 translation at exit

NumIntSteps - Number of integration steps

MaxOrder - Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. Fieldname can be called by calling the passmethod

[req opt] = StrMPoleSymplectic4Pass

where req are mandatory field and opt are optional fields

2. atquadrupole(famname,length,k,passmethod,’fieldname1’,value1,…)

each pair {‘fieldname’,value} is added to the element

3. Quadrupole fringe field can be activated at element entrance or exit

with option FringeQuadEntrance/FringeQuadExit=0,1,2

Version 0: no fringe field

Version 1: Lee-Whiting formula

Version 2: Lee-Whiting Elegant-like formula where 5 integral need to

be provided

atmultipole, atthinmultipole, atmarker, atcorrector, atringparam

See also atdrift(), atsextupole(), atsbend(), atrbend(), atskewquad()

atrbend(famname, length, bendingangle, k, passmethod)#: Creates a rectangular bending magnet element with class ‘Bend’

Two calling methods (that can be combined)

atrbend(famname,length,bendingangle,k,passmethod)

INPUTS

1. FNAME - Family name

2. LENGTH - Length of the arc for an on-energy particle

[m], default to 0

3. BENDINGANGLE - Total bending angle [rad], defaults to 0

4. K - Focusing strength, defaults to 0

5. PASSMETHOD -Tracking function, defaults to ‘BndMPoleSymplectic4Pass’

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. atrbend(famname,length,bendingangle,k,passmethod,’fieldname1’,value1,…)

each pair {‘fieldname’,value} is added to the element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = BndMPoleSymplectic4Pass

where req are mandatory field and opt are optional fields

2. Model for BndMPoleSymplectic4Pass (Rad) can be selected with extra

fields

FringeBendEntrance/FringeBendExit = 0,1,2,3

Version 0 no dipole fringe fields

Version 1 legacy version Brown First Order (K. Brown. A First and Second Order

Matrix Theory for the Design of Beam Transport Systems and Charged

Particle Spectrometers. Internal report, SLAC-75, 1982)

Version 2 SOLEIL close to second order of Brown (J. Bengtsson and M. Meddahi.

Modeling of Beam Dynamics and Comparison with Measurements for

the Advanced Light Source. London, UK, 1994.)

Version 3 THOMX (Dipole Fringe Field Effects in the ThomX Ring, J. Zhang and

A. Loulergue, Proceedings of IPAC2013, Shanghai, China)

FringeQuadEntrance/FringeQuadExit = 0,1,2

Version 0 no quadrupole fringe fields

Version 1 Lee-Whiting Formula

Version 2 Linear quadrupole fringe field using the 5 integrant a la

Elegant

atmultipole, atthinmultipole, atmarker, atcorrector

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atskewquad()

atrbendtune(elem)#: Set X0ref and RefDZ for rectangular bending magnets

newelem=atrbendtune(elem)

Set the X0ref and RefDZ attributes for rectangular bending magnets

This function must be called after creating a rectangular bending magnet

or after setting its polynomA/B attributes. It will set the correct X0ref

and RefDZ attributes to get a zero closed orbit for the reference particle.

Example:

>> % Identify the rectangular bends

>> rbends=atgetcells(ring,…);

>> % Set their correct attributes

>> ring(rbends)=cellfun(@**atrbendtune**,ring(rbends),’UniformOutput’,false);

Does nothing if the passmethod is not a rectangular bend passmethod

atrfcavity(famname, length, voltage, frequency, harmonicnumber, energy, passmethod)#: Creates an rfcavity element with Class ‘RFCavity’

atrfcavity(famname,length,voltage,frequency,harmonicnumber,energy,passmethod)

INPUTS

1. FAMNAME Family name

2. LENGTH Length [m]

3. VOLTAGE Peak voltage [V]

4. FREQUENCY RF frequency [Hz]

5. HARMNUMBER Harmonic Number

6. ENERGY Energy [eV]

7. PASSMETHOD Tracking function, defaults to ‘RFCavityPass’

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

atrfcavity(famname,…,passmethod,’fieldname1’,value1,…)

Each pair {‘FIELDNAME’,VALUE} is added to the element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = atrfcavity

where req are mandatory field and opt are optional

fields

atmultipole, atthinmultipole, atmarker, atcorrector

See also atdrift(), atsextupole(), atsbend(), atrbend(), atskewquad()

atringparam(famname, e0, nbperiods)#: Creates a RingParameter Element which should go at the beginning of the ring

atringparam(famname,e0,nbperiods)

INPUTS

1. FAMNAME - Family name which may be used as name of Ring

2. E0 - Energy of electrons

3. NBPERIODS - Periodicity of the ring (1 if ring is already expanded)

OUTPUTS

1. elem - RingParam class elem

atmultipole, atthinmultipole

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atrbend()

atsbend(famname, length, bendingangle, k, passmethod)#: Creates a sector bending magnet element with class ‘Bend’

Two calling methods (that can be combined)

atsbend(famname,length,bendingangle,k,passmethod)

INPUTS

1. FNAME Family name

2. LENGTH Length of the arc for an on-energy particle

[m], default to 0

3. BENDINGANGLE Total bending angle [rad], defaults to 0

4. K Focusing strength, defaults to 0

5. PASSMETHOD Tracking function, defaults to ‘BndMPoleSymplectic4Pass’

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

atsbend(famname,length,bendingangle,k,passmethod,’fieldname1’,value1,…)

Each pair {‘FIELDNAME’,VALUE} is added to the element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = BndMPoleSymplectic4Pass

where req are mandatory field and opt are optional

fields

2. Model for BndMPoleSymplectic4Pass (Rad) can be selected with extra

fields

FringeBendEntrance/FringeBendExit = 0,1,2,3

Version 0 no dipole fringe fields

Version 1 legacy version Brown First Order (K. Brown. A First and Second Order

Matrix Theory for the Design of Beam Transport Systems and Charged

Particle Spectrometers. Internal report, SLAC-75, 1982)

Version 2 SOLEIL close to second order of Brown (J. Bengtsson and M. Meddahi.

Modeling of Beam Dynamics and Comparison with Measurements for

the Advanced Light Source. London, UK, 1994.)

Version 3 THOMX (Dipole Fringe Field Effects in the ThomX Ring, J. Zhang and

A. Loulergue, Proceedings of IPAC2013, Shanghai, China)

FringeQuadEntrance/FringeQuadExit = 0,1,2

Version 0 no quadrupole fringe fields

Version 1 Lee-Whiting Formula

Version 2 Linear quadrupole fringe field using the 5 integrant a la

Elegant

atmultipole, atthinmultipole, atmarker, atcorrector

See also atdrift(), atquadrupole(), atsextupole(), atrbend()

atsextupole(famname, length, s, passmethod)#: Creates a sextupole element with class ‘Sextupole’

atsextupole(famname,length,s,passmethod)

INPUTS

1. FNAME family name

2. LENGTH length [m]

3. S strength [m-2]

4. PASSMETHOD tracking function, defaults to ‘StrMPoleSymplectic4Pass’

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

atsextupole(famname,length,s,passmethod,’fieldname1’,value1,…)

Each pair {‘FIELDNAME’,VALUE} is added to the element

atrbend,atskewquad, atmultipole, atthinmultipole, atmarker,

atcorrector

See also atdrift(), atquadrupole(), atmultipole(), atsbend()

atskewquad(famname, length, qs, passmethod)#: Creates a skew quadrupole element with Class ‘Multipole’

atskewquad(famname,length,qs,passmethod)

INPUTS

1. FAMNAME - Family name

2. LENGTH - Length [m]

3. Qs - Skew quad strength [m-2]

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

1. atskewquad(fname, l, qs, method)

atmultipole, atthinmultipole, atmarker, atcorrector

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atrbend()

atsolenoid()#: Creates a new solenoid element with Class ‘Solenoid’

Elem =solenoid(‘FAMILYNAME’,Length [m],KS,’METHOD’)

INPUTS

1. FamName family name

2. Length length[m]

3. KS solenoid strength KS [rad/m]

4. PassMethod name of the function to use for tracking

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = BndMPoleSymplectic4Pass

where req are mandatory field and opt are optional

fields

atthinmultipole, atmarker, atcorrector

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atrbend(), atskewquad()

atthinmultipole(famname, polynoma, polynomb, passmethod)#: Creates a thin multipole element

atthinmultipole(famname,polynoma,polynomb,passmethod)

INPUTS

1. FNAME family name

2. POLYNOMA skew [dipole quad sext oct];

3. POLYNOMB normal [dipole quad sext oct];

4. PASSMETHOD tracking function. Defaults to ‘ThinMPolePass’

OPTIONS (order does not matter)

R1 6 x 6 rotation matrix at the entrance

R2 6 x 6 rotation matrix at the entrance

T1 6 x 1 translation at entrance

T2 6 x 1 translation at exit

NumIntSteps Number of integration steps

MaxOrder Max Order for multipole (1 up to quadrupole)

OUTPUTS

1. ELEM - Structure with the AT element

EXAMPLES

atthinmultipole(famname,polynoma,polynomb,passmethod,’fieldname1’,value1,…)

Each pair {‘FIELDNAME’,VALUE} is added to the element

NOTES

1. Fieldname can be called by calling the passmethod

[req opt] = BndMPoleSymplectic4Pass

where req are mandatory field and opt are optional

fields

ATMULTIPOLE, ATMARKER, ATCORRECTOR

See also atdrift(), atquadrupole(), atsextupole(), atsbend(), atrbend(), atskewquad()

atvariablemultipole(famname,mode,passmethod,[key,value]...)#: Creates a variable thin multipole element

atvariablemultipole(famname,mode,passmethod,[key,value]…)

INPUTS

FNAME Family name

MODE Excitation mode: ‘SINE’, ‘WHITENOISE’ or ‘ARBITRARY’.

Default: ‘SINE’

PASSMETHOD Tracking function. Default: ‘VariableThinMPolePass’

OPTIONS (order does not matter)

AMPLITUDEA Vector or scalar to define the excitation amplitude for

PolynomA

AMPLITUDEB Vector or scalar to define the excitation amplitude for

PolynomA

FREQUENCYA Frequency of SINE excitation for PolynomA

FREQUENCYB Frequency of SINE excitation for PolynomB

PHASEA Phase of SINE excitation for PolynomA

PHASEB Phase of SINE excitation for PolynomB

MAXORDER Order of the multipole for a scalar amplitude

SEED Input seed for the random number generator

FUNCA ARBITRARY excitation turn-by-turn kick list for PolynomA

FUNCB ARBITRARY excitation turn-by-turn kick list for PolynomB

PERIODIC If true (default) the user input kick list is repeated

RAMPS Vector (t0, t1, t2, t3) in turn number to define the ramping of the excitation

* t<t0: excitation amlpitude is zero

* t0<t<t1: exciation amplitude is linearly ramped up

* t1<t<t2: exciation amplitude is constant

* t2<t<t3: exciation amplitude is linearly ramped down

* t3<t: exciation amplitude is zero

OUTPUTS

1. ELEM - Structure with the AT element

NOTES

1. For all excitation modes at least one amplitude (A or B) is

required. The default excitation is SINE

2. For SINE excitation modes the FREQUENCY corresponding to the input

AMPLITUDE is required

3. For ARBITRARY excitation modes the FUNC corresponding to the input

AMPLITUDE is required

EXAMPLES

% Create a sinusoidal dipole with amplitude 0.1 mrad and frequency 1 kHz

>> atvariablemultipole(‘acm’,’sine’,’amplitudeb’,1.e-4,’frequencyb’,1.e3);

% Create a white noise dipole excitation of amplitude 0.1 mrad

>> atvariablemultipole(‘acm’,’whitenoise’,’amplitudeb’,1.e-4);

atwiggler(famname, length, lw, bmax, energy, passmethod)#: Creates a wiggler

elem=atwiggler(famname, length, lw, bmax, energy, passmethod)

FAMNAME family name

LENGTH total length

LW Period length

BMAX Peak magnetic field [T]

ENERGY Beam energy [eV]

PASSMETHOD Tracking function. Default ‘GWigSymplecticPass’

elem=atwiggler(…,’keyword’,value…)

Keywords:

Nstep number of integration steps per period (default 5)

Nmeth symplectic integration method, 2nd or 4th order: 2 or 4 (default 4)

By harmonics of the horizontal wiggler. Default [1;1;0;1;1;0]

6xNH matrix, with NH number of harmonics

Bx harmonics of the vertical wigglers. Default []

6xNV matrix, with NV number of harmonics

see also: GWigSymplecticPass