LATTICEDEMO self-running tutorial#
Table of Contents#
clear
Create elements#
An element in Accelerator Toolbox is a 1-by-1 MATLAB STRUCTURE.
Functions are provided to easily create such structures with adequate fields.
The following code creates a structure D1 for a drift space and a structure QF for a quadrupole.
D1 = atdrift('DR01', 3.0);
QF = atquadrupole('QF', 1.0, 0.2);
Use whos, disp or just type variable’s name without closing semicolon to print the element’s info:
whos D1 QF
Name Size Bytes Class Attributes
D1 1x1 600 struct
QF 1x1 1366 struct
disp(D1);
FamName: 'DR01'
PassMethod: 'DriftPass'
Length: 3
Class: 'Drift'
QF
QF = struct with fields:
FamName: 'QF'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: 0.200000000000000
PolynomB: [0 0.200000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
The next few lines will create another drift structure D2 from the exiting D1 and modify the values of fields ‘FamName’ and ‘Length’
D2 = D1;
D2.FamName = 'DR02';
D2.Length = 2;
Create another quadrupole element structure QD from QF and modify the values of fields ‘K’ and ‘PolynomB’ to make it defocusing
QD = QF;
QD.FamName = 'QD';
QD.K = -0.4;
The field ‘PolynomB' is a vector of coefficients of the polynomial field expansion.
The second element (quadrupole coefficient) must be consistent with field ‘K’
QD.PolynomB(2) = QD.K;
disp(QD);
FamName: 'QD'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: -0.400000000000000
PolynomB: [0 -0.400000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
We have created four elements:
whos
Name Size Bytes Class Attributes
D1 1x1 600 struct
D2 1x1 600 struct
QD 1x1 1366 struct
QF 1x1 1366 struct
Build lattices#
We are ultimately interested in sequences of elements to model storage ring lattices or single-pass beam transport lines.
The next section illustrates building such sequences. Accelerator Toolbox represents sequences of elements as MATLAB cell arrays where individual cells are 1-by-1 structures describing elements.
The following command creates a simple FODO cell by copying previously created element structures into a cell array fodocell:
fodocell = {QF D1 QD D2 QF};
whos fodocell
Name Size Bytes Class Attributes
fodocell 1x5 5898 cell
length is useful to find the number of elements in a sequence:
L = length(fodocell)
L = 5
Use the {:} cell array syntax to print some or all elements:
fodocell{1}
ans = struct with fields:
FamName: 'QF'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: 0.200000000000000
PolynomB: [0 0.200000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
fodocell{:}
ans = struct with fields:
FamName: 'QF'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: 0.200000000000000
PolynomB: [0 0.200000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
ans = struct with fields:
FamName: 'DR01'
PassMethod: 'DriftPass'
Length: 3
Class: 'Drift'
ans = struct with fields:
FamName: 'QD'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: -0.400000000000000
PolynomB: [0 -0.400000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
ans = struct with fields:
FamName: 'DR02'
PassMethod: 'DriftPass'
Length: 2
Class: 'Drift'
ans = struct with fields:
FamName: 'QF'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: 0.200000000000000
PolynomB: [0 0.200000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
Let’s build a cell array fodoring that represents a closed ring with 10 periods of fodocell the same way we would build any other array in MATLAB from the command line:
fodoring = [fodocell fodocell fodocell fodocell fodocell...
fodocell fodocell fodocell fodocell fodocell];
whos fodoring
Name Size Bytes Class Attributes
fodoring 1x50 58980 cell
The first element in fodoring is:
fodoring{1}
ans = struct with fields:
FamName: 'QF'
PassMethod: 'StrMPoleSymplectic4Pass'
Length: 1
Class: 'Quadrupole'
K: 0.200000000000000
PolynomB: [0 0.200000000000000]
PolynomA: [0 0]
MaxOrder: 1
NumIntSteps: 10
To inspect or change the value of a specific field we can use MATLAB syntax for accessing cells in cell arrays and field in structures
oldK = fodoring{1}.K
oldK = 0.200000000000000
fodoring{1}.K = 0.25;
newK = fodoring{1}.K
newK = 0.250000000000000
The lattice fodoring is a variable in MATLAB workspace.
We can use it in accelerator physics functions and scripts.
For example: the function findm44 finds 4-by-4 transverse transfer matrix
M = findm44(fodoring,0)
M = 4x4
-0.635168208131458 11.030527257692606 0 0
-0.076281158176798 -0.249663952717313 0 0
0 0 -0.970624346209193 0.311457414865072
0 0 -0.047116691539558 -1.015145726463917
Summary#
Individual elements are represented by 1-by-1 MATLAB structures,
Sequences of elements (lattices) are represented by 1-dimensional MATLAB cell arrays of structures,
MATLAB syntax for handling structures and cell arrays applies.
No special language is required to define a lattice.