96
W. Herr and E. Forest
Defined assignments:
M = z,
constructs a map M using the coefficients z
NORMAL = M,
computes a normal form NORMAL using the map M
In FORTRAN95 derived “type” plays the role of “structures” in C, and NORMAL
contains:
NORMAL%tune
is the tune Q
NORMAL%dtune_da
is the detuning with amplitude
dQ
da
NORMAL%R, NORMAL%A, NORMAL%A**-1 are the matrices
such that: M = A R A −1
from the normal form transformation one obtains α, β, γ . . .
Below a comparison is shown in Fig. 3.10 using the lattice function (e.g. β) obtained
with this procedure and the optical functions from the corresponding MAD-X
output.
One finds that β max ≈ 300 m, β min ≈ 170 m and perfect agreement.
160
180
200
220
240
260
280
300
320
0
200
400
600
800
1000
betax
s
beta function from tracking
Optics from TPSA
Optics from MAD
Fig. 3.10 Comparison: β-function from the model and the corresponding result from MAD-X
W. Herr and E. Forest
Defined assignments:
M = z,
constructs a map M using the coefficients z
NORMAL = M,
computes a normal form NORMAL using the map M
In FORTRAN95 derived “type” plays the role of “structures” in C, and NORMAL
contains:
NORMAL%tune
is the tune Q
NORMAL%dtune_da
is the detuning with amplitude
dQ
da
NORMAL%R, NORMAL%A, NORMAL%A**-1 are the matrices
such that: M = A R A −1
from the normal form transformation one obtains α, β, γ . . .
Below a comparison is shown in Fig. 3.10 using the lattice function (e.g. β) obtained
with this procedure and the optical functions from the corresponding MAD-X
output.
One finds that β max ≈ 300 m, β min ≈ 170 m and perfect agreement.
160
180
200
220
240
260
280
300
320
0
200
400
600
800
1000
betax
s
beta function from tracking
Optics from TPSA
Optics from MAD
Fig. 3.10 Comparison: β-function from the model and the corresponding result from MAD-X