Lattice Modules
233
FIGURE 9.10: The lattice functions β x , β y and dispersion multiplied by
10 in the MAX IV multiple-bend achromat (MBA) lattice at Lund University,
Lund, Sweden. ( c
1996 IEEE. Reprinted, with permission, from D. Einfeld,
et. al., in Proc. PAC 1995, 1, 177, 1996 [26].)
in the ring. The linear map between them is
ˆ
M 12 =
⎛
⎜
⎝
(x|x) 12 (x|a) 12 (x|δ) 12
(a|x) 12 (a|a) 12 (a|δ) 12
0
0
1
⎞
⎟
⎠ ,
and the dispersion of those two points are related through the relation
⎛
⎜
⎝
D 2
D
2
1
⎞
⎟
⎠ =
⎛
⎜
⎝
(x|x) 12 (x|a) 12 (x|δ) 12
(a|x) 12 (a|a) 12 (a|δ) 12
0
0
1
⎞
⎟
⎠
⎛
⎜
⎝
D 1
D
1
1
⎞
⎟
⎠ .
Hence, we have
H 2 =γ 2 D
2
2 + 2α 2 D 2 D
2 + β 2 D
2
2
= (D 2 , D
2 )
γ 2 α 2
α 2 β 2
D 2
D
2
=
(D 1 , D
1 )
(x|x) 12 (a|x) 12
(x|a) 12 (a|a) 12
+ ((x|δ) 12 , (a|δ) 12 )
γ 2 α 2
α 2 β 2
·
(x|x) 12 (x|a) 12
(a|x) 12 (a|a) 12
D 1
D
1
+
(x|δ) 12
(a|δ) 12