Accelerator Physics Homework #5
P470 (Problems: 1-5)
1. In a lossless transverse electromagnetic (TEM) wave transmission line, the equation
for the current and voltage is
V
I
= L ,
s
t
I
V
= C
,
s
t
w
Accelerator Physics Homework #7
P470 (Problems: 1-4)
1. This exercise derives the linear transfer matrix for a skew quadrupole, where the magnetic eld is
Bz = B0 a1 z,
Bx = B0 a1 x,
Bs = 0;
with B0 a1
Solution:
1. In thin length approximation, 2R = 2N L, L = , =
c =
2
2N
1
2
DD
1
2N L2
DF
=
=
N
L+
L=
2R
2R sin2
sin2
2
2
2
2N sin
2
2
Similarly, we nd c = 2 /6R for DBA lattices.
2. The energy gai
Solution:
1. Floquet transformation:
(a) Dening a new coordinate = y/ and = (1/ )
and
s
0
ds/ , we nd ds/d = ,
d
1
ds d
1
1
=
= y 3/2 y = 1/2 y 1/2 y ,
d
d ds
2
2
d2
1
1
2
= 2 1/2 y 1/2 y 3/2 y .
2
d
Solution:
1. Without loss of generality, we use the Frenet-Serret coordinate system of Fig. 2.1 and
derive equation of motion for positively charged ions in the accelerator. It is easy to
modify the e
Solution:
1. Lorentz force provides the central force of circular motion:
F = qv B =
mv 2
B =
mv
p
=
,
Ze
Ze
where Z is the charge number of the particle. Using 1 [GeV/c]=109 [eV]/(2.9979
108 [m/s])=
Answer to the Midterm exam
1. In (, E ) space, the phase-space area A is proportional to a factor F = /| |. When
0
< T , F increases monotonously with , and when > T , the factor F has a
minimum at =