84
An Introduction to Beam Physics
SDUDEROD
FIGURE 4.5: An electric capacitor consisting of two parallel plates. The
orbit of a particle is parabolic.
5
FIGURE 4.6: A concentric electric deflector.
chooses a curved one in such a way that the reference orbit is concentric
together with the plates as shown in Fig. 4.6.
To obtain the linearized equations of motion for such a device, we first
observe that
E x0
χ e0
= h
while
B = 0, and using eqs. (3.16),
χ e0 =
p 0 v 0
Ze
=
1
Ze
· mc
η 0 (2 + η 0 ) · c
η 0 (2 + η 0 )
1 + η 0
=
mc
2
Ze
η 0 (2 + η 0 )
1 + η 0
.
We describe the linearized electric field using the field inhomogenuity n, similar to the magnetic case, as
E x = −E x0 ·
1 − n
x
R 0
,
hence n e in eqs. (4.2) is given by n e = −n/R 0 , and h = 1/R 0 . The linearized
An Introduction to Beam Physics
SDUDEROD
FIGURE 4.5: An electric capacitor consisting of two parallel plates. The
orbit of a particle is parabolic.
5
FIGURE 4.6: A concentric electric deflector.
chooses a curved one in such a way that the reference orbit is concentric
together with the plates as shown in Fig. 4.6.
To obtain the linearized equations of motion for such a device, we first
observe that
E x0
χ e0
= h
while
B = 0, and using eqs. (3.16),
χ e0 =
p 0 v 0
Ze
=
1
Ze
· mc
η 0 (2 + η 0 ) · c
η 0 (2 + η 0 )
1 + η 0
=
mc
2
Ze
η 0 (2 + η 0 )
1 + η 0
.
We describe the linearized electric field using the field inhomogenuity n, similar to the magnetic case, as
E x = −E x0 ·
1 − n
x
R 0
,
hence n e in eqs. (4.2) is given by n e = −n/R 0 , and h = 1/R 0 . The linearized