RÃ %
1
2p Ã
x
% 1=62
ð8:3:9Þ
γ
max
% p
Ã
x a
2
0 ¼ 3100 % 1:5GeV
ð
Þ
ð8:3:10Þ
The numerical result is shown in Fig. 8.6 as a function of the x-coordinate of an
electron located at x ¼ 0 and t ¼ 0. An adiabatic motion of the electron is seen before
the interaction with E x . The figure (a) is the normalized x-momentum, showing 2ω
oscillation given in (8.2.3), where the black line is the case without E x and the blue
line is the case affected by E x . The amplitude “a” in figure (b) is equal to the
normalized y-momentum and oscillates in the form (8.2.2). After a very short time
when the electron is accelerated in x-direction by the longitudinal filed (8.3.7), the
motion changes to that of (8.2.7) with α ¼ R*.
300
200
100
10
5
0
a
P
x /m
e c
γ-P
x /m
e c
γ
-5
-10
0
0
5 0
(a)
(b)
(c)
(d)
100
150
x [μm]
x [μm]
x [μm]
x [μm]
200
250
300
350
400
0
50
100
150
0
0
1
1.5
0.5
50
100
150
600
400
200
0
0
1000
500
200
250
300
350
400
Fig. 8.6 Electron dynamics in a laser field and static field Ex located in the highlighted region. The
dashed curve is the axial momentum in the absence of Ex. [Figure 1 in Ref. 1]
8.3 Direct Acceleration after Interaction with Longitudinal Field
299