On the Schwinger limit attainability with extreme power lasers

The pairs are created in a small 4-volume near the electric field maximum
(maximum of F ) with the characteristic size
TM
Here normalized Schwinger field is
5 a
16 aS 3/ 2 4
2 0 0
0 0 0 5
r z ct
2
mc e 5.110
Integrating over the 4-volume the probability of the pair creation
we obtain the number of pairs produced per wave period,
a
S
0
3/ 2
5 4 a S
N W
dVdt a 3 0 exp
e e e e
4
a
The first pairs can be observed for an one-micron wavelength laser intensity of the order of
27 2
10 W/cm , which corresponds to a0 / aS0.05 , i.e. a characteristic size, 0 ,
Is approximately equal to
r
0.04
0
5
2
F a
TM /
0
2
z0
r0