LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
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Intensity (a.u.)<br />
Intensity (W/cm 2 )<br />
10 7<br />
10 6<br />
10 5<br />
10 4<br />
10 3<br />
10 2<br />
10 1<br />
10 0<br />
10 -1<br />
10 -2<br />
10 -3<br />
10 -4<br />
Wavelength (nm)<br />
10 4 10 3 10 2 10 1<br />
10.6 m<br />
CO 2<br />
0<br />
= 0.001<br />
= 0.01<br />
Relativistic Domain<br />
800 nm<br />
Ti:sapph<br />
z f = 1 (2U p = mc 2 )<br />
= 0.1<br />
= 1<br />
100 eV<br />
E=1a.u.<br />
10 -3 10 -2 10 -1 10 0 10 1<br />
Field frequency (a.u.)<br />
10 23<br />
10 22<br />
10 21<br />
10 20<br />
10 19<br />
10 18<br />
10 17<br />
10 16<br />
10 15<br />
10 14<br />
10 13<br />
The line at 2U p = mc 2 is where the minimum interaction energy of an electron with the laser<br />
field is of the order of the rest energy of the electron. The left / upper corner of the graph is an<br />
extreme relativistic zone. Laser-induced ionization is not a static limit.<br />
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