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Formulas

An e-m wave with k || B has an index of refraction given by

n± = [I - uj2e/uj(uj =p cuce)]1/2,

where ± refers to the helicity. The rate of change of polarization angle 6 as a function of displacement s (Faraday rotation) is given by

dO/ds = (fc/2)(n_ - n+) = 2.36 X 104NBf~2 cm-1,

where N is the electron number density, B is the field strength, and f is the wave frequency, all in cgs.

The quiver velocity of an electron in an e-m field of angular frequency to

is

vq = eEma>x/muj = 25.6/1^2 Ao cm sec-1

in terms of the laser flux I = c£?m2x/8tv, with I in watt/cm2, laser wavelength Ao in jum. The ratio of quiver energy to thermal energy is

Wqu/Wth = mev02/2kT = 1.81 X 10-13A02//T,

where T is given in eV. For example, if I = 1015 W cm-2, Aq = 1 /xm, T = 2 keV, then Wqu/W-th ~ 0.1.

Pondermotive force:

T = NV(E2)/8TTNC,

where

Nc = 1.1 x 1021A0-2cm-3.

For uniform illumination of a lens with /-number F, the diameter d at focus (85% of the energy) and the depth of focus I (distance to first zero in intensity) are given by

d & 2AAF\e/9DL and I & ±2F2 \0/0DL.

Here 6 is the beam divergence containing 85% of energy and 6dl is the diffraction-limited divergence:

odl = 2.44A/6,

where b is the aperture. These formulas are modified for nonuniform (such as Gaussian) illumination of the lens or for pathological laser profiles.

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