Diffraction Radiation in the Ultraviolet and Soft X-Ray Regions
The majority of the problems on diffraction radiation that have been already studied theoretically were solved for ideally conducting targets. The perfect-conductivity model is applicable at large values of the imaginary part of the relative permittivity,
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Diffraction Radiation in the Ultraviolet and Soft X-Ray Regions
4.1 Polarization Current and the Radiation Field The majority of the problems on diffraction radiation that have been already studied theoretically were solved for ideally conducting targets. The perfect-conductivity model is applicable at large values of the imaginary part of the relative permittivity, i.e., for most metals at optical, infrared, and radio frequencies. However, the relative permittivity decreases sharply near the frequency ωL =
4π n e e2 /m = A 2π α λ¯ e n e ,
(4.1)
where λ¯ e is the electron Compton wavelength, n e is the number of the conduction electrons per unit volume, m is the electron mass, and e is the elementary charge. This frequency is usually called the Langmuir frequency. For the frequenciesω > ω L , the relative permittivity of metals is close to unit and the perfect-conductivity model becomes inapplicable. For most metals, frequency ω L is located in the near ultraviolet region and even in the visible spectrum for some metals such as copper or gold, which is responsible for their red color: only the harmonics with ω < ω L from the incident-wave field are reflected (see [1], page 525). At frequencies higher than the eigenfrequencies of the electrons in an atom, an external field interacts with the electrons bound in atoms so as with conduction electrons. For this reason, beginning with the frequency ωp =
4π N Z e2 /m = A 2π α λ¯ e N Z ,
(4.2)
the responses of dielectrics and conductors to the external field become the same and are determined by only the total number of electrons per unit volume of the medium, N Z , where N is the atomic number density and Z is the atomic number of the element. Note that, in metal optics and plasma physics, frequency (4.1) is called the Langmuir frequency and plasma frequency, respectively, whereas frequency (4.2) is not considered. The characteristic ω p values for typical metals of the target are several tens of electron volts [2]. A.P. Potylitsyn et al., Diffraction Radiation from Relativistic Particles, STMP 239, 105–136, DOI 10.1007/978-3-642-12513-3_4, C Springer-Verlag Berlin Heidelberg 2010
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4 Diffraction Radiation in the Ultraviolet and Soft X-Ray Regions
It is convenient to represent the relative permittivity in the form ε (ω) = 1 + χ (ω) + iχ (ω) .
(4.3)
ω ωp
(4.4)
For the frequencies
beyond the absorption region, the real part of the electric susceptibility χ (ω) has the form χ (ω) = −
ω2p ω2
0 can be satisfied and χ (ω) and χ (ω) can be on the same order of magnitude [3]. Note that expression (4.3) is independent of the coordinates. For this reason, the results obtained with the use of formula (4.3) are applicable only for the wavelengths aB < λ
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