By G.N. Afanasiev

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"The booklet having 9 chapters experiences primary actual and mathematical difficulties of the Vavilov-Cherenkov impact of media. the following the readers might discover a dialogue of all easy difficulties of the Vavilov-Cherenkov influence and of synchrotron radiation. … This booklet should be valuable for complex graduate scholars and for pro scientists, either experimentalists and theoreticians." (Oleg A. Sinkevich, Zentralblatt MATH, Vol. 1067 (18), 2005)

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Additional info for Vavilov-Cherenkov and Synchrotron Radiation: Foundations and Applications

Example text

In the z > ργn + z0 region these waves arrive in the reverse order. In the ργ − z0 < z < (ρ2 γn2 + z02 /βn2 )1/2 region the observer consecutively detects the CSW, BS1 shock wave and the BS2 shock wave. In the region (ρ2 γn2 + z02 /βn2 )1/2 < z < ργn + z0 the latter two waves arrive in the reverse order. The CSW Sc is tangential to the BS1 shock wave at the point where Sc intersects the surface z = ργ − z0 and to the BS2 shock wave at the point where Sc intersects the surface z = ργ + z0 (see Fig.

R2 rm We now clarify the physical meaning of particular terms entering into this equation. The first term in the first line describes the electrostatic field of a charge resting at the point z = −z0 up to an instant t = −t0 . It differs from zero outside the sphere S1 of radius cn(t + t0 ) with its center at z = −z0 . The second term in the same line describes the electrostatic field of a charge at rest at the point z = z0 after the instant t = t0 . It differs from zero inside the sphere S2 of radius cn(t−t0 ) with its center at z = z0 .

For t > t0 the charge is again at rest at the point z = z0 . In the spectral representation the non-vanishing z of the vector potential (VP) is given by Aω = µ c 1 jω(x , y , z ) exp (−inωR/c)dx dy dz , R where R = [(x−x )2 +(y−y )2 +(z−z )2 ]1/2 and jω is the Fourier component of the current density defined as jω = 1 2π j(t) exp(−iωt)dt. 33 The Tamm Problem in the Vavilov-Cherenkov Radiation Theory For a charge moving uniformly in the interval (−z0 , z0 ) one finds j(t) = evδ(x)δ(y)δ(z − vt)Θ(z + z0 )Θ(z0 − z) and jω = e δ(x)δ(y) exp(−iωz/v)Θ(z + z0 )Θ(z0 − z).

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