By G.N. Afanasiev
From the reviews:
"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)
Read Online or Download Vavilov-Cherenkov and Synchrotron Radiation: Foundations and Applications PDF
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Additional info for Vavilov-Cherenkov and Synchrotron Radiation: Foundations and Applications
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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