Formation region effects in transition radiation, bremsstrahlung, and ionization loss of ultrarelativistic electrons

The processes of transition radiation and bremsstrahlung by an ultrarelativistic electron as well as the effect of transition radiation influence upon the electron ionization loss in thin layer of substance are theoretically investigated in the case when radiation formation region has macroscopically large size. Special attention is drawn to transition radiation (TR) generated during the traversal of thin metallic plate by the electron previously deflected from its initial direction of motion. In this case TR characteristics are calculated for realistic (circular) shape of the electron deflection trajectory. The difference of such characteristics under certain conditions from the ones obtained previously with the use of approximation of anglelike shape of the electron trajectory (instant deflection) is shown. The problem of measurement of bremsstrahlung characteristics in the prewave zone is investigated. The expressions defining the measured radiation distribution for arbitrary values of the size and the position of the detector used for radiation registration are derived. The problem of TR influence upon the electron ionization loss in thin plate and in a system of two plates is discussed. The proposal for experimental investigation of such effect is formulated.

Figure 1

The traversal of metallic plate by deflected half-bare electron.

Figure 2

(a) TR angular distribution for $l=2\mathrm{m}$, $\lambda =2\mathrm{mm}$; (b) dependence of TR intensity on $l$ for $\theta =1/\gamma$, $\lambda =2\mathrm{mm}$.

Figure 3

Normal incidence of the deflected electron upon thin metallic plate.

Figure 4

Half-bare electron TR angular distribution for $\gamma =100$, $\lambda =3\mathrm{mm}$, $\chi =\pi /4$, $R=50\mathrm{cm}$ (electron path within the deflection region $\delta =R\chi \approx 40\mathrm{cm}$) and (a) $l=40\mathrm{cm}$, (b) $l=2\mathrm{m}$. Red lines—calculation with the use of (2), black lines—with the use of (1), green line—TR by electron with equilibrium field.

Figure 5

Measurement of forward bremsstrahlung by a point detector in the prewave zone.

Figure 6

Radiation angular distributions for different distances $z$ between the deflection point and the detector. Green line—$z>{\gamma }^2\lambda =30\mathrm{m}$, red line—$z=3\mathrm{m}$, blue line—$z=1\mathrm{m}$.

Figure 7

Parabolic mirror with the edge of radius ${\rho }_0$ lying in the plane $z=z_0$.

Figure 8

Radiation distribution with respect to $\alpha$ for $\gamma =100$, $\lambda =3\mathrm{mm}$, $z_0=20\mathrm{cm}$ and (a) ${\rho }_0=3\mathrm{cm}$, (b) ${\rho }_0=10\mathrm{cm}$. Red lines—numerical calculation with the use of expression (20), blue lines—0-approximation (21), dashed lines—1-approximation (23), green line—asymptotic distribution (11) for ${\rho }_0\gg \gamma \lambda /2\pi$.

Figure 9

The same as in Fig. 8 but for $z_0=100\mathrm{cm}$.

Figure 10

Schematic picture of evolution of the electron’s field during its traversal of a system of two plates.

Figure 11

Dependence of the electron ionization loss in the second (thin) plate on the distance between the plates for the electron energy 500 MeV.