Radiation generated by single and multiple volume reflection of ultrarelativistic electrons and positrons in bent crystals

Recently discovered processes of volume reflection and multiple volume reflection of charged particles in bent crystals are accompanied by specific electromagnetic (e.m.) radiation. The mechanism of radiation emission is quite complex due to the coexistence of different regimes for particle dynamics, resulting in e.m. generation with features characteristic of each regime. We present a simulation taking into consideration both the nondipole nature and arbitrary multiplicity of radiation accompanying volume reflection. This approach is worked out for electrons or positrons of any energy and is based on the local straight-crystal approximation and Baier-Katkov formula for radiation, the integration of which is considerably facilitated by the fast Fourier transform method. The radiation generated by multiple volume reflection with vertical and skew planes has been studied, too. A large axial contribution to the hard part of the radiative energy loss spectrum as well as the strengthening of planar radiation, with respect to the single volume reflection case, in the soft part of the spectrum are demonstrated. Both the wide spectrum and high intensity make this type of radiation quite suitable for the conversion of electron and positron beams to hard $\gamma$ radiation.

Figure 1

General view of particle volume reflection (left). The particle moves in the horizontal $xz$ plane and is reflected from the vertical plane parallel to the $y$ axis. Trajectories of 120 GeV positrons (right) reflecting from the $\left(110\right)$ plane of the 2-mm $\text{Si}$ crystal bent with radius of 11 m, evaluated with consideration (bottom) and in neglection (top) of the incoherent scattering. Positrons initially move at 100 $\mu \text{rad}$ with respect to the reflecting bent planes.

Figure 2

Effective potential (positron potential energy) of bent crystal planes. The nearest maxima reached by the effective potential in coordinates $x_{nmx}$ or $x_{nmx}^{\prime }$ are used both to determine is the particle channeled or not and to evaluate the minimal transverse velocity $v_{\min }$ for the unchanneled one. $v_{\min }$ is used both to tabulate and interpolate the intensity of radiation of the latter, while the turning point coordinate $x_{\mathrm{turn}}$ is used for the same if the particle is channeled.

Figure 3

Spectra of radiation of 120 GeV positrons channeled in the field of Si(110) planes with turning point coordinates 0.1, 0.3, and 0.5 Å.

Figure 4

Spectra of radiation of 120 GeV positrons moving in nonchanneling regime in the field of (110) Si planes with minimal transverse velocities 10, 30 and 50 $\mu \mathrm{rad}$.

Figure 5

Energy distribution of 180 GeV positron energy losses in the 0.84 mm Si (111) crystal bent with 12 m radius. Experimental data (circles with bars) and simulation results for the FTPR (solid line) and DIBK (crosses) methods.

Figure 6

Same distributions as in Fig. 5 for 180 GeV electrons and 8 m bending radius.

Figure 7

Same distributions as in Fig. 5 for 120 GeV positron radiation in $2mm$ $Si\left(110\right)$ crystal bent with the radius of 11 m.

Figure 8

Same distributions as in Fig. 7 for 4.7 m bending radius.

Figure 9

Particles hitting the crystal at small angles with respect to $\langle 111\rangle$ axis, experience VR from both the $vertical$, ${\left(1\overline{1}0\right)}_V$, and numerous skew planes. (a) The comoving reference system $ryz$ rotates with the bent axis direction $z$ when a particle is moving through the crystal. (b) Evolution of particle transverse velocity in the $ry$ plane. Figure also contains the projections of the crystal planes intersecting along the $\langle 111\rangle$ axis (solid) and the borders of the regions of influence by each plane (dashed). Small multiple arrows indicate the directions of particle reflection from different planes. The vertical projections of the angles of reflection from symmetric skew planes compensate each other while the horizontal ones sum up leading to the MVROC effect.

Figure 10

Energy loss spectrum of 120 GeV positrons in 2 mm Si (110) crystal, bent by $\varphi =$ 700 $\mu \mathrm{rad}$. Plot (1) is for planar MVROC, (2) for VR by only ${\left(110\right)}_V$ plane and (3) for the radiation in the field of $\langle 111\rangle$ axes. Positrons initially move with 50 $\mu \mathrm{rad}$ divergence and average incidence angles of 350 and 150 $\mu \mathrm{rad}$ with respect to the axis in horizontal and vertical planes.

Figure 11

Same distributions as in plot 3 of Fig. 10 for both 120 GeV positron (crosses) and electron (circles) radiation in the field of $\langle 111\rangle$ axes.

Figure 12

Same distributions as in plot 3 of Fig. 10 for both 120 GeV electron beams with 50 $\mu \mathrm{rad}$ (line) and 150 $\mu \mathrm{rad}$ (circles) divergence.