Optimal radius of crystal curvature for planar channeling of high-energy negatively charged particles in a bent crystal

The problem of planar channeling of high-energy negatively charged particles in a bent crystal was considered on the basis of analytical calculation and numerical simulation. We show the existence of an optimal radius of crystal curvature for planar channeling, corresponding to the maximum deflection of the particle beam. The analytical calculation was carried out in the parabolic planar potential approximation, and in the numerical simulation the Doyle-Turner approximation was used.

Figure 1

The potential energy of a particle with a charge, that equals to the charge of an electron, in the field of (110) atomic planes of Si. Black solid line corresponds to the Doyle-Turner approximation (DT), red dashed line corresponds to the parabolic approximation (3).

Figure 2

The shape of the dependence of the deflection angle up to which the fraction of channeled particles is higher than $f$ on the radius of curvature.

Figure 3

The dependence of the ratio of the optimal radius of curvature to the critical radius of planar channeling on the fraction of channeled particles in the parabolic approximation of planar potential.

Figure 4

The orientation of Si crystal towards the impinging beam of ${\pi }^{-}$-mesons.

Figure 5

The dependence of the deflection angle up to which the fraction of channeled particles is higher than 5% (solid lines) and 15% (dash-dotted lines) on the ratio of radius of curvature to the critical radius of planar channeling.