Channeling, volume reflection, and volume capture study of electrons in a bent silicon crystal

We present the experimental data and analysis of experiments conducted at SLAC National Accelerator Laboratory investigating the processes of channeling, volume-reflection and volume-capture along the (111) plane in a strongly bent quasimosaic silicon crystal. These phenomena were investigated at 5 energies: 3.35, 4.2, 6.3, 10.5, and 14.0 GeV with a crystal with bending radius of 0.15 m, corresponding to curvatures of 0.053, 0.066, 0.099, 0.16, and 0.22 times the critical curvature, respectively. Based on the parameters of fitting functions we have extracted important parameters describing the channeling process such as the dechanneling length, the angle of volume reflection, the surface transmission, and the widths of the distribution of channeled particles parallel and orthogonal to the plane.

Figure 1

A plot of the effective potential of Eq. (5) for a flat crystal and for the relevant electron energies with bending radius $R=0.15\mathrm{m}$.

Figure 2

A figure comparing the surface transmission for electrons using the exact Doyle-Turner potential and the parabolic approximation. We have also plotted the parabolic approximation for positrons to show the difference between positive and negative particles.

Figure 3

A sketch of the experimental setup.

Figure 4

The probability density relative to the maximum probability density of the deflected particles as a function of the crystal angle for the case of 3.35 GeV electrons.

Figure 5

The probability density relative to the maximum probability density of the deflected particles as a function of the crystal angle for the case of 4.2 GeV electrons.

Figure 6

The probability density relative to the maximum probability density of the deflected particles as a function of the crystal angle for the case of 6.3 GeV electrons.

Figure 7

The probability density relative to the maximum probability density of the deflected particles as a function of the crystal angle for the case of 10.5 GeV electrons.

Figure 8

The probability density of the deflected particles when the crystal is in the channeling orientation for the different energies in the experiment.

Figure 9

The probability density of the deflected particles when the crystal is at half of the full bending angle. The large leftmost peaks are the volume reflected portions and the small rightmost peaks are the volume captured particles.

Figure 10

A fit to the 10.5 GeV experimental data in the channeling orientation.

Figure 11

A fit to the 3.5 GeV experimental data in the channeling orientation.

Figure 12

A fit to the 10.5 GeV experimental data at half the crystal bending angle.

Figure 13

A fit to the 3.5 GeV experimental data at half the crystal bending angle.

Figure 14

The probability density of the deflected particles obtained from the dynecharm simulation when the crystal is in the channeling orientation for the different energies in the experiment.

Figure 15

The width of the channeling peak in the direction parallel to the plane is fitted to obtain Eq. (16).

Figure 16

The width of the channeling peak in the direction orthogonal to the plane is fitted with a power function (Fit 1), see Eq. (17) and to a function of the type $a/\sqrt{E}$ (Fit 2), see Eq. (18).

Figure 17

The angle of volume reflection is fitted with a power function (Fit 1) and to a function of the type $a/\sqrt{E}$ (Fit 2).

Figure 18

The volume capture efficiency as given by $1-P_1$ from Table 6. “Fit 1” is a fit to a function of the type $a{E}^{-3/2}$ and “Fit 2” is a fit to a power function $(a{E}^b)$.

Figure 19

A plot of the “simple” dechanneling formulas of Eqs. (7), (9), (23) and of the experimental and simulated values.

Figure 20

The experimental and simulated values of the surface transmission given by $1-P_1$ is compared with the model of Eq. (11).