Influence of bending parameters on crystalline undulator radiation peak stability for 530 MeV positron channelling

TL;DR

This work analyzes how bending amplitude $a$ and bending period $\lambda$ affect the stability and properties of crystalline undulator radiation (CUR) peaks for $530~\text{MeV}$ positron channelling in periodically bent C$(110)$ crystals. It combines a fast continuous-potential analysis (using the bending parameter $C$ and first harmonic energy $\hbar\omega_1$) with relativistic molecular dynamics simulations to map peak energy and intensity across a grid of $(a,\lambda)$ values. The results show that the CUR peak energy tracks $\hbar\omega_1$ and remains stable along isolines, with a predicted peak near $0.515$ MeV for MAMI-like parameters; intensity trends depend on $a$ and $\lambda$, with dechannelling limiting performance at short periods. A four-period undulator scenario consistent with MAMI parameters further supports a CUR peak around $0.515$ MeV and provides practical manufacturing tolerances for crystal-based gamma-ray sources, while demonstrating a transferable methodology for exploring CUR stability at higher energies and other facilities.

Abstract

We investigate the stability of crystalline undulator radiation (CUR) peaks emitted by 530 MeV positron channelling in periodically bent C(110) crystals with varying bending amplitudes and bending periods. Relativistic molecular dynamics simulations were performed to quantify how these parameters affect the intensity and position of the CUR peak. The continuous potential approximation was used to identify isolines of constant peak energy, providing a reference for regions of spectral stability. MD results show that increasing the bending amplitude shifts the CUR peak to lower photon energies, while decreasing the period shifts it to higher energies, with both trends accompanied by enhanced dechannelling. For crystal parameters similar to recent experiments conducted at the MAinz MIkrotron (MAMI), the simulated CUR peak appears near 0.515 MeV. These results demonstrate that the CUR peak remains stable across a broad range of bending amplitudes and periods, establishing estimates of manufacturing tolerances for the design of gamma-ray crystal-based light sources.

Figures (7)

• Figure 1: Heatmaps showing the variation in the values of the bending parameter $C$(left panel) and first harmonic position $\hbar\omega_1$(right panel) as a function of the bending period $\lambda$ and bending amplitude $a$. Both plots share the same y axis. Each plot indicates various lines of constant $C$ and $\hbar\omega_1$ using dashed white lines with their corresponding values. Circular markers on the right panel indicate specific values along the isoline for $\hbar\omega_1=0.526MeV$, discussed in detail later.
• Figure 2: Channelling fractions $f_{\text{ch},0}$ (dashed lines) and $f_{\text{ch}}$ (solid lines) as a function of penetration distance for bending periods of $\lambda=5.5µm$(left panel) and 3.5µm (right panel). Both plots show bending amplitudes of $a=0.60$, 1.44, and 2.50. A representation of the bending profile is included at the top of each plot, with vertical lines corresponding to the maxima and minima of the profile. Note that the fractions are normalised to the number of accepted particles.
• Figure 3: Spectral distributions of crystalline undulator radiation for 530MeV positrons for different bending profiles. The top row corresponds to the emission cone $\theta_0=133.8µrad\approx0.139/\gamma$, and the bottom row $5/\gamma \approx 4821µrad$. The left column corresponds to a bending period of $\lambda=8.0µm$, the middle column 6.5µm, and the right column 5.0µm. All cases show the same range of bending amplitudes $a$, indicated by the top legend. In all cases markers indicate the spectral peaks.
• Figure 4: Spectral distributions of crystalline undulator radiation for 530MeV positrons for the emission cones $\theta_0=133.8µrad\approx0.139/\gamma$(left panel) and $\theta_0=5/\gamma\approx4821µrad$(right panel). Both cases are for a bending period of $\lambda=3.5µm$. In all cases markers indicate the peak spectral peaks.
• Figure 5: Number of photons in units of photons per per solid angle $\Delta\Omega \approx\pi\theta_0^2$ for the emission cones $\theta_0=133.8µrad\approx0.139/\gamma$(left panel) and $\theta_0=5/\gamma4821µrad$(right panel). Both cases are for a bending period of $\lambda=5.0µm$. In all cases markers indicate the peak number of photons. The dashed lines in the left panel indicate the spectral peaks from \ref{['fig:Spectra_All']}.