Simulation of inverse Compton scattering and its implications on the scattered linewidth

Rising interest in inverse Compton sources has increased the need for efficient models that properly quantify the behavior of scattered radiation given a set of interaction parameters. The current state-of-the-art simulations rely on Monte Carlo–based methods, which, while properly expressing scattering behavior in high-probability regions of the produced spectra, may not correctly simulate such behavior in low-probability regions (e.g. tails of spectra). Moreover, sampling may take an inordinate amount of time for the desired accuracy to be achieved. In this paper, we present an analytic derivation of the expression describing the scattered radiation linewidth and propose a model to describe the effects of horizontal and vertical emittance on the properties of the scattered radiation. We also present an improved version of the code initially reported in Krafft et al. [Phys. Rev. Accel. Beams 19, 121302 (2016)], that can perform the same simulations as those present in cain and give accurate results in low-probability regions by integrating over the emissions of the electrons. Finally, we use these codes to carry out simulations that closely verify the behavior predicted by the analytically derived scaling law.

Figure 1

The comparison between the scattering linewidth given by Eq. (14) of Ref. [18] (green line) and Eqs. (14) and (23) of this paper (red line), compared to the simulations with iccs (blue dots). The simulation parameters are those given for case $A_a$ in Sec. 2b3.

Figure 2

Relationship between the energy spread of photon beam ${\sigma }_L/E_L$ and the resulting linewidth of scattered radiation. Electron beam energy spread is held constant at ${\sigma }_{\gamma }/E_{\gamma }=0$ and emittance at ${\epsilon }_{x,y}=0$. Panels represent cases $D_{\mathrm{la}}–F_{\mathrm{la}}$, given in Table 2, from top to bottom. Results given in Eq. (23) are labeled “analytical.” Numerical simulations carried out with iccs are labeled “simulated.” Panels are not on the same scale.

Figure 3

Relationship between the energy spread of electron beam ${\sigma }_{\gamma }/E_{\gamma }$ and the resulting linewidth of scattered radiation. Photon beam energy spread is held constant at ${\sigma }_L/E_L=2\times {10}^{-4}$ and emittance at ${\epsilon }_{x,y}=0$. Panels correspond to cases $D_{\mathrm{el}}–F_{\mathrm{el}}$, given in Table 3, from top to bottom. The impact of electron beam spread is nearly halved in large electron recoil regimes. Values were chosen so that electron beam bandwidth dominated the linewidth of scattered radiation. Results given in Eq. (23) are labeled analytical. Numerical simulations carried out with iccs are labeled simulated. Panels are not on the same scale.

Figure 4

Relationship between the aperture and resulting linewidth of scattered radiation. The electron beam energy spread is held constant at ${\sigma }_{\gamma }/E_{\gamma }=0$ and emittance at ${\epsilon }_{x,y}=0$, photon beam at ${\sigma }_L/E_L=2\times {10}^{-2}$. Parameters for all cases are reported in Table 4. Results given in Eq. (23) are labeled analytical. Numerical simulations carried out with iccs are labeled simulated. Panels are not on the same scale. Top row (left to right): Cases $A_a$ and $D_a$. Bottom row: Cases $E_a$ and $F_a$.

Figure 5

Relationship between the horizontal emittance of the electron beam ${\epsilon }_x$ and the resulting linewidth of scattered radiation. Parameters for all cases are reported in Table 5. Analytical results given in Eq. (23) are labeled analytical. Numerical simulations carried out with iccs are labeled simulated. Panels are not on the same scale. Top row (left to right): Cases $D_{\mathrm{em},1}$ and $D_{\mathrm{em},2}$. Bottom row: Cases $E_{\mathrm{em},1}$ and $E_{\mathrm{em},2}$.

Figure 6

Relationship between the emittance and resulting linewidth of scattered radiation. Top: Case $D_{\mathrm{em},3}$. Bottom: Case $D_{\mathrm{em},4}$. Including covariance, given in Eq. (23) and labeled analytical, covariance, does predict better in the regime of asymmetrical spectra than the case without covariance, given in Eq. (22), and labeled analytical, no covariance. Apertures were increased greatly to make the covariance more pronounced (top panel). For small apertures (bottom panel), the curve with covariance rises less sharply and closely follows the curve without covariance. Parameters for all cases are reported in Table 6.

Figure 7

The numerically simulated spectrum for increasing resolutions for cain [19] and iccs for the case given in Table 7. The number of macroparticles $N_p$ samples the electron beam distribution. Top row: cain simulations on the linear (left) and log scale (right). Bottom row: iccs simulations on the linear (left) and log scale (right).