Modeling classical and quantum radiation from laser-plasma accelerators

The development of models and the “Virtual Detector for Synchrotron Radiation” (vdsr) code that accurately describe the production of synchrotron radiation are described. These models and code are valid in the classical and linear (single-scattering) quantum regimes and are capable of describing radiation produced from laser-plasma accelerators (LPAs) through a variety of mechanisms including betatron radiation, undulator radiation, and Thomson/Compton scattering. Previous models of classical synchrotron radiation, such as those typically used for undulator radiation, are inadequate in describing the radiation spectra from electrons undergoing small numbers of oscillations. This is due to an improper treatment of a mathematical evaluation at the end points of an integration that leads to an unphysical plateau in the radiation spectrum at high frequencies, the magnitude of which increases as the number of oscillation periods decreases. This is important for betatron radiation from LPAs, in which the betatron strength parameter is large but the number of betatron periods is small. The code vdsr allows the radiation to be calculated in this regime by full integration over each electron trajectory, including end-point effects, and this code is used to calculate betatron radiation for cases of experimental interest. Radiation from Thomson scattering and Compton scattering is also studied with vdsr. For Thomson scattering, radiation reaction is included by using the Sokolov method for the calculation of the electron dynamics. For Compton scattering, quantum recoil effects are considered in vdsr by using Monte Carlo methods. The quantum calculation has been benchmarked with the classical calculation in a classical regime.

Figure 1

Calculated radiation spectrum showing the effects of $N_{\beta }$ and the term $R_1$ in Eq. (4). The betatron strength parameter here is $a_{\beta }=2.0874$. The yellow dashed lines show the envelope of high frequency oscillation plateau (HFP) induced by end-points effect. The white dashed line shows the envelope of the oscillations induced by numerical integration noise.

Figure 2

Schematic view of vdsr calculations for betatron radiation, undulator radiation, Thomson and Compton scattering.

Figure 3

(a) Radiated photon energy and angular distributions. (b) Angularly integrated radiation spectrum distribution. (c) Evolution of the root mean square (rms) spread of the transverse position. (d) Evolution of the rms spread of the longitudinal momenta of the traced electrons.

Figure 4

Radiation distribution ($\mathrm{photons}/\mathrm{sr}/0.1\%\mathrm{BW}$) in angle-energy space in the plane perpendicular to the laser polarization direction $\varphi =90°$ [(a),(c),(e)] and in the plane parallel to the laser polarization direction $\varphi =0°$ [(b),(d),(f),(h)]. (g) Typical radiation intensity distribution on a CCD camera which is 4.7 m far away from the radiation source. Here no filter and corresponding effects of the virtual CCD are considered. Only raw radiation data is shown. Beam parameters for (a) and (b) are $r_b=1.0\mu \mathrm{m}$ and energy spread is 0.2%, for (c) and (d) are $r_b=1.0\mu \mathrm{m}$ and energy spread is 2%, and for (e), (f), (g), and (h) are $r_b=10.0\mu \mathrm{m}$ and energy spread is 2%. The beam-laser collision point is at the laser focus for simulations of (a)–(f), and it is 4.968 mm in front of the focus for simulations of (g) and (h).

Figure 5

Comparison between classical Thomson scattering calculations (C) and quantum Compton scattering calculations (Q). The signal is integrated in the $\theta$ direction. Here $X=[(p+k{)}^2-(m_{e}c{)}^2]/(m_{e}c{)}^2\simeq 0.002\ll 1$, quantum recoil effect is negligible and the classical calculation is applicable. In the quantum calculation an integration range for $\varphi$ has been used. The averaged line means the average for the $\varphi =0°$ and $\varphi =90°$.

Figure 6

(a) Radiation intensity distribution using quantum calculations (Monte Carlo method). Here $X=[(p+k{)}^2-(m_{e}c{)}^2]/(m_{e}c{)}^2\simeq 0.23$, quantum recoil effect is important. Different macroparticle numbers from 50 to 200 K and amplification factors from 0.333 to 10.0 are used to make the calculations. The blue dotted line shows a too much larger $f$ number can result in multiscattering artificially, and a broadened spectrum is seen. (b) Spectrum calculated by classical method. Both the radiation spectra including radiation reaction effect (red line) or without (black line) are shown. The only difference between them is the slight peak position shift.

Figure 7

A schematic view of the vdsr programing flowchart.