Saturation of the laser-induced narrowband coherent synchrotron radiation process: Experimental observation at a storage ring

We study the efficiency limitation affecting laser-induced coherent synchrotron radiation (CSR) at high laser power. Experiments are made on the UVSOR-II storage ring in conditions of narrowband terahertz CSR emission. While, at moderate power, CSR power increases quadratically with laser power, a noticeable decrease in efficiency and eventually a decrease in CSR power is observed experimentally at high power. Details of the underlying process are analyzed numerically. As the saturation effect depends almost instantaneously on the laser intensity, the saturation occurs locally in longitudinal space. This has important consequences on the modulation pattern induced on the electron bunch.

Figure 1

Illustration of the saturation process in a simplified case where the laser pulse is infinitely long, and the magnetic transport involves only longitudinal dynamics (more precisely $r_{51}=r_{51}=0$ and $r_{56}\ne 0$). The upper [(a)–(d)] and lower rows [(e)–(h)] represent the longitudinal phase space, and the longitudinal density profile $\rho (z)$ respectively, at the emission point for increasing laser power. The tilt of the modulation pattern has a fixed angle determined by the magnetic transport parameter $r_{56}$. The increase in laser power leads to a monotonic increase of energy modulation. However, the modulation amplitude in the vertical projection (or equivalently the bunching factor) increases up to an absolute maximum [from (a) to approximately (c)]. Then the amplitude of the density modulation begins to decrease and remains below this absolute maximum. The model used in this simulation is described in Ref. 11, and the parameters used for the illustration are $r_{56}=0.4$, $k_m=40$, $w_0=0.03$ for (a), $w_0=0.06$ for (b), $w_0=0.3$ for (c), and $w_0=0.6$ for (d) . The longitudinal coordinate is expressed in units of the initial bunch length. Calculations made in the paper will be performed including 3D beam transport and a finite duration laser pulse.

Figure 2

Global organization of the experiment at the UVSOR-II storage ring. We produce long laser pulses with an adjustable duration and a sinusoidal intensity modulation. The period is adjustable in the cm-submillimeter range, and the duration is typically chosen from few ps to 190 ps (FWHM). The laser pulses interact with the electron bunch inside an undulator (FEL beam line) and produce an energy modulation. The transport through magnetic elements (in particular dipoles) converts this energy modulation into a charge density modulation, and narrowband CSR terahertz emission is produced at bending magnet beam lines. CSR emission is monitored at the BL6B beam line. T: $0.5\times \mathrm{\text{telescope}}$; HWP: half-wave plate; PC: polarizing cube; L1: 5 m focusing lens; L2: 2.5 m imaging lens; F: partially rejecting filter at 800 nm, adjusted to obtain simultaneously synchrotron radiation and laser images with similar intensities on the camera. The imaging system (camera and lens L2) provides an image of laser and SR transverse profiles in the first undulator (typically the center). Details of transport mirrors are not represented.

Figure 3

Laser and pulse-shaper setup. The amplified laser system (from Coherent Inc.) is composed of a Mira oscillator, a Legend regenerative amplifier, and a Hidra multipass amplifier, whose uncompressed (chirped) output is used. The pulse shaper is composed of a Michelson interferometer and an adjustable compressor. The CCR2 Michelson retroreflector is mounted on a motorized translation stage, allowing to adjust the output pulse period $T_m$. The pulse duration $T_D$ can be changed by adjusting the distance between gratings. The parts displayed in green (mirror and G2 grating) are fixed on the carrier of a single translation stage with wide range (60 cm). With this configuration, the output pulse delay is not significantly affected by the large displacements of the translation stage. CCR1 and CCR2 are protected gold-coated corner cube retroreflectors with low angular error (0.5 arc sec). RRF: roof retroreflector; M: mirrors (HR at 800 nm); BS: 50% beam splitter; G1 and G2: $1800\mathrm{l}/\mathrm{mm}$ compression gratings from Spectrogon. Transport mirrors are not represented in detail. The compressor produces pulses whose duration is adjustable from $\approx 130\mathrm{fs}$ to 190 ps FWHM.

Figure 4

Typical scalings of terahertz signal versus laser power for three power ranges: (a) reference quasiquadratic behavior that was already observed at low power, with a 2 mJ amplifier and 300 ps long-pulses (the dots and the full line represent respectively the experimental data and a quadratic fit); (b) and (c) behaviors obtained with the current 70 mJ amplifier and shorter pulses: 191 ps FWHM (b) and 28.5 ps (c). The dashed lines represent a reference quadratic slope. Modulation period is identical ($\approx 2.4\mathrm{ps}$, i.e., $14{\mathrm{cm}}^{-1}$) for each recording. Note that electron bunch duration is $\approx 240\mathrm{ps}$ FWHM (length 3.1 cm rms).

Figure 5

Numerical calculation of the efficiency, represented in conditions similar to the experimental ones (Fig. 4). Note that dimensionless units are used. The quantity ${\sigma }_L{w}_0^2$ is proportional to laser pulse energy. The integrated form factor is proportional to the terahertz pulse energy (and the bolometer signal). The laser pulse duration ${\sigma }_L$ is expressed in units of the electron bunch duration. The two thick full lines (${\sigma }_L=0.1$ and ${\sigma }_L=0.8$) approximately correspond to the pulse durations of Fig. 4 (28.5 ps, i.e., ${\sigma }_L=0.117$ and 191 ps, i.e., ${\sigma }_L=0.78$). The modulation wave number is $k_m=272$, which corresponds to $14{\mathrm{cm}}^{-1}$. We took $\varphi =0$, and other parameters are listed in Tables .

Figure 6

Least square fit of Eq. (9) on experimental data. $w_0$ is the energy modulation in units of the initial energy spread. The vertical values are expected to be overestimated, as the laser beam has a smaller diameter than the electron bunch. Equal weights are attributed to every experimental points.

Figure 7

Local saturation process visible on the normalized charge density profile ${\rho }_0(z)$ of the electron bunch. Numerical calculations were made using $w_0=1$ (a), $w_0=10$ (b), and $w_0=50$ (c). Panels (d), (e), and (f) show the form factors (i.e., power spectra) associated to (a), (b), and (c), respectively. Dimensionless laser pulse duration is ${\sigma }_L=0.117$ (i.e., 28.5 ps). Other parameters are the same as for Fig.  5.

Figure 8

Form factor versus wave number and energy modulation, for a modulation wave number $k_m=272$ (i.e., $\approx 14{\mathrm{cm}}^{-1}$). In the left column we have represented the raw form factor $|\tilde{\rho }{|}^2$. In the right column, we have plotted $|\tilde{\rho }{|}^2/w_0^4$. With this representation, we can clearly notice the quadratic scaling with laser power [the yellow line of almost constant value in the left part of (g)], expected at low powers [more precisely when $w_0\ll 1/(k_m{r}_{56})\approx 1.26$ here]. Note that laser power is proportional to $w_0^2$. Parameters are identical to the ones used for Fig. 7 and the experimental results displayed in Fig. 6. For clarity, we have not represented the data in the extremely low wave number part [note that Eq. (7) implies that we must have ${\tilde{\rho }}^2(\overline{\nu })=1$ at $\overline{\nu }=0$]. More precisely, the sharp horizontal white regions near $\overline{\nu }=0$ correspond to ${\tilde{\rho }}^2>4\times {10}^{-3}$ in (d), and ${\tilde{\rho }}^2/w_0^4>1\times {10}^{-10}$ in (h).