⇦Chinese Physics Letters, 2017, Vol. 34, No. 1, Article code 015202 Imaging Laser wake fields by Thomson Scattering a Co-Propagating Pulse * Hong-Jie Liu(刘红杰)1,2**, Yu-Qiu Gu(谷渝秋)1,2, Gang Li(李纲)1,2, Feng Lu(卢峰)1,2, Bo Cui(崔波)1,2, Zeng-Hai Dai(戴曾海)1,2, Yan-Yun Ma(马燕云)3, Wei-Min Zhou(周维民)1,2, Lei-Feng Cao(曹磊峰)1,2, Bao-Han Zhang(张保汉)1,2 Affiliations 1Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900 2Science and Technology on Plasma Physics Laboratory, Mianyang 621900 3Department of Physics, National University of Defense Technology, Changsha 410073 Received 18 August 2016 *Supported by the National Natural Science Foundation of China, and the Foundation of Science and Technology on Plasma Physics Laboratory.
**Corresponding author. Email: buyijie@163.com Citation Text: Liu H J, Gu Y Q, Li G, Lu F and Cui B et al 2017 Chin. Phys. Lett. 34 015202 Abstract Thomson scattering imaging (TSI) is proposed and experimentally demonstrated to observe the fine structure of the laser wake field. By Thomson scattering a co-propagating laser pulse, we obtain clear images indicating that the wake field is like an acaleph swimming behind the pump laser. The wavelength of the wake field observed at different electron densities agrees well with the theory. Since no mathematics transformation is involved, TSI could be potentially used as an online monitor for future 'tabletop' plasma accelerators. DOI:10.1088/0256-307X/34/1/015202 PACS:52.35.Fp, 52.80.Dy, 52.40.Db © 2017 Chinese Physics Society Article Text Generation of energetic electrons based on laser plasma accelerators can provide compact and high-brightness beam sources,[1-6] opening the door to many applications such as medicine and material science. In these accelerators, laser wake fields play a key role in the generation of monoenergetic electrons with high energy. The wake fields are usually excited by an intense laser interacting with gas jet and have a phase velocity equal to the group velocity of the driven laser. Recent advances in laser plasma accelerators dramatically illustrated the link between beam quality and wake fields structure. The ability to measure the wake fields microstructure directly is important for addressing fundamental issues such as the wake fields generation by optimized pulse trains,[7] design of particle injectors synchronized to the laser pulse on a femtosecond timescale,[8] growth dynamics of plasma wave instabilities,[9] and self-consistent propagation of laser pulse and wake in plasma channels.[10] In the last few years, frequency-domain interferometry (FDI) and frequency-domain holography (FDH) were used to explore the laser wake fields.[11-15] In FDI, a focused femtosecond probe pulse can be used to measure local electron density $n_{\rm e}(t)$ at only a single time delay $t$ behind the driving pulse within the co-propagating wake for each shot. Wake structure was then accumulated painstakingly by probing a different $t$ on each subsequent shot. Nevertheless, multi-shot techniques can obtain the average over shot-to-shot variations of the laser wake fields, and could not provide rapid feedback for optimizing experimental parameters. Recently, snapshots of laser wake fields were achieved by FDH,[16] which uses a long and wide probe pulse that illuminates the entire object $n_{\rm e}(r,t)$ at once. However, both FDI and FDH could hardly be used for online diagnostic because complicated mathematic transformations can involve processing the raw interferometric data, reconstructing the wave structure. Heretofore, the fine structure of laser wake fields has not yet been observed. In this Letter, we propose the Thomson scattering imaging, a completely direct way to observe the fine structure of the laser wake fields. The Thomson scattering is originally used to describe the light scattering from a free electron. When an electromagnetic wave ($\omega _{0}$) is incident on a charged particle, the electric and magnetic components of the wave exert a Lorentz force on the particle, setting it into motion. The scattering light was radiated at harmonics of the frequency of the incident light. The harmonic number $n$ depends upon the normalized amplitude of the vector potential of the incident laser, $a_{0}=0.85\times10^{-9}\lambda _{0}I_{0}^{1/2}$, where $\lambda _{0}$ and $I_{0}$ are the wavelength and intensity of the incident laser, in units of μm and W/cm$^{2}$, respectively. When $a_{0}\ll1$, the Thomson scattering occurs in the linear regime and radiation is generated at the fundamental frequency $\omega=\omega _{0}$. In contrast, when $a_{0}\ge1$, the Thomson scattering occurs in the nonlinear regime and radiation is generated at harmonics in addition to the fundamental, $\omega=\omega _{n}=n\omega _{0}$, $n=1$, 2, 3, ${\ldots}$. In the nonlinear regime, it is known that the distribution of the scattered radiation provides information about the spatial distribution of electron density in the medium.[17] The dependence of the intensity of the Thomson scattering light on plasma density and laser intensity has been reported by Chen et al.[18] To observe the structure of laser wake field, which is propagating with a velocity close to the pump laser, a co-propagating probe is needed. The laser wake field, pump laser, and co-propagating probe together make a moving reference frame. Only in this reference frame can we image the laser wake fields by the Thomson scattering a co-propagating pulse. To obtain a Thomson scattering image, three challenges have to be met: (1) the generation of large amplitude laser wake field, (2) sufficient intensity of the probe beam, and (3) the proper delay time between the pump laser beam and the probe beam.
cpl-34-1-015202-fig1.png
Fig. 1. Experimental setup. The He gas jet is produced in a supersonic expansion of high pressure gas into a vacuum through a 0.5 mm coniform nozzle, in length 22 mm. A Mach–Zehnder interferometer (not shown here) is built up using a 532 nm, 10 ns and 1 mJ laser beam, to measure the density of the He gas jet. The pump pulse and probe pulses deliver 2.25 J and 0.75 J energies, respectively. The delay time between them is determined by a strip camera.
The experiments were performed on the SILEX-I 800 nm, 300 terawatt Ti:sapphire laser facility at the Research Center of Laser Fusion,[19] China Academy of Engineering Physics (RCLF, CAEP). The contrast ratio of this system is typically 10$^{7}$ on nanosecond scale. It can produce two pulses ($\tau=31$ fs) with a 30 ps interval between them (see Fig. 1). The first one (hereafter 'pump pulse') is focused by an f/20 off axis parabolic (OAP) on a He gas jet to create a plasma wave. The focal spot consists of a Gaussian spot with full width at half maximum (FWHM) of 40 μm (containing 50% of the total energy) and a dim ring. The post-pulse serves as a probe pulse. Because the probe pulse is focused by the same OAP, like a flashlight, it can illuminate all the region of hot plasma generated by the pump pulse. The energy of the pump pulse is three times that of the probe pulse. The vacuum-focused laser intensity is $3\times10^{18}$ W/cm$^{2}$ ($a_{0} =1.2$) and $1\times10^{18}$ W/cm$^{2}$ ($a_{0}=0.7$) for pump pulse and probe pulse, respectively. For the high laser intensity, the helium gas was fully ionized by the leading edge of the laser pulse and ionization did not play a role in the interaction. The first harmonic ($\omega _{1}$) from the probe plasma interaction region was imaged (by a lens, $f=300$ mm) onto a Bitran CCD camera (6.45 μm resolution) through a band-pass filter with a 10 nm wavelength window centered at 800 nm. The CCD is orientated perpendicular to the laser polarization and to the laser propagation direction. To obtain a large-amplitude plasma wave, we varied the plasma density from $1\times10^{17}$/cm$^{3}$ to $1\times10^{18}$/cm$^{3}$ by controlling the gas jet backing pressure. In such a plasma with low density, the laser pulse can excite a good-quality wake plasma wave below the wave-breaking threshold for the first period of the wake.[20] The wavelength of relativistic plasma wave ($\lambda _{\rm p}=2\pi c/\omega _{\rm p}$) is of the order of 50 μm, where $\omega _{\rm p}=\sqrt {4\pi n_{\rm e} e^2/m_{\rm e}}$. According to the theory,[21-23] the harmonic signal generated from the nonlinear Thomson scattering is linearly proportional to the electron density because it is an incoherent single-electron process. In our experiment, the measured incoherent signal equals the single-electron results multiplied by the total number of electrons, $I_{\rm s} d{\it \Omega}=I_0 N_{\rm e} r_{\rm e}^2 \sin^2\beta S(k,\omega )d{\it \Omega}$, where $I_{0}$ is the intensity of the incident laser, $N_{\rm e}$ is the number of electrons, $r_{\rm e}$ is the electron classical radius, $\beta$ is the angle between the incident laser polarization and scattering direction ($\beta=90^{\circ}$ in our experiment), and $S(k,\omega)$ is the dynamical form factor, giving the frequency shifts resulting from the effect of correlation between the electrons.
cpl-34-1-015202-fig2.png
Fig. 2. (a) Typical Thomson scattering image (raw) of plasma wave, obtained by the Bitran CCD camera, at 4.47$\times$10$^{17}$/cm$^{3}$. The corresponding wavelength 47.85 μm can be read directly from the image. (b) Image obtained without probe pulse, while keeping the other experimental conditions unchanged.
Considering the high intensity of the probe pulse, we placed several neutral filters before the CCD camera. Figure 2 represents the typical Thomson scattering image. A clear image of the scattered light (first harmonic) was observed in the region where the laser wake field was excited. It is known that the laser wake fields propagate forward with a similar velocity to the driven laser. Actually, the oscillating electrons themselves do not leave their oscillating region before wave breaking. Thus with the co-propagating laser pulse in the experiment, we can obtain a series of periodic wake fields at each shot. Once established, the wake fields will grow until wave-breaking takes place. At the beginning (shown in Fig. 2(a)) the number of the electrons captured by the wake fields is limited. As the wake fields propagated forward, more and more electrons with energy above the trapping threshold were captured until the largest amplitude formation of the plasma wave.[24,25] As described in Ref. [2], wave breaking is not always catastrophic and a part of the electrons in the wave can escape, reducing its amplitude, while maintaining the wave structure. To confirm the Thomson scattering radiation of the post-pulse contributing to the observed signal, we repeated the experiment without post pulse, in which instead of the periodic wave structure, just a very feeble image of the plasma channel was observed, as shown in Fig. 2(b). This excludes the possibility that our TSI is a result of laser gas jet interaction or other stray light. The main focal spot of the laser will undergo relativistic self-channeling when the intense laser interacts with the high dense gas jet.[26] However, the Thomson scattering images show that the diameter of the plasma thread is about 500 μm, which is produced by the spot wings with intensity above the ionization threshold.
Table 1. The measured wavelength and the theoretical calculation.
$n_{\rm e}$ (10$^{17}$) 6.29 4.47 3.69 3.33 2.81
$\lambda _{\rm ex}$ (μm) 42.89 47.85 56.49 59.10 66.32
$\lambda _{\rm p}$ (μm) 42.07 49.91 54.94 57.83 62.95
The variation of the initial gas density has an expected effect on the laser wake field. The measured wavelengths ($\lambda _{\rm ex}$) of the laser wake field at different electron densities are listed in Table 1, which are in good agreement with the theoretical results considering the resolution of the Bitran CCD. The wavelength of different periods is slightly different even in the same image. This is associated with the nonuniformity of the density distribution of the gas jet. The wavelength in Table 1 is the average of each shot. To gain a greater insight into the fine structure of the laser wake field, we adjusted the neutral filters, which were chosen to observe the largest amplitude period (the most intense scattering light) only (see Fig. 3). The plasma wave is really beautiful like an acaleph swimming along the laser propagating axis in the plasma. Here one can see how the wake field is excited. The electrons pushed by the ponderomotive force of the laser pulse move in the forward and transverse directions. Since the ponderomotive force is proportional to the laser intensity gradient, these pushed electrons were directed primarily in the longitudinal direction because the laser pulse length ($c\tau =9$ μm) is much shorter than its focal spot size in our experiment.[24] On the other hand, the ions do not respond to the ponderomotive force because their mass is much larger than electrons. Under the restoring force (backward and centripetal) due to the electric field of the space charge separation, the electrons would be dragged back towards their original position.[25] Thus a large amplitude laser wake field is generated along the propagating axis of the driven laser pulse.
cpl-34-1-015202-fig3.png
Fig. 3. Fine structure of the typical plasma wave.
cpl-34-1-015202-fig4.png
Fig. 4. Electron densities at (a) 160 T and (b) 410 T in 2D simulation for $a=3$ and $n=6.1\times 10^{18}$/cm$^3$.
Another very interesting phenomenon is the micro-structure of the wake field in Fig. 2, which has never been reported in any other experiment before. In our experimental results, there are numerous sparkles in the wake field. To reach a deeper understanding of the experiment, we carried out two-dimensional (2D) particle-in-cell (PIC) simulations using PLASIM (2D), which is a fully relativistic particle-in-cell code. A uniform plasma with length $L=500\lambda_{0}$ is used in the simulations, where $\lambda _{0}=800$ nm is the wavelength of the incident laser in vacuum. The Gaussian laser pulse is given by $a=a_0\exp[-(t-t_0)^2/2\tau ^2]\exp[-(y-y_0)^2/2\sigma ^2]$, where $\sigma=10.56$ μm and $\tau=5.62T$ ($T$ is the laser duration). In the simulations, $a=2$ and $a=3$ are used for the plasma density range from 0.0001$n_{\rm c}$ to 0.004$n_{\rm c}$, where $n_{\rm c}$ is the critical density. However, a surprising thing is that very analogous phenomena appeared in our simulations for higher laser intensity and plasma density. The simulation results show that some instability may arise in the wake field. The instability can be attributed to laser filamentation, Raman scattering and self-modulation. The more detailed physics are still being studied. In conclusion, the Thomson scattering imaging is experimentally demonstrated to observe the fine structure of the laser wake fields. By Thomson scattering a co-propagating laser pulse, we obtain clear images of the wake fields. The wavelength of the wake field observed at different electron densities agrees well with the theoretical analysis. With the development of the laser and detectors, we expect that TSI will become a real-time diagnostic tool for the relativistic laser plasma accelerator in the near future. We would like to thank Dr. Zhang Bo for critically reading the manuscript, and the staff of the SILEX-I laser system for their assistance during the experiments. References GeV electron beams from a centimetre-scale acceleratorMonoenergetic beams of relativistic electrons from intense laser–plasma interactionsHigh-quality electron beams from a laser wakefield accelerator using plasma-channel guidingA laser–plasma accelerator producing monoenergetic electron beamsGeV electron beams from a centimeter-scale channel guided laser wakefield acceleratorElectron bunch acceleration in the wake wave breaking regimeNonlinear Plasma Waves Resonantly Driven by Optimized Laser Pulse TrainsObservation of Ultrahigh Gradient Electron Acceleration by a Self-Modulated Intense Short Laser PulseElectron acceleration from the breaking of relativistic plasma wavesLight pipe for high intensity laser pulsesSnapshots of laser wakefieldsDirect measurement of coherent ultrahigh wakefields excited by intense ultrashort laser pulses in a gas-jet plasmaObservation of spatial asymmetry of THz oscillating electron plasma wave in a laser wakefieldLaser Wakefield Excitation and Measurement by Femtosecond Longitudinal InterferometrySingle-shot measurement of temporal phase shifts by frequency-domain holographyStudies of laser wakefield structures and electron acceleration in underdense plasmasLaser light scattering in laboratory plasmasExperimental observation of relativistic nonlinear Thomson scatteringSpace discharge and gas lasersElectron bunch acceleration in the wake wave breaking regimeIncoherent harmonic emission from strong electromagnetic waves in plasmasNonlinear Thomson scattering of intense laser pulses from beams and plasmasThomson Scattering from Ultrashort and Ultraintense Laser PulsesSimulation of ultrashort electron pulse generation from optical injection into wake-field plasma wavesTrapping and acceleration in nonlinear plasma wavesPlasma Channel Formation and Guiding during High Intensity Short Pulse Laser Plasma Experiments
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