Direct imaging of the dynamics of a laser-plasma accelerator operating in the bubble -regime

Transcription

1 arxiv: v1 [physics.plasm-ph] 13 Feb 2014 Direct imaging of the dynamics of a laser-plasma accelerator operating in the bubble -regime A. Sävert 1, S. P. D. Mangles 2, M. Schnell 1, J. M. Cole 2, M. Nicolai 1, M. Reuter 3, M. B. Schwab 1, M. Möller 1, K. Poder 2, O. Jäckel 1,3, G. G. Paulus 1,3, C. Spielmann 1,3, Z. Najmudin 2, and M. C. Kaluza 1,3, 1 Institut für Optik und Quantenelektronik, Max-Wien-Platz 1, Jena, Germany. 2 The John Adams Institute, The Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom. 3 Helmholtz-Institut Jena, Fröbelstieg 3, Jena, Germany. Corresponding author: Malte.Kaluza@uni-jena.de 1

2 Laser-plasma accelerators operating in the bubble -regime [1] generate quasi-monoenergetic multi-gigaelectronvolt electron beams [2, 3] with femtosecond duration [4, 5] and micrometre size [6, 7]. These beams are produced by accelerating in laser-driven plasma waves in only centimetre distances. Hence they have the potential to be compact alternatives to conventional accelerators [8]. However, since the plasma wave moves at ultra-relativistic speed making detailed observation extremely difficult, most of our current understanding has been gained from high-performance computer simulations. Here, we present experimental results from an ultra-fast optical imaging technique visualising for the first time the non-linear dynamics in a laser-plasma accelerator. By freezing the relativistic motion of the plasma wave, our measurements reveal insight of unprecedented detail. In particular, we observe the plasma wave s non-linear formation, breaking, and transformation into a single bubble for the first time. Understanding the acceleration dynamics is essential to further improve the quality of laser-plasma accelerators as a source for brilliant and ultra-short x-rays [9, 10, 11]. In a laser-plasma accelerator [8], the intense pressure of a short-pulse laser displaces plasma electrons from the stationary background ions. Due to the generated space charge fields the electrons return, creating an accelerating plasma wave that co-propagates with the laser at almost c, the speed of light, through the plasma. The wavelength of this relativistic plasma wave in the linear regime, i.e. for sufficiently low plasma densities n e, is λ plasma = 2πc ε 0 m e /(n e e 2 ), where e, m e, and ε 0 are electron charge, mass and the vacuum permittivity respectively. Since this constitutes a variation in plasma density and in associated refractive index, the plasma wave can induce phase changes on a co-propagating probe beam. Hence the plasma wave can be directly observed by either time-domain interferometry (TDI) [12, 13], or in a single shot by frequency-domain holography (FDH) [14]. For these techniques to work well, though, the wave must not be evolving strongly within the interaction distance, since this would cause blurring. 2

3 To reach the bubble -regime, where electrons break from the coherent fluid motion and become trapped and accelerated within the plasma wave, multi-tw laser powers are required. Particle-in-cell (PIC) simulations show that, in this domain, the first period of the plasma wave also self-traps the driving laser pulse, leading to its self-focussing and compression. This in turn further increases the plasma wave amplitude, eventually leading to bubble formation. Since the density gradients are so large in this domain, the plasma wave s peaks strongly refract the probe, so that FDH gives no information about the wave structure [15]. Also since FDH is integrated over the whole plasma, information about the wave s evolution is lost. However, refractive index gradients in transparent media, such as those associated even with non-linear plasma waves, can be directly observed by shadowgraphy. This is provided that the probe propagating perpendicularly to the main pulse is much shorter than one plasma wave period, τ probe T plasma = λ plasma /v g λ plasma /c, where v g is the laser s group velocity in the plasma. For n e = cm 3, λ plasma = 8.1µm corresponding to T plasma = 27 fs. Hence resolving the plasma wave requires a probe duration as short as a few optical cycles of the IR-probe light only. Recent experiments with 8.5-fs multi-tw laser pulses [5] demonstrated visualisation of a plasma wave with shadowgraphy. These measurements though were in the linear regime of plasma-wave generation due to the relatively low energy of the (also) ultrashort drive pulse. Also the high densities at which these experiments were performed mean that the shape of the wave is poorly resolved. In the study presented here, a pulse with durationτ L = 35 fs of much higher energy (750 mj) accelerated highly relativistic electron bunches (>100 MeV) in the bubble -regime (cf. Supplementary Information). A fraction was split from the main pulse, spectrally broadened in a noble-gas filled hollow-core fiber and then recompressed to a few optical cycles. This created a synchronised probe pulse with a duration as short as τ probe = (5.9±0.4) fs, that was used to probe perpendicularly to the laser-plasma accelerator [16]. 3

4 The resulting images reveal snapshots of the plasma wave that has essentially been frozen despite its relativistic velocity (cf. Fig. 1). This is due to the extremely short shutter duration of the probe pulse, which is amongst the shortest ever used to take an optical image. These features are completely washed out (by motion blur) when τ probe is increased to 30 fs. The resulting detail in our images has previously only been seen in simulations. The curvature of the wave fronts is clearly visible and remains constant for the first ten periods of the plasma wave showing a radius of curvature ofρ = (2.9±0.5)µm. This rounded shape is indicative of operating in the full blow-out regime [1]. After the tenth period, the curvature increases further due to the mismatch between the longitudinal and transverse plasma-oscillation frequencies [17]. This leads to phase-mixing and eventually destruction of the wave structure, giving the first ever measurement of the length of the bunch train supported by a plasma accelerator. By varying the delay between probe and main pulse, we directly observe the evolution of the plasma wave s structure as the pump propagates through the plasma. This time-series is compared with electron density maps from a PIC simulation (cf. Supplementary Information) at corresponding distances in Fig. 2. This is not a direct comparison since the shadowgrams are formed as a result of the deflection of probe rays by density gradients, and are closer to following the second derivative of n e. Nevertheless, the experimental shadowgrams and the electron density maps from the PIC simulation bear a striking resemblance to each other. An artificial shadowgram generated from the simulation data (cf. Fig. 2 d-f and Supplementary Information) confirms this correspondence, which can be expected since the second derivative of density in the moving frame is related to density by Poisson s equation. The experimental shadowgrams clearly show how the plasma wave s evolution plays a key role in the injection and acceleration process. As the pump pulse propagates up the initial density ramp, a low-amplitude, quasi-linear plasma wave is generated (after a propagation distance of v g t = 65µm in Fig. 2). During this focussing of the laser pulse, the transverse extent of 4

5 the plasma wave reduces and the amplitude of the wave increases (v g t = 350µm). Further evolution of the laser pulse due to self-focussing and pulse compression leads to an increase in intensity and the plasma wave s amplitude grows further. This is noticeable in a significant increase of the curvature of the plasma-wave train and, in particular, in the lengthening of the first (v g t = 654µm) and second (v g t = 1030µm) plasma periods. Our simulations show that the increase ofλ plasma is not due to beam-loading after the injection of electrons, but is a result of the intensity amplification of the laser pulse; λ plasma λ plasma(1 + a 2 0 /2)1/4 [18], where a 0 = (I L λ 2 L/W) 1/2 and I L and λ L are laser intensity and wavelength, respectively. Significant charge is only injected into the wake (around v g t = 1000µm) once the wavelength of the first period (or bubble ) has started to increase as observed previously in simulations [19, 20, 21]. We also observe bright, broadband radiation emitted from this point which can be attributed to wavebreaking radiation [22] (cf. Fig. 3 a and Supplementary Information), confirming that injection is aided by the plasma wavelength increase. After wavebreaking, the wave becomes highly non-linear, as indicated by reversal in the direction of curvature of the trailing wave periods (v g t = 1100µm) in the shadowgrams. Our 2D-PIC simulations only partially reproduce this feature, though it is observed in 3D simulations [18, 23]. These features are intimately tied to the process of transverse wavebreaking [24]. Finally the wave s amplitude becomes so large that the trailing wake is destroyed as wavebreaking has washed out all of the downstream structure (v g t = 1450µm), leaving a single plasma bubble [1] co-propagating with the main pulse. We also measured the length of the second period, which should not be affected by intensity amplification, as a function of density at a fixed position in the plasma ( 900µm after the focal position). The measurement was made sufficiently far into the gas jet to ensure that it was in the uniform density plateau and that the wave s amplitude has had time to grow fully (Fig. 3b). At low density, the length is well matched to the standard expression, but at high 5

6 density, λ plasma is significantly longer. The density at which this transition occurs corresponds to the expected onset of self-injection [25], also supported by measurements of the electron beam profile (insets in Fig. 3b). As n e is increased beyond cm 3, the wavelength observed at this fixed position remains approximately constant, rather than decreasing n 1 e as expected. This lengthening is a direct consequence of beam-loading [26], and shows that significant charge can be injected into the trailing periods of the wave train. Our ability to take snapshots of the interaction, rather than time integrated measurements as with other methods (TDI, FDH), allows us to show for the first time that the dynamic process of bubble lengthening is intimately tied to self-injection. To emphasise the importance of bubble expansion on injection, we plot in Fig. 4 the evolution of the plasma wave s longitudinal structure from the simulation shown in Fig. 2. The laser pulse travels at slightly less than c so that the front of the plasma wave (on the right of Fig. 4) moves back in the(x ct)-frame. Early in the interaction (ct = 0.5 mm), the wave is periodic. Betweenct = 0.5 and 1 mm, the distance between the density spike in front of the laser and the first density spike behind the laser, i.e. the length of the first bubble, increases. It is during this expansion that electrons are self-injected into the bubble. Injected electrons move forward at very close to c creating vertical features in this image. At (x ct) 73 and 82µm a sizeable charge can be seen emanating from the rear of the first and second wave periods at ct 1 mm. This means that during the period of rapid bubble expansion two electron bunches were formed, which exit the plasma at the end. Superimposing the experimental bubble length data onto this image of the plasma wave evolution shows excellent agreement, demonstrating that bubble expansion indeed plays a key role in electron self-injection in this laser-wakefield accelerator. Applying our approach to visualise the full non-linear evolution of the plasma wave is likely to allow to study the acceleration process with unprecedented precision in the future. As well as providing greater understanding of acceleration in the bubble -regime, our technique can 6

7 easily be adopted to more complex acceleration geometries, e.g. staging [27], or for beamdriven acceleration [28, 29]. This promises to optimise the table-top acceleration of high-quality electron beams. It is widely speculated that these beams could be applied to the generation of ultra-short secondary radiation pulses. Hence, our results promise to have far-reaching impact in the many fields where such sources are in demand such as biomedical imaging and ultrafast condensed-matter study. References [1] Pukhov, A. & Meyer-ter-Vehn, J. Laser wake field acceleration: the highly non-linear broken-wave regime. Appl. Phys. B 74, 355 (2002). [2] Leemans, W. P. et al. GeV electron beams from a centimetre-scale accelerator. Nature Phys. 2, 696 (2006). [3] Wang, X. et al. Quasi-monoenergetic laser-plasma acceleration of electrons to 2 GeV. Nature Commun. 4, 2988 (2013). [4] Lundh, O. et al. Few femtosecond, few kiloampere electron bunch produced by a laserplasma accelerator. Nature Phys. 7, 219 (2011). [5] Buck, A. et al. Real-time observation of laser-driven electron acceleration. Nature Phys. 7, 543 (2011). [6] Schnell, M. et al. Deducing the electron-beam diameter in a laser-plasma accelerator using x-ray betatron radiation. Phys. Rev. Lett. 108, (2012). [7] Plateau, G. R. et al. Low-emittance electron bunches from a laser-plasma accelerator measured using single-shot x-ray spectroscopy. Phys. Rev. Lett. 109, (2012). 7

8 [8] Hooker, S. M. Developments in laser-driven plasma accelerators. Nature Photon. 7, 775 (2013). [9] Rousse, A. et al. Production of a kev x-ray beam from synchrotron radiation in relativistic laser-plasma interaction. Phys. Rev. Lett. 93, (2004). [10] Kneip, S. et al. Bright spatially coherent synchrotron x-rays from a table-top source. Nature Phys. 6, 980 (2010). [11] Powers, S. M. Quasi-monoenergetic and tunable X-rays from a laser-driven Compton light source. Nature Photon. 8, 28 (2014). [12] Marques, J. R. et al. Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse. Phys. Rev. Lett. 76, 3566 (1996). [13] Siders, C. W. et al. Laser wakefield excitation and measurement by femtosecond longitudinal interferometry. Phys. Rev. Lett. 76, 3570 (1996). [14] Matlis, N. H. et al. Snapshots of laser wakefields. Nature Phys. 2, 749 (2006). [15] Dong, P. et al. Formation of optical bullets in laser-driven plasma bubble accelerators. Phys. Rev. Lett. 104, (2010). [16] Schwab, M. B. et al. Few-cycle optical probe-pulse for investigation of relativistic laserplasma interactions. Appl. Phys. Lett. 103, (2013). [17] Dawson, John M. Nonlinear electron oscillations in a cold plasma. Phys. Rev. 113, 383 (1959). [18] Lu, W. et al. Generating multi-gev electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime. Phys. Rev. ST Accel. Beams 10, (2007). 8

9 [19] Bulanov, S., Naumova, N., Pegoraro, F. & Sakai, J. Particle injection into the wave acceleration phase due to nonlinear wake wave breaking. Phys. Rev. E 58, R5257 (1998). [20] Mangles, S. P. D. et al. Monoenergetic beams of relativistic electrons from intense laserplasma interactions. Nature 431, 535 (2004). [21] Kalmykov, S., Yi, S. A., Khudik, V. & Shvets, G. Electron self-injection and trapping into an evolving plasma bubble. Phys. Rev. Lett. 103, (2009). [22] Thomas, A. G. R. et al. Measurements of wave-breaking radiation from a laser wakefield accelerator. Phys. Rev. Lett. 98, (2007). [23] Faure, J. et al. A laser-plasma accelerator producing monoenergetic electron beams. Nature 431, 541 (2004). [24] Bulanov, S. V., Pegoraro, F., Pukhov, A. M. & Sakharov, A. S. Transverse-wake wave breaking. Phys. Rev. Lett. 78, 4205 (1997). [25] Mangles, S. P. D. et al. Self-injection threshold in self-guided laser wakefield accelerators. Phys. Rev. ST Accel. Beams 15, (2012). [26] Rosenzweig, J. B., Breizman, B., Katsouleas, T. & Su, J. J. Acceleration and focusing of electrons in two-dimensional nonlinear plasma wake fields. Phys. Rev. A 44, R6189 (1991). [27] Gonsalves, A. J. et al. Tunable laser plasma accelerator based on longitudinal density tailoring. Nature Phys. 7, 862 (2011). [28] Blumenfeld, I. et al. Energy doubling of 42 GeV electrons in a metre-scale plasma wakefield accelerator. Nature 445, 741 (2007). 9

10 [29] Caldwell, A., Lotov, K., Pukhov, A. & Simon, F. Proton-driven plasma-wakefield acceleration. Nature Phys. 5, 363 (2009). [30] Fonseca, R. A. et al. OSIRIS: A three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. in: Lecture Notes in Computer Science Vol. 2329, III-342 (Springer, Heidelberg, 2002). Acknowledgements: We thank B. Beleites, W. Ziegler, and F. Ronneberger for running the JETI-laser system. This study was sponsored by DFG (grants TR18 B9 and KA 2869/2-1), BMBF (contracts 05K10SJ2 and 03ZIK052), European Regional Development Fund (EFRE), STFC (grant ST/J002062/1) and EPSRC (grant EP/H00601X/1). The collaboration was funded by LASERLAB-EUROPE (grant agreement n , EC s Seventh Framework Programme). Author contributions: A.S., S.P.D.M, Z.N., and M.C.K. designed the experiment and wrote the manuscript. A.S., M.S., M.N., M.R., J.M.C., and K.P. carried out the experiments. A.S., M.B.S., M.M., G.G.P., C.S., M.C.K., and O.J. designed and operated the probe beam. A.S. and S.P.D.M did the main data analysis. S.P.D.M., J.M.C., K.P., and Z.N. performed the simulations. All authors discussed the results and contributed to the completion of the manuscript. Additional information: Supplementary information is available in the online version of the paper. Correspondence and requests for materials should be addressed to M.C.K. (malte.kaluza@uni-jena.de). Competing financial interests: The authors declare no competing financial interests. 10

11 Fig. 1: High-resolution probing of the plasma wave Shadowgraphy image after 1.1 mm of propagation into the plasma at a density n e = cm 3. Fig. 2: Snapshots of the wakefield Early in the interaction the wake is quasi-linear (first row). As the laser pulse focuses the 11

12 transverse extent of the wake reduces (second and third row). Around the injection point (fourth row) significant lengthening of the first and second wake periods occurs. After injection the amplitude of the trailing periods is reduced, leading to a single plasma bubble (last row). a) Plasma target density profile (dashed line: focus position). Injection (cf. Supplementary Information) occurred around x = 1000 µm. b) Experimental shadowgrams observed at various distances. c) Corresponding electron density maps from PIC simulations. d-f) Example of a numerically generated shadowgram (e), showing the correspondence between shadowgrams (d) and electron density distribution (f). Fig. 3: Evolution of the first and second plasma period a) Length of the first plasma period ( bubble ) as a function of propagation distance v g t taken 12

13 from the shadowgrams [error bars represent combination of uncertainty in determining the bubble length (±2µm) in a single shot reduced by N where repeat shots are available]. Blue horizontal line is the expected plasma wavelength for n e = cm 3. Between v g t = 0.9 and 1.05 mm (grey shaded area) wavebreaking radiation was frequently detected. b) Wavelength of second plasma period versus n e at a fixed position v g t = 1.1 mm. Red line shows expected theoretical value. Open circles represent measured and averaged data points with the standard error of the mean. Small insets: Electron beam profiles for various n e averaged over shots. Fig. 4: Bubble expansion Each horizontal row of the image corresponds to a line-out of the on-axis electron density at a time t in the simulation. Early in the interaction (top) the wave is still periodic. Between ct = 0.5 and 1 mm, the first wave period rapidly expands. Electron bunches are injected into the back of the first and second plasma period, indicated by vertical features in the image exiting the plasma at (x ct) 73 and 82µm. We have superimposed bubble lengths from Fig. 3 a onto this image assuming that the front of the bubble in experiment and simulation appear at the same value ofct. 13

14 Supplementary Information: Laser System and Experimental Techniques: In the present study, the JETI-laser system at the Institut für Optik und Quantenelektronik in Jena, Germany delivered pulses of 750 mj energy and 35 fs duration. The pulses were focused into a supersonic helium gas jet by an f/13 off-axis parabolic mirror to peak intensities of I L = W/cm 2 (corresponding to a peak normalised vector potential of a 0 = 1.7), generating a plasma with n e in the range cm 3, cf. Supp. Fig. 1 a. The energy of the accelerated electron bunches were characterised with a magnetic spectrometer which could measure from 3 MeV to 1 GeV. Additionally, the electron beam profile could be measured by inserting a scintillator screen into the beam (cf. Supp. Fig. 1 b). The position of the gas jet with respect to the laser focus was optimised to reproducibly generate electron pulses exhibiting a quasi-monoenergetic feature (cf. Supp. Fig. 1 c). An imaging system resolution of 1.5µm allowed high-resolution images of the plasma wave to be taken (cf. Fig. 1). Frequently, broadband wavebreaking radiation [22] was emitted from the plasma indicating the position of injection of plasma electrons into the wake (cf. Supp. Fig. 2). The probe images were normalised to reduce the influence of probe intensity modulations and improve contrast by usingi norm = (I I 0 )/I 0, withi being the pixel value at each individual position and I 0 the value received from a low order spline fit in the horizontal direction. Particle-In-Cell Simulations: We performed two-dimensional simulations of the interaction using the PIC code OSIRIS [30]. A laser pulse with an intensity FWHM duration of 36 fs was focused to a waist of 16µm (corresponding to a peak a 0 = 1.4) into a plasma density profile that matched the experimentally measured one (with a peak densityn e = cm 3 ). The simulation was performed in a box size of c/ω L with grid cells with 14

15 Supplementary Figure 1: Experimental set-up. Supplementary Figure 2: Detection of wavebreaking radiation. 15

16 four macro electrons per cell and a stationary ion background. The box moved at the speed of light in the laboratory frame of reference. Shadowgraphy Simulations: We generated artificial shadowgrams using the snapshots of the local electron density from the PIC-simulations. First, the 2D-electron map was converted into a cylindrically symmetric 3D-refractive index distribution; next, a bundle of geometric probe rays were propagated through this plasma volume using Fermat s principle, taking into account the longitudinal motion of the wakefield. The intensity of the probe beam after the plasma was calculated from the density of rays arriving at a plane just after the rays left the plasma region. Once the ray paths were calculated, the phase shift was integrated along the path of each ray and the intensity and phase shift of the electric field of the probe beam were determined at a point just after the wakefield. We then used the phase and amplitude information from the ray-tracing calculation as the boundary conditions for a diffraction integral calculation to take into account the finite resolution and depth of field of the imaging system. Finally, the finite probe duration τ probe was accounted for by blurring the image in the main laser-propagation direction using the measured temporal profile of the probe pulse. 16