Abstract
1 Introduction
The past two decades or so have witnessed the rapid development of laser wakefield acceleration (LWFA) since the experimentally obtained mono-energetic electron beam[1–3]. From the early stage of tens of percent level energy spread and few mm mrad-level emittance, LWFA electron beams have now achieved electron beams with nC-level charge[4,5], few per-mille-level relative energy spread[6–9] and sub-mm mrad-level emittance[10]. Benefitted from the ultra-high acceleration gradient of LWFA[11–15], ultra-compact radiation sources, such as betatron radiation[16–18], Compton scattering[19–22] and tabletop free electron lasers (FELs)[23–25], injectors for future colliders[26] will be possible. Most LWFA-based applications require an excellent 6D electron beam brightness[27,28], defined by
Owing to the large instability in the plasma acceleration process, a single-shot high-resolution diagnostic method is preferable. At present, one of commonly used single-shot emittance measurement methods is the ‘pepper-pot’ method[29]. It uses a beam-intercepting mask to construct the electron beam phase space distribution through the divergence and charge of electrons passing through the hole, in which it is preferrable to have a beam with a large charge (higher than tens of pC level). Ref. [30] reports that this method is not suitable for LWFA beams owing to large divergence. The radiation-based method[31–33] measures the transverse size of the electron beam inside the bubble and the divergence outside the bubble. Neglecting the evolution as the electron beam leaves the bubble will make the measured result deviate from its true emittance[34]. In comparison, the direct energy-dispersed measurement method using a focused beam transfer line and an energy spectrometer has greater feasibility, and is suitable for low-charge electron beam diagnostics[10,35]. Unlike the early quadrupole scanning method[36], the electron beam has energy-dependent transverse deflection through the dipole, which separates the influence of chromaticity effects[37] while measuring sizes. This method can not only measure the emittance, but also obtain the transverse phase space distribution of the electron beam.
In this paper, a single-shot method for measuring the energy-sliced emittance of the electron beam was demonstrated experimentally. Through analyzing the evolution of the electron transverse trajectory in the bubble, the phase difference of the electrons with respect to the central energy can be estimated. Phase compensation unifies the electron beam phase, which makes the phase space present the slice information of the electron beam. The slice emittance is then calculated by fitting to the vertical sizes of the electron beam sliced at different energies. In order to more accurately reflect the whole process of the electron beam from its inception to final measurement, Fourier–Bessel particle-in-cell (FBPIC) simulation was also carried out. The simulation results are in good agreement with the experimental results, indicating the accuracy of the analysis.
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2 Theory and experiment setup
While accelerated in the nonlinear plasma wake (the so-called bubble), the electrons experience transverse oscillation[38], which causes the evolution of the beam emittance. Considering a relativistic electron accelerates and oscillates in the bubble, the transverse trajectory can be expressed as
where
where
Figure 1.The phase space trajectories of the low-energy part (a) and the high-energy part (b) in one electron beam; the electron beam transverse phase space distribution without (c) and with (d) phase compensation.
In the framework of beam optics, the single-electron state can be characterized by a 6D vector. In the case of ignoring the second-order effect, the trajectory of the single electron through the transfer line can be expressed as follows:
where
where
Figure 2(a) shows a schematic diagram of the experimental setup for the emittance diagnostic of high-quality electron beams produced by the LWFA. The experiments were performed on a Ti:sapphire chirped pulse amplification laser system with 30-fs pulse duration, 200-TW peak power and 1 Hz repetition rate at the Shanghai Institute of Optics and Fine Mechanics (SIOM)[43]. An 800-nm laser pulse with an on-target power of approximately 120 TW was focused onto a gas target by an f/30 off-axis parabolic mirror, and the vacuum beam radius ω0 was measured to be 32 μm full width at half maximum (FWHM). The fractional laser energy contained in the laser spot was measured to be approximately 61% at 1/e2, and the peak intensity was estimated to be 4.3 × 1018 W/cm2, corresponding to a normalized amplitude of a0 ≈ 1.3.
Figure 2.(a) Schematic diagram of the experimental setup for single-shot measurement of electron emittance by using a focused beamline; (b) shock wave in the shadow graph; (c) statistics of the spot center position of the consecutive 62-shot electron beam on profile; (d) typical spectra of electron beams from the LWFA for 10 consecutive shots[24].
The pure helium gas was sprayed from a supersonic gas nozzle to the metal target to conduct a structured gas flow with a shock front. The longitudinal density profile can be adjusted by varying the relative position between the nozzle and the target and the gas back pressure. A Michelson-type interferometer with a 4-f optical imaging system was used for measuring the plasma density, as shown in Figure 2(b). The shock front has a peak density of (4 ± 0.5) × 1018 cm–3, following which is a 3-mm-long plateau with the density of (2.2 ± 0.4) × 1018 cm–3. The beamline is composed of three quadrupole magnets, where the first two are permanent quadrupoles with a magnetic field gradient of 250 T/m, and the third one is an electromagnetic quadrupole whose magnetic field gradient is tunable in the range of 0–80 T/m. The accelerated electron beam is deflected onto a Lanex phosphor screen (Y3Al5O12:Ce3+) by a 90-cm-long tunable dipole magnet. The energy spectrometer has an energy resolution of 0.011% at 500 MeV. The total beamline has a length of approximately 2.4 m from the gas target to the electron spectrometer, and the components in the beamline were aligned within ±100 μm of coaxiality with the main optical axis.
3 Experimental results
It is noted that only the linear beam optics are applied in the aforementioned theoretical model for simplification. The transport effects up to the second order and the space charge are considered in the simulation. By adjusting the relative position between the two permanent magnetic quadrupoles and the magnetic field gradient of the electromagnetic quadrupole, the focused beamline was optimized with a cancelling term
Figure 3(a) shows a typical energy spectrum of the focused electron beam deflected by the dipole, with the intensity corresponding to the relative charge density. The root-mean-square (RMS) energy-resolved beam size can be obtained by weighted counting of the distance of the electrons from the beam center in the vertical direction. Intensities lower than 10% of the peak intensities in each energy slice are set to zero to avoid overestimation of the sizes. The blue line in Figure 3(b) represents the vertical size corresponding to different energy slices in Figure 3(a), and the red line is the fitting curve. Quasi-3D particle-in-cell simulations were performed using the FBPIC code[44–46] to estimate the initial phase difference after injection, which cannot be directly measured in the experiment. The simulation parameters were chosen according to the experiments. The initial phase difference was estimated to be 34.2° after injection, as shown in Figure 3(c), where the horizontal axis represents the final relative energy of the tracking electrons. The range from
Figure 3.(a) Single-shot image for the energy spectrum of a focused electron beam and (b) the corresponding energy-resolved sizes (blue line) and fitted curve (red line); (c) the phase difference of the energy offset relative to the center energy immediately after injection (red solid line) and acceleration (blue solid line) from FBPIC, and the calculated value of the final phase difference (pink dotted line).
Figure 4 shows the measured normalized emittance for various beam charges with the back pressures of 1.5 and 2 bar, respectively. Each data point represents 20 consecutive shots. The electron beam emittance is lower at the back pressure of 1.5 bar and fluctuates in the range of 0.27–0.34 mm mrad. Most of the emittance fluctuates in the range of 0.28–0.36 mm mrad, and the highest value can reach approximately 0.45 mm mrad under the condition of 2 bar back pressure. In general, the energy-sliced emittance shows no significant correlation with the beam charge. Compared with the back pressure of 2 bar, the electron beam emittance fluctuation is smaller when the back pressure is 1.5 bar. In particular, when the charge amount is higher than 20 pC, the electron beam emittance fluctuates greatly.
Figure 4.Electron beam slice emittance statistics at 1.5 bar (red) and 2 bar (blue) back pressures.
The assumption that the electron beam transports along the main optical axis is made in the aforementioned theoretical model. However, positional deviation occurs due to the shot-to-shot pointing fluctuations of the electron beam from the LWFAs. An initial pointing deviation of P will result in a positional offset
Figure 5.(a) A typical electron beam spectrogram with initial pointing jitter, with two dashed-dotted lines perpendicular to the electron beam (red line) and at the same horizontal distance from the main optical axis (white line). (b) Corresponding relationship between the electron beam size and energy of the two slicing methods (the blue line corresponds to the white line in
The red dashed line in Figure 5(a) is a slice perpendicular to the electron beam distribution, and the white dashed line is a slice with the same horizontal offset relative to the main optical axis. The red and the blue curves in Figure 5(b) indicate the RMS energy-resolved beam size by weighted counting of the distance of the electrons from the beam center along the dashed red and white lines in Figure 5(a). Although the design ensures that the horizontal focal point locates at the end of the beamline, the coupling of the horizontal position deviation and the deflection angle in the dipole means that any slice on the screen with the same horizontal offset is not absolutely mono-energetic. The measured sizes increase as electron beams with different energies generate additional vertical offset, owing to pointing jitter. Figure 5(c) shows the relative charge distributions of the two profiles corresponding to Figure 5(a), in which the subgraphs are locally enlarged graphs. The dashed line represents the Gaussian fitting profiled by the red line, with a fitting threshold of 50% of the peak value. It can be seen from the Figure 5(c) that the electron beam is approximately Gaussian in the vertical direction. The greater weight of the background noise in the low-intensity signal and the transverse divergence of the electron beam owing to space charge effects make the beam profile slightly larger than the Gaussian curve. Figure 2(c) shows the center position of 62 consecutive electron beams, and the vertical RMS pointing jitter of the electron beam is 0.52 mrad (the pointing fluctuation was measured by a beam position monitor located 4 m from the gas target, where the quadrupoles were turned off). Considering the effect of the pointing jitter within the double-RMS range, the red and blue lines in Figure 5(d) represent the imaging beam slope and the measured relative emittance derivation for different pointing jitters, respectively.
4 Conclusion
We experimentally performed single-shot measurements of electron beam slice emittance using a focused transfer line. The electron beam significantly follows envelope oscillations in the bubble owing to the linear focusing field. The coupling of the longitudinal acceleration field and the transverse focusing field results in an energy-dependent electron beam phase. Each slice phase is unified by means of phase compensation based on the relationship between the electron phase and energy. The emittance can be obtained through fitting the energy-dependent size calculated by weighted statistics. Electron beams with an average slice emittance as low as 0.27 mm mrad are currently experimentally available. Based on the transfer matrix, the pointing jitter can be obtained from the energy-dependent electron beam centroid offset, and the corresponding emittance derivation can also be measured. The simulation results based on the experimental parameters are in good agreement with the actual measurement results.
References
[1] J. Faure, Y. Glinec, A. Pukhov, S. Kiselev, S. Gordienko, E. Lefebvre, J. P. Rousseau, F. Burgy, V. Malka. Nature, 431, 541(2004).
[2] C. G. R. Geddes, C. Toth, J. van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, W. P. Leemans. Nature, 431, 538(2004).
[3] S. P. D. Mangles, C. D. Murphy, Z. Najmudin, A. G. R. Thomas, J. L. Collier, A. E. Dangor, E. J. Divall, P. S. Foster, J. G. Gallacher, C. J. Hooker, D. A. Jaroszynski, A. J. Langley, W. B. Mori, P. A. Norreys, F. S. Tsung, R. Viskup, B. R. Walton, K. Krushelnick. Nature, 431, 535(2004).
[4] J. P. Couperus, R. Pausch, A. Kohler, O. Zarini, J. M. Kramer, M. Garten, A. Huebl, R. Gebhardt, U. Helbig, S. Bock, K. Zeil, A. Debus, M. Bussmann, U. Schramm, A. Irman. Nat. Commun., 8(2017).
[5] J. Gotzfried, A. Dopp, M. F. Gilljohann, F. M. Foerster, H. Ding, S. Schindler, G. Schilling, A. Buck, L. Veisz, S. Karsch. Phys. Rev. X, 10, 041015(2020).
[6] L. T. Ke, K. Feng, W. T. Wang, Z. Y. Qin, C. H. Yu, Y. Wu, Y. Chen, R. Qi, Z. J. Zhang, Y. Xu, X. J. Yang, Y. X. Leng, J. S. Liu, R. X. Li, Z. Z. Xu. Phys. Rev. Lett., 126, 214801(2021).
[7] Y. P. Wu, J. F. Hua, Z. Zhou, J. Zhang, S. Liu, B. Peng, Y. Fang, Z. Nie, X. N. Ning, C. H. Pai, Y. C. Du, W. Lu, C. J. Zhang, W. B. Mori, C. Joshi. Phys. Rev. Lett., 122, 204804(2019).
[8] R. D’Arcy, S. Wesch, A. Aschikhin, S. Bohlen, C. Behrens, M. J. Garland, L. Goldberg, P. Gonzalez, A. Knetsch, V. Libov, A. M. de la Ossa, M. Meisel, T. J. Mehrling, P. Niknejadi, K. Poder, J. H. Rockemann, L. Schaper, B. Schmidt, S. Schroder, C. Palmer, J. P. Schwinkendorf, B. Sheeran, M. J. V. Streeter, G. Tauscher, V. Wacker, J. Osterhoff. Phys. Rev. Lett., 122, 034801(2019).
[9] V. Shpakov, M. P. Anania, M. Bellaveglia, A. Biagioni, F. Bisesto, F. Cardelli, M. Cesarini, E. Chiadroni, A. Cianchi, G. Costa, M. Croia, A. Del Dotto, D. Di Giovenale, M. Diomede, M. Ferrario, F. Filippi, A. Giribono, V. Lollo, M. Marongiu, V. Martinelli, A. Mostacci, L. Piersanti, G. Di Pirro, R. Pompili, S. Romeo, J. Scifo, C. Vaccarezza, F. Villa, A. Zigler. Phys. Rev. Lett., 122, 114801(2019).
[10] S. K. Barber, J. van Tilborg, C. B. Schroeder, R. Lehe, H. E. Tsai, K. K. Swanson, S. Steinke, K. Nakamura, C. G. R. Geddes, C. Benedetti, E. Esarey, W. P. Leemans. Phys. Rev. Lett., 119, 104801(2017).
[11] W. P. Leemans, B. Nagler, A. J. Gonsalves, C. Toth, K. Nakamura, C. G. R. Geddes, E. Esarey, C. B. Schroeder, S. M. Hooker. Nat. Phys., 2, 696(2006).
[12] W. P. Leemans, A. J. Gonsalves, H. S. Mao, K. Nakamura, C. Benedetti, C. B. Schroeder, C. Toth, J. Daniels, D. E. Mittelberger, S. S. Bulanov, J. L. Vay, C. G. R. Geddes, E. Esarey. Phys. Rev. Lett., 113, 245002(2014).
[13] A. J. Gonsalves, K. Nakamura, J. Daniels, C. Benedetti, C. Pieronek, T. C. H. de Raadt, S. Steinke, J. H. Bin, S. S. Bulanov, J. van Tilborg, C. G. R. Geddes, C. B. Schroeder, C. Toth, E. Esarey, K. Swanson, L. Fan-Chiang, G. Bagdasarov, N. Bobrova, V. Gasilov, G. Korn, P. Sasorov, W. P. Leemans. Phys. Rev. Lett., 122, 084801(2019).
[14] X. M. Wang, R. Zgadzaj, N. Fazel, Z. Y. Li, S. A. Yi, X. Zhang, W. Henderson, Y. Y. Chang, R. Korzekwa, H. E. Tsai, C. H. Pai, H. Quevedo, G. Dyer, E. Gaul, M. Martinez, A. C. Bernstein, T. Borger, M. Spinks, M. Donovan, V. Khudik, G. Shvets, T. Ditmire, M. C. Downer. Nat. Commun., 4(2013).
[15] M. Turner, A. J. Gonsalves, S. S. Bulanov, C. Benedetti, N. A. Bobrova, V. A. Gasilov, P. V. Sasorov, G. Korn, K. Nakamura, J. van Tilborg, C. G. Geddes, C. B. Schroeder, E. Esarey. High Power Laser Sci. Eng., 9, e17(2021).
[16] J. B. Svensson, D. Guenot, J. Ferri, H. Ekerfelt, I. G. Gonzalez, A. Persson, K. Svendsen, L. Veisz, O. Lundh. Nat. Phys., 17, 639(2021).
[17] M. Kozlova, I. Andriyash, J. Gautier, S. Sebban, S. Smartsev, N. Jourdain, U. Chulagain, Y. Azamoum, A. Tafzi, J. P. Goddet, K. Oubrerie, C. Thaury, A. Rousse, K. T. Phuoc. Phys. Rev. X, 10, 011061(2020).
[18] J. C. Wood, D. J. Chapman, K. Poder, N. C. Lopes, M. E. Rutherford, T. G. Whites, F. Albert, K. T. Behm, N. Booth, J. S. J. Bryant, P. S. Foster, S. Glanzer, E. Hill, K. Krushelnick, Z. Najmudin, B. B. Pollock, S. Rose, W. Schumaker, R. H. H. Scott, M. Sherlock, A. G. R. Thomas, Z. Zhao, D. E. Eakins, S. P. D. Mangles. Sci. Rep., 8(2018).
[19] S. Chen, N. D. Powers, I. Ghebregziabher, C. M. Maharjan, C. Liu, G. Golovin, S. Banerjee, J. Zhang, N. Cunningham, A. Moorti, S. Clarke, S. Pozzi, D. P. Umstadter. Phys. Rev. Lett., 110, 155003(2013).
[20] K. Khrennikov, J. Wenz, A. Buck, J. Xu, M. Heigoldt, L. Veisz, S. Karsch. Phys. Rev. Lett., 114, 195003(2015).
[21] K. T. Phuoc, S. Corde, C. Thaury, V. Malka, A. Tafzi, J. P. Goddet, R. C. Shah, S. Sebban, A. Rousse. Nat. Photonics, 6, 308(2012).
[22] J. M. Cole, K. T. Behm, E. Gerstmayr, T. G. Blackburn, J. C. Wood, C. D. Baird, M. J. Duff, C. Harvey, A. Ilderton, A. S. Joglekar, K. Krushelnick, S. Kuschel, M. Marklund, P. McKenna, C. D. Murphy, K. Poder, C. P. Ridgers, G. M. Samarin, G. Sarri, D. R. Symes, A. G. R. Thomas, J. Warwick, M. Zepf, Z. Najmudin, S. P. D. Mangles. Phys. Rev. X, 8, 011020(2018).
[23] K. Nalkajima. Nat. Phys., 4, 92(2008).
[24] W. T. Wang, K. Feng, L. T. Ke, C. H. Yu, Y. Xu, R. Qi, Y. Chen, Z. Y. Qin, Z. J. Zhang, M. Fang, J. Q. Liu, K. N. Jiang, H. Wang, C. Wang, X. J. Yang, F. X. Wu, Y. X. Leng, J. S. Liu, R. X. Li, Z. Z. Xu. Nature, 595, 516(2021).
[25] C. Emma, J. Van Tilborg, R. Assmann, S. Barber, A. Cianchi, S. Corde, M. E. Couprie, R. D’Arcy, M. Ferrario, A. F. Habib, B. Hidding, M. J. Hogan, C. B. Schroeder, A. Marinelli, M. Labat, R. Li, J. Liu, A. Loulergue, J. Osterhoff, A. R. Maier, B. W. J. McNeil, W. Wang. High Power Laser Sci. Eng., 9, e57(2021).
[26] K. Nakajima, J. Wheeler, G. Mourou, T. Tajima. Int. J. Mod. Phys. A, 34, 1943003(2019).
[27] G. G. Manahan, A. F. Habib, P. Scherkl, P. Delinikolas, A. Beaton, A. Knetsch, O. Karger, G. Wittig, T. Heinemann, Z. M. Sheng, J. R. Cary, D. L. Bruhwiler, J. B. Rosenzweig, B. Hidding. Nat. Commun., 8, 15705(2017).
[28] S. Di Mitri, M. Cornacchia. Phys. Rept. Lett., 539(2014).
[29] C. M. S. Sears, A. Buck, K. Schmid, J. Mikhailova, F. Krausz, L. Veisz. Phys. Rev. Spec. Top. Accel. Beams, 13, 092803(2010).
[30] A. Cianchi, M. P. Anania, M. Bellaveglia, M. Castellano, E. Chiadroni, M. Ferrario, G. Gatti, B. Marchetti, A. Mostacci, R. Pompili, C. Ronsivalle, A. R. Rossi, L. Serafini. Nucl. Instrum. Methods Phys. Res. Sect. A, 720, 153(2013).
[31] G. R. Plateau, C. G. R. Geddes, D. B. Thorn, M. Chen, C. Benedetti, E. Esarey, A. J. Gonsalves, N. H. Matlis, K. Nakamura, C. B. Schroeder, S. Shiraishi, T. Sokollik, J. van Tilborg, C. Toth, S. Trotsenko, T. S. Kim, M. Battaglia, T. Stohlker, W. P. Leemans. Phys. Rev. Lett., 109, 064802(2012).
[32] M. Schnell, A. Savert, B. Landgraf, M. Reuter, M. Nicolai, O. Jackel, C. Peth, T. Thiele, O. Jansen, A. Pukhov, O. Willi, M. C. Kaluza, C. Spielmann. Phys. Rev. Lett., 108, 075001(2012).
[33] C. Emma, A. Edelen, M. J. Hogan, B. O’Shea, G. White, V. Yakimenko. Phys. Rev. Accel. Beams, 21, 112802(2018).
[34] M. C. Downer, R. Zgadzaj, A. Debus, U. Schramm, M. C. Kaluza. Rev. Mod. Phys., 90, 035002(2018).
[35] S. K. Barber, J. H. Bin, A. J. Gonsalves, F. Isono, J. van Tilborg, S. Steinke, K. Nakamura, A. Zingale, N. A. Czapla, D. Schumacher, C. B. Schroeder, C. G. R. Geddes, W. P. Leemans, E. Esarey. Appl. Phys. Lett., 116, 234108(2020).
[36] R. Weingartner, S. Raith, A. Popp, S. Chou, J. Wenz, K. Khrennikov, M. Heigoldt, A. R. Maier, N. Kajumba, M. Fuchs, B. Zeitler, F. Krausz, S. Karsch, F. Gruner. Phys. Rev. Spec. Top. Accel. Beams, 15, 111302(2012).
[37] J. van Tilborg, S. Steinke, C. G. R. Geddes, N. H. Matlis, B. H. Shaw, A. J. Gonsalves, J. V. Huijts, K. Nakamura, J. Daniels, C. B. Schroeder, C. Benedetti, E. Esarey, S. S. Bulanov, N. A. Bobrova, P. V. Sasorov, W. P. Leemans. Phys. Rev. Lett., 115, 184802(2015).
[38] J. Feng, Y. F. Li, J. G. Wang, D. Z. Li, C. Q. Zhu, J. H. Tan, X. T. Geng, F. Liu, L. M. Chen. High Power Laser Sci. Eng., 9, e5(2021).
[39] X. L. Xu, J. F. Hua, F. Li, C. J. Zhang, L. X. Yan, Y. C. Du, W. H. Huang, H. B. Chen, C. X. Tang, W. Lu, P. Yu, W. An, C. Joshi, W. B. Mori. Phys. Rev. Lett., 112, 035003(2014).
[40] A. Koehler, R. Pausch, M. Bussmann, J. P. C. Cabadag, A. Debus, J. M. Kramer, S. Schobel, O. Zarini, U. Schramm, A. Irman. Phys. Rev. Accel. Beams, 24, 091302(2021).
[41] S. Corde, K. T. Phuoc, G. Lambert, R. Fitour, V. Malka, A. Rousse, A. Beck, E. Lefebvre. Rev. Mod. Phys., 85(2013).
[42] M. B. Reid. J. Appl. Phys., 70, 7185(1991).
[43] F. X. Wu, Z. X. Zhang, X. J. Yang, J. B. Hu, P. H. Ji, J. Y. Gui, C. Wang, J. C. Chen, Y. J. Peng, X. Y. Liu, Y. Q. Liu, X. M. Lu, Y. Xu, Y. X. Leng, R. X. Li, Z. Z. Xu. Opt. Laser Technol., 131, 106453(2020).
[44] M. Kirchen, R. Lehe, S. Jalas, O. Shapoval, J. L. Vay, A. R. Maier. Phys. Rev. E, 102, 013202(2020).
[45] S. Jalas, I. Dornmair, R. Lehe, H. Vincenti, J. L. Vay, M. Kirchen, A. R. Maier. Phys. Plasmas, 24, 033115(2017).
[46] R. Lehe, M. Kirchen, I. A. Andriyash, B. B. Godfrey, J. L. Vay. Comput. Phys. Commun., 203, 66(2016).
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