[1] S.Corde, S.Fourmaux, K. T.Phuoc et al. Single shot phase contrast imaging using laser-produced Betatron x-ray beams. Opt. Lett., 36, 2426(2011).

[2] F.Dollar, S.Kneip, C.McGuffey et al. X-ray phase contrast imaging of biological specimens with femtosecond pulses of betatron radiation from a compact laser plasma wakefield accelerator. Appl. Phys. Lett., 99, 093701(2011).

[3] K.Khrennikov, S.Schleede, J.Wenz et al. Quantitative X-ray phase-contrast microtomography from a compact laser-driven betatron source. Nat. Commun., 6, 7568(2015).

[4] J. M.Cole, N. C.Lopes, J. C.Wood et al. Laser-wakefield accelerators as hard x-ray sources for 3D medical imaging of human bone. Sci. Rep., 5, 13244(2015).

[5] D. J.Chapman, K.Poder, J. C.Wood et al. Ultrafast imaging of laser driven shock waves using betatron x-rays from laser wake-field accelerator. Sci. Rep., 8, 11010(2018).

[6] M.Koenig, S.Le Pape, A.Ravasio et al. Hard x-ray radiography for density measurement in shock compressed matter. Phys. Plasmas, 15, 060701(2008).

[7] J.Lindl. Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas, 2, 3933(1995).

[8] X.Davoine, J.Ferri, S. Y.Kalmykov, A.Lifschitz. Electron acceleration and generation of high brilliance x-ray radiation in kilojoule, sub-picosecond laser-plasma interactions. Phys. Rev. Accel. Beams, 19, 10130(2016).

[9] F.Albert, A. G. R.Thomas. Applications of laser wakefield accelerator-based light sources. Plasma Phys. Controlled Fusion, 58, 103001(2016).

[10] K. T.Phuoc, A.Rousse, R.Shah et al. Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction. Phys. Rev. Lett., 93, 135005(2004).

[11] A.D?pp, J.Ju, K.Svensson et al. Enhancement of x-rays generated by a guided laser wakefield accelerator inside capillary tubes. Appl. Phys. Lett., 100, 191106(2012).

[12] S.Cipiccia, B.Ersfeld, M. R.Islam et al. Gamma-rays from harmonically resonant betatron oscillation in plasma wake. Nat. Phys., 7, 867(2011).

[13] V.Malka. Laser plasma accelerators. Phys. Plasmas, 19, 055501(2012).

[14] J. M.Dawson, T.Tajima. Laser electron accelerator. Phys. Rev. Lett., 43, 267(1979).

[15] N. E.Andreev, L. M.Gorbunov, V. I.Kirsanov et al. Resonant excitation of wake-fields by a laser pulse in a plasma. JETP Lett., 55, 571-577(1992).

[16] N. E.Andreev, L. M.Gorbunov, V. I.Kirsanov. Stimulated processes and self-modulation of short intense laser pulses in laser wake field accelerator. Phys. Plasmas, 2, 2573-2582(1995).

[17] F.Albert, N.Lemos, J. L.Shaw et al. Observation of betatron x-ray radiation in a self-modulated laser wakefield accelerator driven with picosecond laser pulses. Phys. Rev. Lett., 118, 134801(2017).

[18] F.Albert, N.Lemos, J. L.Shaw et al. Betatron x-ray radiation in the self-modulated laser wakefield acceleration regime: Prospects for a novel probe at large scale laser facilities. Nucl. Fusion, 59, 032003(2018).

[19] B.Liu, H. Y.Wang, X. Q.Yan, M.Zepf. Gamma-ray emission in near critical density plasmas at laser intensities of 10²¹ W/cm². Phys. Plasmas, 22, 033102(2015).

[20] T. W.Huang, A. P. L.Robinson, C. T.Zhou et al. Characteristics of betatron radiation from direct-laser-accelerated electrons. Phys. Rev. E, 93, 063203(2016).

[21] N. E.Andreev, O. N.Rosmej, S.Zaehter et al. Interaction of relativistically intense laser pulses with long-scale near critical plasmas for optimization of laser based sources of MeV electrons and gamma-rays. New J. Phys., 21, 043044(2019).

[22] M. M.Günther, M.Gyrdymov, O. N.Rosmej et al. High-current laser-driven beams of relativistic electrons for high energy density research. Plasma Phys. Controlled Fusion, 62, 115024(2020).

[23] S. Y.Gus’kov, J.Limpouch, P.Nicola?, V. T.Tikhonchuk. Laser-supported ionization wave in under-dense gases and foams. Phys. Plasmas, 18, 103114(2011).

[24] N. G.Borisenko, A. M.Khalenkov, V.Kmetik et al. Plastic aerogel targets and optical transparency of undercritical microheterogeneous plasma. Fusion Sci. Technol., 51, 655-664(2007).

[25] J.Meyer-ter-Vehn, A.Pukhov, Z.-M.Sheng. Particle acceleration in relativistic laser channels. Phys. Plasmas, 6, 2847(1999).

[26] A.Pukhov. Strong field interaction of laser radiation. Rep. Prog. Phys., 66, 47-101(2003).

[27] N. E.Andreev, P. R.Levashov, L. P.Pugachev, O. N.Rosmej. Acceleration of electrons under the action of petawatt-class laser pulses onto foam targets. Nucl. Instrum. Methods Phys. Res., Sect. A, 829, 88-93(2016).

[28] B.Aurand, V.Bagnoud, A.Blazevic et al. Commissioning and early experiments of the PHELIX facility. Appl. Phys. B, 100, 137-150(2010).

[29] F.Consoli, R.De Angelis, T. S.Rosinson et al. Generation of intense quasi-electrostatic fields due to deposition of particles accelerated by petawatt-range-laser-matter interactions. Sci. Rep., 9, 8551(2019).

[30] A.Pukhov. Tree-dimensional electromagnetic relativistic particle-in-cell code VLPL (virtual laser plasma lab). J. Plasma Phys., 61, 425-433(1999).

[31] J. D.Jackson. Classical Electrodynamics(1998).

[32] S.Kiselev, I.Kostyukov, A.Pukhov. X-ray generation in strongly nonlinear plasma waves. Phys. Rev. Lett., 93, 135004(2004).

[33] C. S.Brady, R.Duclous, C. P.Ridgers et al. Dense electron-positron plasmas and ultraintense γ rays from laser-irradiated solids. Phys. Rev. Lett., 108, 165006(2012).

[34] H. X.Chang, X. B.Li, B.Qiao et al. Identifying the quantum radiation reaction by using colliding ultraintense lasers in gases. Phys. Rev. A, 98, 052119(2018).

[35] N. E.Andreev, L. P.Pugachev. Characterization of accelerated electrons generated in foams under the action of petawatt lasers. J. Phys.: Conf. Ser., 1147, 012080(2019).

[36] L.Antonelli, F.Barbato, D.Mancelli et al. X-ray phase-contrast imaging for laser-induced shock-waves. Europhys. Lett., 125, 35002(2019).

[37] S.Atzeni, F.Barbato, D.Batani et al. Quantitative phase contrast imaging of a shock-wave with a laser-plasma based X-ray source. Sci. Rep., 9, 18805(2019).

[38] J. M.Cowley. Diffraction Physics, 481(1995).

[39] J. O.Kane, D. A.Martinez, V. A.Smalyuk et al. Evidence for a bubble-competition regime in indirectly driven ablative Rayleigh-Taylor instability experiments on the NIF. Phys. Rev. Lett., 114, 215004(2015).

[40] R.Betti, R.Nora, W.Theobald et al. Gigabar spherical shock generation on the OMEGA laser. Phys. Rev. Lett., 114, 045001(2015).