• Matter and Radiation at Extremes
  • Vol. 6, Issue 3, 034001 (2021)
F. B. Rosmej1、2、3、4, V. A. Astapenko3, and E. S. Khramov3
Author Affiliations
  • 1Sorbonne University, Faculty of Science and Engineering, UMR 7605, Case 128, 4 Place Jussieu, F-75252 Paris Cedex 05, France
  • 2LULI, Ecole Polytechnique, CEA, CNRS, Laboratoire pour l’Utilisation des Lasers Intenses, Physique Atomique dans les Plasmas Denses, F-91128 Palaiseau, France
  • 3Moscow Institute of Physics and Technology—MIPT, Institutskii per. 9, Dolgoprudnyi 141700, Russia
  • 4National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow 115409, Russia
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    DOI: 10.1063/5.0046040 Cite this Article
    F. B. Rosmej, V. A. Astapenko, E. S. Khramov. XFEL and HHG interaction with matter: Effects of ultrashort pulses and random spikes[J]. Matter and Radiation at Extremes, 2021, 6(3): 034001 Copy Citation Text show less

    Abstract

    The theory of photoionization describing the interaction of x-ray free-electron laser (XFEL) pulses and high-harmonic-generated (HHG) radiation is generalized to ultrashort laser pulses, where the concept of the standard ionization probability per unit time in Fermi’s golden rule and in Einstein’s theory breaks down. Numerical calculations carried out in terms of a generalized photoionization probability for the total duration of pulses in the near-threshold regime demonstrate essentially nonlinear behavior, while absolute values may change by orders of magnitude for typical XFEL and HHG pulses. XFEL self-amplified spontaneous emission pulses are analyzed to reveal general features of photoionization for random and regular spikes: the dependences of the nonlinear photoionization probability on carrier frequency and spike duration are very similar, allowing an analytical expectation value approach that is valid even when there is only limited knowledge of random and regular parameters. Numerical simulations carried out for typical parameters demonstrate excellent agreement.
    K2L8Mx+ehotK1L8Mx+2eK2L7Mx+2e+ωKα,

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    K2L8Mx+ωXFELK1L8Mx+ephoto,

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    W(ωc,τ)=c4π20+σabs(ω)|E(ω,ωc,τ)|2ωdω,

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    σabs(ω)=4πωcImα(ω).

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    α(ω)=f1(ω)+i·f2(ω)ω2,

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    σabs(ω)=4πcωf2(ω).

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    σn(ω)8π33/2Zeff4cn5ω3,

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    |E(ω,ωc,τ)|2π2E02τ2ω2τ21+ωc2τ2exp(ωcω)2τ2,

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    Wn4π1/233/2E02En2τ̃51+τ̃2ω̃2erfc[τ̃(1ω̃)],

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    E(t)=E0j=1nexptj22T2exp(ttj)22τ2cos[ωc(ttj)+φj],

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    E(ω)=π2E0τj=1nexptj22T2+iωtjexpiφj(ωωc)2τ22+expiφj(ω+ωc)2τ22,

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    tj0=ϰT22j1n1,j=1,,n,n<Tτ.

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    Δt=ϰ2Tnτ.

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    M|E(ω)|2=π3/2τ2T8Δtexp(ωωc)2τ2+exp(ω+ωc)2τ2×j=1nerftj0+ΔtTerftj0ΔtT,

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    εtot=+E2(t)dt=π2E02τj=1nk=1nexptj2+tk22T2(tjtk)24τ2×expωc2τ2cos(φj+φk)+cos[ωc(tjtk)(φjφk)],

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    W(ω,τ)εtot=cσabs(ω)4πω,

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    σabs(ω,Θ)C1+4πcωC2F(Θ),

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    F(Θ)=11exp(ωωion+Θfμ(Θ))/Θ+1,

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    F. B. Rosmej, V. A. Astapenko, E. S. Khramov. XFEL and HHG interaction with matter: Effects of ultrashort pulses and random spikes[J]. Matter and Radiation at Extremes, 2021, 6(3): 034001
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