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    Journals >Matter and Radiation at Extremes >Volume 8 >Issue 6 >Page 064002 > Article
    • Matter and Radiation at Extremes
    • Vol. 8, Issue 6, 064002 (2023)
    Simulations of spin/polarization-resolved laser–plasma interactions in the nonlinear QED regime
    Feng Wan1, Chong Lv2, Kun Xue1, Zhen-Ke Dou1..., Qian Zhao1, Mamutjan Ababekri1, Wen-Qing Wei1, Zhong-Peng Li1, Yong-Tao Zhao1 and Jian-Xing Li1,a)|Show fewer author(s)
    Author Affiliations
  • 1Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, China
  • 2Department of Nuclear Physics, China Institute of Atomic Energy, P.O. Box 275(7), Beijing 102413, China
    • show less
    DOI: 10.1063/5.0163929 Cite this Article
    Feng Wan, Chong Lv, Kun Xue, Zhen-Ke Dou, Qian Zhao, Mamutjan Ababekri, Wen-Qing Wei, Zhong-Peng Li, Yong-Tao Zhao, Jian-Xing Li. Simulations of spin/polarization-resolved laser–plasma interactions in the nonlinear QED regime[J]. Matter and Radiation at Extremes, 2023, 8(6): 064002 Copy Citation Text show less

    Abstract

    Strong-field quantum electrodynamics (SF-QED) plays a crucial role in ultraintense laser–matter interactions and demands sophisticated techniques to understand the related physics with new degrees of freedom, including spin angular momentum. To investigate the impact of SF-QED processes, we have introduced spin/polarization-resolved nonlinear Compton scattering, nonlinear Breit–Wheeler, and vacuum birefringence processes into our particle-in-cell (PIC) code. In this article, we provide details of the implementation of these SF-QED modules and share known results that demonstrate exact agreement with existing single-particle codes. By coupling normal PIC simulations with spin/polarization-resolved SF-QED processes, we create a new theoretical platform to study strong-field physics in currently running or planned petawatt or multi-petawatt laser facilities.
    dpdt=qm(E+β×B),

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    dxdt=pγ,

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    pn+1/2−pn−1/2Δt=qmEn+pnγn×Bn,

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    xn+1−xnΔt=vn+1/2,

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    pn−1/2=p−−qΔt2mEn,

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    pn+1/2=p++qΔt2mEn,

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    p′=p−+p−×τ,

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    p+=p−+p′×ς,

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    τ=qΔt2mγnBn,

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    ς=2τ1+τ2,

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    ∇⋅E=ρ,

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    ∇⋅B=0

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    ∇×E=−∂B∂t,

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    ∇×B=∂E∂t+J.

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    Eyn+1−EynΔti+1/2=−Bi+1−BiΔxzn+1/2−Jy,i+1/2n+1/2,Bzn+1/2−Bzn−1/2Δti=−Ei+1/2−Ei−1/2Δxyn;

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    Eyn+1−EynΔti+1/2,j=−Bi+1,j−Bi,jΔxzn+1/2−Jy,i+1/2,jn+1/2,Bzn+1/2−Bzn−1/2Δti+1/2,j=−Ei+1/2,j−Ei+1/2,jΔxyn+Ei+1/2,j+1/2−Ei+1/2,j−1/2Δyxn+1/2;

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    Eyn+1−EynΔti+1/2,j,k+1/2=−Bi+1,j,k+1/2−Bi,j,k+1/2Δxzn+1/2+Bi+1/2,j,k+1−Bi+1/2,j,kΔzxn+1/2−Jy,i+1/2,j,k+1/2n+1/2,Bzn+1/2−Bzn−1/2Δti,j,k+1/2=−Ei+1/2,j,k−Ei−1/2,j,kΔxyn+Ei+1/2,j+1,k−Ei+1/2,j,kΔyxn.

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    ∂tρ+∇⋅J=0,

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    ρi,j,kn+1/2=1ΔV∑rWxrn+12vn+1/2Δtqr,

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    ρi,j,kn−1/2=1ΔV∑rWxrn−12vnΔtqr,

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    δnρ=ρn+1/2−ρn−1/2,

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    Wspline=34−δ2,forj,1212±δ,forj±1,

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    FRR,classical=2e33mc3γ∂∂t+pγm⋅∇E+pγmc×∂∂t+pγm⋅∇B+emcE×B+1γmcB×(B×p)+1γmcE(p⋅E)−eγm2c2pE+pγmc×B2−1γ2m2c2(E⋅p)2.

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    FRR,classical=23αfξLγ∂∂t+pγ⋅∇E+pγ×∂∂t+pγ⋅∇B+E×B+1γB×(B×p)+E(p⋅E)−γpE+pγ×B2−1γ2(E⋅p)2,

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    FRR,cl≃23αfχe2ξLβ,

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    R≡|FRR|/|FL|∼23αfγeχe≃2×10−8a0γe2(for wavelength 1μm).

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    FRR,quantum=q(χ)FRR,classical,

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    q(χ)=IQEDIC,

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    IQED=mc2∫c(k⋅k′)dWfidηdr0dr0,

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    IC=2e4E′23m2c3,

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    q(χe)≈11+4.8(1+χe)ln(1+1.7χe)+2.44χe22/3,

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    q(χe)≈1(1+8.93χe+2.41χe2)2/3.

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    FRR,quantum=q(χ)Pclχe2β/β2c.

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    pn+1/2−pn−1/2Δt=Fn=FLn+FRn.

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    pLn+1/2−pLn−1/2Δt=FLn,

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    pRn+1/2−pRn−1/2Δt=FRn,

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    pn+1/2=pLn+1/2+pRn+1/2−pn−1/2=pLn+1/2+FRnΔt.

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    p(τ)=p0−A(τ)+k̂A2(τ)−2p0⋅A(τ)2(γ0−p0⋅k̂)

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    γ(τ)=γ0+A2(τ)−2p0⋅A(τ)2(γ0−p0⋅k̂)

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    dSdtT=S×Ω≡S×−g2−1γeγe+1β⋅B⋅β+g2−1+1γeB−g2−γeγe+1β×E,

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    dSdt=dSdtT+dSdtR,

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    dSdtR=−Pψ1(χ)S+ψ2(χ)(S⋅β)β+ψ3(χ)n̂B.

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    S′=Sn−1/2+Sn−1/2×t,

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    Sn+1/2=Sn−1/2+S′×o,

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    t=qΔt2Ωn,

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    o=2t1+t2.

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    STn−1/2=Sn−1/2+Δt2dSdtR,

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    Sn+1/2=STn+1/2+Δt2dSdtR.

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    d2Wfidudt=WR2(F0+ξ1F1+ξ2F2+ξ3F3),

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    F0=−(2+u)2IntK1/3(u′)−2K2/3(u′)(1+Sif)+u2(1−Sif)IntK1/3(u′)+2K2/3(u′)+2u2SifIntK1/3(u′)−(4u+2u2)(Sf+Si)⋅n̂×âK1/3(u′)−2u2(Sf−Si)⋅n̂×âK1/3(u′)−4u2IntK1/3(u′)−K2/3(u′)×(Si⋅n̂)(Sf⋅n̂),

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    F1=−2u2IntK1/3(u′)(Si⋅â)Sf⋅n̂×â+(Sf⋅â)Si⋅[n̂×â]+4u(Si⋅â)(1+u)+(Sf⋅â)K1/3(u′)+2u(2+u)n̂⋅[Sf×Si]K2/3(u′),

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    F2=−2u2(Si⋅n̂)Sf⋅n̂×â+(Sf⋅n̂)Si⋅n̂×â+2u(2+u)â⋅[Sf×Si]K1/3(u′)−4u(Si⋅n̂)+(Sf⋅n̂)(1+u)IntK1/3(u′)+4u(2+u)×(Si⋅n̂)+(Sf⋅n̂)K2/3(u′),

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    F3=41+u+1+u+12u2Sif−12u2(Si⋅n̂)(Sf⋅n̂)K2/3(u′)+2u2Si⋅n̂×âSf⋅n̂×â−(Si⋅â)(Sf⋅â)IntK1/3(u′)−4u(1+u)Sin̂×â+Sfn̂×âK1/3(u′),

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    d2Wfidudt=WR−(2+u)2IntK1/3(u′)−2K2/3(u′)(1+Sif)+u2IntK1/3(u′)+2K2/3(u′)(1−Sif)+2u2SifIntK1/3(u′)−(4u+2u2)(Sf+Si)[n×â]×K1/3(u′)−2u2(Sf−Si)[n×â]K1/3(u′)−4u2IntK1/3(u′)−K2/3(u′)(Si⋅n)(Sf⋅n),

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    d2W̄fidudt=8WR−(1+u)IntK1/3(u′)+(2+2u+u2)K2/3(u′)−uSi⋅n×âK1/3(u′).

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    SfR=gw+f⋅Si.

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    d2Wraddudt=Wr(w+f⋅Si+g⋅Sf),

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    P̂=cos(θα)P̂1+sin(θα)P̂2eiθβ,

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    ρ=121+ξ⋅σ=121+ξ3ξ1−iξ2ξ1+iξ21−ξ3,

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    P̂1′=P̂1cos(ψ)+P̂2sin(ψ),

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    P̂2′=−P̂1sin(ψ)+P̂2cos(ψ).

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    ξ1′=ξ1cos(2ψ)−ξ3sin(2ψ),ξ2′=ξ2,ξ3′=ξ1sin(2ψ)+ξ3cos(2ψ),

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    ξ1′ξ2′ξ3′=cos2ψ0−sin2ψ010sin2ψ0cos2ψξ1ξ2ξ3≡ROT(ψ)⋅ξ.

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    d2Wpair±dε+dt=12(G0+ξ1G1+ξ2G2+ξ3G3),

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    G0=W02IntK1/3(ρ)+ε−2+ε+2ε−ε+K2/3(ρ)+IntK1/3(ρ)−2K2/3(ρ)(S−⋅S+)+K1/3(ρ)−εγε+(S+⋅b̂+)+εγε−(S−⋅b̂+)+ε−2+ε+2ε−ε+IntK1/3(ρ)−(ε+−ε−)2ε−ε+K2/3(ρ)×(S+⋅v̂+)(S−⋅v̂+),

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    G1=W02K1/3(ρ)−εγε−(S+⋅â+)+εγε+(S−⋅â+)+ε+2−ε−22ε−ε+K2/3(ρ)(S−×S+)⋅v̂+−εγ22ε−ε+IntK1/3(ρ)×(S+⋅â)(S−⋅b̂)+(S−⋅â+)(S+⋅b̂+),

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    G2=W02εγ22ε−ε+K1/3(ρ)(S−×S+)⋅â++ε+2−ε−22ε−ε+K1/3(ρ)×(S−⋅v̂+)(S+⋅b̂+)+(S+⋅v̂+)(S−⋅b̂+)+εγε−IntK1/3(ρ)−ε+2−ε−2ε−ε+K2/3(ρ)(S−⋅v̂+)+εγε+IntK1/3(ρ)+ε+2−ε−2ε−ε+K2/3(ρ)(S+⋅v̂+),

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    G3=W02−K2/3(ρ)+ε−2+ε+22ε−ε+K2/3(ρ)(S−⋅S+)−K1/3(ρ)×εγε+(S−⋅b̂+)−εγε−(S+⋅b̂+)+εγ22ε−ε+IntK1/3(ρ)×(S+⋅b̂+)(S−⋅b̂+)−(S+⋅â+)(S−⋅â+)−(ε+−ε−)22ε−ε+K2/3(ρ)(S+⋅v̂+)(S−⋅v̂+),

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    d2Wpair+dε+dt=W0IntK1/3(ρ)+ε−2+ε+2ε−ε+K2/3(ρ)−εγε+K1/3(ρ)(S+⋅b̂+)−ξ1εγε−K1/3(ρ)(S+⋅â+)+ξ2ε+2−ε−2ε−ε+K2/3(ρ)+εγε+IntK1/3(ρ)(S+⋅v̂+)−ξ3K2/3(ρ)−εγε−K1/3(ρ)(S+⋅b̂+).

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    d2Wpair+dε+dt=W0(C+S+⋅D),

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    C=IntK1/3(ρ)+ε−2+ε+2ε−ε+K2/3(ρ)−ξ3K2/3(ρ),

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    D=−εγε+−ξ3εγε−K1/3(ρ)b̂+−ξ1εγε−K1/3(ρ)â++ξ2ε+2−ε−2ε−ε+K2/3(ρ)+εγε+IntK1/3(ρ)v̂+.

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    d2Wpair−dε+dt=W0(C+S−⋅D′),

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    D′=εγε−−ξ3εγε+K1/3(ρ)b̂++ξ1εγε+K1/3(ρ)â+−ξ2ε+2−ε−2ε−ε+K2/3(ρ)−εγε−IntK1/3(ρ)v̂+.

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    d2Wpairdε+dt=2W0IntK1/3(ρ)+ε−2+ε+2ε−ε+K2/3(ρ)−ξ3K2/3(ρ).

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    dσeZdω(ω,y)=αr02ω43−43y+y2Z2ϕ1−43ln⁡Z−4f+Zψ1−83lnZ+23(1−y)[Z2(ϕ1−ϕ2)+Z(ψ1−ψ2)],

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    dσbrdω=Z2β21ωχ(Z,Ee,y),

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    dσbr+dω=Fp(Z,Ee)dσbr−dω,

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    n≈1−αχγ2m216πω2∫−11dυ(1−υ2)121+13υ21−13υ2×πx4/3Gi′(x2/3)−ix23K2/323x,

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    Re(n)=1−454D∫01dυ(1−υ2)121+13υ21−13υ2×πx4/3Gi′(x2/3),

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    Im(n)=454D∫01dυ(1−υ2)121+13υ21−13υ2x23K2/323x.

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    M(χγ)=−454∫01dυ(1−υ2)121+13υ21−13υ2πx4/3Gi′(x2/3),

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    Re(n)=1+M(χγ)D≡1+M(χγ)α90πχγ2ω2/m2.

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    Re(n)=1+D4+7−

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    ξ1′ξ2′ξ3′=cosδϕ−sinδϕ0sinδϕcosδϕ0001ξ1ξ2ξ3≡QED(δϕ)⋅ξ.

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    Feng Wan, Chong Lv, Kun Xue, Zhen-Ke Dou, Qian Zhao, Mamutjan Ababekri, Wen-Qing Wei, Zhong-Peng Li, Yong-Tao Zhao, Jian-Xing Li. Simulations of spin/polarization-resolved laser–plasma interactions in the nonlinear QED regime[J]. Matter and Radiation at Extremes, 2023, 8(6): 064002
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