• Matter and Radiation at Extremes
  • Vol. 5, Issue 6, 064201 (2020)
F. B. Rosmej1、2、3、4、a), V. A. Astapenko3, V. S. Lisitsa3、4、5, and L. A. Vainshtein6
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, CNRS-CEA, Physique Atomique dans les Plasmas Denses (PAPD), Route de Saclay, F-91128 Palaiseau Cedex, France
  • 3Moscow Institute of Physics and Technology MIPT (National Research University), Dolgoprudnyi 141700, Russia
  • 4National Research Nuclear University—MEPhI, Department of Plasma Physics, Moscow 115409, Russia
  • 5National Research Center “Kurchatov Institute”, Moscow, Russia
  • 6P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russia
  • show less
    DOI: 10.1063/5.0014158 Cite this Article
    F. B. Rosmej, V. A. Astapenko, V. S. Lisitsa, L. A. Vainshtein. Dielectronic recombination in non-LTE plasmas[J]. Matter and Radiation at Extremes, 2020, 5(6): 064201 Copy Citation Text show less

    Abstract

    Novel phenomena and methods related to dielectronic capture and dielectronic recombination are studied for non-local thermodynamic equilibrium (LTE) plasmas and for applications to non-LTE ionization balance. It is demonstrated that multichannel autoionization and radiative decay strongly suppress higher-order contributions to the total dielectronic recombination rates, which are overestimated by standard approaches by orders of magnitude. Excited-state coupling of dielectronic capture is shown to be much more important than ground-state contributions, and electron collisional excitation is also identified as a mechanism driving effective dielectronic recombination. A theoretical description of the effect of angular-momentum-changing collisions on dielectronic recombination is developed from an atomic kinetic point of view and is visualized with a simple analytical model. The perturbation of the autoionizing states due to electric fields is discussed with respect to ionization potential depression and perturbation of symmetry properties of autoionization matrix elements. The first steps in the development of statistical methods are presented and are realized in the framework of a local plasma frequency approach. Finally, the impact of collisional–radiative processes and atomic population kinetics on dielectronic recombination is critically discussed, and simple analytical formulas are presented.

    dielectroniccapture:A+Z(α0)+eA+(Z1)**(αnl).(1.1)

    View in Article

    autoionization:A+(Z1)**(αnl)A+Z(α0)+eAuger.(1.2)

    View in Article

    corestabilization:A+(Z1)**(αnl)A+(Z1)*(α0nl)+ωcore,(1.3)

    View in Article

    spectatorelectronstabilization:A+(Z1)*(α0nl)A+(Z1)(γ)+ωnl.(1.4)

    View in Article

    Z2RyE=Zαcve2η21,(1.5)

    View in Article

    EEf=ΔE=ωcoreE+RyZeff2/nf2.(2.1)

    View in Article

    njZΓjkZ,Z+1=nkZ+1neDCkj,(2.2)

    View in Article

    njZnkZ+1=negjZ2gkZ+12π2mekTe3/2expΔEk,jZ+1,ZkTe,(2.3)

    View in Article

    ΔEk,jZ+1,Z=EkjDC,(2.4)

    View in Article

    DCkj=gjZ2gkZ+12π2me3/2ΓjkZ,Z+1exp(EkjDC/kTe)(kTe)3/2,(2.5)

    View in Article

    DCkj=1.656×1022gjZgkZ+1ΓjkZ,Z+1exp(EkjDC/Te)Te3/2(cm3/s)(2.6)

    View in Article

    DRkjZ+1,Z=Pj,grZDCkjZ+1,Z.(2.7)

    View in Article

    DCkj=π232me3/2gjZgkZ+1ΓjkZ,Z+1F(EkjDC)EkjDC,(2.8)

    View in Article

    DCkj=2.9360×1040ΓjkZ,Z+1gjZgkZ+1ΓjkZ,Z+1F(EkjDC)EkjDC(cm3/s).(2.9)

    View in Article

    Pj,grZ=Pj,grZ(ne,Te).(3.1)

    View in Article

    Pj,grZiBjiZ=iAjiZlAjlZ+kΓjkZ,Z+1.(3.2)

    View in Article

    DRkjZ+1,ZiBjiZ.DCkjZ+1,Z=iAjiZlAjlZ+kΓjkZ,Z+1DCkjZ+1,Z.(3.3)

    View in Article

    DRkjZ+1,Z12gkZ+12π2me3/2exp(EkjDC/kTe)(kTe)3/2igjZΓjkZ,Z+1AjiZlAjlZ+kΓjkZ,Z+1.(3.4)

    View in Article

    Qk,jiZ+1,Z=gjZΓjkZ,Z+1AjiZlAjlZ+kΓjkZ,Z+1,(3.5)

    View in Article

    DRtotZ+1,Z=kjDRkjZ+1,Z=kjPj,grZDCkjZ+1,Z.(3.6)

    View in Article

    DRkjZ+1,Z:=DZ+1,Z(α0α,nl).(3.7)

    View in Article

    DRtotZ+1,Z:=DZ+1,Z=α0αnl=0n1DZ+1,Z(α0α,nl).(3.8)

    View in Article

    DZ+1,Zαnl=0n1DZ+1,Z(α0α,nl).(3.9)

    View in Article

    DZ+1,Z(α0α,nl)=4.8×1011fα0αBdβ3/2eβχd(cm3/s),(3.10)

    View in Article

    β=(z+1)2RykTe,(3.11)

    View in Article

    χd=χ1+0.015z3(z+1)2,(3.12)

    View in Article

    χ=ΔE(α0α)(z+1)2Ry.(3.13)

    View in Article

    Bd=zχz2+13.41/211+0.105(z+1)χ+0.015(z+1)2χ2.(3.14)

    View in Article

    Bd=zχz2+13.41/20.51+0.210(z+1)χ+0.030(z+1)2χ2.(3.15)

    View in Article

    DZ+1,ZDZ+1,Z(α0α1)+DZ+1,Z(α0α2),(3.16)

    View in Article

    DZ+1,Z(α0α):=nl=0n1DZ+1,Z(α0α,nl).(3.17)

    View in Article

    He1+(1s)+eHe0+**(nlnl)He0+(1s2).(3.18)

    View in Article

    3lnl1s+eAuger2l+eAuger.(3.19)

    View in Article

    DZ+1,Z(α0α,nl)=108×m2l0+1Bdβ3/2eβχd(cm3/s),(3.20)

    View in Article

    β=Z2RykTe,(3.21)

    View in Article

    DRk,jiZ+1,Z12gkZ+12π2me3/2gjZΓjkZ,Z+1AjiZlAjlZ+kΓjkZ,Z+1exp(EkjDC/kTe)(kTe)3/2.(5.1)

    View in Article

    ΓjkZ,Z+1=2.5×1014s1,AjiZ=1.4×1012s1,(1)

    View in Article

    lAjlZ=1.4×1013s1,kΓjkZ,Z+1=2.5×1014s1.(1)

    View in Article

    ΓjkZ,Z+1=0,AjiZ=6.0×1011s1,(1)

    View in Article

    lAjlZ=1.4×1012s1,kΓjkZ,Z+1=0,(1)

    View in Article

    njZlAjlZ+kΓjkZ,Z+1+neCjj=nkZ+1neDCk,jZ+1,Z+nenjZCjj,(5.2)

    View in Article

    njZlAjlZ+kΓjkZ,Z+1+neCjj=nkZ+1neDCk,jZ+1,Z+nenjZCjj,(5.3)

    View in Article

    DCk,qZ+1,Z=12gkZ+12π2me3/2gqZΓqkZ,Z+1exp(EkqDC/kTe)(kTe)3/2,(5.4)

    View in Article

    nq(0),Z=nkZ+1ne12gkZ+12π2me3/2gqZΓqkZ,Z+1lAqlZ+kΓqkZ,Z+1exp(EkqDC/kTe)(kTe)3/2,(5.5)

    View in Article

    lAjlZ+kΓjkZ,Z+1neCjj.(1)

    View in Article

    DRcolltotZ+1,Z=DRcollk,jiZ+1,Z+DRcollk,jiZ+1,Z,(5.6)

    View in Article

    DRcolltotZ+1,ZDRtotZ+1,Z=DRcollk,jiZ+1,Z+DRcollk,jiZ+1,ZDRk,jiZ+1,Z+DRk,jiZ+1,Z.(5.7)

    View in Article

    DRcollk,jiZ+1,ZnjZAjiZ,(5.8)

    View in Article

    DRcolltotZ+1,ZDRtotZ+1,Z=njZAjiZ+njZAjiZnj(0),ZAjiZ+nj(0),ZAjiZ,(5.9)

    View in Article

    DRcolltotZ+1,ZDRtotZ+1,Z=njZnj(0),Z+njZAjiZnj(0),ZAjiZnj(0),ZAjiZnj(0),ZAjiZ+1.(5.10)

    View in Article

    nj(0),Znj(0),ZgjZΓjkZ,Z+1gjZΓjkZ,Z+1lAjlZ+kΓjkZ,Z+1lAjlZ+kΓjkZ,Z+10,(5.11)

    View in Article

    njZlAjlZ+neCjjnenjZCjj(5.12)

    View in Article

    njZlAjlZ+kΓjkZ,Z+1nkZ+1neDCk,jZ+1,Z.(5.13)

    View in Article

    njZnj(0),Z.(5.14)

    View in Article

    DRcolltotZ+1,ZDRtotZ+1,Z1+neCjjlAjlZ+neCjjAjiZAjiZ.(5.15)

    View in Article

    DRcolltotZ+1,ZDRtotZ+1,Z1+gjZgjZAjiZAjiZ11+lAjlZ/neCjj.(5.16)

    View in Article

    AjiZ/lAjlZ+kΓjkZ,Z+1=6.0×1011/1.4×1012=0.43(1)

    View in Article

    AjiZ/lAjlZ+kΓjkZ,Z+1=1.4×1012/2.6×1014=0.0088(1)

    View in Article

    E=Zeff2Ryn2=(Znσ)2Ryn2(1)

    View in Article

    Fcrit6.8×108Zeff3nF4[V/cm],(6.1)

    View in Article

    Fmean3.41F0=3.4×4π4152/3Ryea0ZPNP2/31.3×106ZPNP2/3[cm3][V/cm],(6.2)

    View in Article

    nFnmaxspectator4.8×103Zeff3/4ZP1/4NP1/6(cm3).(6.3)

    View in Article

    Arad(αα0)neIn,(6.4)

    View in Article

    Aradαα0,Δn>01.57×1010Zeff4nα0nα3(nα2nα02)[s1],(6.5)

    View in Article

    In6×108RyEn3/2βneβnln1+0.562+1.4βnβn(1+1.4βn)[cm3/s],(6.6)

    View in Article

    βn=EnkTe.(6.7)

    View in Article

    En(Zeff1)2Ryn2.(6.8)

    View in Article

    Arad(nlgr)neIn.(6.9)

    View in Article

    Arad(nlgr,Δn>0)1.57×1010(Zeff1)4ngrn3(n2ngr2)[s1].(6.10)

    View in Article

    Γ(dc)=2πdVc2δ(EdEc),(6.11)

    View in Article

    Γ(ac)=2π|daQEddVc(EaEd)+i(Γd+Ad)/2|2δ(EaEc),(6.12)

    View in Article

    nλm=l=mn1nlmnlmnλm,(6.13)

    View in Article

    Γ(n,λ,m)=lminlmaxP(nl;λm)Γ(nl)dl,(6.14)

    View in Article

    lmin2=12{[(n1)2+m2λ2][(n1)2+m2λ2]24(n1)2m2}(6.15)

    View in Article

    lmax2=12{[(n1)2+m2λ2]+[(n1)2+m2λ2]24(n1)2m2},(6.16)

    View in Article

    P(nl;λm)1π2l(l2lmin2)(lmax2l2).(6.17)

    View in Article

    Γ(n,λ,m)=fijπn3I(tmin,tmax),(6.18)

    View in Article

    I(tmin,tmax)2lmax3Z2ω2/3Ylmin(ω/3Z2)1/3,(6.19)

    View in Article

    Y(x)0.284exp(2x3),(6.20)

    View in Article

    DR(Te)=4πRykTe3/2a03gfgiAn,lΓ(n,l)A+Γ(n,l)expωkTe+Zi2Ryn2kTe,(7.1)

    View in Article

    A=2ω2fifc3,(7.2)

    View in Article

    (2l+1)gfΓ(n,l)=Z2n3ωgiσex(n,l)π2a02.(7.3)

    View in Article

    σex(n,l)=8π3mVe2gfgififZi2(l+12)2Gω(l+12)33Zi2,(7.4)

    View in Article

    G(u)=u[K1/32(u)+K2/32(u)],(7.5)

    View in Article

    G(u)3.4exp(2u).(7.6)

    View in Article

    Γ(n,l)0.72ω(l+12)fijn3exp2ω(l+12)33Zi2.(7.7)

    View in Article

    Ne=ffif(7.8)

    View in Article

    Ne=ne(r,q,Zn)dV.(7.9)

    View in Article

    ffif0r0dr4πr2ne(r,q,Zn)(7.10)

    View in Article

    Eifω=4πne(r,q,Zn).(7.11)

    View in Article

    DR[cm3/s]=0.61×108DR(a.u.),(7.12)

    View in Article

    DR(a.u.)=54.5Te3/2ZnZi20x0dxx2φ(x,q)x9/41dtexpω(x)Te11t2×0lmax=tn11dl(l+12)exp[2ω(x)(l+12)3/3Zi2]t3+A(x,l),(7.13)

    View in Article

    A(x,l)=5.2×106(l+12)exp[2ω(x)(l+12)3/3Zi2]Zi3ω(x),(7.14)

    View in Article

    ω(x)=1.2Znφ(x,q)x3/4,(7.15)

    View in Article

    Ei=ωZi22n2,(7.16)

    View in Article

    0=ωZi22n12,(7.17)

    View in Article

    n1=Zi2ω.(7.18)

    View in Article

    ne(x,q,Zn)=329π3Zn2φ(x,q)x3/2,(7.19)

    View in Article

    x=rrTF,(7.20)

    View in Article

    rTF=9π31281/31Zn1/3=0.8853Zn1/3,(7.21)

    View in Article

    q=ZZn,(7.22)

    View in Article

    φ(x,q)=φ0(x)11+z(x)1+z0(x)λ1/λ2,(7.23)

    View in Article

    z(x)=x1443/2λ2,(7.24)

    View in Article

    z0(x)=x0(q)1443/2λ2,(7.25)

    View in Article

    φ0(x)=11+z(x)λ1/2,(7.26)

    View in Article

    λ1=0.57+73=7.77200,(7.27)

    View in Article

    λ2=0.57+73=0.77200.(7.28)

    View in Article

    x0dφ(x0)dx=q.(7.29)

    View in Article

    x0(q)=2.961qq2/3if0.2<q1,6.841q3ifq<0.05.(7.30)

    View in Article

    IZ=Zn2Ry1289π21/32ZZn5/3x0(q,Zn).(7.31)

    View in Article

    IZ0.221Ry(1+Z)4/310.961+ZZn0.257.(7.32)

    View in Article

    n,lΓ(n,l)A+Γ(n,l),(1)

    View in Article

    DR(a.u.)=39.2Te3/2ZnZi2ZnZi20x0dxx2φ(x)x31dtt2expω(x)T11t2×0tn1dl(l+12)2exp[2ω(x)(l+12)3/3Zi2]t3+A(x,l),(7.33)

    View in Article

    WA(n,l)=1.7fifZi2πn5ω.(7.34)

    View in Article

    DR(a.u.)=0.86×102Te3/2ZnZi20x0dxx2φ(x,q)x9/4×1dtexp1.2ZTeφ(x,q)x3/411t2t5+A(x),(7.35)

    View in Article

    A(x)=4.56×106Zi3Znφ(x,q)x3/8.(1)

    View in Article

    F. B. Rosmej, V. A. Astapenko, V. S. Lisitsa, L. A. Vainshtein. Dielectronic recombination in non-LTE plasmas[J]. Matter and Radiation at Extremes, 2020, 5(6): 064201
    Download Citation