Ionization Cross Sections of Ions in Dense
plasmas modified by the Transient Space
Localization of Continuum Electrons
Jianmin Yuan
Graduate School, China Academy of Engineering Physics
jmyuan@gscaep.ac.cn
Department of Physics, National University of Defense
Technology
jmyuan@nudt.edu.cn
MoD-PMI2019, June 18-20, 2019

NIFS, JAPANIntroduction
Nature 517, 56 (2015)

IntroductionuMean free path: l =nPεl is the radius wave function offree electron and is renormalized.

In free space

In plasmaatom()Pel r = Poldelæ rör exp ç - ÷è lø()pij  i Tˆ  j2

Opacity with Debye like screening

N A bbKn =
 (hn )   bf (hn )   ff (hn )  (1 - e - hv / kT )  K sc
A Z12
ˆH = [c  p   mc - ]     f (ri )ri i  j rij ii
R0  1 ri f ( ri ) = 4   r1    r1  f ( r1 ) dr10rir
 i

 f (r ) =1

p 2 dp 2 p ( r )0æexp ççèp 2 c 2  c 4 - c 2 - U (r ) -  ö÷1÷
k BT
ø

2s22p63s, 2s22p53s, 2s22p43s

Opacity with Debye like screening

Finite quantum coherence length for the thermal continuum electronsFinite quantum coherence length for the thermal continuum electronsFinite quantum coherence length for the thermal continuum electronsFinite quantum coherence length for the thermal continuum electronsFinite quantum coherence length for the thermal continuum electrons

Te=194 eV, ne=41022 /cm3

Comparison with experiment using CSD by Saha equation

Expt.: J. Bailey et al.. Nature 517, 56 (2015).
Theo. (Isolated): using free-atom data
Theo. (w/i localization): using atomic datawith electron localization effectNuclear thermal motion driven electronic states
 QMD:Quantum Molecular Dynamics– Electronic states are described by using DFT– ions’ moving on smooth potential surface is described by
Newton’s equation

 Langevin molecular dynamics in condensed matterand material sciences– ions in Langevin equation

 = F -  M R
 NMIRItIII
 t represents the contribution of thermostat for controlling thetemperature of the system.

14Nuclear thermal motion driven electronic states
Simulation for Sandia’s experimental plasma conditions

Nuclear thermal motion driven electronic states
The electron density distribution around the ions in the cell

38.9 a.u.

Nuclear thermal motion driven electronic states
DFT basedcalculations
with 16
atoms in aunit cellNuclear thermal motion driven electronic states
Two typical atoms chosen in the cell, one is close
to another and one is separated from others.

Comparison with experiment using diagnosed CSDs
CSDs by Saha equation and diagnostics
Ion1314195eVDiag Saha
nose Eq.
00
0.01 015

0.01

161718
1920
21

0.14
0.32
0.28
0.18
0.01
0.05

0.01
20.11
0.30
0.35
0.18
0.04
0.022

0.0

0.0

181eV
Diag Saha
nose Eq.
0.02 0.0
0.07 0.00
30.10 0.22

169eV
Diag Saha
nose Eq.
0.05 0.0
0.05 0.00
40.20 0.03

164eV
Diag Saha
nose Eq.
0.0
0.0
0.0
0.0

0.15
0.25
0.23
0.12
0.01
0.05

0.18
0.24
0.17
0.02
0.01
0.08

0.18
0.39
0.30
0.09
0.01
0.0

0.28
0.30
0.18
0.01
0.04
0.03

0.00

0.0

0.16

0.0

0.16
0.36
0.32
0.12
0.02
0.00
10.0

0.0

0.00
50.07
0.27
0.40
0.22
0.04
0.00
30.0

Electron impact ionization processes

Electron impact ionization processes

Electron impact ionization processes

Electron impact ionization processes

Electron impact ionization processes

Summary
1. Here we propose the notion of a transient space localizationof electrons produced during the ionization of atoms
immersed in a hot dense plasma.
2. A theoretical formalism is developed to study thewavefunctions of the continuum electrons that takes into
consideration the quantum de-coherence caused bycoupling with the plasma environment.
3. We find that the cross section is considerably enhanced
compared with the predictions of the existing isolated-atommodel.
4. And thereby partly explains the big difference between themeasured opacity of Fe plasma and the existing standard
models for short wavelengths, and also explains the big gap
between the extracted electron impact ionization rates
from laser heated Mg plasma and the calculated values
using the existing models.

Acknowledgements:
Colleagues:
Pengfei Liu （刘鹏飞），Cheng Gao（高诚），Dongdong Kang（康冬冬）， Yong Hou（侯永），Jiaolong Zeng （曾交龙）Supported by:
Science Challenge Project and National Natural
Science Foundation of China