BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Effect of partially ionized high-Z atoms on fast electron dynamics
in tokamak plasmas
DTSTART;VALUE=DATE-TIME:20210511T101000Z
DTEND;VALUE=DATE-TIME:20210511T103000Z
DTSTAMP;VALUE=DATE-TIME:20210413T220318Z
UID:indico-contribution-17186@conferences.iaea.org
DESCRIPTION:Speakers: Yves Peysson (CEA)\nThe dynamics of fast electrons d
riven inductively or by resonant interactions with radio- frequency waves
is known to be highly sensitive to the presence of impurities in hot magne
tized hydrogen plasmas. The possibility to use tungsten for the ITER diver
tor\, thanks to its low tritium retention and high melting temperature\, h
as raised the question of the impact of partially ionized high-Z atoms on
current drive efficiency by enhancing pitch-angle scattering but also coll
isional slowing-down. Pioneering work on the impact of the partial screeni
ng effect in kinetic calculations was carried out primarily for the proble
m of runaway electron mitigation in very cold post-disruptive plasmas [1].
In this paper the approach is adapted and extended to regular plasma regi
mes\, allowing to take into account any type of high-Z metallic impurity i
n the plasma core on the fast electron dynamics. In addition\, the enhance
ment of non-thermal bremsstrahlung by partially ionized high-Z atoms in th
e plasma is calculated.\nEffect of partial screening is investigated in th
e framework of the Born approximation by calculating the usual form factor
to account for the spatial extent of the high-Z ion using atomic electron
densities deduced from simplified models (Thomas-Fermi\, Yukawa potential
) or from the Density Functional Theory (DFT) describing accurately many-b
ody exchange and correlation interactions. In order to reduce computationa
l effort either for kinetic calculations or bremsstrahlung emission\, anal
ytical formulas of the form factor deduced from Thomas- Fermi and Yukawa p
otential atomic models are used\, with effective ion sizes determined for
each ionization state by a best fit of the form factor deduced numerically
from quantum relativistic calculations using the GAUSSIAN chemistry softw
are package [2]. While Thomas- Fermi model form factor gives better result
s when high-Z atoms are weakly ionized\, Yukawa potential model turns out
to be more appropriate when the screened ion charge is greater than Z/3\,
where Z is the atomic number\, a condition encountered for tungsten in sta
ndard core tokamak plasma conditions where electron temperature reaches fe
w keV.\nFrom the spinless relativistic Rutherford elastic scattering cross
-section\, the modified pitch-angle collision operator is used in Fokker-P
lanck calculations\, taking into account of the partial screening for each
species and all corresponding ionization states. It is proportional to th
e factor (Z-N)2lnΛ(p)+g(Z-N\,p)\, where lnΛ(p) is the usual momentum-dep
endent Coulomb logarithm\, N\, the number of bound electrons\, and g an an
alytical function describing the enhanced pitch-angle scattering by inner
populated atomic shells. When g is small as compared to the usual Coulomb
logarithm term\, screening effect on pitch-angle is small. Inelastic scatt
ering resulting from the mean excitation of partially-ionized high-Z atoms
is also considered from the Bethe formula for the electron relativistic s
topping power.\nFor non-thermal bremsstrahlung\, Yukawa potential model is
usually preferred for describing screening effect of bounded electrons\,
since inner atomic shells contribute significantly\, whatever the ionizati
on state [3]. In this case\, an original semi-analytical formula is derive
d for the doubly differential quantum relativistic cross-section in photon
energy and in photon emission angle from the most general Bethe-Heitler b
remsstrahlung cross-section [4]\, which greatly enhances calculation speed
\, while keeping a high numerical accuracy. It is shown that bremsstrahlun
g scales like Z^2\, with an enhanced reduction factor as the ratio k/Ec de
creases\, where k is the photon energy and Ec the incoming fast\nelectron
kinetic energy (Fig. 1). Screening effects tends to disappear progressivel
y when the angle between the photon emission and the incoming electron vel
ocity increases.\nConsequences on the current drive efficiency have been i
nvestigated using the kinetic solver LUKE of the 3-D linearized relativist
ic bounce-averaged electron Fokker-Planck equation [5] and on the fast ele
ctron bremsstrahlung using the quantum relativistic radiation code R5-X2 [
6]. Thermal ionization states for all species are determined by ADAS code
[7]. A full simulation of the high-power WEST tokamak discharge #55539 is
investigated\, where most of the plasma current is driven by the Lower Hyb
rid wave\, taking into account of the tungsten level deduced from radiativ
e power losses using the METIS tokamak code [8]. With an estimated concent
ration of tungsten of 4x10-4\, it is shown that the reduction of the LH dr
iven current is about 4%\, while conversely\, bremsstrahlung is increased
by a factor 3 approximately as compared to the fully screened ion case. Fr
om simulations of high-power WEST tokamak Lower Hybrid discharges [9]\, th
e general impact of partially ionized metallic impurities on RF current dr
ive is discussed\, as well as on fast electron bremsstrahlung diagnosis ca
pability.\nAcknowledgements. This work has been partially funded by Nation
al Science Centre\, Poland (NCN) grant HARMONIA 10 no. 2018/30/M/ST2/00799
. We thank the PLGrid project for computational resources on the Prometheu
s cluster.\n\n![Screening reduction factor for forward bremsstrahlung for
an incoming electron of Ec = 200 keV interacting with a tungsten ion whose
fully screening charge is ranging from 0 to 70. Screening effects are lar
ge when k/Ec << 1.][f1]\n\nReferences\n\n1 L. Hesslow\, et al.\, Phys. Rev
. Letter 118 (2017) 255001\n2 M. J. Frisch\, et al.\, Gaussian 09\, Revisi
on E.01\, Gaussian\, Inc.\, Wallingford CT\, 2016. 3 M. Lamoureux and N. A
vdonina\, Phys. Rev. E\, 55 (1997) 912\n4 H. W. Koch and J. W. Motz\, Rev.
Mod. Phys.\, 31 (1959) 920\n5 Y. Peysson and J. Decker\, Fusion Science a
nd Technology\, 65 (2014) 22\n6 Y. Peysson and J. Decker\, Phys. Plasmas\,
15 (2008) 092509\n7 H. P. Summers\, the ADAS User Manual\, version 2.6 ht
tp://www.adas.ac.uk (2004)\n8 J.F. Artaud\, et al.\, Nuc. Fusion 58 (2018)
105001\n9 C. Bourdelle\, et al.\, Nucl. Fusion 55 (2015) 063017\n\n\n\n
[f1]: https://yvespeysson.fr/iaea2020/Fig_synopsis1.png\n\nhttps://confere
nces.iaea.org/event/214/contributions/17186/
LOCATION:Virtual Event
URL:https://conferences.iaea.org/event/214/contributions/17186/
END:VEVENT
END:VCALENDAR