Neutral gas modelling
Ben Dudson1
1
York Plasma Institute, Department of Physics, University of York,
Heslington, York YO10 5DD, UK
BOUT++ Workshop 16th September 2014
Ben Dudson, University of York
BOUT++ Workshop 2014 (1 of 13)
Outline
Neutral gas and plasma turbulence
Neutral gas physics: Cross-sections and mean free paths
Typical length-scales
Approaches used in BOUT++
Discussion
Ben Dudson, University of York
BOUT++ Workshop 2014 (2 of 13)
Neutrals and plasma turbulence (1/2)
2D transport codes include molecular and atomic physics
→ Essential for e.g. divertor physics, detachment
3D turbulence codes have typically assumed fully ionised,
single ion species plasma
Strong motivations for including neutral gas physics in 3D code:
1 Effect of neutrals on turbulence
Sources and sinks of density and momentum
Damping from ion-neutral interactions
Electron-neutral interaction may have more complex effect on
drift-wave stability
Ben Dudson, University of York
BOUT++ Workshop 2014 (3 of 13)
Neutrals and plasma turbulence (2/2)
2
Effect of turbulence on neutrals
Ion-neutral cross-sections are strongly nonlinear:
n hσv i =
6 nhσv i
Neutral gas profiles affected by fluctuations
2D ITER simulations with and without synthetic fluctuations1
Caused by hardening of CX neutral spectrum
1
S.Mekkaoui
Ben Dudson, University of York
BOUT++ Workshop 2014 (4 of 13)
Neutral gas processes
Several processes involved:
Charge Exchange (CX) H + H + → H + + H
Ionisation (electron impact) H + e − → 2e − + H +
Also produces radiation through excitation
Recombination has several pathways:
Radiative recombination: e − + H + → H + hν
Three-body recombination: e − + e − + H + e − + H
Negative-ion mediated recombination (MAR):
e − + H2
→
H2− → H + H −
−
→
H +H
+
H +H
Ion-conversion mediated recombination (MAR):
H + + H2
→ H + H2+
e − + H2+
→ H +H
1
EIRENE: http://www.eirene.de/
2
KN1D: http://www.psfc.mit.edu/l̃abombard/KN1D Source Info.html
Ben Dudson, University of York
BOUT++ Workshop 2014 (5 of 13)
Interaction cross-sections
10-13
10-14
10-15
Rate <σv > [m3 s−1 ]
Analytic forms used
for ionisation,
recombination, and
charge exchange cross
sections2
10-17
10-18
10-19
10-20
10-21 0
1
Ionisation
Recombination (n = 1018 m−3 )
Recombination (n = 1020 m−3 )
Recombination (n = 1022 m−3 )
Charge exchange
10-16
5
10
15
20
Electron temperature [eV]
Thanks to Eva Havlickova, CCFE
Ben Dudson, University of York
BOUT++ Workshop 2014 (6 of 13)
25
30
Interaction mean free paths
10cm
1017
1m
10 100
101
102
Temperature [eV]
1mm
19
1018
10
1cm
10
103
Ionisation mean free path
1020
cm
1017
1016100
Ben Dudson, University of York
1cm
1018
10m
Charge exchange results in a
population of fast neutrals,
which can have much longer
m.f.p.
1019
16
Electron density [m−3 ]
Often a 3.5 eV
“Frank-Condon” energy is
assumed instead
Charge exchange mean free path
1mm
Mean free paths shown for a
300K (0.025eV) neutral gas
atom using a crude
analytical model for
cross-sections
Electron density [m−3 ]
1020
1m
101
102
Temperature [eV]
BOUT++ Workshop 2014 (7 of 13)
103
BOUT++ neutral models
Three approaches being followed to neutral modelling
Simple drag model for CX in LAPD1
Fluid modelling2
1
2
Valid for short mean-free-path
interactions
Conputationally lower cost than
Montecarlo methods
Montecarlo modelling
3
Can be applied when m.f.p is long
Much more expensive
computationally, but parallelises very
well
Coupling to EIRENE
Currently testing in linear geometry3
1
P.Popovich, M.V.Umansky, T.A.Carter and B.Friedman arXiv:1005.2418 (2010)
2
Z.H.Wang, X.Q.Xu, T.Y.Xia, T.D.Rognlien Nucl. Fusion 2013
3
S.Mekkaoui et al. PSI conference 2014
Ben Dudson, University of York
BOUT++ Workshop 2014 (8 of 13)
Simple model
Sensitivity of turbulence to neutral gas studied in LAPD
simulations1
Treat charge-exchange as a sink of vorticity with ion-neutral
collision rate νin ∼ 10−3 Ωci
∂t ω = . . . − νin ω
1
P.Popovich, M.V.Umansky, T.A.Carter and B.Friedman arXiv:1005.2418 (2010)
Ben Dudson, University of York
BOUT++ Workshop 2014 (9 of 13)
Fluid neutral model
Fluid model developed1 which takes into account dissociation and
ionisation:
H2 → 2H 0 → 2H + + 2e
and charge-e Currently models neutrals along a 1D beam (SMBI).
Provides a source of density for fuelling
1
Z.H.Wang, X.Q.Xu, T.Y.Xia, T.D.Rognlien Nucl. Fusion 2013
Ben Dudson, University of York
BOUT++ Workshop 2014 (10 of 13)
Ongoing work with neutral fluid models
1D modelling of detachment fronts
20
15
Time t = 2.505800e-03 s
At high density (low divertor
temperature), volume
recombination can detach plasma
from the target plates
Ionisation-recombination front
can move upstream
Stability and control of this front
is essential
10
5
0
5
150
Ben Dudson, University of York
Plasma density
Neutral density
Plasma temperature
Plasma sink
10
5
10
Length [m]
BOUT++ Workshop 2014 (11 of 13)
15
20
25
Ongoing work with neutral fluid models
Plasma temperature [eV]
0
1D modelling of detachment fronts
At high density (low divertor
temperature), volume
recombination can detach plasma
from the target plates
Ionisation-recombination front
can move upstream
Stability and control of this front
is essential
2D modelling of plasma turbulence
- neutral gas interactions
Diffusive model for neutral gas
So far low power cases → small
variation in density
50
28
24
100
20
16
150
12
8
200
4
250
0
50
100
150
200
250
Neutral temperature [eV]
0
3.2
50
2.8
2.4
100
2.0
1.6
150
1.2
0.8
200
0.4
250
0
Ben Dudson, University of York
50
100
150
BOUT++ Workshop 2014 (11 of 13)
200
250
BOUT++ / EIRENE coupling
Work ongoing to couple BOUT++ to EIRENE
Starting in linear geometry (LAPD, PSI-2, Magnum-PSI)
Technical coupling completed. Both codes run in parallel
(MPI), passing data in memory
Initial turbulence simulations beginning
→ Some issues related to initialisation transients
Ben Dudson, University of York
BOUT++ Workshop 2014 (12 of 13)
Summary
Simple models used in BOUT++ to study broad trends
Fluid models can be run for long times relatively cheaply
A kinetic treatment is probably needed
Need to capture changes in neutral energy spectrum
Mean-free-paths can be comparable to turbulent scales
Ongoing work with BOUT++ and EIRENE3
3
S.Mekkaoui, EFDA fellowship 2014. Poster at PSI 2014
Ben Dudson, University of York
BOUT++ Workshop 2014 (13 of 13)