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Title
CQL3D-Hybrid-FOW modeling of the temporal dynamics of NSTX NBI+HHFW discharges
Permalink
https://escholarship.org/uc/item/9qk2g6kx
Journal
AIP Conference Proceedings, 1580(1)
ISSN
0094-243X
ISBN
9780735412101
Authors
Harvey, RW
Petrov, YV
Liu, D
et al.
Publication Date
2014
DOI
10.1063/1.4864551
Copyright Information
This work is made available under the terms of a Creative Commons Attribution License,
availalbe at https://creativecommons.org/licenses/by/4.0/
Peer reviewed
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University of California
CQL3D-HYBRID-FOW Modeling of the Temporal
Dynamics of NSTX NBI+HHFW Discharges
R.W. Harvey
1
, Yu. V. Petrov
1
, D. Liu
2
, W.W. Heidbrink
2
,
G. Taylor
3
, P.T. Bonoli
4
1
CompX, Del Mar, California, USA
2
University of California, Irvine, California, USA
3
Princeton Plasma Physics Laboratory, Princeton, NJ, USA, California, USA
4
Massachusetts Institute of Technology, Cambridge, MA, USA
Abstract. The CQL3D Fokker-Planck code[1] has been upgraded to include physics of finite-orbit-width
(FOW) guiding-center orbits[2,3], as compared with the previous zero-orbit-width (ZOW) model, and a
recent first-order orbit calculation[2]. The Fast Ion Diagnostic FIDA[4,5] signal resulting from neutral beam
(NBI) and high harmonic fast wave (HHFW) RF power injected into the NSTX spherical tokamak can now
be modeled quite accurately, using ion distributions from the CQL3D-Hybrid-FOW code, a rapidly executing
variant that includes FOW+gyro-orbit losses to the plasma edge, FOW effects on NBI injection and HHFW
diffusion, but does not include neoclassical radial diffusion. Accurate simulation of prompt fast ion (FI)
losses is a key feature of the marked modeling improvement relative to previous ZOW results. By
comparing NBI-only and NBI+HHFW shots, independent confirmation of the usual 35% edge loss of HHFW
in NSTX is obtained. Further, HHFW prompt losses from the plasma core are shown to be 3X as large
(>25%) as the NBI-only case. The modulated NBI and time-dependent background plasma variations and
charge exchange losses of fast ions are accounted for, and the temporal neutron variation is in approximate
agreement with NSTX observations.
Keywords: ICRF, QL, quasilinear, orbit integration
PACS: 52.25.Dg, 52.25.Xz, 52.35.Hr, 52.65.Cc, 52.65.Ff
INTRODUCTION
Most of the CQL3D applications to date have been in the zero-orbit-width (ZOW) approximation[1],
neglecting most effects of radial drift on the transiting and trapped tokamak orbits. Recent work has
added finite-orbit-width (FOW) effects to the code[2,3]. Presently, the FOW effects are included in a
“hybrid” mode[3], to be explained more fully below; the results have shown much more accurate
simulation of radial orbit shift effects and prompt losses in NSTX FIDA experiments.
The development of the CQL3D guiding center FOW code is based on two main steps. At the first step,
partial FOW capabilities have been implemented, which add FOW features into the particle source (NB)
operator, RF quasilinear operator and diagnostics. Collisions remain ZOW, thus omitting banana regime
neoclassical diffusion. Guiding center orbit losses with gyro-radius correction are included. The Fokker-
Planck (FP) equation remains in its ZOW form, except the above mentioned modification of coefficients.
To find the local distributions, transformations must be made going from the calculated bounce-averaged
(BA) distributions versus particle BA position, to the local point. At the second step, the FP equation is
being modified to include the radial transformation coefficients in the collision coefficients; and the
boundary conditions are revised, introducing discontinuities in FOW orbit diffusion. This work,
completed except for further work on the internal boundary conditions, will give full guiding center orbit-
based neoclassical diffusion coefficients and transport, and can be compared with the NEO code[6]
results. It differs from NEO in being a full guiding center (GC) code, rather than an expansion in GC
orbit width. This will be an important differencefor energetic particles, particularly in NSTX.
Radiofrequency Power in Plasmas
AIP Conf. Proc. 1580, 314-317 (2014); doi: 10.1063/1.4864551
© 2014 AIP Publishing LLC 978-0-7354-1210-1/$30.00
314
RESULTS
The first step, referred to as CQL3D-HYBRID-FOW, has greatly improved agreement with FOW effects
measured by the experimental NSTX FIDA diagnostic, yet the required execution time is only increased
by 30% for the NBI-only case, and by 75% for NBI+HHFW compared to CQL3D-ZOW.
Figure 1 shows the applied powers versus time in a modulated NBI and HHFW in an NSTX experiment
[5]. The HHFW power is reduced by the usual 35%,
accounting for edge losses. Two shots are focused
on, 129842 is with modulated beam only, and
128739 is with both the modulated beam and
HHFW. CQL3D simulations utilizing input of time-
dependent radial plasma profiles for electron and
ion density and temperature, and neutral density,
from the TRANSP analysis of this shot, were
advanced in time.
The FIDA signal, a measure of the major radius
profile of the fast ions, is given in Fig. 2(a), NBI-
only, and (b), NBI+HFW, as derived from the
CQL3D distributions and the FIDASIM code[7], in
comparison with the the experimental curve in
black[5]. NBI FIDA signals are normalized to the
same peak value, and this normalization is also used
with the NBI+HHFW.
Results of three different CQL3D models are shown
for comparison: (1) the original ZOW analysis
(blue) which is shifted inwards from the
experimental profile (black), indicated the need to
include finite orbit width effects[5]; (2) A first order
correction for orbit width (green), which turned out
to overestimate the radial shift, not too surprising in
view of the very large NSTX orbits[2]; and (3) the
Hybrid-FOW treatment including the GC orbit
effects (red). Evidently inclusion of the GC FOW
effects is crucial for reasonably accurate simulation
of the experiment.
In Figure 2(a), the NBI-only case, attempts were
made to further refine the code so as to account for
the somewhat elevated calculated FIDA signal (the
red curve) versus the experimental data (black) at
the smaller major radii. NUBEAM[8] calculated
hot ion birth-points were read into the CQL3D in
place of those from the older-cross-section-based
NFREYA code. It was found that neutral beam
stopping, i.e., ionization was reduced, and this
somewhat broadened the calculated FIDA signal.
Adding charge exchange losses of the fast ions,
based on time-dependent radial profiles from the
flux-surface FRANTIC neutral code[9], as read in
from the TRANSP code, compensated for the
Fig. 1. NBI and HHFW powers as a function of
time for two NSTX shots, one with the modulated
beam only, and a second comparison shot with
added HHFW power [Liu, 2010]. CQL3D gives
f(v,theta,rho,t). The FIDA signal is obtained in
experiment and simulation by averaging over the
indicated time periods.
Fig. 2. Experimental FIDA signal indicative of fast
ion radial distribution (a) for modulated NBI, and
(b) for modulated NB I+HHFW. The black curves
are experimental results, blue is ZOW, green is a 1
st
order approximation, and red is the hybrid-FOW
result.
NBI
NBI+HHFW
(a)
(b)
315
NUBEAM deposition broadening, with the profile
shown in Fig. 2 remaining almost unchanged.
A key feature of FOW is accurate calculation of the
orbit loss region, which at the higher energies in the
NBI+HHFW experiment in NSTX and extends
inwards to particles (at certain pitch angles) near the
magnetic axis. Figure 3 shows the power lost to the
plasma edge. Fig. 3(a) compares total power loss in
the NBI and NBI+HHFW shots. The prompt FI loss
is 7% of the NBI power, but rises to 28% of the
HHFW power, the latter being due to quasilinear
(QL) velocity space diffusion into the orbit loss
region. Fig. 3(b) shows the radial origin of the orbit-
loss particles versus time, showing substantial near-
central loss of HHFW generated fast ions. The
explanation of enhanced HHFW losses, compared to
NBI, is that the NBI is injected into a low loss region
of phase space, and the particles mainly slow down at constant pitch, whereas the HHFW causes QL
perpendicular velocity diffusion into the FOW loss regions in velocity space which extend into the
magnetic axis.
Synthetic diagnostic signals are available, based on the time- and spatial-varying electron and ion
distributions. An example, for the NSTX shot we are discussing is shown in Fig. 4. Several basic plasma
time scales are evident, which can be tested against experiment. Neutrons in CQL3D match the time-
history of the experimental data quite well (Fig. 5), except for a 20%(NBI-only)-40%(NBI+HHFW)
underestimate of the calculations compared to the experimental values. Results with a more complete 3D
neutral code will be investigated to determine if the 1D model is the origin of the neutron simulation
underestimate.
Fig.3. Fast ion orbit power loss versus time. (a)
Comparison of the loss power for NBI only (green)
and the NIB+HHFW simulation (blue).
(b) Fast ion loss versus bounce-average position
and time. Both plots exhibit a marked increase
of loss when the the HHFW is turned on at
t=0.200 secs.
0.360
time
(sec)
0.152
(b)
0.25 1.0
Bounce Avg radius
(a)
NBI+HHFW
NBI
Fig. 4. Time-dependent energy-spectra of NPA
calculated from simulated ion distributions in a
modulated NBI+HHFW NSTX experiment. The
HHFW is turned on a 0.2 secs. Heating, collisional,
QL diffusion time scales, and neutrals, all play
testable roles in the results.
316
It also anticipated that, pending the completion of the fully neoclassical CQL3D-FOW, the additional
radial transport will fill in the calculated FIDA signal near the plasma periphery.
CONCLUSIONS
It is possible, even with HHFW such as in the NSTX case, to calculate accurate ion distribution functions
with desktop computer resources, and to test the resulting synthetic diagnostic signals against many
available tail ion diagnostics, such as FIDA, NPA and neutron rates. This detailed comparison will
validate that calculated sources are accurate. A detailed, physics-verifiable representation of tokamak
plasma physics will need to focus on plasma phase-space distributions.
Research supported by USDOE Grants SC0006614, ER54744, and ER54649.
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Fig. 5. Comparison of experimental neutrons (red) with simulation results (blue). Fast ion charge
exchange losses are included from a 1D neutral code
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