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SUMMARY:Multi-machine Scalings of Thresholds for n=1 and n=2 Error Field C
orrection
DTSTART;VALUE=DATE-TIME:20210511T101000Z
DTEND;VALUE=DATE-TIME:20210511T103000Z
DTSTAMP;VALUE=DATE-TIME:20211026T032104Z
UID:indico-contribution-17143@conferences.iaea.org
DESCRIPTION:Speakers: Nikoas Logan (Princeton Plasma Physics Laboratory)\n
New power law scalings of the error field (EF) penetration thresholds acro
ss a wide range of tokamaks have been developed for toroidal mode numbers
n=1 and 2 and project values for ITER that the construction tolerances and
correction coils satisfy. This paper presents a multi-variable n=2 thresh
old regression across a wide range of densities\, toroidal fields\, and pr
essures in 3 machines (DIII-D\, EAST\, and COMPASS) using a common metric
to quantify the EF in each device. It compares this new n=2 scaling to up
dated n=1 scalings using a larger 6 machine ITPA database. The results val
idate nonlinear single-fluid MHD simulation scalings\, which are used to l
end confidence to the projected scalings to ITER. These projections set th
e tolerances for non-axisymmetric components (like Test Blanket Modules) a
nd the corresponding requirements for EF correction coil arrays in ITER.\n
![Distribution of the n=2 database across scaling parameters for each mach
ine. Projected ITER scenario values are designated by dashed lines.][1]\n!
[Experimental threshold and scaling fit for every shot in the experimental
database. Dashed lines delineate factor of 2 and 0.5 discrepancies.][2]\n
\nNonaxisymmetric fields four orders of magnitude smaller than the axisymm
etric field can drive islands that cause disruptions in tokamaks\; and the
GPEC overlap metric\, $\\delta$\, provides a way of identifying and quant
ifying the most dangerous of these asymmetries. The metric uses a resonant
field spectrum determined from a combination of the applied field and the
plasma response (amplification and/or shielding of various components)$^{
1\, 2}$\, surpassing the robustness of the old “3-mode” vacuum model$^
{3}$. Tolerances for the design and optimization of tokamak coils have bee
n projected to ITER using fit scalings of this overlap metric with macrosc
opic 0D parameters that are easily identified both in current and for futu
re devices. \n\nThe n=2 database\, consisting of 3 devices and a paramete
r range shown in Figure 1\, reveals tolerances of a similar order of magni
tude to those for n=1 in current devices. Experimental thresholds are dete
rmined by ramping up artificial EFs using 3D field coil arrays until a cor
e island penetration event is observed and recording the corresponding amp
litude in EF overlap $\\delta$. The predictions of a power law fit to this
data using a kernel density weighted regression are compared to the true
experimental thresholds in Figure 2. The full regression used has a densit
y scaling exponent of 1.07±0.09\, a toroidal field exponent of -1.52±0.2
\, a major radius exponent of 1.46±0.09 and a normalized pressure ($\\bet
a_N/\\ell_i$) exponent of 0.36±0.11. This fit projects very high n=2 thre
sholds for ITER due to the strong size scaling. \n\n![Unique density scans
in different regimes (top)\, and a unified density scaling (bottom) norma
lizing for the other parametric dependencies from the full database regres
sion.][3]\n\nAlthough single parameter scans across regimes accessible by
a single machine can reveal varied behaviors\, the multi-variable\, multi-
machine scaling provides the most robust projection to new devices. Figure
3 shows individual density scans in DIII-D can exhibit a wide variety of
trends depending on the initial target plasma. The second panel\, however\
, shows how the seemingly discrepant DIII-D experiments are unified when n
ormalizing by the general toroidal field and pressure scalings. Observatio
ns at even higher density show that ohmic confinement regime transitions i
n any given device can drastically alter the density scaling in that parti
cular experiment. The ratio of non-resonant to resonant 3D field applied i
n a given experiment also alters the dynamics through neoclassical toroida
l viscosity (NTV) braking. Recent advances in optimization of nonresonant
fields for robust quasi-symmetry minimizing such secondary effects are bey
ond the scope of this dominant-order resonant field analysis. The local an
d secondary phenomena are purposely smoothed out in the multi-machine scal
ing presented here\, in an intentionally analogous manner to the treatment
of single-machine variations in the international confinement scalings th
at have proven so useful for the fusion community. \n\nThe nonlinear\, sin
gle fluid MHD code TM1 has been used to model the experimental scalings\,
providing confidence in some scalings and insight into experimental needs.
The model reproduces the experimentally observed toroidal field and $\\be
ta_N/\\ell_i$ scaling\, and shows the scalings hold out to ITER values. Th
e density scaling exponent calculated by TM1 falls below the experimental
n=2 fit\, closer to the better constrained n=1 empirical fit. This\, and a
large discrepancy between n=1 and 2 size scalings\, identifies what n=2 d
ata is needed to improve ITER projections. The code projects n=2 threshold
s in ITER roughly 2-3 times that of the projected n=1 thresholds\, consist
ent with observations in existing devices to date. \n\nThis combination of
robust\, cross-regime experimental scalings and tightly coupled modeling
project EF tolerances of above a Gauss for both n=1 and 2 EFs in ITER\, wh
ich are criteria the ITER construction tolerances and correction coils eas
ily satisfy. \n\nThis work was supported by the U.S. Department of Energy\
, Office of Science\, Office of Fusion Energy Sciences\, using the DIII-D
National Fusion Facility\, a DOE Office of Science user facility\, under A
wards DE-AC02-09CH11466 and DE-FC02-04ER54698.\n\n1. J.-K. Park\, A.H. Boo
zer\, et. al\, Physics of Plasmas 16\, 056115 (2009).\n2. N.C. Logan\, C.
Paz-Soldan\, et. al\, Physics of Plasmas 23\, 056110 (2016).\n3. J.-K. Par
k\, N. C. Logan\, et. al\, ITPA MHD\, ITER Report #ITER_D_UMLSUW (2017).\n
\n\n [1]: https://fusion.gat.com/conference/event/104/attachments/161/146
8/Logan.Nikolas.IAEA2020.Fig1.jpg\n [2]: https://fusion.gat.com/conferenc
e/event/104/attachments/161/1469/Logan.Nikolas.IAEA2020.Fig2.jpg\n [3]: h
ttps://fusion.gat.com/conference/event/104/attachments/161/1470/Logan.Niko
las.IAEA2020.Fig3.jpg\n\nhttps://conferences.iaea.org/event/214/contributi
ons/17143/
LOCATION:Virtual Event
URL:https://conferences.iaea.org/event/214/contributions/17143/
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