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SUMMARY:An efficient MHD equilibrium solver for control oriented transport
models
DTSTART;VALUE=DATE-TIME:20190515T090000Z
DTEND;VALUE=DATE-TIME:20190515T092000Z
DTSTAMP;VALUE=DATE-TIME:20200918T210046Z
UID:indico-contribution-14350@conferences.iaea.org
DESCRIPTION:Speakers: Pablo Garcia-Martinez (CONICET - Centro Atomico Bari
loche)\nSuccessful reproduction of advanced tokamak scenarios in burning p
lasmas like ITER will strongly rely on sophisticated plasma control system
s. Among the novel control physics challenges required to accomplish the c
ontrol needed for scenario execution\, the internal profile regulation pla
ys a fundamental role [1]. The non-linear dynamics involved in current pro
file control are described by the resistive magnetic diffusion equation (M
DE) expressed in flux coordinates. These coordinates are constructed out f
rom the magnetic geometry imposed by the MHD plasma equilibrium condition.
During a tokamak discharge the plasma equilibrium\, its internal profiles
and the magnetic geometry change\, therefore\, the flux coordinates shou
ld be updated during this evolution. However\, the equilibrium is held fix
ed and the update of the flux coordinates is not yet performed by the newe
st control-oriented transport codes [2\,3].\nThis simplification is made f
or practical reasons. On one hand\, the solution of the Grad-Shafranov equ
ation for general axisymmetric equilibria involves two nested loops (one i
nner loop to treat the non-linearity and one outer loop to treat the eigen
value nature of this equation [4]) that make standard equilibrium solvers
unacceptably expensive and poorly convergent. On the other hand\, the resu
lting inconsistency is\, in many cases\, not severe and effective feedback
control of the current profile has been achieved for some relevant scenar
ios [2]. Despite this partial success\, an efficient method to couple the
equilibrium problem with the MDE solver in control-oriented transport code
s would represent a significant improvement. With such self-consistent app
roach\, more accurate feedback controllers could be designed\, better feed
fordward controllers for scenario planning would be available and a fast a
nd reliable control-oriented predictive simulation tool could be developed
.\nIn this work\, a new flux mapping method that allows a rapid estimation
of the RHS of the Grad-Shafranov equation\, including the eigenvalue\, is
introduced. This method significantly accelerates the outer loop and impr
oves the convergence properties of the solver. In particular\, equilibria
with arbitrary prescribed safety factor and pressure profiles can be obtai
ned with few outer iterations (less than five for low-beta plasmas). Moreo
ver\, the change in the equilibrium and the magnetic geometry during a con
trol-oriented transport simulation can be recovered without the outer loop
\, using only few Newton iterations in the inner loop to treat the non-lin
earity. We show that the new mapping method can also be used to compute th
e internal plasma equilibrium using only the total plasma current\, the sh
ape of the separatrix and the spatial profile of the field line pitch angl
e. This approach differs from the traditional equilibrium reconstruction m
ethod (which uses the pitch angle information as a constraint [5]) and hav
e many potential applications in the design of control systems requiring s
patial information of the plasma parameters.\n[1] D. Humphreys et al\, Phy
s. Plasmas 22\, 021806 (2015).\n[2] E. Schuster et al\, Nucl. Fusion 57\,
116026 (2017).\n[3] F. Felici et al\, Nucl. Fusion 58\, 096006 (2018).\n[4
] L. LoDestro et al\, Phys. Plasmas 1\, 90 (1994).\n[5] J. Ferron et al\,
Nucl. Fusion 38\, 1055 (1998).\n\nhttps://conferences.iaea.org/event/180/c
ontributions/14350/
LOCATION:Daejeon\, Republic of Korea
URL:https://conferences.iaea.org/event/180/contributions/14350/
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