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SUMMARY:Models and scalings for the disruption forces in large tokamaks
DTSTART;VALUE=DATE-TIME:20210512T101000Z
DTEND;VALUE=DATE-TIME:20210512T103000Z
DTSTAMP;VALUE=DATE-TIME:20210418T025955Z
UID:indico-contribution-17279@conferences.iaea.org
DESCRIPTION:Speakers: Vladimir Pustovitov (Kurchatov Institut)\n**Abstract
**. The study is devoted to theoretical analysis of the models for calcula
ting the disruption forces in tokamaks. It is motivated by the necessity o
f reliable predictions for ITER. The task includes the evaluation of the e
xisting models\, resolution of the conflicts between them\, elimination of
contradictions by proper improvements\, elaboration of recommendations fo
r dedicated studies. A better quality of the modelling and higher accuracy
are the ultimate theoretical goals. \n**Impact**. The disruption forces m
ay strongly restrict the operational range in tokamaks. This can be illust
rated by the JET tokamak normally operated with plasma current up to about
3 MA\, though originally the discharges with current up to 4.8 MA were co
nsidered possible (with the elliptical cross section and toroidal field up
to 34.5 kG) and even 6 MA has been mentioned [1] as the design plasma cur
rent in JET. For ITER with expected 15 MA current\, the most pessimistic s
calings give the sideways force above the tolerable level\, but a great sc
atter in theoretical predictions (about two orders of magnitude) shows tha
t the problem still remains open. \n**Novelty**. In recent years\, there w
as a steady progress in developing a better physics basis for calculating
the forces\, which gave rise to new trends and ideas. It was discovered\,
in particular\, that the wall resistivity\, penetration of the magnetic pe
rturbation through the wall\, the poloidal current induced in the wall\, t
he kink-mode coupling\, plasma position in the vacuum vessel must be the e
lements essentially affecting the disruption forces. These and related pre
dictions along with earlier less sophisticated concepts and results are an
alyzed here. \n**Quality**. The key question is the quality of the proofs
behind them. A convenient base for analysis\, comparison\, revision and co
nclusions is the approach built starting from the most reliable and univer
sal part for all cases of interest\, i.e. the Maxwell equations and the Oh
m’s law for the wall. The plasma enters the task through the boundary co
nditions\, which makes them the critical element responsible for proper in
corporation of the plasma physics. The presented approach is careful in th
is aspect and provides a universal basis for comparison of the existing mo
dels. The study is focused on the problems important for the ITER scenario
s.\n**The addressed problems**. In terms of mathematics\, the main goal mu
st be the calculation of **jxB** or some integrals of this force density i
n the vacuum vessel wall\, where **B** is the magnetic induction and **j**
is the current density. The plasma enters this purely electromagnetic tas
k as a distributed current with evolving distribution. The main complicati
ons arise from the related changes of the plasma shape and position to gua
rantee the force balance for the plasma. Because of small plasma mass and
relatively slow development of disruptions the plasma must remain force-fr
ee at each time step\, while the disruption force on the wall can exceed t
he inertial force by 6-8 orders of magnitude [2\, 3]. Proper description o
f the plasma reaction becomes a necessary part in the task.\n This is a de
veloping area\, and several points require clarification. Among them is th
e effect of the plasma position and the poloidal current on the disruption
force. Recent theories show [4\, 5] that each of them can strongly affect
the force\, but some studies [6] ignore them.\n Another disputable subjec
t is the kink mode structure: should it be a single harmonic m/n = 1/1 [7
] or a pair of coupled modes (1/1) and (1/–1) [8] to satisfy the force-f
ree condition for the plasma and simultaneously produce a significant side
ways force on the wall?\n The sideways force itself is a mystery which mak
es difficult extrapolations from JET to ITER. It becomes clear that so-cal
led Noll’s formula cannot be used for that: it is a product of oversimpl
ified modelling with a result [9] 25 times larger than a similar estimate
[8]\, but with a more refined plasma model.\n Various models attribute the
sideways force to different stages of the discharge\, starting from the p
re-disruption kink mode and ending by halo currents and other events after
the plasma-wall contact. A pure sideways force can appear due to n = 1 pe
rturbation only\, but theory also predicts that a large integral radial fo
rce can develop in an axially symmetric configuration during TQ or CQ. The
n a question is which of the two forces can be more dangerous? Also\, is i
t possible to distinguish the difference between them in experiment? Was t
he JET damaged by a pure sideways force or a combined action of several fo
rces? \n**The model**. The study is mainly based on the Maxwell equations
and\, therefore\, is general. The induced currents in the vacuum vessel wa
ll are described by the standard Ohm’s law. A particular attention is pa
id to the plasma-wall electromagnetic coupling under constraints imposed b
y the force balance for the plasma.\n\n**References**\n\n[1] V. Riccardo\,
P. L. Andrew\, A. S. Kaye\, and P. Noll\, “Disruption design criteria f
or Joint European Torus in-vessel components”\, Fusion Sci. Technol. 43\
, 493 (2003).\n[2] L. E. Zakharov and X. Li\, “Tokamak magneto-hydrodyna
mics and reference magnetic coordinates for simulations of plasma disrupti
ons”\, Phys. Plasmas 22 062511 (2015).\n[3] V. D. Pustovitov\, “Genera
l approach to the problem of disruption forces in tokamaks”\, Nucl. Fusi
on 55 113032 (2015).\n[4] V. D. Pustovitov\, “Disruption forces on the t
okamak wall with and without poloidal currents”\, Plasma Phys. Control.
Fusion 59 055008 (2017).\n[5] N. Isernia\, V. D. Pustovitov\, F. Villone a
nd V. Yanovskiy\, “Cross-validation of analytical models for computation
of disruption forces in tokamaks”\, Plasma Phys. Control. Fusion 61 115
003 (2019).\n[6] S. Wang\, Q. Xu\, K. Zhang and H. Chen\, “Electromagnet
ic-mechanical coupling method and stress evaluation of the Chinese Fusion
Engineering Test Reactor helium cooled solid breeder under a vertical disp
lacement event scenario”\, Nucl. Fusion 59 106048 (2019).\n[7] A. A. Mar
tynov and S. Yu. Medvedev\, “Resistive wall modes and related sideways f
orces in tokamak”\, Phys. Plasmas 27 012508 (2020).\n[8] D. V. Mironov a
nd V. D. Pustovitov\, “Sideways force due to coupled kink modes in tokam
aks”\, Phys. Plasmas 24\, 092508 (2017).\n[9] L. E. Zakharov\, S. A. Gal
kin\, S. N. Gerasimov\, and JET-EFDA Contributors\, “Understanding disru
ptions in tokamaks”\, Phys. Plasmas 19\, 055703 (2012).\n\nhttps://confe
rences.iaea.org/event/214/contributions/17279/
LOCATION:Virtual Event
URL:https://conferences.iaea.org/event/214/contributions/17279/
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