306:
a much more rapid drop in the central plasma temperature of hot tokamaks than predicted by the resistive reconnection in the
Kadomtsev model. Some insight into fast sawtooth crashes was provided by numerical simulations using more sophisticated model equations and by the Wesson model. Another discrepancy found was that the central safety factor was observed to be significantly less than unity immediately after some sawtooth crashes. Two notable explanations for this are incomplete reconnection and rapid rearrangement of flux immediately after a relaxation.
65:
265:. As the flux in the core is reconnected, an island grows on the side of the core opposite the reconnection layer. The island replaces the core when the core has completely reconnected so that the final state has closed nested flux surfaces, and the center of the island is the new magnetic axis. In the final state, the safety factor is greater than unity everywhere. The process flattens temperature and density profiles in the core.
31:
377:
In large tokamaks with larger
Lundquist numbers, sawtooth relaxations are observed to occur much faster than predicted by the resistive Kadomtsev model. Simulations using two-fluid model equations or non-ideal terms in Ohm's law besides the resistive term, such as the Hall and electron inertia terms,
305:
The
Kadomtsev picture of sawtoothing in a resistive MHD model was very successful at describing many properties of the sawtooth in early tokamak experiments. However as measurements became more accurate and tokamak plasmas got hotter, discrepancies appeared. One discrepancy is that relaxations caused
369:
The first results of a numerical simulation that provided verification of the
Kadomtsev model were published in 1976. This simulation demonstrated a single Kadomtsev-like sawtooth relaxation. In 1987 the first results of a simulation demonstrating repeated, quasi-periodic sawtooth relaxations was
314:
The Wesson model offers an explanation fast sawtooth crashes in hot tokamaks. Wesson's model describes a sawtooth relaxation based on the non-linear evolution of the quasi-interchange (QI) mode. The nonlinear evolution of the QI does not involve much reconnection, so it does not have Sweet-Parker
268:
After a relaxation, the flattened temperature and safety factor profiles become peaked again as the core reheats on the energy confinement time scale, and the central safety factor drops below unity again as the current density resistively diffuses back into the core. In this way, the sawtooth
68:
Magnetic reconnection during a numerical resistive MHD simulation of a sawtooth relaxation. The arrows showing the direction of the flow are overlaid on top of a plot of the toroidal current density. The size of the arrows corresponds to the magnitude of the flow
80:, first reported in 1974. The relaxations occur quasi-periodically and cause a sudden drop in the temperature and density in the center of the plasma. A soft-xray pinhole camera pointed toward the plasma core during sawtooth activity will produce a
235:. The mode amplitude will grow exponentially until it saturates, significantly distorting the equilibrium fields, and enters the nonlinear phase of evolution. In the nonlinear evolution, the plasma core inside the
386:
Large, hot tokamaks with significant populations of fast particles sometimes see so called "giant sawteeth". Giant sawteeth are much larger relaxations and may cause disruptions. They are a concern for
679:
Tian-Peng, Ma; Li-Qun, Hu; Bao-Nian, Wan; Huai-Lin, Ruan; Xiang, Gao; et al. (2005-09-23). "Study of sawtooth oscillations on the HT-7 tokamak using 2D tomography of soft x-ray signal".
370:
published. Results from resistive MHD simulations of repeated sawtoothing generally give reasonably accurate crash times and sawtooth period times for smaller tokamaks with relatively small
955:
Campbell, D. J.; Start, D. F. H.; Wesson, J. A.; Bartlett, D. V.; Bhatnagar, V. P.; et al. (1988-05-23). "Stabilization of
Sawteeth with Additional Heating in the JET Tokamak".
315:
scaling and the crash can proceed much faster in high temperature, low resistivity plasmas given a resistive MHD model. However more accurate experimental methods for measuring
300:
359:
58:
416:
132:
92:
which effectively limits the pressure gradient at the plasma edge and the fishbone instability which effectively limits the density and pressure of fast particles.
259:
233:
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von Goeler, S.; Stodiek, W.; Sauthoff, N. (1974-11-11). "Studies of
Internal Disruptions and m=1 Oscillations in Tokamak Discharges with SoftâX-Ray Tecniques".
333:
181:
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34:
The safety factor profile shortly before and shortly after a sawtooth relaxation in a numerical resistive MHD simulation. After the relaxation,
361:
as needed by Wesson's description of the sawtooth. Nevertheless, Wesson-like relaxations have been observed experimentally on occasion.
418:
drops well below unity during the long period of stabilization, until instability is triggered, and the resulting crash is very large.
335:
profiles in tokamaks were developed later. It was found that the profiles during sawtoothing discharges are not necessarily flat with
378:
can account for the fast crash times observed in hot tokamaks. These models can allow much faster reconnection at low resistivity.
84:. Sawteeth effectively limit the amplitude of the central current density. The Kadomtsev model of sawteeth is a classic example of
104:(MHD) description of the plasma. If the amplitude of the current density in the plasma core is high enough so that the central
17:
262:
391:. In hot tokamaks, under some circumstances, minority hot particle species can stabilize the sawtooth instability.
906:
100:
An often cited description of the sawtooth relaxation is that by
Kadomtsev. The Kadomtsev model uses a resistive
765:
Denton, Richard E.; Drake, J. F.; Kleva, Robert G. (1987). "The m=1 convection cell and sawteeth in tokamaks".
105:
183:
is the poloidal mode number. This instability may be the internal kink mode, resistive internal kink mode or
209:
tearing mode. The eigenfunction of each of these instabilities is a rigid displacement of the region inside
1012:
508:
Beidler, M. T.; Cassak, P. A. (2011-12-13). "Model for
Incomplete Reconnection in Sawtooth Crashes".
160:
809:
272:
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Biskamp, D.; Drake, J. F. (1994-08-15). "Dynamics of the
Sawtooth Collapse in Tokamak Plasmas".
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Sykes, A.; Wesson, J. A. (1976-07-19). "Relaxation
Instability in Tokamaks".
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88:. Other repeated relaxation oscillations occurring in tokamaks include the
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Halpern, Federico D.; Lßtjens, Hinrich; Luciani, Jean-François (2011).
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A sawtooth is a relaxation that is commonly observed in the core of
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74:
907:"Diamagnetic thresholds for sawtooth cycling in tokamak plasmas"
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860:"Nonlinear studies of m=1 modes in highâtemperature plasmas"
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477:
Kadomtsev, BB. (1975). Disruptive instability in tokamaks,
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and the q profile has a broader, more square-like shape.
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628:Wesson, J A (1986-01-01). "Sawtooth oscillations".
963:(21). American Physical Society (APS): 2148â2151.
443:(20). American Physical Society (APS): 1201â1203.
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269:relaxation occurs repeatedly with average period
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810:"Numerical simulations of sawteeth in tokamaks"
730:(3). American Physical Society (APS): 140â143.
585:(7). American Physical Society (APS): 971â974.
516:(25). American Physical Society (APS): 255002.
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1018:Science and technology in the Soviet Union
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27:Relaxation in the core of tokamak plasmas
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494:(1976). Resistive Internal Kink Modes,
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14:
1005:
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808:Vlad, G.; Bondeson, A. (1989-07-01).
630:Plasma Physics and Controlled Fusion
864:Physics of Fluids B: Plasma Physics
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870:(11). AIP Publishing: 3469â3472.
687:(10). IOP Publishing: 2061â2067.
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823:(7). IOP Publishing: 1139â1152.
773:(5). AIP Publishing: 1448â1451.
496:Soviet Journal of Plasma Physics
479:Soviet Journal of Plasma Physics
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636:(1A). IOP Publishing: 243â248.
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920:(10). AIP Publishing: 102501.
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701:10.1088/1009-1963/14/10/023
650:10.1088/0741-3335/28/1a/022
457:10.1103/physrevlett.33.1201
295:{\displaystyle \tau _{saw}}
10:
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829:10.1088/0029-5515/29/7/006
744:10.1103/physrevlett.37.140
599:10.1103/physrevlett.73.971
354:{\displaystyle q\approx 1}
261:surface is driven into a
90:edge localized mode (ELM)
163:will be unstable, where
957:Physical Review Letters
858:Aydemir, A. Y. (1992).
724:Physical Review Letters
579:Physical Review Letters
510:Physical Review Letters
481:, vol. 1, pp. 389--391.
437:Physical Review Letters
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876:1992PhFlB...4.3469A
779:1987PhFl...30.1448D
736:1976PhRvL..37..140S
693:2005ChPhy..14.2061M
642:1986PPCF...28..243W
591:1994PhRvL..73..971B
532:2011PhRvL.107y5002B
449:1974PhRvL..33.1201V
254:{\displaystyle q=1}
228:{\displaystyle q=1}
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422:References
985:0031-9007
942:1070-664X
892:0899-8221
837:0029-5515
795:0031-9171
752:0031-9007
709:1009-1963
666:250841622
658:0741-3335
607:0031-9007
548:0031-9007
523:1111.0590
465:0031-9007
346:≈
278:τ
69:velocity.
993:10038272
615:10057587
556:22243083
965:Bibcode
922:Bibcode
872:Bibcode
845:3904646
775:Bibcode
732:Bibcode
689:Bibcode
638:Bibcode
587:Bibcode
564:3077047
528:Bibcode
445:Bibcode
78:plasmas
75:tokamak
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492:et al.
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910:(PDF)
841:S2CID
813:(PDF)
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560:S2CID
518:arXiv
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611:PMID
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552:PMID
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389:ITER
45:>
973:doi
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116:q
48:1
42:q
20:)
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