Abstract
Simulations of JET and TFTR discharges with the BALDUR integrated modeling code are used to test a sawtooth model that consists of sawtooth triggering mechanisms [Porcelli et al., Plasma Phys. Contolled Fusion 38, 2163 (1996)] together with a modified version of the Kadomtsev sawtooth reconnection model [Kadomtsev, Sov. J. Plasma Phys.1, 389 (1975)]. In simulations of 12 TFTR low confinement (Lmode) and 5 JET high confinement (Hmode) discharges, sawtooth triggering conditions are examined in order to determine which physical mechanisms are responsible for the crashes. It is found that most sawtooth crashes in the simulations are triggered by the resistive internal kink instability in plasmas that are in the semicollisional regime. However, in some discharges, some of the sawtooth crashes are triggered as a consequence of the driving force for the internal kink instability overcoming the fast ion stabilization. In rare instances, a sawtooth crash is triggered when the driving force for the internal kink instability overcomes the stabilization produced by the diamagnetic rotation of thermal ions. Generally, the median sawtooth period is found to increase as the magnetic reconnection fraction is increased. Optimal agreement with experimental data for the discharges considered is obtained with a magnetic reconnection fraction of approximately 37% although there is considerable scatter in the sawtooth periods observed in each discharge, both in the experimental data and in the simulations.
We thank Dr. Thawatchai Onjun, Dr. Alexei Pankin, and Dr. Filomena Nave for helpful suggestions with regard to this project.
This work was supported by U.S. Department of Energy under Contract No. DEFG0292ER54141.
I. INTRODUCTION
II. SAWTOOTH TRIGGERING MECHANISM
A. Kadomtsev reconnection model
B. Porcelli model for triggering sawteeth
C. Modified Kadomtsev magnetic reconnection model combined with the Porcelli model for triggering sawteeth
III. SIMULATION RESULTS
A. Simulation of sawtooth oscillations
B. Effect of varying fraction of magnetic reconnection
C. Calibration of the Porcelli model
IV. SUMMARY AND CONCLUSION
Key Topics
 Magnetic reconnection
 63.0
 Macroinstabilities
 37.0
 Diamagnetism
 16.0
 Plasma temperature
 15.0
 Magnetohydrodynamics
 9.0
Figures
Magnetic profile as a function of the minor radius just before and just after a sawtooth crash for JET discharge 33131 with magnetic reconnection fraction, , set at 40% (top panel) and 80% (bottom panel).
Magnetic profile as a function of the minor radius just before and just after a sawtooth crash for JET discharge 33131 with magnetic reconnection fraction, , set at 40% (top panel) and 80% (bottom panel).
Time evolution for the measured central electron temperature is shown in the top panel for JET discharge 33140, with vertical dotted lines marking the sawtooth crashes. Components of the Porcelli model are shown in the other four panels from a simulation using a 50% magnetic reconnection fraction. The left and right hand sides of Eq. (2) and Eq. (3) are shown in the second and third panels from the top, respectively. The three terms in the first part of Eq. (4) are shown in the fourth panel and the two terms in the second part of Eq. (4) are shown in the fifth panel.
Time evolution for the measured central electron temperature is shown in the top panel for JET discharge 33140, with vertical dotted lines marking the sawtooth crashes. Components of the Porcelli model are shown in the other four panels from a simulation using a 50% magnetic reconnection fraction. The left and right hand sides of Eq. (2) and Eq. (3) are shown in the second and third panels from the top, respectively. The three terms in the first part of Eq. (4) are shown in the fourth panel and the two terms in the second part of Eq. (4) are shown in the fifth panel.
Time evolution of the measured central electron temperature is shown for JET discharge 33131 in the top panel. The rf heating power (dotted line) and NBI power (solid line) are shown in the middle panel. The measured sawtooth period (solid line) and the sawtooth period from simulations with 45% magnetic reconnection (dashed line) are shown in the bottom panel.
Time evolution of the measured central electron temperature is shown for JET discharge 33131 in the top panel. The rf heating power (dotted line) and NBI power (solid line) are shown in the middle panel. The measured sawtooth period (solid line) and the sawtooth period from simulations with 45% magnetic reconnection (dashed line) are shown in the bottom panel.
Sawtooth period as a function of the magnetic reconnection fraction for TFTR discharge 105294. The central electron temperature is shown as a function of time in the top panel. The experimental sawtooth periods are indicated as solid lines in the lower three panels. The sawtooth periods are indicated with a dotted line in the second panel, a dashed line in the third panel, and a chained line in the fourth (bottom) panel for a simulation using a 30%, 40%, and 60% magnetic reconnection fraction.
Sawtooth period as a function of the magnetic reconnection fraction for TFTR discharge 105294. The central electron temperature is shown as a function of time in the top panel. The experimental sawtooth periods are indicated as solid lines in the lower three panels. The sawtooth periods are indicated with a dotted line in the second panel, a dashed line in the third panel, and a chained line in the fourth (bottom) panel for a simulation using a 30%, 40%, and 60% magnetic reconnection fraction.
The resistive effective growth rate in the effective ionkinetic regime, , is shown as a solid line and the thermal ion diamagnetic frequency, , is shown as a dashed line as a function of time from simulations of TFTR discharge 45980 with a 30% magnetic reconnection fraction in the top panel and a 60% magnetic reconnection fraction in the bottom panel.
The resistive effective growth rate in the effective ionkinetic regime, , is shown as a solid line and the thermal ion diamagnetic frequency, , is shown as a dashed line as a function of time from simulations of TFTR discharge 45980 with a 30% magnetic reconnection fraction in the top panel and a 60% magnetic reconnection fraction in the bottom panel.
Time evolution for the measured central electron temperature is shown in the top panel for TFTR discharge 105340, with vertical dotted lines marking the sawtooth crashes. Components of the Porcelli model are shown in the other four panels from a simulation using a 35% magnetic reconnection fraction. The left and right hand sides of Eq. (2) and Eq. (3) are shown in the second and third panels from the top, respectively. The three terms in the first part of Eq. (4) are shown in the fourth panel and the two terms in the second part of Eq. (4) are shown in the fifth panel.
Time evolution for the measured central electron temperature is shown in the top panel for TFTR discharge 105340, with vertical dotted lines marking the sawtooth crashes. Components of the Porcelli model are shown in the other four panels from a simulation using a 35% magnetic reconnection fraction. The left and right hand sides of Eq. (2) and Eq. (3) are shown in the second and third panels from the top, respectively. The three terms in the first part of Eq. (4) are shown in the fourth panel and the two terms in the second part of Eq. (4) are shown in the fifth panel.
Average relative offset as a function of magnetic reconnection fraction for the median sawtooth periods predicted by the Porcelli model in BALDUR simulations of the 8 JET discharge time intervals (dashed line) and the 12 TFTR discharge time intervals (dotted line), as well as the total of the 20 discharge time intervals.
Average relative offset as a function of magnetic reconnection fraction for the median sawtooth periods predicted by the Porcelli model in BALDUR simulations of the 8 JET discharge time intervals (dashed line) and the 12 TFTR discharge time intervals (dotted line), as well as the total of the 20 discharge time intervals.
Tables
Definition of variables.
Definition of variables.
Plasma parameters for the TFTR Lmode and JET Hmode discharges.
Plasma parameters for the TFTR Lmode and JET Hmode discharges.
Median sawtooth periods for the TFTR Lmode and JET Hmode discharges.
Median sawtooth periods for the TFTR Lmode and JET Hmode discharges.
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