Mechanism for rapid sawtooth crashes in tokamaks

Abstract

The standard picture of the Kadomtsev reconnection process predicts sawtooth crash times that are longer than those observed in present-day large tokamaks. Ideal kink modes are investigated as a possible mechanism for these fast crashes, by use of fully toroidal, compressible, full magnetohydrodynamic equations. In systems with low shear, parallel-current and pressure-driven modes are identified well below the previously accepted poloidal-/? limits. Linear and nonlinear calculations show good agreement with experiments and indicate that such modes may explain fast collapse times reported in the recent literature.PACS numbers: 52.55.FaThe sawtooth oscillations in the soft x-ray signals observed in tokamaks are associated with periodic changes in the central electron temperature, T e . l Typically, a slow phase during which the central temperature slowly rises is followed by a fast drop in T e , associated with flattening of the central temperature. The time scale of the slow phase is determined by various transport processes such as Ohmic heating. The resistive internal kink mode was invoked by Kadomtsev 2 to explain the crash phase of the oscillations. In this model, anm = l island (m is the poloidal mode number), associated with a safety factor q less than unity on axis, grows, forming a helical deformation of the internal plasma column. This kink structure subsequently relaxes to a symmetric state through complete reconnection of the helical flux inside the q = 1 surface with the flux from outside. The Kadomtsev model has been generally believed to explain the sawtooth oscillations in earlier tokamaks.Recent observations, however, indicate that tokamaks exhibit various types of sawtooth oscillations that cannot be fully explained by the Kadomtsev model. In addition to the simple sawtooth associated with this model, there are double or compound sawteeth 3 ' 4 thought to be caused by the presence of two or more q = 1 surfaces in the plasma. Moreover, both TFTR and JET tokamaks report crash times that cannot be easily reconciled with the Kadomtsev reconnection process. 5 Previous numerical studies of the sawtooth oscillations have concentrated on the m = 1 resistive tearing mode. Waddell et al. 6 performed the first nonlinear studies and found the current-flattening times to be in agreement with the internal disruption times reported in the ST tokamak. Sykes and Wesson 7 included self-consistent evolution of the temperature and resistivity in order to follow periodic sawtooth oscillations. However, in their simulations, sawteeth decayed away after a few periods. Denton et al., by including parallel thermal conductivity, have produced repeating sawtooth oscillations. 8 They were able to reproduce qualitatively many of the experimentally observed features of sawtooth oscillations, in-cluding compound sawteeth, by adjusting the transport coefficients. However, their studies did not adequately address the quantitative features of sawteeth, in particular anomalously fast crash times observed in the present-day large to...

Shear flows at the tokamak edge and their interaction with edge-localized modes

“…21 and used in a number of toroidal calculations, some in shaped geometries. [22][23][24] It has been continually going through improvements and updates over the years, but many of the algorithmic details can be found there. Briefly, a toroidal ͑r , , ͒ coordinate system is used.…”

Compressible magnetohydrodynamic sawtooth crash

“…It involves a helical displacement of the entire central core of the plasma inside the magnetic surface with q ¼ m/n ¼ 1. Two main types of MHD instability with n ¼ 1 can be driven by the equilibrium pressure gradient over q < 1 when the central q o < 1-the internal kink in ideal MHD [8][9][10] and resistive [11][12][13][14][15] versions, or at low magnetic shear with q Շ 1, the quasi-interchange [16][17][18] or current-driven 18 modes. For the incompressible ideal MHD internal kink, 10 large aspect ratio expansion, R=a ) 1, shows that higher order m 6 ¼ 1 poloidal harmonics driven by toroidal mode coupling introduce a minimum value of poloidal beta for toroidal instability, compared to zero beta in a cylinder.…”

Helical core tokamak MHD equilibrium states

“…We propose an alternative description associated with the development of a novel equilibrium state with the allure of a saturated ideal m = 1, n = 1 internal kink. These type of kink modes have been shown to be nonresonantly destabilized in a circular axisymmetric tokamak when the value of q min is in the range of unity to 1.014 [27]. We shall discuss our perspective for snake formation later in this text.…”