Comparison of electron drift waves in numerical and analytical tokamak equilibria

Abstract

In this paper, we demonstrate the importance of the details of the equilibria on the stability of electron drift waves. A comparison of electrostatic electron drift waves in numerical and analytical tokamak equilibria is presented in fully three-dimensional circular and non-circular tokamaks. The numerical equilibria are obtained using the variational moments equilibrium code and the analytical equilibria used is the generalizedŝ-α model. An eigenvalue equation for the model is derived using the ballooning mode formalism and solved numerically using a standard shooting technique. The stability and the localization of the electron drift wave is found to be strongly dependent on the local shear of the magnetic field. Large values of the local shear are found to be stabilizing. A disagreement in the results is found between analytical and numerical equilibria at aspect ratios of typical tokamaks, suggesting that the latter approach should be used in the transport calculations. The effects of the local shaping of the magnetic surfaces are complicated and can be both stabilizing and destabilizing, depending on the details of the equilibria.

Electron drift waves in an advanced tokamak plasma

“…The full equilibrium is computed using the magnetohydrodynamic (MHD) equilibrium code VMEC [23] and is then mapped to the Boozer coordinates. Details of the magnetic field configurations and its mapping to different coordinate systems can be found elsewhere [10,11]. In this study, we have used 16 maximum poloidal Fourier components, one toroidal Fourier component and a set of 96 magnetic surfaces to obtain the equilibrium.…”

“…However, the situation at the edge is different where strong influence of electron-ion collisions gives a resistive nature to the drift modes. The properties of these modes have been extensively studied in tokamak and stellarator geometries for a number of years [1][2][3][4][5][6][7][8][9][10][11][12][13]. It has been found [3] that drift wave instabilities can be stabilized by a strong magnetic shear.…”

“…Further, the shear stabilization effect can be annulled by the toroidal effects [4]. In recent studies [10,11,13], we have reported the effects of local magnetic shear (LMS) and other geometrical quantities on drift wave stability. However, in these studies we focused on geometries which are characterized either by an increasing (tokamak-like) profile of safety factor q [11] or by a decreasing (stellarator-like) q-profile [10,13].…”

“…In recent studies [10,11,13], we have reported the effects of local magnetic shear (LMS) and other geometrical quantities on drift wave stability. However, in these studies we focused on geometries which are characterized either by an increasing (tokamak-like) profile of safety factor q [11] or by a decreasing (stellarator-like) q-profile [10,13]. It is thus instructive to study the properties of drift waves in an ITERrelevant tokamak geometry with a q-profile having both these characteristics.…”

“…This equilibrium, as will be seen later, is characterized by a q-profile having negative magnetic shear surfaces (decreasing q) as well as positive magnetic shear surfaces (increasing q). A simple iδ-model [10,11] for the electron drift waves is adopted in which the ions are treated as a cold fluid and the electrons response is assumed to be close to adiabatic. The non-adiabaticity in the response of electrons is included by adding arbitrary fixed iδ, which may be due to collisions, wave-particle resonance, dissipation due to electron trapping, etc.…”