Influence of plasma boundary shape on helical core/long-lived mode in tokamak plasmas

Abstract

Helical distortion of the core part of tokamak plasma, which is called a helical core or a long-lived mode, is investigated by means of three-dimensional magnetohydrodynamic equilibrium calculations. It is found that the magnitude of the helical distortion strongly depends on the shape of the plasma boundary for weakly reversed shear plasmas. The triangularity of the boundary enhances the amplitude of helical distortion. In addition, reversed D-shape plasmas also exhibit a helical core. It is also found that the triangularity lowers the critical b for the onset of a helical core; furthermore, the critical b vanishes when the triangularity exceeds a certain value. On the other hand, the influence of the ellipticity on the amplitude of helical distortion strongly depends on b. The ellipticity enhances the amplitude at high b, while it reduces the amplitude at low b.

Two types of helical-core equilibrium states in tokamak plasmas

“…It is also found that such a shaped tokamak can exhibit another bifurcated equilibrium state due to external kink/peeling modes [18]. In addition, reversed D-shape plasmas are found to exhibit a helical core [17].…”

“…The inputs for the VMEC code are the profiles of the rotational transform ι(s) = ∑ 6 n=0 l n s n = 1/q(s) and pressure p(s) = p 0 ∑ 5 n=0 p n s n that are obtained by interpolating the output from the MEU-DAS code with the method of least squares, where the normalized toroidal flux is given by the poloidal flux as s = ´ψt 0 q(ψ p )dψ p / ´1 0 q(ψ p )dψ p . We impose a fixed boundary condition that has up-down symmetry, and the boundary shape of the plasma is represented in terms of the ellipticity κ, triangularity δ, and aspect ratio A = 3, as described in [17]. To obtain helical cores in the low q min regime, we need to increase the number of radial grid points from N s = 251 to N s = 3001, as discussed in [17].…”

“…We impose a fixed boundary condition that has up-down symmetry, and the boundary shape of the plasma is represented in terms of the ellipticity κ, triangularity δ, and aspect ratio A = 3, as described in [17]. To obtain helical cores in the low q min regime, we need to increase the number of radial grid points from N s = 251 to N s = 3001, as discussed in [17]. We use eight modes for the toroidal and poloidal spectrum, i.e.…”

“…The q min scan shows that the maximum distortion is at a q min of around unity [1,11,12,15], although a helical core appears at a q min of above unity. Recently, it has been found that the plasma boundary shape influences the amplitude of the helical distortion: for instance, the triangularity enhances the helical distortion and lowers the critical onset β value for the formation of a helical core [17]. It is also found that such a shaped tokamak can exhibit another bifurcated equilibrium state due to external kink/peeling modes [18].…”

“…The development of a helical core is related to the linear stability of (m, n) = (1, 1) internal-kink modes [19][20][21], so that the magnetic shear at the q = 1 surface suppresses the formation while the pressure gradient enhances it [16,21,22,[24][25][26]. The enhancement of the distortion, by increasing the triangularity [17], is consistent with the shape dependence of the linear stability of internal-kink modes [21,25]. A direct link between a helical equilibrium state and linear stabilities is demonstrated by nonlinear MHD simulations [23,24].…”