Stability Analysis of Neoclassical Tearing Mode

Shigeki Yoshida1), Sanae-I.Itoh2), Masatoshi Yagi2) , Masafumi Azumi3)

1)Interdiscliplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga 816-8580, Japan
2)Research Institute for Aplied Mechanics, Kyushu University, Kasuga 816-8580, Japan
3)Japan Atomic Energy Research Institute, Naka, Ibaraki, 311-0193, Japan

The magnetic islands are often observed in high β tokamak plasmas [1], where the plasma confinement is degraded or sometimes discharges become disruptive due to the formation of islands. To achieve high performance in fusion plasmas, it is necessary to understand (1) the physical mechanism of island excitation and its saturation level in high β plasma and (2) the associated collapse phenomena.
We have investigated neoclassical tearing mode (NTM) based on the four-field reduced MHD model which includes the ion parallel flow and ion neoclassical viscosity. Up to now, it is found that NTM is unstable when Δ' > Δ'c [2] and the linear neoclassical tearing mode is stabilized by synergetic effect between the finite Larmor radius, ion neoclassical viscosity and ion parallel flow in the banana regime even if Δ' > Δ'c [3]. It is also found that there is a new instability for weak shear case in banana regime, where NTM is stabilized for a normal q profile.
In this paper, the dependences of growth rate on magnetic shear and Δ' are systematically investigated. Four-field reduced MHD model {φ,A,v//,p} is numerically solved via Matrix Method and these eigen values are evaluated, where {φ,A,v//,p} are the fluctuating electrostatic potential, vector potential parallel to the magnetic field, parallel velocity and electron density, respectively (Details of the model are shown in Ref.[3]). q profile is given as q(r)=qa(1+(r/rs)a)b+qb where rs is rational surface. The magnetic shear parameter s is changed in accordance with variation of a and/or b. We set qa=0.8, qb=0.4, a=3, b=1 as default values. If the rational surface of (m,n)=(2,1) mode is located at rs=0.6ap(ap:minor radius), free energy source and magnetic shear are given by Δ'=10.3(>0), s=1.2, respectively. The threshold value Δ'c is examined changing pressure gradient at rational surface.
To clarify the onset condition or its excitation mechanism of the NTM, the nonlinear simulation with multi-helicity should be performed including the ballooning coupling terms, and so on. The result will be also reported in this confernce.

References

[1]Z. Chang, J. D. Callen, E. D. Fredrickson, et al., Phys. Rev. Lett. 74 4663(1995).
[2]A. H. Glasser, J. M. Greene and J. L. Johnson, Phys. Fluids 18 875(1975).
[3]A. Furuya, M. Yagi and S.-I. Itoh, J. Phys. Soc. Jpn 72 2(2003).