Speaker
Description
See the full abstract here http://ocs.ciemat.es/EPS2019ABS/pdf/P5.1009.pdf
Analytic derivation and numerical calculation of pressure driven MHD instabilities in toroidal plasmas is notoriously difficult. Instability is determined by apparently weak effects in the toroidal metric tensor. A classical example is the m = n = 1 internal kink mode, where previous numerical and analytic results obtained in a cylinder were shown [M. N. Bussac et al, Phys. Rev. Lett. 35, 1638 (1975)] to be exactly cancelled by toroidal corrections, even in the limit of infinite aspect ratio. With such lessons well learnt by many MHD code and analysis developers, there are now new generations of gyro-kinetic codes (e.g. EUTERPE [1], GTC [2], LIGKA [3], ORB5 [4]) that are being deployed to model MHD instabilities. Some of these codes are, or have been, only partially electromagnetic. It is usually assumed that the perturbed vector potential is parallel to the equilibrium field (so that the perturbed parallel magnetic field is nearly zero), though in some codes the parallel magnetic potential assumption is deployed together with a change to the equilibrium magnetic field that is consistent with an effective adiabatic parallel magnetic field. Similar such reduced models are also assumed in some non-linear MHD codes deployed for the study of edge localised modes (e.g. JOREK [5]), and non-linear kinetic-MHD codes (e.g. HXMGC [6]). The present contribution investigates the impact of code-relevant models for the parallel magnetic field on pressure driven instabilities in axisymmetric toroidal equilibria. The work therefore provides analytic benchmarks for codes that are not yet fully electromagnetic. For example, for the case where the parallel magnetic field is not compensated, it is shown that neglecting parallel field fluctuations allows the drive for pressure driven instabilities to be artificially absorbed by the energy required to perturb the magnetic curvature. While ballooning modes in tokamaks are only weakly affected by the neglect of the parallel magnetic field, the internal kink mode, infernal modes and interchange modes are strongly, or entirely, stabilised by neglecting B . For example, for interchange modes, the effect is dominant if the ballooning parameter > 4(1 - q2r ), where qr = m/n is the rational safety factor of the main mode, and is the local inverse aspect ratio. The effect in a cylinder, reverse field pinch, and the core of the tokamak is seen to be particularly important.
References
[1] M. Cole et al, Phys. Plasmas 21, 072123 (2014)
[2] J. McClenaghan et al, Phys. Plasmas 21, 122519 (2014)
[3] Ph. Lauber et al, J. Comp. Phys. 226, 447 (2007)
[4] A. Biancalani et al, Phys. Plasmas 23, 012108 (2016)
[5] G.T.A Huysmans and O. Czarny Nucl. Fusion 47 659 (2007)
[6] S. Briguglio et al, Phys. Plasmas 2, 3711 (1995)
