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PHOENIX: MHD spectral code for rotating laboratory and gravitating astrophysical plasmas. (English) Zbl 1310.76189
Summary: The new PHOENIX code is discussed together with a sample of many new results that are obtained concerning magnetohydrodynamic (MHD) spectra of axisymmetric plasmas where flow and gravity are consistently taken into account. PHOENIX, developed from the CASTOR code [W. Kerner et al., J. Comput. Phys. 142, No. 2, 271–303, Art. No. CP985910 (1998; Zbl 0921.76100)], incorporates purely toroidal, or both toroidal and poloidal flow and external gravitational fields to compute the entire ideal or resistive MHD spectrum for general tokamak or accretion disk configurations. These equilibria are computed by means of FINESSE [A. J. C. Beliën et al., J. Comput. Phys. 182, No. 1, 91–117 (2002; Zbl 1021.76026)], which discriminates between the different elliptic flow regimes that may occur. PHOENIX makes use of a finite element method in combination with a spectral method for the discretization. This leads to a large generalized eigenvalue problem, which is solved by means of Jacobi-Davidson algorithm [G. L. G. Sleijpen and H. A. van der Vorst, SIAM J. Matrix Anal. Appl. 17, No. 2, 401–425 (1996; Zbl 0860.65023)].
PHOENIX is compared with CASTOR, PEST-1 and ERATO for an internal mode of Soloviev equilibria. Furthermore, the resistive internal kink mode has been computed to demonstrate that the code can accurately handle small values for the resistivity. A new reference test case for a Soloviev-like equilibrium with toroidal flow shows that, on a particular unstable mode, the flow has a quantifiable stabilizing effect regardless of the direction of the flow. PHOENIX reproduces the Toroidal Flow induced Alfvén Eigenmode (TFAE, [B. van der Holst et al., “New Alfvén continuum gaps and global modes induced by toroidal flow”, Phys. Rev. Lett. 84, No. 13, 2865–2868 (2000; doi:10.1103/PhysRevLett.84.2865)]) where finite resistivity in combination with equilibrium flow effects causes resonant damping. Localized ideal gap modes are presented for tokamak plasmas with toroidal and poloidal flow. Finally, we demonstrate the ability to spectrally diagnose magnetized accretion disk equilibria where gravity acts together with either purely toroidal flow or both toroidal and poloidal flow. These cases show that the MHD continua can be unstable or overstable due to the presence of a gravitational field together with equilibrium flow-driven dynamics [J. P. Goedbloed et al., “Unstable continuous spectra of transonic axisymmetric plasmas”, Phys. Plasmas 11, No. 1, 28–54 (2004; doi:10.1063/1.1631812)].

MSC:
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
85-04 Software, source code, etc. for problems pertaining to astronomy and astrophysics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76U05 General theory of rotating fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
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