Symplectic map and mathematica for calculations of magnetic field lines and compressible resistive MHD spectra in a tokamak with hydrogen plasma

Abstract

This paper attempted to consider Symplectic mappings called the Tokamap to describe the magnetic field lines in the Poincaré map. These maps are compatible with the toroidal geometry and are considered in a tokamak with a large aspect ratio. The Tokamap depends on the two parameters ε and q, and with increasing ε chaos appears in the maps. In the current study, Tokamap and symmetric Tokamap are considered for two types of q, monotonic and non-monotonic. The non-monotonic is different from the original q in these mappings. The location of the created transport barriers depends on the q. Moreover, the compressible resistive MHD equations are solved for IR-T1 tokamak configuration with arbitrary currents and density mass profiles. The equations were linearized around an equilibrium state. Then, the eigenvalues and normal modes were obtained numerically by Mathematica software for homogeneous and inhomogeneous plasma. The results show that the eigenvalues are complex and lie on specific curves. Also, the normal modes are damped.