The Theoretic Analysis Of Rotating Magnetic Field Driving Plasma Current In Rotamak Under The Spherical Coordinate

A Rotamak is one kind of compact magnetic confinement plasma experimental device, which is different to the traditional Tokamak. The plasma current in Tokamak is obtained by Ohm pulse discharge, and the plasma current in Rotamak is driven by the rotating magnetic field(RMF). When the frequency of rotating magnetic field meetsω_ci <<ω<<ω_ce , theion is considered static background and the electronic is captured by RMF and rotate with the same frequency of its', which resulting in plasma current.The existing analysis mostly carries out the fundamental research of RMF driving plasma current under the cylindrical coordinate. Although the cylindrical coordinate simplifies the analysis and calculation, the practical device is not infinitely long straight column, and the nonlinear effects of spherical configuration may be not understood. Therefore it is necessary to carry out the fundamental research of RMF current drive in Rotamak under the spherical coordinate, and the RMF penetration, the current drive efficiency, and the structure of the magnetic field configuration in the real configuration of Rotamak.Starting from Maxwell's equations and the equation of the Ohm's law, and considering the symmetry of the Rotamak system and the fact that the divergence of magnetic field must be zero, the magnetic field is expressed in terms of two sets of scalar functions by using the spherical harmonics. Then we use Crank - Nicolson finite difference method, program and calculate the magnetic field equation without the additional toroidal field. Finally we analysis the penetration process of the rotating magnetic field, the current drive efficiency, and the structure of the magnetic field configuration under the spherical coordinate.Calculation results show that during interaction with plasma, RMF has a penetration process, which is from the edge to the center. The penetration time is about 0.5 oscillation cycle of the rotating magnetic field under the used parameters. Respectively, the driven plasma current develops from the edge to the center. When there isn't additional vertical field, the current drive efficiency has a process of a rapid increase at the beginning, slow rise in the middle stage and finally come to saturation. But when there is additional vertical field, the current drive efficiency has a dropped process. The analysis shows that the additional vertical field can improve the current drive efficiency.The results also show that there exists a toroidal field which has opposite directions but the same amplitude in the two hemispheres. When there isn't additional vertical field, the maximum value of the toroidal field is about 2 percent of that of RMF. But when there is additional vertical field, the maximum value of the toroidal field is about 4 percent of that of RMF. And at the beginning, the toroidal field is not only opposite in the two hemispheres but it also reverses its sign from the inner area of the plasma to the outer area one. When the driven plasma current is saturated, the toroidal field is also saturated to possess two opposite polarity. The results of the calculation match with the experimental results. The reason of the self-generation of the toroidal magnetic field is the interaction of RMF and the plasma current. In a spherical plasma, the screening current associated with a rotating magnetic field b=(br,b_θ,b_φ) has two components j_θand Jφ. The both components of the time-averaged Hall force acts on the electron fluid, driving the steady toroidal current, and in addition the poloidal current generates the bi-directional toroidal magnetic field.