Rigid rotation symmetry of a marginally stable minimum B field and analytical expressions of the flux coordinates

摘要

One of the main issues of the open ended plasma confining devices is to provide a magnetohydrodynamic stable plasma equilibrium. A nonaxisymmetric, marginally stable confining magnetic field for a conventional, single mirror device has been studied for a long thin flux tube. The marginally stable minimum B magnetic field is proven to have quadrupolar symmetry under the assumptions of a straight paraxial central flux line and zero plasma beta. The quadrupolar symmetry geometrically means that the flux lines are not twisted. The perpendicular drift of the gyro centers is zero. A possible external current distribution which can generate the magnetic field is determined. The most convenient set of flux coordinates for this magnetic field are (x(0), y(0), s), where x(0) and y(0) are Cartesian-like Clebsch coordinates and s is the arclength of the magnetic field line. Analytical expressions for the magnetic flux coordinates are derived for this magnetic field. (c) 2005 American Institute of Physics.