Finite Gyro-Radius Equation with Inhomogeneous Electric Field and Stabilizing Effect for Flute Instabilities

Abstract

For the flute instabilities of a plasma in the presence of inhomogeneous electric field E_o (x) and a uniform magnetic field B, the Finite Gyro-Radius (F. G. R.) eigenvalue equation is derived on the basis of the simple guiding center picture with appropriate F. G. R. corrections. This is the same equation which Rosenbluth and Simon derived by using a formal expansion of the Viasov equations. Then, the stable condition is examined in the case of b²<<1, dV_E/dx=const and k≡-dln^ρ/dx-const, where ρ is the mass density, b²=B²/4πρc² and V_E=-cE_o (x) /B, with the light velocity c. It is concluded that the presence of the inhomogeneous electric field always tend to destroy the F.G.R.stabilizing effect irrespective of the sign of dV_E/dx.