An analytical theory of electron-cyclotron-resonance plasmas

Summary form only given, as follows. An analytical theory of the electron-cyclotron-resonance (ECR) plasmas is developed. In the steady-state, plasma generation is in balance with plasma loss due to diffusion. Based on the ambipolar diffusion and Poisson equation caused by charge separation, coupled differential equations are obtained for electron density and electric field, which are described interns of the position x, the normalized ionization rate /spl alpha/, the current density /spl zeta/ and the maximum plasma density n/sub 0/. Making use of these coupled differential equations, we obtain simple analytical expressions for electron and ion densities, and therefore the electric field and potential. Particularly, the conditions for ion sheath development, and a simple scaling law of the ion sheath strength and associated electric field are found. Several points are noteworthy from the analytical study. First, normalized strength of the ion sheath at the beginning is inversely proportional to the one-third power of the plasma density n/sub 0/. Electric field at the beginning of the sheath is proportional to the one-third power of the plasma density, thereby showing that the field strength increases as the plasma density increases. Second, the cathode ion sheath is stronger than the anode ion sheath. The anode ion sheath disappears when the current density /spl zeta/ is larger than the square root of the ionization rate /spl alpha/. Third, the electric potential for the current density satisfying 0\n\n\t\t