Spectral collocation method for collisional power absorption in radially inhomogeneous helicon plasmas

A spectral collocation method using Chebyshev polynomials is applied to compute the electromagnetic fields and the collisional power absorption in radially inhomogeneous helicon plasmas. The governing equation has a singularity at the cylindrical axis, which has been resolved by imposing the appropriate boundary conditions. The results are compared with those of the finite difference method. The present work not only shows the superior accuracy of the spectral collocation method with a proper treatment of the singularity, but also discusses the advantages of using Chebyshev nodes for helicon plasmas in particular. It is possible to extend the range of parameters efficiently in cases for which the finite difference method fails to obtain reliable solutions without drastically decreasing the grid size. The spectral collocation method is shown to be especially useful near the lower hybrid resonance condition.