A new method of solution for one-dimensional quasi-neutral bounded plasmas

A new method is proposed for calculating the potential distribution Φ(z) in a one-dimensional quasi-neutral bounded plasma; Φ(z) is assumed to satisfy a quasi-neutrality condition (plasma equation) of the form nⁱ{Φ(z)} = n^e(Φ), where the electron density n^e is a given function of Φ and the ion density nⁱ is expressed in terms of trajectory integrals of the ion kinetic equation. While previous methods relied on formally solving a global integral equation (Riemann, Phys. Plasmas, vol. 13, 2006, paper no. 013503; Kos et al., Phys. Plasmas, vol. 16, 2009, paper no. 093503), the present method is characterized by piecewise analytic solution of the plasma equation in reasonably small intervals of z. As a first concrete application, Φ(z) is found analytically through order z⁴ near the center of a collisionless Tonks-Langmuir discharge with a cold-ion source.