Heuristic Solution of Langmuir Problem in Arbitrary Domain
The Langmuir problem for a collisionless plasma was formulated and solved for some simple domains at 1921. But, for more complicated cases, no robust method is known till now except for the macro particle simulation. We propose a new method applicable to domains with arbitrary boundary shape. The method is based on the solution of the well-known eigenvalue roblem for diffusion-type equations. The comparison of test solutions obtained by this technique with the Particle-In-Cell method demonstrates an acceptable accuracy despite the lack of theoretical validation of this method.
L. Tonks, I. Langmuir. A general theory of the plasma of an arc. Phys. Rev. 34, 876 (1929).
S.A. Dvinin, A.A. Kuzovnikov. A two-dimensional equation for a plasma and a layer in the positive column of a gas discharge. Vestn. Mosk. Univ. Ser. 3. 5, 18 (2005).
V.A. Godyak, N. Sternberg. Smooth plasma-sheath transition in a hydrodynamic model. IEEE Trans. Plasma Sci. 18, 159 (1990).
R.N. Franklin. You cannot patch active plasma and collisionless sheath. IEEE Trans. Plasma Sci. 30, 352 (2002).
I.D. Kaganovich. How to patch active plasma and collisionless sheath: Practical guide. Phys. Plasmas 9, 4788 (2002).
V.I. Zasenko. Formation of a charged layer in a bounded nonuniform magnetized plasma in RF field. Ukr. J. Phys. 57, 1011 (2012).
C.K. Birdsall. Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PICMCC. IEEE Trans. Plasma Sci. 19, 65 (1991).
J.P. Verboncoeur. Particle simulation of plasmas: review and advances. Plasma Phys. Control. Fusion 47, A231 (2005)].
J.P. Verboncoeur, A.B. Langdon, N.T. Gladd. An objectoriented electromagnetic PIC code. Comp. Phys. Comm. 87, 199 (1995).
A.V. Gapon, A.N. Dahov, S.V. Dudin, A.V. Zykov, N.A. Azarenkov. 2D fluid model for interactive development of ICP technological tools. Problems of Atomic Science and Technology 12, No. 6, 186 (2006)