Perturbation of singular chasma equationPerturbation of singular chasma equation
Faculty of Sciences. Physics
Department of Physics
Cambridge :Electromagnetics Academy, 2007[*]2007
Engineering sciences. Technology
Progress in Electromagnetics Research Symposium (PIERS 2007), March 26-30, 2007, Beijing, Peoples Republic of China
University of Antwerp
An ionizing beam (electrons, ions, atoms, photons) between plane-parallel plates, either parallel or perpendicular to the plates (like in the multipactor effect and hf cavities) may create an accumulating ion charge. The resulting steady state of the chasma ('non-quasi-neutral plasma') has a potential W satisfying a quasi-singular non-linear integro-differential equation. The investigation of the perturbations reveals problems due to the singular character of the integrand. However, in the case that the beam density (b) and the ion production (P) are constant the potential is given by phi = -kx(2), where k is the positive root of a cubic equation. Perturbing and linearizing the latter equation yields the change dk for a disturbance db and dP, which may be time dependent provided slow enough that the ions may readapt to the new steady state. Some particular cases are studied. For more involved cases one should return to the singular equation or it may be better to the original set of partial differential equations, which avoids the singularity problem. However, this makes the investigation much more wide and much more involved.