Calculation of Quasistatic Eigen-Field of a Charge, which Moves Arbitrarily in Cylindrical Drift Chamber *

In the Darwin approximation using the Green functions method, we found the solutions for the quasistatic (quasistationary) vector potential excited in cylindrical drift chamber with perfectly conducting walls by arbitrary charge and current densities (e.g., by a charged beam), which satisfy the continuity equation. The found Green functions are expressed as decomposition into the eigen functions of the Laplace operator within the cylindrical coordinate system with the Dirichlet and Neumann boundary conditions. Based on the obtained solutions for potentials, we find expressions for the induced magnetic field and relativistic correction to the electric field. Taking into account relativistic corrections to the order of field of radiation, we also found contribution from charges and currents being beam-induced on the drift chamber walls into the Lorentz force acting on the isolated charged particles of a beam. The method is proposed which enables the problem for vector potential to be reduced to a system of the scalar Poisson equation in cylindrical coordinate system. A separation of the excited e.m. field into "wave field" (the propagating one) and the so called "field of spatial charge" (the non-propagating one) is a generally recognized procedure in theoretical investigation of the oscillation mechanism in electron devices of various kinds. Notice that the field of spatial charge has analogy to the fastdropping part of the e.m. field of the moving charge in the near zone of the free space. Structural determination of the eigen field of the charge is a very complicated however necessary problem for the physical electronics. In the literature there are suggested the methods for estimation of the influence of the spatial charge field upon the operation of the