Electric Fields Produced by Cosmic Rays

With recognition of the existence in interstellar space of a finite density of matter, the following four assumptions are made regarding the conditions under which electric currents flow in interstellar space: (1) The current is related to the electric field producing it by Ohm's law; (2) the interchange of electric charge between a star and its surroundings has reached a steady state; (3) the conditions around a star are spherically symmetric, which implies that the star has no magnetic moment; (4) the forces due to gravity, radiation pressure, and diffusion can be neglected simultaneously. The validity of these assumptions is discussed. The electric field $E$ in the neighborhood of a single star is given by the equation, $A=-\sigma r^{2}E$, where $A$ is proportional to the rate at which the star intercepts, or emits, cosmic-ray particles all of the same charge, $\sigma$ is the electrical conductivity in interstellar space, and $r$ is the distance of the point under consideration from the center of the star. It is found that both charge density and current density vanish in interstellar space. Numerical calculations indicate that the star will acquire a very small potential when it only intercepts cosmic rays. For a typical star this is of the order of ${10}^{-12\mathrm{}}$ volt. In the case of emission an upper limit to the potential is found to be approximately one volt. The limitations of the applicability of the present analysis for the case of emission are discussed. It is concluded that the existence in interstellar space of cosmic rays as charged particles predominantly of one sign will result in the production of negligible electric fields. Calculations are made to determine the dimensions of the ion sheath that will be produced around a star by the ions in interstellar space.