Electromagnetic emission from pairs of water drops exchanging charge

Abstract

Laboratory studies of two oppositely charged water drops, each having a radius of 500 μ, a charge of 50×10−12 coul, and falling through air at a pressure of about 1 atm along a trajectory which brings it close to the other drop, indicate that the dipole moment of the pair changes by about 1×10−14 coul m in a time 2τ less than 10−9 sec. The sparklike charge transfer occurs when deformed portions of the drop surfaces become sufficiently close to one another. The change in moment Δp and the time τ are parameters that can be used in estimating a minimum efficiency for conversion of electrostatic energy into radiation. Values for τ less than 1.2×10−12 sec are energetically impossible and correspond to efficiencies greater than 1. An assumed value of 2×10−11 sec for τ is consistent with speeds typical of electronic processes. A swarm of drops, pairs of which at random times discharge so as to produce the minimum radiation consistent with τ = 2 × 10−11 sec and with the approximation that for any given pair no change in the dipole moment occurs outside an interval of duration 2τ, radiates power with a spectral density that peaks at 17 Ghz. Polarized radiation from a single pair of drops has been detected at 10 Ghz. The spectral density in the low-frequency limit is proportional to the square of the frequency ƒ. In this limit the coefficient of proportionality depends on Δp but does not depend on τ or on the exact manner in which the moment p varies with time. Because in the low-frequency limit blackbody radiation is also proportional to ƒ2, radiation from a swarm of discharging drops can be mistaken for thermal radiation. Radiation equivalent in the low-frequency limit to that from a blackbody at a temperature of 650°K, the apparent microwave temperature of Venus at wavelengths between 3 and 30 cm, can be produced by a transparent cloud in which drop-to-drop encounters result in dipole moment changes of 10−14 coul m occurring at a rate of 1.4×106 changes per second per square meter column of cloud lying along the direction of observation.