National Academies Press: OpenBook

The Earth's Electrical Environment (1986)

Chapter: Diffusion Charging

Suggested Citation:"Diffusion Charging." National Research Council. 1986. The Earth's Electrical Environment. Washington, DC: The National Academies Press. doi: 10.17226/898.
Page 115

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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 115 CLOUD STAGE As the first clouds form on a warm summer afternoon, the environment is already set for cloud electrification. The air is filled with ions whose concentrations and mobilities determine the effective conductivity of the atmosphere. In many practical situations the air is an electric insulator, but the conductivity is large enough to permit a relaxation time of less than 7 minutes for discharging the lower atmosphere (Israël, 1971). The discharge current results from the drift of small ions with the mass of a few molecules. Charge separation begins immediately when a field is applied to a mixture of positive and negative ions. Within a cloud the usual result of ion motion is capture by water droplets. The electric background in which the cloud forms contains vertical gradients in ion concentration with a negative charge at the Earth's surface that is maintained by thunderstorms. The electric field above the ground is reduced by a screening layer of positive ions attracted by the Earth. Positive ions from aloft accumulate near the ground because the field-induced drift is reduced by collisions as the density of the air increases. Capture of ions by aerosols greatly reduces the drift velocity and, during times of heavy pollution, 500 V/m have been measured between the positive space charge and the ground. A field of 130 V/m is more typical of a summer day with a well-mixed boundary layer. This is reduced by about 1 order of magnitude at a 3 km height. Thus, a fresh cumulus cloud forms in an environment of vertical gradients in space-charge density, electric field, ion concentration, and conductivity (see Figure 9.1). The field is oriented toward negative earth with a strong increase in positive space charge below 1 km and a small ion concentration and conductivity that increase with height. In this electric environment there are several ion capture mechanisms that lead to charged droplets in shallow cumulus clouds. In the following discussion, microscale charge separation is described for diffusion charging, drift charging, and selective ion charging. The cloud-scale separation of charge for these nonprecipitation clouds is discussed below under drift charging. Diffusion Charging For the early stage of cloud charging we consider the collection of ions by cloud droplets. The ion-transport equation on the microscale near a cloud droplet gives the charge flux (C/m2 sec) or the current density for an ion component as Figure 9.1 Average electric properties of the lower atmosphere during fair weather. The variation of the electric field with height is due to Gish (e.g., see Pruppacher and Klett, 1978). The spacecharge density is a direct result of Gauss's law, whereas the conductivity is obtained by assuming a constant current (2.7 pC m–1 sec–1). The concentration of small ions is proportional to the conductivity and varies inversely with the ion mobility. where ρi is the ion-charge density (C/m3) of a particular species, U is the air velocity, Bi is the ion mobility (about 2 Χ 10-4 m2/V sec for small ions in the lowest few kilometers), E is the electric field, and Di is the molecular diffusivity (m2/sec). The flux term for the microscale airflow (ρi U) is relatively weak because of the low fall speed for cloud droplets. In addition the field is small enough in the cloud stage to ignore the ion drift term (ρiBi E). Thus the charging of small cloud droplets is found by evaluation of the standard diffusion equation. An important consequence of diffusion charging is a reduction of ion concentration within the cloud by several orders of magnitude. The time constant for depletion can be obtained from the solution to the diffusion equation for a steady-state attachment of ions to a cloud of similar size droplets. The solution is where R is the droplet radius and N is their concentration. For a typical size and concentration in the cloud

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This latest addition to the Studies in Geophysics series explores in scientific detail the phenomenon of lightning, cloud, and thunderstorm electricity, and global and regional electrical processes. Consisting of 16 papers by outstanding experts in a number of fields, this volume compiles and reviews many recent advances in such research areas as meteorology, chemistry, electrical engineering, and physics and projects how new knowledge could be applied to benefit mankind.

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