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Handel 1985
Handel, P.H. (1985). Polarization catastrophe theory of cloud electricity—speculation on a new mechanism for thunderstorm electrification. Journal of Geophysical Research 90: doi: 10.1029/JD090iD03p05857. issn: 0148-0227.

During the last two decades, ice has been recognized as a hindered ferroelectric, i.e., a substance that is supposed to be ferroelectric at 0 ¿K, but turns out to have the protonic disorder frozen in, and to persist in a metastable finite-entropy state down to arbitrarily low temperatures. Small, heterogeneously nucleated aggregates of water and ice may therefore be saturation-polarized and may keep most of their polarization while they grow, perhaps up to sizes of the order of 1 μ for water and more than 10 μ for ice crystallites. This upper size limit is likely to increase with the growth rate. More important, if the criterion N&ngr;2>2.5 1021cm-3 is satisfied, a polarization catastrophe occurs, rendering the cloud ferroelectric. Here N is the concentration of aggregates, &ngr; the number of H2O molecules in each. The direction of the spontaneous polarization is usually determined by the fair-weather field vector, leading to negative polarization charges on top of the cloud and positive on the lower end of the polarization catastrophe region. Masking charges of opposite sign accumulate in these regions during the formation of the cloud, compensating most of the polarization charges. When the aggregates grow too large, they lose their dipole moment, i.e., when the cloud dissipates, the polarization catastrophe disappears, and the masking charges generate lightning if the process of dissipation is fast.

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Journal of Geophysical Research
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