Symmetrical and asymmetrical ideal cylindrical radiation transformers and concentrators

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Abstract
Ideal cylindrical radiation transformers and concentrators are examined in both asymmetrical and symmetrical forms. Symmetrical ideal transformers are found to give the lowest peak concentration for a given angle of acceptance. Average concentration for uniform diffuse radiation or a distant point source of constant apparent angular velocity is found to be independent of the symmetry of the transformer; for an apparently accelerating source such as the sun, however, an asymmetrical transformer can give higher performance than a symmetrical unit when averaged over time.