Cosmic Strings Lens Phenomenology: Model of Poisson Energy Distribution

10 pages, 5 figures.We present a novel approach for investigating lens phenomenology of cosmic strings in order to elaborate detection strategies in galaxy deep field images. To account for the complexity of the projected energy distribution of string networks we assume their lens effects to be similar to those of a straight string carrying a {\\em random} lineic energy distribution. In such a model we show that, unlike the case of uniform strings, critical phenomena naturally appear. We explore the properties of the critical lines and caustics. In particular, assuming that the energy coherence length along the string is much smaller than the observation scale, we succeeded in computing the total length of critical lines per unit string length and found it to be $4/\\sqrt{3} {\\bf E}(3/4)$. The length of the associated caustic lines can also be computed to be $16/(\\pi \\sqrt{3}) {\\bf E}(3/4)$. The picture we obtain here for the phenomenology of cosmic string detection is clearly at variance with common lore