32 Chapter 2: Motivation and Pisarksi [225–227] (for a review of HTL, see [228]); the energy loss was found by deriving the work done on the source current by the induced fields in the dielectric medium. Braaten and Thoma [229, 230], expanding upon the work of Svetitsky [231], separately evaluated the high momentum part of the dynamics using the vacuum matrix element and the low momentum piece with linear response and connected the two at a scale q ∗ which, to leading order, drops out of the problem [232]. These leading log results were compared to asymptotic radiative loss ap- proximations and found to be small [233, 234], not surprising as this is a well known result from E&M [235]. Further work on elastic mechanisms slowed until [236] showed that with realistic kinematic limits at Rhic energies ra- diative and elastic losses are of the same order. This and the experimental evidence of surprisingly strong heavy quark quenching [237–240] motivated work to incorporate both radiative and collisional processes in jet quenching models (see Chapter 4) and has generated a flurry of interest in improving elastic calculations. Some more recent developments in elastic loss include considerations of run- ning coupling, finite creation time effects, and the importance of the higher moments of the distribution. Peshier [241] saw a large energy loss enhancement when he allowed the coupling to run; [242] found a qualitatively similar result. Wicks [243], however, showed that for Rhic and Lhc kinematics this is actu- ally a small effect. All previously mentioned calculations used asymptotic jets created in the infinite past. Peigne, Gossiaux, and Gousset [244] claimed that