content_image/325071.jpg content_image/325072.jpg content_image/325074.jpg content_image/325073.jpg content_image/325075.jpg
For the same momenta, Eq. (D.4), the leading order lightcone coordinate representation, 

<img src='content_image/325071.jpg'>

<img src='content_image/325072.jpg'>

yields exactly the same formation time, Eq. (D.6), but with p$_{z}$ replaced by E $^{+}$. 

## D.1.2 Bethe-Heitler to LPM 

The “speed limit” at which incoherent Bethe-Heitler turns over to coherent LPM, γ$_{c}$ , is found when the formation length for the produced radiation is on the order of the radiation’s mean free path: 

where τ$_{f}$ is given by Eq. (D.2) and 

<img src='content_image/325074.jpg'>

<img src='content_image/325073.jpg'>

<img src='content_image/325075.jpg'>

