found by solving the diffusion-loss equation [@diffusion]: $$\begin{aligned}
\frac{\partial}{\partial t}\frac{dn_{e^{+}}}{dE_{e^{+}}} = \vec{\bigtriangledown} \cdot \bigg[K(E_{e^{+}},\vec{x})  \vec{\bigtriangledown} \frac{dn_{e^{+}}}{dE_{e^{+}}} \bigg] + \frac{\partial}{\partial E_{e^{+}}} \bigg[b(E_{e^{+}},\vec{x})\frac{dn_{e^{+}}}{dE_{e^{+}}}  \bigg] + Q(E_{e^{+}},\vec{x}),
\label{dif}\end{aligned}$$ where $dn_{e^{+}}/dE_{e^{+}}$ is the number density of positrons per unit energy, $K(E_{e^{+}},\vec{x})$ is the diffusion constant, $b(E_{e^{+}},\vec{x})$ is the rate of energy loss and $Q(E_{e^{+}},\vec{x})$ is the source term, which contains all of the information about the dark matter annihilation modes, cross section, and distribution. To solve the diffusion-loss equation, a set of boundary conditions must be adopted. In this application, the boundary condition is described as the distance from the galactic plane at which the positrons can freely escape, $L$. These diffusion parameters can be constrained by studying the spectra of various species of cosmic ray nuclei, most importantly the boron-to-carbon ratio [@btoc].

In Fig. \[heat\], the ratio of positrons to positrons plus electrons in the cosmic ray spectrum is shown as a function of energy, including a possible contribution from dark matter annihilations. Also shown are the measurements from the HEAT experiment [@heat], which may possibly contain an excess in comparison to standard astrophysical expectations at energies above 7 GeV or so. While positrons from dark matter annihilations are indeed able to generate 