Runaway Positrons in Fusion Plasmas

Runaway positrons can be produced in the presence of runaway electron avalanches in magnetized plasmas. In this Letter, we determine the positron distribution, the fraction of runaway positrons, and the parametric dependences of their synchrotron radiation spectrum. We show that the maximum production occurs around ${\gamma }_e\simeq 30$, where ${\gamma }_e$ is the Lorentz factor of the fast electrons. For an avalanching positron distribution typical of tokamak plasmas, the maximum of the synchrotron radiation spectrum should be around a micron. The radiated power and spectrum shape are sensitive to the plasma parameters. Apart from its intrinsic interest, detection of radiation from positrons could be a diagnostic tool to understand the properties of the medium they propagate through.

Figure 1

Total cross section in $\mu b$ for $Z=1$, as a function of the electron Lorentz factor. The dash-dotted line is the ultrarelativistic approximation ${\sigma }_{\gamma \gg 1}$, the dashed line is the threshold approximation ${\sigma }_{\mathrm{th}}$, and the solid line is the numerically calculated cross section (1). The annihilation cross section (2) is a function of the positron Lorentz factor and is shown by a dotted line.

Figure 2

Differential production rate normalized to $n_i{n}_{r}c/c_z$ as function of runaway energy from (4) using the runaway distribution from (3). The dash-dotted red line uses the ultrarelativistic approximation of the cross section ${\sigma }_{\gamma \gg 1}$, and the solid line the numerically calculated cross section (1). Thin lines are for $\ln \Lambda =10$ and thick lines are for $\ln \Lambda =15$.

Figure 3

(a) Normalized positron distribution as a function of normalized momentum. (b) Fraction of positrons that run away as a function of the normalized electric field.

Figure 4

Synchrotron radiation spectrum normalized to the positron number density, for an avalanching distribution from (3). Unless otherwise stated, the parameters are the following: magnetic field $B=2.27\mathrm{T}$, parallel electric field $E_{\parallel }=20\mathrm{V}/\mathrm{m}$, major radius $R=1.8\mathrm{m}$, effective charge $Z_{\mathrm{eff}}=1.6$, Coulomb logarithm $\ln \Lambda =10$, and electron density $n_e=3\times {10}^{20}{\mathrm{m}}^{-3}$. The rest of the parameters are changed according to the legend of the figures: (a) major radius, (b) density, (c) effective charge, (d) magnetic field, (e) Coulomb logarithm, and (f) parallel electric field.