## 1 Introduction  
X-rays/gamma-rays (in lightning research, the boundary between the two is usually placed at 1 MeV) are produced by all types of downward lightning leaders when they are typically within 100 m or so of the ground ([PERSON] (2004) [1], [PERSON] et al. (2012) [2]). Lightning leaders emit X-rays/gamma-rays when the electric field and channel properties are such that free electrons can run away; that is, they gain more energy from the electric field than they lose by collisions with air molecules. The emission occurs when runaway electrons experience deflection by the electric field of other charged particles (typically atomic nuclei), a process that is referred to as Bremsstrahlung or braking radiation. The rate of electron energy loss per unit distance is often called the friction force and its dependence on electron energy is represented by the so-called friction curve. Two such curves, for cold air and for air at 3000 K, are shown in Figure 1.  
Table 1 compares the various scenarios of acceleration and multiplication of runaway electrons in terms of the source of seed electrons, air temperature, and characteristic electric field. Conventional (non-relativistic) avalanches are additionally included as a reference. In Table 1, the ambient electron-energy distribution includes electrons with energies less than 30 eV or so, while the so-called cosmic-ray secondaries (electrons produced by very high  
energy (10\({}^{15}\)-10\({}^{16}\) eV or greater) cosmic-ray particles) have energies exceeding 0.1-1 MeV. For comparison, the average energy of electrons in conventional electric breakdown is just a few electron-volts. It follows from Table 1 that there are three main factors that can serve to initiate and sustain the multiplication of runaway electrons: (1) super-high electric field, (2) energetic electrons supplied by external sources, and (3) elevated air temperature (reduced air density). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Process** & \begin{tabular}{c} **Source of Seed** \\ **Electrons** \\ \end{tabular} & \begin{tabular}{c} **Air Temperature**, \\ **K** \\ \end{tabular} & \begin{tabular}{c} **Electric Field**, \({}^{*}\) \\ **MV/m** \\ \end{tabular} \\ \hline \hline Relativistic avalanches in & \begin{tabular}{c} Two-step process \\ cold air (cold runaway \\ breakdown) \\ \end{tabular} & \begin{tabular}{c} 300 \\ distribution \\ \end{tabular} & \(\gtrsim\)30 \\ \hline \hline Relativistic avalanches in & \begin{tabular}{c} Cosmic-ray \\ cold air (RREA) \\ \end{tabular} & \begin{tabular}{c} 300 \\ secondaries \\ \end{tabular} & \(\sim\)0.2 \\ \hline \hline Relativistic avalanches in & \begin{tabular}{c} Ambient distribution \\ \end{tabular} & \(3000\) & \(\gtrsim\) \\ \hline \hline Conventional & \
\begin{tabular}{c} Ambient distribution \\ (non-relativistic) avalanches in cold air \\ \end{tabular} &
\begin{tabular}{c} 300 \\ \end{tabular} & \(\sim\)3 \\ \hline \hline \end{tabular}  
* Approximate values at sea level.  
\end{table} 
Table 1: Acceleration and multiplication of runaway electrons. Figure 1: The dynamic friction curves showing the friction force (rate of energy loss per unit distance) experienced by an electron as a function of electron energy for cold air and for air at 3000 K. The curves include the effects of both inelastic scattering of the electron with air molecules and Bremsstrahlung emission. The horizontal lines represent the Coulomb force acting on the electron (eE, where E is the electric field intensity and e is the electron charge) corresponding to E = 1 MV/m and E = 5 MV/m (see the right vertical scale). Electrons can run away to relativistic energies when the Coulomb force is greater than the friction force. For cold air and E = 5 MV/m, only electrons with energy greater than 5 keV can run away, while for the air at 3000 K, all electrons can do so. Adapted from [PERSON] (2004) [1] and [PERSON] et al. (2019) [3].