# Atmospheric Charge Separation Mechanism Due to Gas Release from the Crust before an Earthquake
## 2 Physical Modeling
Notably, radon, thoron and other radioactive elements released underground continue to release energy as they decay into \(\alpha\), \(\beta\) and \(\gamma\) particles, and the decay process continuously occurs underground or aboveground. Then, the process of \(\alpha\) particle decay that promotes the ionization of molecules in the atmosphere also causes heat release. In the continuous microfracturing process of the Earth's crust, heat from the underground is released into the near-surface atmosphere. In addition, coupled with the consideration of longwave radiation anomalies prior to earthquakes [7], there must be a thermal driver \(F\) before the earthquake, but the variation in the F value is complex. Therefore, here, \(F\) is described only qualitatively. In general, a charged particle in the air experiences four forces: atmospheric quasi-stable electrostatic force \(qE\), gravity force mg, air drag force \(kv^{2}\) and thermal convection (upward thermal pressure) force \(F\), where \(q\) is the ion charge, \(E\) is the average atmospheric electrostatic field, m is the ion mass, g is the gravitational acceleration, \(k\) is the drag coefficient and \(v\) is the ion velocity. Single positive and negative ion particles are considered in the following equations:A single atmospheric positive ion satisfies the following equation:  
\[m_{+}\frac{\mathrm{d}v_{+}}{\mathrm{d}t}=-q_{+}E-m_{+}g-kv_{+}^{2}+F \tag{1}\]  
A single atmospheric negative ion satisfies the following:  
\[m_{-}\frac{\mathrm{d}v_{-}}{\mathrm{d}t}=q_{-}E-m_{-}g-kv_{-}^{2}+F \tag{2}\]  
Then, the average atmospheric electrostatic field E can be obtained as:  
\[E=E_{0}e^{-\alpha z} \tag{3}\]  
where \(m_{+}\) and \(m_{-}\) are positive and negative ion masses, respectively, \(q_{+}\) and \(q_{-}\) are the amounts of positive and negative ion charges, respectively, \(g\) is the gravitational acceleration, \(k\) is the air drag coefficient and \(F\) is the upward thermal driving force. The above equations constitute a simplified fundamental model, where \(F\) is regarded as a constant and \(v_{+}\) and \(v_{-}\) are the velocities of positive and negative ions, respectively. Accounting for the actual measured distributions of the atmospheric electric field with altitude, we considered the background electric field E here as a quantity that only varies with height; it varies vertically downward under normal fair-weather conditions, and the change in height follows an exponential distribution [24]:  
The parameters in the quantitative model and their physical explanations are as follows:  
\(m_{+}\): 1.63 \(\times\) 10\({}^{-17}\) kg (the mass of positive ions including many molecules);  
\(m_{-}\): 4.08 \(\times\) 10\({}^{-18}\) kg (the mass of negative ions including many molecules);  
\(g\): 9.8 m/s\({}^{2}\) (gravitational acceleration);  
\(q_{+}\): 1.6 \(\times\) 10\({}^{-18}\) C (the charge of positive ions including many molecules);  
\(q_{-}\): 1.6 \(\times\) 10\({}^{-18}\) C (the change in positive ions including many molecules);  
\(k\): 0.45 (drag coefficient);  
\(E_{0}\): 100 V/m (average value of the atmospheric electrostatic field under fair weather conditions);  
\(a\): 1.7 \(\times\) 10\({}^{-5}\)/m. Assuming that F is an exponentially decreasing quantity with time, substituting Equation (3) into Equations (1) and (2), with some constant values set as described above, leads to the simulation results, and the results can be obtained within 300 s, as shown in Figure 4.  
Figure 4: Simulation results illustrating the atmospheric charged particle process in which positive and negative ions are rapidly separated over time (blue and yellow colors indicate the movement of positive and negative ions, respectively. ).