The atomic ionization exists in gas when the absolute temperature is not 0 K, which means that there exist other charged particles besides the neutral particles. Only when the density of these particles is massive enough to form the space charge, limiting movement itself, could other charged particles affect the gas characteristics heavily.

This limitation tends to be important with the enhancement of the density. As the ample density, the macroscopic electrical neutrality is kept by the interaction between the positive and negative charged particles in a certain volume of gas (the gas volume has analogy with the space of the charged particles) whose destructive effect could induce electric field, thus the resumptive time would be shorten. Aerial discharge is one of the ways transforming gas into plasma, however not all the discharged gas could reveal the plasma characteristics. Only when the ionization is strong enough, would the plasma properties be presented. Up to dozens to several hundred kA currents could be induced by lightning instantly and such large currents could heat the lightning channel to tens of thousands K. At normal temperature, various molecules and atoms in the atmosphere would be dissociated and ionized instantaneously in such high circumstance temperature, which leads to diverse elements atoms and various levels ionized ions in the channel. Meanwhile, a mass of electrons are generated simultaneously and the whole channel is in a plasma state. Because of the complexity and the transient of the lightning discharge, it is difficult to test the physical parameters of the channel directly. The research could be implemented by the quantitative analyses of the lightning spectrum to obtain the inner physical parameters. In the analytical process, the theoretical assumption should be met as follows

(1) lightning channel is optically thin for the researched spectral lines; (2) lightning channel is in local ther-modynamic equilibrium (LTE) status.

The LTE Model

Plasmas only satisfy the LTE to guarantee that the velocities of the plasmas meet the Maxwell distribution, each charged ion and atom conform to the Saha distribution and each energy level conform to the Boltzmann statistical distribution. Thereby the quantitative relationships having clear physical meanings are established between the radiation quantity of the plasmas and diverse state parameter17. The LTE condition would be tenable, only when the collision processes of electron-atom and electron-ion are achieved within several microseconds and play a leading role in the plasma velocity equation. So only when the Ne electron density is large enough, could the LTE be achieved in the system, meaning that the plasmas should meet the following LTE necessary condition

where:

N e is the electron density of the lightning channel plasmas, eV/cm3; ΔE is the energy difference between the involved energy states; T e is the temperature of electrons, K. It is often set as the measure standard that the difference between the first excited state and the ground state to ensure the energy levels meet the above conditions.

The lower excited state of NII dominates the lightning channel plasmas, the temperature range being in 2 × 104 K~3 × 104 K, ΔE being in 10 eV~30 eV. Based on equation (1), the plasmas satisfy the LTE condition in the channel when the electron density range from 1017 to 1018 cm−3. The value of the plasma density is about 1017 cm−3, which is calculated utilzing the Stark widening method. Thereout, it could be judged that the plasmas in the lightning channel satisfy the LTE condition.

According to the corresponding characteristics of the lightning spectrum, it is required to ensure the electron density in the return stroke channel that the lightning channel is optically thin. Only when the channel keep in balance on radiation and absorption could the return stroke channel be formed. Orville et al. analyzed the lightning spectrum by time accumulation and resolution, gaining that the ion channel was optically thin for NII particles preliminarily17.

The measuring theory for lightning channel temperature

Based on the atom spectrum theory, the charged particles in lower energy state would be excited to higher energy state. Then the excited charged particles are quite unstable and would return to the lower energy state from the higher after being excited 10−8 s. When the excited charged particles transit from the higher energy level to the lower energy level, the energy radiated in form of light is given as

where: E m is energy of the particles in the higher energy level; E n is energy of the particles in the lower energy level; m, n are the energy levels; h is the Planckconstant; v mn is the frequency of the radiation spectrum generated by the particle transition.

In the LTE condition, it is assumed that the neutral atom in the channel is in a state of excitation when the lightning channel is at a certain temperature. Based on the Boltzmannformula, the number of particles in each excited state is

where: N i is the number of particles in the excited state i in a unit volume of in the lightning channel; N 0 is the number of particles in the ground state; g i and g 0 are the statistical weights of the excited state and the ground state; E i is the excited potential, standing for the energy level of the excited state i, eV; k is the Boltzmann constant; T is the temperature of the lightning channel, K. From the equation (3), when the excitation temperature of the plasmas in the lightning channel is high enough, the neutral atom is easy to be excited to the higher energy level and more atoms are in the excited state. Meanwhile, the excited plasmas is unstable in the channel, and is easy to return to the ground state quickly, thus radiate photons. It is assumed that one particle should be excited to the i energy level, and when it recovers from the higher energy level to the lower energy level, the transitions between various energy levels have a variety of likelihood. Set the transition probability between i and m energy level as A im , then the difference between i and m is

where f im are the frequencies of the transition spectral lines between i and m energy level.

The transition spectral line intensities are I im :

where: I im are the spectral line intensities, transiting between i and m energy level, J/(cm3·s); A im is the transition probability between two energy levels.

According to the above equations, the spectral line intensities yield to be

The intensity ratio of the two bands of the same kind of particle should satisfies

where: I λ 1 and I λ 2 are the intensities of spectral lines whose wave lengths are λ 1 and λ 2 ; A 1 and A 2 are the transition probabilities of diverse lines; g 1 and g 2 are the statistical weights of the excited states; E 1 and E 2 are the excited state energies of different lines.

From equation (7), it can be found that

For the two lines whose wave lengths are λ 1 and λ 2 , A 1 , A 2 , g 1 , g 2 , E 1 , E 2 and k are the foregone constants, therefore the temperature T of the lightning channel could be acquired by equation (8) only by measuring the two spectral line intensities I λ 1 and I λ 2 .

Equation (8) provides the direct relation between the lightning intensity and temperature in the lightning channel which can be used as the basic theory of temperature measurement by the atomic emission spectroscopy and as the foundation of the technology by measuring the temperature by relative intensity spectrum of lightning channel.