In this work, we use the plasma module in COMSOL Multiphysics software to establish the neon discharge model, and obtain the plasma characteristic parameters and electric field distribution parameter diagram, and verify whether the model realizes the glow discharge and the feasibility of the model by comparing with the existing theoretical and experimental results.

Assuming that the system is in an ideal plasma environment, the plasma discharge area is filled with pure neon gas. A two-dimensional axisymmetric model was established as shown in Figure 1. The outer length of the model is 6 mm and the width is 8 mm . The white rectangles on the upper and lower sides are electrodes. The length is 4 mm , the width is 0.5 mm , and the electrode spacing is 6 mm . The gray area between two electrodes is neon discharge area, the gas inside the plate is divided into outer region and inner region. Because the fluid does not distinguish between internal and external boundary, errors are easy to occur in calculation if the electrode is set to a metal. Due to this reason the electrodes regions were “hollowed out”.

The discharge area includes discharge module, particle drift diffusion module and energy module.

Discharge module: Neon’s discharge region includes four kinds of particles, namely electron ( e ) , neon atom ( Ne ) , metastable neon atom ( Ne ∗ ) and neon ion ( Ne + ) . In the calculation of the variation of the dynamic parameters of the gas discharge system, the particle collision of Ne and Ne + , including elastic collision, excitation and ionization, and the surface reaction on the electrode surface should also be considered. The reaction formulas and reaction types are shown in Table 1.

Ion drift diffusion module: it contains the electron drift diffusion equation and the input of model parameters, the setting of gas temperature, gas pressure and reduced electron mobility parameters.

Energy module: it includes insulation surface, initial value, metal contact (anode), grounding (cathode), dielectric contact, wall, as so on. The initial value is the initial electron density and the applied voltage value. Metal contact include the setting of type setting and circuit type setting. The circuit types include RC circuit, ballast resistance, DC isolation resistance and DC isolation capacitor. In this paper, we choose RC circuit.

According to the volt-ampere characteristic curve of gas discharge, at first, due to the migration movement of electrons and positive ions, a small current is generated in the discharge tube, and the space charge formed by positive ions is conducive to the movement of electrons towards the anode in the tube. As the electrons slowly gather at the anode, they collide and ionize frequently with the gas atoms near the anode, and a large number of electrons and positive ions generate. The electrons continue to collide with the gas atoms, and the positive ions move to the cathode under the action of the electric field, bombard the cathode and emit secondary electrons, which then collide with the gas particles. And finally the discharge reaches a stable state.

In the 2D Neon discharge model, the electrode spacing is set to 6 mm , the discharge voltage is 200 V , and the initial plasma density is 1 × 10 13 m − 3 , and the resulting trend distribution of electron density, electron temperature and electric potential are shown in Figures 2–4.

Figure 2 shows the distribution of electron density at different time. In Figure 2A ,  when t = 1.0 × 10 − 8 s , a large number of electrons and positive ions are generated near the anode due to the collision between electrons and gas atoms, and the electron density is relatively high. In Figures 2B,C, from  t = 1.0 × 10 − 6 s to  t = 1.0 × 10 − 4 s , the positive ion moves to the cathode under the action of the electric field, the cathode produces secondary electrons under the bombardment of the positive ion, and the electron density near the cathode is increasing. In Figures 2C,D, after when t = 1.0 × 10 − 4 s , the electron density near the cathode reaches the maximum value, until when  t = 1.0 × 10 − 2 s , the electron density distribution does not change any more, and the discharge reaches a stable state.

Figure 3 shows the distribution of electron temperature at different time. Electron temperature is used to describe the thermal energy of particles. In Figure 3A, when t = 1.0 × 10 − 8 s , electrons continue to move to the anode under the action of the electric field, and the temperature of the electron near the anode is relatively high. In Figure 3B, when t = 1.0 × 10 − 6 s , due to the bombardment of positive ions on the cathode, a large number of electrons are generated near the cathode, which increases the temperature of the electrons near the cathode. The electrons reach the anode from the cathode under the bias electric field. In Figure 3C, when  t = 1.0 × 10 − 4 s , the electron’ energy decreases due to collision. Until Figure 3D, when t = 1.0 × 10 − 2 s , there is no change in the electron temperature distribution, and finally the discharge reaches a stable state.

Figure 4 shows the distribution of electric potential at different time. In Figure 4A, when t = 1.0 × 10 − 8 s , the discharge has just begun, and the electric potential distribution is linear between the two electrodes. In Figures 4B,C, with the increase of secondary electrons emitted by the cathode, the voltage drop gradually approaches the cathode. In Figure 4D, when  t = 1.0 × 10 − 2 s , there is no change in the electric potential distribution and a stable state is reached.

According to the analysis of simulation results, our model is consistent with the glow discharge theory, so the model can be used to simulate a gas glow discharge. In our simulation, we have simulated the glow discharge respectively when the electrode spacing is 3 mm , 4 mm , 5 mm , 6 mm and 7 mm , the discharge voltage is 50 V , 100 V , 150 V , 200 V and 250 V , the initial electron density is 1 × 10 11 m − 3 , 1 × 10 13 m − 3 and 1 × 10 15 m − 3 , respectively. And we found that the neon gas glow discharge is the most stable when the electrode spacing is 6 mm , the discharge voltage is 200 V , and the initial electron density is 1 × 10 13 m − 3 .

Based on the results of part 2, we established the interaction model of neon gas and THz wave as shown in Figure 5. The model is divided into five regions. Region one is the incident region; region 2 is the transmission region with a size of 6 mm × 2 mm ; region 3 is the cathode which is grounded; region four is the anode which is connected to the bias voltage, and the size of regions 3 and four is 0.5 mm × 4 mm ; region 5 is a gas discharge area with a size of 6 mm × 4 mm . THz radiation perpendicularly incident to the discharge area.

We suppose that the electric field is no loss in the incident area. When the THz wave illuminates the discharge area, the part of incident energy is absorbed by the electrons, which will enhance the interaction between the charged particles and the neutral particles in the discharge area. The temperature of the electrons rises to the extent that new electrons can be generated through ionization, and the ionization rate is increased. With the increase of the kinetic energy of electrons, the ionization rate and the number of electrons increases, which increases the frequency of collisions between electrons and neutral particles. The effect of frequency on the interaction between THz wave and plasma was investigated by simulating the electric field distribution of THz wave with different THz frequencies before and after passing through the neon discharge region. The simulated results are shown in Figures 6A,C,E.

Take a horizontal line parallel to the discharge section at y = − 2.5 mm in Figure 5, and then get the distribution of THz electric field along the line after it passing through the discharge region. The distribution curves of electric field intensity are shown in Figures 6B,D,F which illustrates the energy changes of the THz wave after passing through the discharge region.

When the THz wave enters the discharge region, the plasma absorbs the energy of the THz wave to improve its internal energy, collision frequency increases, and a large number of electrons, neon ions and excited neon atoms are constantly produced. After that, high-energy electrons and excited neon atoms are consumed in large quantities, new electrons generated and the electron density in the discharge region increases. The external energy input is difficult to maintain the frequent and violent inelastic collision reaction, and the plasma gradually reaches a new balance. It can be seen from the Figure 6, the peak value of the electric field intensity distribution curve is increasing and different peaks appear. The reason is that the interaction of electrons and neutral particles in the plasma is strengthened, which leads to the decrease of energy absorbed by electrons from THz waves with the increase of frequencies. The transmittance of THz wave increases in the discharge region, and the electric field intensity increases in the transmission region. The absorbed THz waves change the plasma density and the potential between the two electrodes also will changes, the THz intensity can be detected according the potential change.