Atmospheric pressure non-equilibrium plasma (APNP) has received increasing attention largely because of its low cost and simplified operation in comparison with low pressure discharge.^[1] It has application prospects in a variety of fields, such as surface modification, ozone generation, biological sterilization and pollution control.^[2–5] Streamer discharge is usually involved in APNP,^[6] which is almost intrinsically inhomogeneous. As far as some special applications such as surface modification are concerned, it is more important to generate atmospheric pressure uniform discharge (APUD). According to the discharge mechanism, APUD can be categorized into atmospheric pressure glow discharge (APGD) and atmospheric pressure Townsend discharge (APTD).

Dielectric barrier discharge (DBD) is a traditional way of initiating APUD.^[7,8] The DBD in helium has been originally reported by Kanazawa et al.^[9] Since then, many investigations have been carried out in different kinds of working gases.^[10–14] The evolution from APTD to APGD has been found experimentally within a discharge pulse by Lee et al.^[10] According to a one-dimensional fluid model, Zhang and Kortshagen have found that it is APTD at a lower frequency but APGD at a higher frequency in a mixture of helium and oxygen.^[11] The mode transition from APTD to APGD has also been numerically investigated by varying the external driving frequency in helium mixed with nitrogen.^[12] Through numerical simulation, Wang et al. pointed out that APTD and APGD can be respectively obtained in atmospheric helium DBD under different frequencies.^[13,14]

Compared with DBD, direct current (DC) discharge is one of the easy methods of generating APUD.^[15] It has been realized in helium, argon, hydrogen, nitrogen, and air, moreover, and the discharge characteristics have been analyzed by the visualization of the discharges and the voltage–current curve.^[16] A self-sustained glow discharge in atmospheric-pressure helium has been investigated experimentally.^[17] Leys et al. have found that the DC discharge can also operate in APGD mode, which has similar characteristic regions to the low pressure glow discharge.^[18,19] Deng et al. have pointed out that the DC discharge can be sustained in two different regimes: a self-pulsing regime at low current and a continuous glow regime at high current.^[20] The transition from APTD to APGD has been investigated through two-dimensional numerical simulation on the DC discharge with moderate pd value, where p is gas pressure and d is the electrode spacing.^[21] Recently, the APUD generated by a DC discharge with a semiconductor layer has been investigated numerically.^[22]

Although APUDs have been investigated experimentally and numerically, it is still necessary to gain an in-depth insight into the influences of experimental parameters on the discharge mode in a steady state. Therefore, in this paper the APUD generated by the DC discharge is investigated in detail through one-dimensional fluid simulation.

The discharge initiates between two parallel–plate electrodes^[23,24] as shown in Fig. 1. A DC voltage is applied across the two electrodes and a ballast resistor R is used to restrict the discharge current in order to obtain an APUD. The gas gap width (d_g) is filled with pure helium under atmospheric pressure.

Fig. 1.

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	Fig. 1. Schematic diagram of the DC discharge.

Numerical simulation is based on a one-dimensional fluid model. Electrons and ions are described by the continuity equations:

A set of equations listed above is solved by the Scharfetter–Gummel scheme.^[29] The simulation parameters are chosen as follows. The gas temperature is set to be 300 K in atmospheric pressure helium. Initial densities of electrons and ions in the gas gap are considered to be uniform with n_e (x,0) = n_p (x,0) = 10⁷ cm⁻³.

In the simulation, the electron–ion recombination rate coefficient β and the electron diffusion coefficients D_e are needed. They are calculated from the formula

Fig. 2.

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	Fig. 2. Temporal evolutions of the current density at different electron temperatures (a), and under different gap widths (b). Other parameters: U = 3 kV and R = 100 kΩ.

Figure 3 presents the spatial distributions of electron density, ion density and the electric field at the moments of 0.3 μs, 0.9 μs, 3 μs, and 20 μs, respectively. The electric field is almost uniformly distributed along the gap and the density maxima for electron and ion appear near the anode at the beginning of the discharge as shown in Fig. 3(a). In the Townsend regime, the electron avalanches develop from the cathode to the anode and the densities for electron and ion increase in the process. Hence, the maxima of both electron density and ion density appear near the anode. Therefore, it can be concluded that the discharge belongs to APTD at the beginning. Comparing Fig. 3(a) with Fig. 3(b), it can be found that the maxima of electron density and ion density shift toward the cathode with time elapsing. At the moment of 3 μs, a cathode fall region can be discerned in Fig. 3(c). In the cathode fall region, it is clear that the electric field near the cathode increases almost linearly along the x axis, which is very similar to that observed in a low-pressure glow discharge.^[30] This result also accords with the field profile measured spectroscopically for a helium DC atmospheric pressure glow discharge.^[17] Therefore, the existence of the cathode fall region verifies that the discharge operates in a glow discharge mode. Figure 3(d) shows the spatial distributions of electron density, ion density and the electric field corresponding to the steady discharge state. Obviously, there is an anode region near the anode, which is followed by a positive column, and a cathode fall region near the cathode. In the positive column, the electric field is lower than that in the anode region or the cathode fall region. Therefore, it can be concluded that the discharge has a transition from the APTD to APGD in the discharge process.

Fig. 3.

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	Fig. 3. Spatial distributions of the electron density, the ion density, and the electric field at different times: (a) 0.3 μs, (b) 0.9 μs, (c) 3.0 μs, and (d) 20.0 μs. Other parameters: dg = 4 mm, U = 3 kV, and R = 100 kΩ.

In order to have a better understanding about the DC discharge mode, the discharge voltage–current (V–I) curves in a steady state are investigated for different parameters. Figure 4 presents the V–I curves for the DC discharge under different gap widths. With increasing i_T, gas voltage increases monotonically for a wider gap, such as d_g = 10 mm and d_g = 4 mm, and it decreases monotonically for a narrower gap (d_g = 2 mm). The positive slope of the V–I curve is an indication that the discharge operates in the abnormal glow mode. At the same time, the negative slope indicates that the discharge is in the normal glow mode. It has been originally found in the glow discharge at low pressure.^[16] Recently, it has also been verified in an atmospheric pressure glow discharge.^[22] Therefore, it can be concluded that the discharge operates in the abnormal glow mode for a wider gap and the normal glow mode for a narrower gap. As is well known, an electron avalanche quickly builds up in the gas gap. Apparently, it tends to grow into a bigger avalanche with a wider gap if other parameters remain constant. The bigger the avalanche, the higher the obtained current density will be, which means that the discharge tends to operate in the abnormal glow mode. Therefore, the discharges operate in the normal glow mode for the narrower gap and the abnormal glow mode for the wider gap, respectively.

Fig. 4.

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	Fig. 4. Voltage–current curves for the atmospheric pressure discharge under different gap widths. The ballast resistor is 100 kΩ.

Figure 5 shows the V–I curves with different ballast resistors for d_g = 4 mm. It can be found that with increasing i_T, the V increases monotonically for a small resistor (R = 100 kΩ), decreases monotonically for a large resistor (R = 300 kΩ) and maintains almost a constant at lower current density and then decreases monotonically for R = 200 kΩ. It can be concluded that the discharges operate in the abnormal glow mode for a smaller resistor and in the normal glow mode for a larger resistor, respectively. As mentioned above, the resistor is used to restrict the increase of the discharge current. Therefore, the discharge current will be maintained at a lower value for a larger resistor, which means that the discharge tends to stay in a normal glow mode for a larger resistor. Consequently, the discharges operate in the abnormal glow mode for a smaller resistor and in the normal glow mode for a larger resistor, respectively.

Fig. 5.

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	Fig. 5. Voltage–current curves with different ballast resistors. The gap width is 4.0 mm for the atmospheric pressure helium.

Figure 6 displays the V–I curves with different secondary electron emission coefficients for d_g = 4 mm and R = 100 kΩ. Apparently, with increasing i_T, the gas voltage increases monotonically for different values of secondary electron emission coefficient. It can also be seen that the lower secondary electron emission coefficient corresponds to the larger voltage for the same current density. The positive slope of the V–I curve is an indication that the discharge operates in the abnormal glow mode, which means that a small variance of the secondary electron emission coefficient does not affect the discharge mode.

Fig. 6.

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	Fig. 6. Voltage–current curves with different coefficients for the secondary electron emission. Other parameters: dg = 4 mm and R = 100 kΩ.

Based on a one-dimensional fluid model, the characteristics of DC discharge in atmospheric pressure helium are investigated. Results indicate that the discharge does not reach its steady state till it takes a period of time. Moreover, the required time increases and the current density of the steady state decreases with increasing the gap width. Through analyzing the spatial distributions of the electron density, the ion density and the electric field at different discharge moments, it is found that the DC discharge starts with the Townsend regime, then transits to the glow regime. In addition, the discharge operates in a normal glow mode or an abnormal glow one under different parameters, such as the gap width, the ballast resistors, and the secondary electron emission coefficients, judged by its voltage–current characteristics. The discharge operates in a normal glow mode, a narrower gas gap and larger ballast resistor. For a wider gap or smaller resistor, the discharge operates in an abnormal glow mode. It is also found that the discharge always operates in an abnormal glow mode with a small variance of the secondary electron emission coefficient.