Results and Discussion

3.3.1 Conduction, Displacement and Total Currents

The total current versus with time is shown in Figure 6, and the total current from simulation is match able with experiment data qualitatively and quantitatively.

The figure shows that the total current increases as the increasing voltage and decreases as decreasing voltage.

The total current is the sum of displacement current and conduction current of charged species.

∑

^{± Γ + +}

+

= displacement e,N2,N4

total

J e

J

Therefore, the total can be separate into conduction currents and displacement current shown from Figure 8 a to Figure 8 h. The sketches observe that the variance of displacement and conduction currents during one cycle. In Figure 8 a, the applied voltage approaches to zero at initial, and the total current equals to the displacement current. As the voltage increasing at left electrode, the electron moves toward the left dielectric barrier since the high potential, so the positive conduction current of electron is generated.

On the other hand, the positive conduction currents of ions are produced due to the ions move toward right dielectric at low potential. In Figure 8 b, the maximum value of electron conduction current are higher than ion conduction current, because of the electron is easy to move during electric field since the mass of electron is lighter than ions, N2+ and N4+.

After most electron hits the left dielectric barrier, the positive ions are moving toward the right dielectric barrier as shown in Figure 8 c. And then, the conduction currents approach to zero since the shielding by the accumulated surface charge.

From

Figure 8 a to Figure 8 h, it also verifies that the gradient of total current

equals to zero at all time,

=0

⋅

∇

J

_total

3.3.2 Power Absorptions and Light Emissions

The plasma frequency [M. A. Lieberman and A. J. Lichtenberg, 2005] of charged species i is

i i

i ne m

w = ²/ε₀ Assume

n

_e ≈10¹⁶ , 10¹⁷

2 ≈

N+

n

and 5 10¹⁶

4+ ≈ ×

n

N which are taken from simulated results, so the plasma frequencies can be estimated as 5.6 GHz, 78.8 MHz and 39.4 MHz for electron, N2+ and N4+. Since the frequency of applied voltage is 60

kHz, we expect that the both electron and ions can correspond to the driving

frequency and also absorb energy from the electric field.

The absorbed power of charged species versus with time in one cycle is shows in

Figure 9, and it shows that charged species get energy efficiently while in the stronger

electric field caused by raising and falling of the applied voltage. During the time of applied voltage varies quickly, starts from 0.5 s

μ

to 2.5 s

μ

and 8.5 s

μ

to 11 s

μ

, the N2+ absorb the most energy since the largest number density, and the other energy are absorbed by electron since the electron can respond the electric field quickly.

We take the average over one cycle to calculate the time averaged absorption power of each species listed in Table 3, the power absorbed by electron is 63.5 (J/s), the power absorbed by N2+ is 267.2 (J/s), and the power absorbed by N4+ is 2.8 (J/s).

We take time average to the absorbed power of displacement current

( ^J

dis⋅

^E )

during one cycle, the answer is zero. It reveals that the energy which absorbed by dielectric barrier will be released during the cycle, and there is no net energy absorbed by dielectric barrier. Therefore, the total absorption power is the sum of each species, 333.6(J/s). The result shows that most energy (about 81%) is absorbed by ions and the electron absorbs the other (about 19%).

In Figure 10, the power of the emitted light is shown, and the emitted light of wavelength 336.5 nm has higher intensity than others’ wavelength. The time averaged powers of light emissions are listed in Table 4, and the sum of all powers is less than 0.3%. That means that only a very small percentage of absorbed power is used for the light emissions.

3.3.3 Potential, Electron Temperature and Accumulated Charge

The voltages between the dielectric barriers and the discharge gap versus with time are shown in Figure 7. At initial, the electron moves toward the left dielectric which carried positive charge as increasing voltage, so the negative charged is accumulated on left barrier. Although the accumulated charge approach to stable at about 2 s

μ

, there still has large potential gradient in the gap. Because of there is no quasi-neutral region in discharge, and the potential is not shielded by the accumulated

charge at dielectric barrier. And the gap voltage approaches to zero at about 3.5 s

μ

while the amplitude of applied voltage becomes small.

According to the boundary condition at left dielectric surface,

d s

d

x

x ε φ σ

ε φ

=−

∂

− ∂

∂

∂

0

, the distribution of potential is effected by the accumulated charge, and Figure 7 reveal that the maximum value of accumulated charge is about 1 C/cm². The phase diagrams of potential and electron temperature are shown in Figure 11 and Figure 12.

Since the electron gets energy from the gradient of potential, the two figures show that the electron temperature is increased form 1~2 eV to 4~5 eV during the increasing and decreasing applied voltage. Therefore, the excited species and ions can be produced efficiently while the electron temperature approaches to 5 eV.

3.3.4 Charged Species

The number density of electron increases from 10¹³ (1/m³) to 10¹⁶ (1/m³) during the raising voltage, which shown in Figure 13, because the ionized process has large reaction rate coefficient at high electron temperature,

+ +

→

+

N

₂ 2

e N

₂

e

The phase diagrams of ions species N2+ and N4+ are shown in Figure 14 and

Figure 15, and it show that the increasing of N

2+ number density is depended on the

electron temperature because of the direct ionized process of nitrogen is sensitively to electron temperature. Since the associative ionized processes,

+ +

− + Σ → +

Σ ₂ ³ ₄

1

2(

a

' )

N

(

A

)

e N

N

_{u u}

+

−

− + Σ → +

Σ ₂ ¹ ₄

1

2(

a

' )

N

(

a

' )

e N

N

_{u u}

This is revealed on the phase diagrams of N2(A³) and N2(a’¹) number density,

Figure 16 and Figure 17, and the figures show that the N

4+ increases when the decreasing number density of N2(A³) and N2(a’¹).

The N4+ ion can be generated from N2(A³) and N2(a’¹), so the N4+ can still be produced efficiently during low electron temperature. Therefore, the number density of N2+ is higher than N4+ during the pulse of voltage, and N4+ becomes dominated when the voltage is slightly changing.

From the electron generated or destroyed from each reaction channels, the

Figure 20 shows that the dominant process to generate electron at high electron

temperature (above 3 eV) is direct ionization, + +

→

+

N

₂ 2

e N

₂

e

.

At low electron temperature (below 2 eV), during the cycle, the most electron is produced by,

+ +

− + Σ → +

Σ ₂ ³ ₄

1

2(

a

' )

N

(

A

)

e N

N

_{u u}

The profiles of charged species versus with position are shown in Figure 21 at 5

different time points, from Figure 21 a to Figure 21 e. The number density of electron is less than the positive ions, so there is no quasi neutral region, which is called Townsend-like discharge.

3.3.5 Neutral Species

The phase diagrams of neutral species are shown from Figure 16 to Figure 19, and the number densities of excited species, N2(A³), N2(a’¹), N2(C³) and N2(C³) which sort by the value of number density, are about 10²⁰, 10¹⁸, 10¹⁷ and 10¹⁶. According to simulation, the order does not change during all temporal and spatial space.

As previous discussion, the dominant reaction channels to generate electron at low electron temperature is,

+ +

− + Σ → +

Σ ₂ ³ ₄

1

2(

a

' )

N

(

A

)

e N

N

_{u u}

Since the number densities of N2(A³) and N2(a’¹) are changing slightly during one cycle as shown from Figure 21 a to Figure 21 e, so the N4+ is produced stably through associative ionization.

3.3.6 Influence of Different Dielectric Permittivity

The simulated condition is the same as previous simulation except the different dielectric permittivity. The total current versus with time at different dielectric

permittivity, which is changed from 9 to 12, is shown in Figure 22, and it shows that the total current increases as the dielectric permittivity increasing. Since the total current is the sum of conduction currents and displacement current, the total current is increased due to the increasing conduction current during the time 0.5 s

μ

to 2.5 s

μ

and 8.5 s

μ

to 11 s

μ

. At the other time, the displacement current is the dominant component of total current.

The boundary condition at left dielectric surface is,

d s

d

x

x ε φ σ

ε φ

=−

∂

− ∂

∂

∂

0

, the profile of dielectric permittivity

ε

_d and accumulated charge

σ

_s is shown in

Figure 23. From the figure, it reveal that the accumulated surface charge decreasing

while the decreasing the dielectric permittivity.

3.3.7 Influence of Different Gap Size

The simulated condition is the same as previous simulation, dielectric thickness 1mm with permittivity 11.63 and 60 kHz applied voltage, except that the gap size is changed. The 200 uniform grids are used for discharge gap. The total currents versus with time at different gap size, 0.5 mm, 1 mm and 2 mm, are shown Figure 24.

Compare the total current at different gap size, 0.5 mm and 1 mm, it shows that total current at gap size 0.5 mm is phase lead to the current at the gap size 1 mm. The

thin gap size has larger electric field than the other while applied the same waveform of voltage. While the gap size increases to 2 mm, the plasma is not maintained at this gap size, so there is no conduction current and all the total current is due to displacement current.

The accumulated charge on left dielectric surface with different gap sizes is shown in Figure 25. The surface charge accumulated at 0.5 mm is phase lead to 1 mm since the electron is generated earlier than the 1 mm gap, and the more electron and ions attach to the dielectric barrier at gap size 0.5 mm. The plasma does not maintain at 2 mm, and it is also revealed from the surface accumulated charge in Figure 25, there is almost no charge accumulated on the dielectric surface.

在文檔中 氮氣介電質放電的一維數值模擬 (頁 40-49)