**4. Equivalent circuit model**

In this part, an equivalent circuit model is used to analyze the dependence of the thin copper wire annealing temperature on the dielectric in APDBD. From analysis model, the main factor that determines annealing temperature is the ion bombardment on the wire surface. The average temperature of the thin copper wire in APDBD reactor is calculated as a function of dielectric diameter, dielectric material, applied voltage, ion mass, and gas thermal conductivity. The effect of dielectric on annealing from analysis model is used to compare with that from experiment.

Effect of Dielectric in a Plasma Annealing System at Atmospheric Pressure 193

x 10-5

Voltage Current

**Figure 15.** Voltage and discharge current waveform of argon at 8.5 kV

Combination between the discharge characteristics of plasma annealing and the reflected physical structure of the plasma reactor, the equivalent circuit model is formed as a RLC circuit in which the total impedance is the combination between series and parallel circuit model. The corresponding main physical part of discharge mechanism shows that plasma reactor can be divided into three parts: (1) dielectric wall, (2) dynamic sheathes and (3) plasma bulk as shown in Figure 16(a). The impedances of dielectric, ionization (Zp), and non ionization gas capacitance Cg are shown in Figure 16(b). The equivalent circuit model with impedances of dielectric, sheath and plasma bulk is shown in Figure 16(c). In that the impedance of the dielectric is the parallel combination of dielectric capacitance and dielectric heating resistance [32], the impedance of the sheath is the parallel combination of sheath capacitance and ion heating resistance which is presented by ion current in sheath, and the impedance of the plasma is the parallel combination of the Rp (only the ohm heating by streamer is considered) with the cylindrical space capacitance Cp [33]. The diodes, Da and Db, are used to specify the sign of the input voltage. The gas capacitance of the reactor before

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (s) Argon discharge gas

**4.2. Equivalent circuit model** 






0

Input voltage (V) and discharge current I.10 4 (A)

0.2

0.4

0.6

0.8

1 x 104

discharging is also connected to the parallel Cg.
