56 and 150 MHz and with different power application positions. A two-dimensional (1 m × 0.2 m) plane electrode was modeled, and the impedances of the atmospheric-pressure plasma obtained from IV (current and voltage) measurements and analysis  were used for the calculation. Methods Modeling A one-dimensional model of electrodes and plasma (including
sheath) is shown in Figure 1. Radio-frequency voltage is applied to the upper electrode, and the lower electrode is grounded. We assume that only the upper electrode has resistance and inductance for simplicity. This simplified model is useful enough to calculate a relative voltage between two electrodes, because only relative voltage is important for plasma. Figure 1 One-dimensional model of electrodes Liproxstatin-1 ic50 and plasma (including sheath). Plasma will be generated in the space between the upper and lower electrodes. In this model, electrodes (upper and lower) and plasma are divided into small elements of length ΔX. The voltage U is assumed to be constant within the elements. Symbol δ is the thickness of current flow (skin depth). The currents flowing into and out from the element Selleck PF-573228 are shown by the arrows in Figure 1. The plasma is assumed to be able to be represented by the parallel connection of the capacitance C p and the conductance G p. One can derive a one-dimensional
wave equation from the above mentioned one-dimensional model and extend it to the following two-dimensional wave equation. In the case of a two-dimensional model, the electrode will be divided in two directions, and the widths of the element will be ΔX and ΔY. For MK-0457 mw simplicity, the element widths ΔX and ΔY were set to be equal. (1) Here, L and R are inductance and resistance per unit length (in current flow direction) of the electrodes of element width (ΔX or ΔY), and C p and G p are www.selleck.co.jp/products/MDV3100.html the capacitance and conductance of plasma per unit length of element width, respectively. F(x,y,t) is the external force (causes voltage to change) applied to the upper electrode
at position (x,y). Electrode resistance R and inductance L When radio-frequency power is applied to the electrodes, the current will flow only on the surface of the electrodes owing to the skin effect. The effective electrode resistance per unit length R (of width w) is determined by the following equation : (2) where σ is the conductivity of the electrode material, δ is the skin depth, and w is the width of the current flow. The skin depth δ is determined by (3) where ω is the angular frequency, and μ is the magnetic permeability of the electrode material. The inductance of a pair of two parallel plates (electrodes) per unit length (of width w) can be calculated using  (4) where d is the distance between the upper and lower electrodes, and w is the width of the current flow. When aluminum is used as the electrode material, the conductivity σ is 0.