High-Voltage Probe

The high-voltage (HV) probe was mentioned in Section 2.2, where it was used to calibrate the rf power generator. During actual experiments, this probe is used to measure the voltage that occurs across the rf antenna, which can have values as high as 5 kV depending on the rf input power. Additionally, this voltage is oscillating at 13.56 MHz, so the probe needs to be able to follow these oscillations. The probe used is a pre-calibrated Tektronix

B_z B_θ Br z x y r θ

Fig. 3.16: The orientation of the B-dot probe determines which magnetic field signal (blue arrows) the probe can detect, as indicated in the figure. Thus by rotating the red pickup coil correctly, the

Bz, BrandBθ components of any oscillating magnetic field can be measured.

P6015A (with a 1000 : 1 voltage output ratio), which is connected to the HP 54600A digital oscilloscope. A photograph of the HV probe is shown in Fig. 3.17 (a). The probe consists of a handle with a shield guard, and an insulated probe tip, to which a number of standard end connectors can be attached. In the present case, a crocodile clip is used. This tip is the high voltage measuring point of the probe, which is then attached to different points within the match-box/antenna system, as indicated in the schematic in Fig. 3.17 (b). A separate crocodile clip is then used to provide the second measurement point (which must be ground) and is connected to the grounded side of the match-box.

Cload Ctune Lant Rant Rp Oscilloscope RF current probe Antenna A B V_T Iant (b) (a) Ground clip Measurement tip Electronics

Fig. 3.17: (a) Photograph of the HV probe showing the high-voltage measurement tip, grounding clip, and electronics box. (b) Electrical schematic of the rf power supply and matching net- work/antenna system showing the HV probe measurement locations A and B.

§3.2 RF Circuit Diagnostics 83

Measurements from the HV probe are essentially limited by the resolution of the 8- bit oscilloscope, thus giving a maximum resolution of about 0.4% of the full scale range setting (which is also the main source of measurement uncertainty, and corresponds to an absolute uncertainty of about _±30 V when considering the HV probe’s 1000 : 1 scal- ing factor). The main measurement points of interest in the match-box are located at points A and B in Fig. 3.17 (b). This effectively represents the voltage drop across the antenna (including the antenna feedthroughs and connectors), and allows the quality, or

Q factor to be determined. TheQ factor is a measure of the stored-to-dissipated energy within an electrical circuit, and gives an indication of the resistance present. A small Q

factor indicates a large resistance, which is usually undesirable for a circuit. However, for the antenna/plasma system, a low Q factor is advantageous, as it indicates that a large percentage of the input power is being dissipated within the plasma (that is, the power transfer efficiency of the antenna is high. This will be discussed further in Section 3.2.2). The Qfactor is given by

Q= VB

VA

(3.23)

where VA and VB are the voltages measured with the HV probe at locations A and B in Fig. 3.17 (b) respectively. When operating in a wave mode, helicon reactors of the type used here, typically have Q factors between 3₋6 [136, 137]. The voltage measurements can also be used in limited situations to find the effective resistance of the antenna/plasma system, which is needed to calculate the power transfer efficiency (see Section 3.2.2 below). In the circuit schematic in Fig. 3.17 (b), the antenna/plasma is treated as an effective resistance, RT, and an effective inductance, L. The voltage across the antenna, ∆V, can then be written (using standard complex circuit analysis, together with Ohm’s law) as

∆V =VBejδB −VAejδA

ejωt=ZI (3.24)

wherej =√₋1,ωis the signal frequency,tis a time variable,Z is the antenna impedance,

I is the current flowing through the antenna, andδA andδB are quantities accounting for signal phase shifts at locations A and B respectively. The impedance of the antenna is

Z =RT +jωL, while the current is I = I0ejδejωt, with δ the phase shift in the current.

The resistance of the antenna/plasma is typically very small, of the order of 1 Ω, so that most of the voltage is dropped across the inductance. Thus ignoring this resistance, using the above quantities in Eqn. 3.24, and rearranging, the magnitude of the current is

I0 = |

VB−VAejθ|

ωL (3.25)

where θ is the relative phase shift in the voltage measured between points A and B with the HV probe. Equation 3.25 requires knowledge of the effective inductance, which due

to the presence of the plasma, is in general not equal to the antenna inductance. Never- theless, with a reasonable approximation for this inductance, the current in the antenna can be determined. This then allows the effective antenna resistance to be found, which is discussed in the next section.