# Anomalous Beam Transport through Gabor (Plasma) Lens Prototype
## 3 Plasma Characterisation  
The operation of the lens was tested over the range of available anode voltages and coil currents to identify the regime for which a stable plasma could be produced. Measurements of the plasma in the lens were made using the Medusa voltage sensor shown in Figure 2. The sensor detects the current of ions and electrons discharged by the lens and was composed of 16 equal segments with a total area of 122.5 mm\({}^{2}\). The detector segments were connected either in concentric circles or in a sector arrangement, with four segments combined and fed into one channel of an oscilloscope. The Medusa detector was used to characterise the range of high voltage and current settings which would produce a stable plasma within the lens. A schematic diagram of the experimental setup for these primary studies is given in Figure 3. For a constant current through the coils of the lens, producing a constant magnetic field, the high voltage was increased from zero until plasma was produced in the lens. The presence of a stable plasma in the lens was indicated by a steady voltage read from the Medusa detector. The high voltage was then increased further, until instability in the plasma, characterised by sparking, was observed as an extreme variation in the output voltage reading.  
Figure 4 shows the amplitude responses observed in the Medusa detector that are typical of three modes of operation:  
* Plasma off: high voltage and current through coils. below the threshold for plasma to be produced;
* Stable plasma: plasma produced with high voltage below 25 kV and current below 27 A; and
* Unstable plasma: plasma produced with higher magnetic field causing considerable sparking and therefore large variations in the output amplitude.  
Figure 2: The segmented detector used for measuring the current of electrons and ions exiting the Gabor Lens. The detector is divided in to 16 sections of equal area which were combined in sector (middle) or concentric circle (right) arrangements.  
The mean and standard deviation of the Medusa voltage measurement of the different plasma regions are shown in Table 1. The mean increases slightly when the plasma is switched on, while the standard deviation remains largely unchanged. As the current applied through the coils becomes large, and the unstable region is reached, the mean and standard deviation rose and a large amount of noise was observed. This is shown in Figure 4, where the level of noise is similar with the plasma off and the plasma on. The noise increases appreciably only when the unstable region is reached. The frequency spectrum of the voltage signal was studied in each of the three modes of operation. In the unstable region, the low-frequency noise is increased significantly while the high-frequency noise remains largely unchanged. The characterisation of the operating regimes described in this section was used to verify that the lens produced a stable plasma during the beam test.  
\begin{table}
\begin{tabular}{l l l} \hline  & **Mean (V)** & **Standard Deviation (V)** \\ \hline
**Plasma Off** & 0.008 & 0.019 \\
**Plasma On** & 0.114 & 0.020 \\
**Plasma Unstable** & 0.797 & 0.133 \\ \hline \end{tabular}
\end{table}
Table 1: Mean and Standard Deviation values for Plasma Off, On, and Unstable regions shown in Figure 4.  
Figure 4: Amplitude of signal from the Medusa detector in three regions: plasma off, plasma on, and plasma on in unstable region. The time range is given 0.0004 s, and the time resolution of the measurement is \(4\times 10^{-7}\) s. The voltage range is 0.5 V with a resolution of 0.01 V.  
Figure 3: Schematic of the Gabor lens, current detector, and oscilloscope. The high voltage supply maintains the drop across the electrodes. expelled ions hit the detector, and the current signal is converted to a voltage output signal in the oscilloscope.