# Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification
## 1 Introduction  
Helical antennas, also known as helical resonators, are gaining increased interest nowadays. Newer semiconductor manufacturing processes allow using such designs in closed-loop modes by measuring the number of generated X-rays using CdS/CdTe sensors [1]. Such configurations could have various medical or military applications, where X-ray or ozone generators are required.  
The development of the compact electric field and X-ray generators has become a significant challenge regarding the overall system efficiency and spatial constraints. The implemented system focuses on a hardware solution; the helical resonator acts as a quarter-wave oscillator which makes possible the achievement of high voltages by operating the resonator close to its resonant frequency. It also obtains a standing wave inside the conductor, composed of two components--the incident wave and the reflected wave.  
Beyond alternative methods, such as using an approximate equation form of one of [PERSON]'s laws, similar designs were used in satellite communications [2; 3]. Such approximation leads to a high tolerance in mathematical calculations; the approach presented in this study considers obtaining standing waves inside the helical resonator winding wire. In contrast, using [PERSON]'s equations, the propagation medium with standing waveforms is the waveguide formed by the helical-coil winding air core, with the plasma at the top load providing the required reflection factor. Moreover, having such a low operating voltage makes it possible to power such resonators using only renewable energy, such as solar panels or geothermal probes.  
The main phenomenon used in finding the natural frequency through mathematics is the standing wave. It operates similarly to constraints that appear in SMD circuit designs at very high frequencies--experimentally, reflections are more pronounced along the transmission line as the frequency or line length increases.  
The helical resonator presented here is formerly known as the Tesla coil. By operating the secondary coil close to its natural frequency, the signal propagating towards the top load becomes trapped due to reflection coefficients. During this operation regime, a transition from the inductor to resonator occurs by overlaying the incident wave with the reflected wave, also known as standing-wave summation. Thus, due to constructive and destructive interference, high impedance points and low impedance points are formed, respectively [4].  
The Tesla coil is a circuit known as one of the easiest ways to achieve high voltage, a design also based on a helical resonator. The output voltage value and power consumption depend on the design structure [5]. Quarter wave oscillators are an extremely flexible technology that can be used for such a purpose [6].  
Intensive electric field generation based on high-voltage, ultrafast switching is an easy way to obtain a broad spectrum of high-power microwave (HPM) impulses with many potential applications, including medical treatment, product processing, ultra-wideband (UWB) radar, and electric device testing under an electromagnetic field. Other high-voltage applications may include inert gas welding, electotherapy, and vacuum leak checking [7; 8; 9; 10; 11].  
While the conventional X-ray generators are using components that are not commonly available, such as turbomolecular pump, X-ray tubes, filament power supply, or constant high-voltage power supplies, the currently implemented helical resonator design will result in a smaller size and possibly higher efficiency as the operating frequency reaches values close to the X-ray domain. Thus, such helical resonators could be used to generate intense electric fields while also generating X-ray radiation. Based on the helical antenna mathematics, multiple quarter-wave oscillators' mathematics were determined, having various operating frequencies and covered in the following sections.