Abstract
The helical resonator is a scheme for the production of high voltage at radio frequency, useful for gas breakdown and plasma sustainment, which, through a proper design, enables avoiding the use of a matching network. In this work, we consider the treatment of the helical resonator, including a grounded shield, as a transmission line with a shorted end and an open one, the latter possibly connected to a capacitive load. The input voltage is applied to a tap point located near the shorted end. After deriving an expression for the velocity factor of the perturbations propagating along the line, and in the special case of the shield at infinity also of the characteristic impedance, we calculate the input impedance and the voltage amplification factor of the resonator as a function of the wave number. Focusing on the resonance condition, which maximizes the voltage amplification, we then discuss the effect of the tap point position, dissipation and the optional capacitive load, in terms of resonator performance and matching to the power supply.
Highlights
Resonator: A Scheme for RadioThe generation in the laboratory of an ionized gas, called plasma, requires, in most instances, application to the originally neutral gas of an electric field that is large enough to start an avalanche process of ionization events driven by free electrons
In order to properly model the helical resonator, we first need to understand how electromagnetic disturbances propagate in it, deriving a dispersion relation that is useful for obtaining the basic properties, such as phase velocity and, in a limit case, the characteristic impedance of the resonator seen as a transmission line
The voltage amplification factor at resonance was measured by sending radio frequency (RF) power to the resonator and measuring the input voltage with a 10:1 oscilloscope probe and the output voltage with a 1000:1 Tektronix P6015a high voltage (HV) probe
Summary
The generation in the laboratory of an ionized gas, called plasma, requires, in most instances, application to the originally neutral gas of an electric field that is large enough to start an avalanche process of ionization events driven by free electrons ( called breakdown). The paper is organized as follows: in Section 2, we introduce the geometry of the device we wish to describe, and the different flavors that it can take; in Section 3, we describe the propagation of electromagnetic perturbations in the resonator, deriving the main characteristics of the device, which are characteristic impedance and the velocity factor, as a function of its geometry
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