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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.
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