Plasma can be generated using radio frequency (RF) electromagnetic waves for a large variety of applications, such as energy and propulsion generation. Often, the desire is to achieve higher densities for given input power and helicon sources have demonstrated a high efficiency. The design of the antenna that couples the wave plays a major role in the efficiency of generating the plasma particles. Many geometries were studied and compared, but the relationship between the antenna characteristics and the plasma production is still missing. In this article, we identify the power-law dependence between the plasma density and the Gain of an antenna. The latter is determined using numerical simulations in a vacuum, whereas the former is acquired experimentally. The power-law dependence is obtained using four different antenna elements operating under the same experimental conditions on the Polaris linear plasma device. The design a posteriori of a new inductive antenna with a modified quadrifilar helix topology, exhibits not only a higher gain but also confirms the power law. The confirmation of this law will significantly impact the future of many technologies that leverage helicon plasmas.Index Terms-Antenna design, antenna gain, helicon plasma, magnetized plasma devices, radio frequency (RF) antenna. I. INTRODUCTIONP LASMA generation in laboratories has a wide range of applications in a variety of fields like in nuclear fusion [1], space thrusters [2], and plasma processing [3]. A large number of studies are thus dedicated to the production of hot and dense plasma using electromagnetic waves. In 1997, a first review, done by Chen and Boswell [4] presented an account of the understanding of helicon waves and the experimental results. Later in 2015, Chen [5] gave another comprehensive summary of the physics of helicon discharges. In 2018, Shinohara [6] wrote an overview of the experimental results related to radio frequency (RF) sources and their applications.The first helicon plasma source was achieved in an experiment conducted by Lehane and Thoneman [7]. Later on,

No abstract