Cylindrical rf network antennas for coupled plasma sources Copper legs delayed in time system stability analysis
Keywords:Cylindrical RF network antenna, Delay Differential Equations (DDE), Stability, Bifurcation, Orbit
— In this article, Very Crucial subject discussed cylindrical (closed) RF network antennas for coupled plasma sources copper legs delayed in time system stability analysis. Resonant RF network antennas are important to plasma sources with many applications. The cylindrical resonant RF network antennas run as large volume plasma sources and have stability switching due to system's copper legs parasitic effects. The cylindrical RF network antenna structure is 16-leg cylindrical (Birdcage) RF antenna which has electrical circuit and opposite points of RF feeding and grounding. The vacuum vessel is a glass cylinder closed at the top and bottom by grounding metal plates. Generally there are two popular different resonant RF network assemblies: a cylindrical and a planar RF antenna. The cylindrical RF antenna is built as a high-pass Birdcage coil. The antenna is mounted outside a glass tube. The RF antenna consists of 16 copper legs equally spaced interconnected with capacitors. Due to RF antenna copper leg parasitic effect we get copper leg's current and current derivative with delay τ1-k and τ2-k (k is leg number index, k=1,…,16). The uncooled antenna is fed at the midpoint and operated with opposite grounded. Alternatively, it can be fed by another transmitter unit. Due to cylindrical antenna parasitic delayed in time, there is a stability issue by analyzing its operation. We consider for simplicity that all copper leg's current parasitic time delayed are equal (τ1-1= τ1-2=… =τ1-16) and current derivative parasitic time delayed are equal (τ2-1= τ2-2=… =τ2-16). The cylindrical RF network antennas delayed in time equivalent circuit can represent as a delayed differential equations which depend on variable parameters and delays. The investigation of our cylindrical network antenna with copper leg system, a differential equation is based on bifurcation theory , a study of possible changes in the structure of the orbits of a delayed differential equation depending on variable parameters. Cylindrical RF network antenna analysis is done under two series of different time delays respect to antenna's copper legs current and current derivative. All of that for optimization of a cylindrical RF network antenna circuit parameter analysis to get the best performance. The cylindrical network antenna with copper leg system can be represented as delayed differential equations which, depending on variable parameters and delays. There is a practical guideline that combines graphical information with analytical work to effectively study the local stability of models involving delay dependent parameters. The stability of a given steady state is determined by the graphs of some function of τi-1, ..,τi-16 (i=1, 2)   .
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