An Eigenvalue Approach to Study SPIDER RF Oscillator Operating Space

The SPIDER experiment features four radiofrequency (RF) circuits to heat the plasmagenerated in its inductively coupled ion source. Each circuit includes a tetrode-basedColpitts push-pull oscillator (200kW rated power) operating at 1 MHz frequency, acoaxial transmission line to feed the load composed of a couple of RF antennas anda resonant matching network. The SPIDER operation has shown two phenomena thataffect the performance of the RF circuit: the so-called "frequency flip" that preventsthe operation at the best load impedance matching condition and a limitation on themaximum RF power delivered by the RF generators.Theoretical models of the SPIDER RF circuits have been developed able to predictthe frequency flip occurrence, that has been also experimentally observed. By usingthe validated models, an operational setup to avoid the frequency flip occurrencehas also been synthesized and successfully implemented. However, limitation in themaximum delivered RF power are still present, thus the RF circuit modelling approachhas been further developed exploiting the state space analysis to achieve a deepercomprehension of its operation.The results of the eigenvalue analysis of the circuit gives as outputs both the operatingfrequency of the system and equivalent load seen by the oscillator at that frequency.The equivalent load is used as input for an steady state electrical model of the pushpull connection of the tetrodes, which exploits the algebraic model of the tetrode andpermits the identification of the RF power delivered by the oscillator as a function ofthe tetrodes polarization voltages.A validation of the models developed is presented on the base of the SPIDERexperiments.