# Probing Collisional Plasmas with MCRS: Opportunities and Challenges
## 1 Introduction  
Since the introduction of Microwave Cavity Resonance Spectroscopy (MCRS) as a plasma diagnostic in the 1940s [1], the technique has been solidified by a series of publications [2; 3; 4; 5]. Over the last eight decades, the measurement approach has been used to study various types of low-pressure plasmas: pristine radio-frequency (RF) driven low-pressure plasmas [6; 7], powder-forming plasmas [8; 9; 10], etching plasmas [11], ultracold plasmas [12], and extreme ultraviolet photon-induced plasmas [13; 14; 15]. The measurement approach has also been used to determine properties of materials, i.e., dielectric constants [16] and molar polarizations [17]. A giant leap in this development of the diagnostic tool was the introduction of the multi-mode approach, which enabled resolving spatial distributions of the electron density in low-pressure plasmas [14]. In the exemplary applications of MCRS as plasma diagnostic mentioned above, the change in the spectral position of a resonance peak of an electromagnetic standing wave in a plasma-filled cavity was used to determine the changes in permittivity that subsequently were related to the electron density \(n_{\mathrm{e}}\) of the cavity's content. Only recently has it been demonstrated that MCRS can be used to study the electron dynamics between successive discharges in an atmospheric-pressure pulsed plasma jet in N\({}_{2}\) feed gas [18]. In such atmospheric-pressure discharges, the contributions of the electron density \(n_{\mathrm{e}}\) and the electron momentum transfer collision frequency \(\
u_{\mathrm{m}}\) to the alterations in the complex permittivity \(\bar{\epsilon}\) need to beseparated. The changes in the position as well as the width of a resonance peak were used to separate and determine the individual contributions. This 'atmospheric-pressure' avenue was continued by exploring the full temporal evolution of electron dynamics in the spatial afterglow of an RF-driven atmospheric-pressure plasma jet [19]. In both investigations of these atmospheric-pressure discharges, the changes in resonant behavior were relatively small and for this reason, the resolution in permittivity had to be improved significantly over the last few years. As the resolution of MCRS improved, more phenomena could be probed with the method. This is because the presence of free electrons is only one of the factors affecting the resonant behavior. The importance of separating the different contributors to changes in the resonant behavior during plasma experiments was demonstrated in the study of an RF plasma jet [20]. In that work, the contributions of the plasma dynamics, the acoustic waves, and most likely the gas composition were separated. In contrast to most MCRS studies of low-pressure plasmas, the investigated atmospheric-pressure plasmas did not occupy the whole cavity volume. The electric field profile of the resonant mode and the volume occupied by the plasma were determined in order to correct for the partially-filled cavity. This procedure currently limits the determination of the effective plasma volume, which is the plasma volume weighted by the electric-field-squared, and subsequently the obtained electron density, to its order of magnitude [18]. With the transition towards probing atmospheric-pressure plasmas, the perspective on the limitations of the diagnostic method has changed and the description of the limitations needs to be adapted. The first meticulous theoretical investigation of the validity of the MCRS diagnostic method has been performed by [PERSON] [21]. Unfortunately, the limitations were not presented in an accessible way which reduced the impact of the work. [PERSON] et al. [22] have focused on the perturbation of the resonant field by the plasma and derived an analytical expression for the resonance frequency of a partially-filled cavity. The practical limit \(\omega_{\rm pe}\ll\omega\) is most often used to indicate the maximum measurable electron density [23; 24; 25; 26].