# Description of the Experiment

Fig. 1 - Photo of the experimental setup

Plasmas are inseparable from radio-frequency studies. Effectively the most basic properties of a plasma is derived from its plasma frequency. As such, combining plasma physics studies with electromagnetic (EM) wave propagation is a challenging matter for physics with great advances achieved last century before space conquest due to the necessity of wave reflections on the ionosphere for long range communication. An electromagnetic cavity poses a good opportunity to understand the behavior of EM standing waves and how free charges in a plasma affects its resonant frequency and quality factor, interlinking the properties of matter with wave propagation.

• Control room: Microwave plasma cavity
• Level: ****

# Experimental Apparatus

A microwave cavity refers to a volume enclosed by a conducting surface which can store electromagnetic (EM) energy. It can be thought of as the microwave analog of an LC circuit, albeit with multiple resonance frequencies and much larger quality factors. Three main processes govern the energy losses in a cavity: conduction losses in the cavity walls, conduction loss in the dielectric material filling the cavity, and losses through access ports or holes in the conducting surface. In the first-order approximation, these losses cause the same resonance peak broadening as the resistivity losses in an RLC circuit, causing both a resonance frequency shift and a decrease in the quality factor.

Two types of resonant modes occur in electromagnetic cavities: transverse-electric modes (TE) and transverse-magnetic modes (TM). In the TE (TM) modes, the electric (magnetic) field lines are transverse to the longitudinal direction.

A comprehensive derivation of all the resonant modes of a cavity is available in chapter 6 of the book by David Pozar~\cite{Pozar2011}. In a cylindrical cavity filled by a homogeneous and isotropic medium, the resonant frequencies of the TM modes are:

$$f_{nml}=\frac{c}{2\pi\sqrt{\mu_r\epsilon_r}}\sqrt{\left(\frac{p_{nm}}{a}\right)^2+\left(\frac{l\pi}{d}\right)^2}, \label{eq:resonant-frequency}$$

A detailed description can be found in this paper.

## Discharge chamber

The present cavity is made of copper covered with a tiny surface of nickel to protect it against corrosion. A Cold Cathode Fluorescent Light (CCFL) inverter serves as a current source to generate a Penning discharge inside the cavity~\cite{Knauer1962}. The inverter converts a 12~V DC input to 1~kV/50kHz AC output which is applied to both the electrodes inside the cavity. This electrodes are basically an aluminum meshes and are electrically insulated from the cylinder's lateral surface and close the extremes of the cylinder (see figure~\ref{fig:cav_cut}). This configuration ensures that the discharge permeates the entire cavity uniformly. The CCFL inverter managed to sustain discharges with working gas pressures between 10 and 300~Pa. Two loop antennas lie in the middle of the cylinder wall opposite to each other. The antennas have a 4~mm radius with their axis coincident with the magnetic field line of highest intensity of the $\mathrm{TM}_{010}$ mode, see figure~\ref{fig:tm-010}~a).

One of the antennas injects the microwaves in the cavity, and the other antenna collects the propagated signal. A observed resonance is expected close to a frequency of 3560~MHz (see figure~\ref{fig:band}).

# Protocol

This experiment allow to determine the impact on plasma density by: (i) the influence of different atomic and molecular particles structures in the plasma generation, (ii) the effect produced by magnetic confinement and (iii) various background pressure. All this three parameters are prone to be tuned in the experiment interface. very /*Note that after being not used for a long time, the firsts readings may be misleading due to wall impurities, a few experiments have to be conduced in order to validate the results./*

 e experience  to conduct the experiment


Python interface description Switching ON and OFF procedure Gas Injection and control Data retrieval

Cavity theory

How plasma affects the dielectric constant

Expected results Pressure influence RF Power influence Helium vs Argon - major challenges