Review Reports - The Effect of the Axial Plasma Electron Density Distribution on the Effective Length and Radiation Pattern of a Plasma Antenna

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article is technically sound and well structured. The subject of the study is scientifically relevant. However, it contains several minor technical and editorial issues. Some additional comments and clarifications should be included in the text to make certain aspects clearer.

* Although the used methods are contactless, they still disturb the measurement.
Since the resonant cavity is metallic, it affects the propagation of the surface wave (the wave is partially reflected). Please explain shortly how the presence of the cavity influences the results. The same applies to the waveguide method.

* In the description of the resonant cavity method, it is stated that the result represents a volume-averaged value. The same applies to the waveguide method, which also provides an averaged electron density. Please add a short comment on this point.

* Page 9, calculation section: please complete the input data by specifying:
– the inner radius and dielectric constant of the discharge tube,
– the assumed electron density gradient,
– whether the plasma was assumed to be radially uniform,
– the Drude model requires the electron density and collision frequency; the latter depends on the type of gas, pressure and temperature. What collision frequency was assumed in both cases?

* It would be beneficial to perform additional numerical calculations for the effective electrical length and to present the corresponding radiation patterns.

* The keywords include 'RF discharge', while the abstract mentions 'microwave discharge'. Since 445 MHz is rather in the microwave range, please use consistent terminology throughout the paper.

* The acronym PADA in the abstract is not explained.

* Page 2: Since the reader may not be familiar with antenna terminology, it would be helpful to briefly define the term 'effective electrical length'

* In Figure 1, the discharge tube appears green and opaque. Please specify the material of the tubes.

* Page 4, first line: the symbol inside the parentheses is not visible.

* The text alternates between 'electron density' and 'electron concentration'. Please use consistent terminology. I also suggest replacing the term 'plasma density' with 'electron density' throughout the text, including in the title.

* Page 4, below Equation (3): define the quantity 'E'.

* Page 4, line 130: please clarify that this electron density is typical for low-pressure discharges (at atmospheric pressure it exceeds 10¹⁵ cm⁻³).

* Page 4, line 137: define S₂₁ here (it is currently defined on the next page). In the figures showing this coefficient the indices are written as subscripts, but in the text they appear in normal font. Please make the notation consistent.

* Figures 8 and 9: the radiation characteristics are not normalized. Please provide the units.

* It may be worth mentioning that waveguide methods for measuring electron density were originally developed in the 1970s, e.g.: Vyskocil, J., & Musil, J. (1980). Microwave measurement of electron density and temperature in plasmas produced by a surfatron at atmospheric pressure. J. of Phys. D: App. Phys., 13(2), L25.

Author Response

We extend sincere gratitude to the reviewers for their exceptionally thorough and attentive review of our manuscript. Their insightful questions and constructive comments proved invaluable and have significantly enhanced the quality of our work.

We revised the manuscript to improve its comprehension. In addition to the reviewers' key comments, the abstract and introduction were revised, the reference list was expanded, information that would have made the article more readable was removed, and the figures were significantly improved.

REPLIES for Reviewer 1

* Although the used methods are contactless, they still disturb the measurement. Since the resonant cavity is metallic, it affects the propagation of the surface wave (the wave is partially reflected). Please explain shortly how the presence of the cavity influences the results. The same applies to the waveguide method.

REPLY: The transverse dimensions of both the resonant cavity (9 cm) and waveguide (3.5 cm) were significantly smaller than the excitation wavelength (67 cm), minimizing their intrusive impact. For our plasma parameters (nₑ ~ 2×10¹¹ cm⁻³), a substantial portion of the surface wave energy (~30%) is confined within the plasma bulk, with approximately 50% localized near the tube wall. This energy distribution makes the wave propagation relatively resilient to external perturbations.We systematically monitored plasma luminosity during measurements. While both diagnostics, particularly the longer resonant cavity, caused some plasma column shortening (up to 15 cm for the waveguide), this effect was localized. The perturbation primarily affected the density profile downstream of the diagnostic point but did not significantly alter the local electron density measurement at the probe position. Although minor reflections occurred, they did not distort the fundamental trend of the axial density distribution. The observed linear decay profile remains a robust and representative characteristic of the surface-wave-sustained discharge under investigation.

The following text has been added to the manuscript: “The potential influence of the resonant cavity and waveguide on the surface wave propagation was carefully considered. While partial wave reflection from the metallic boundaries of both diagnostics is expected, several factors mitigate its impact on the measured results. The transverse dimensions of the diagnostics (9 cm for the cavity, 3.5 cm for the waveguide) are substantially smaller than the excitation wavelength (67 cm). Furthermore, for the given plasma parameters, a significant fraction of the surface wave energy is localized within the plasma column and the near-wall region, reducing its susceptibility to external perturbation. Monitoring of the plasma

luminosity confirmed that while the diagnostics, especially the longer cavity, could cause a local shortening of the plasma column, this effect was spatially confined. The perturbation influenced the density profile downstream of the measurement point but did not alter the locally measured value or the overall axial trend, which was the primary focus of this study.”

REPLY: In the corrected manuscript we added: “Both used microwave methods determine the volume-averaged electron density of a plasma part placed in the resonant cavity or in the waveguide cross-section.”

REPLY: Sections 1, 2, and 3 have been supplemented to include the inner radius and permittivity of the discharge tube, the assumed electron density gradient, the radial homogeneity of the plasma, and the electron-electron collision frequency in both the experiment and the simulation. The revised portions of the manuscript are listed below:

“The first antenna (Figure 1a) consists of a transparent bactericidal lamp that is a quartz glass tube (1) with a length of 900 mm and a inner diameter of 24 mm (outer diameter is 26 mm) , a surfatron (2), the design of which is described in detail in [30,31], and a coaxial cable (3). The second antenna (Figure 1b) consists of a commercial fluorescent lamp that is a quartz glass tube (1) with a length of 160 mm and a inner diameter of 10 mm (outer diameter is 12 mm), a copper shield (2), and a coaxial connector with an inner conductor (3) and outer conductor (4).

…

The typical plasma electron density is 10¹¹-10¹² cm^-3 for microwave surface wave low-pressure discharges, and the electron-electron collision frequency for plasma in both tubes is about 10⁷ s⁻¹, which allowed us to use a collisionless approach.

…

The plasma electron density and electron-electron collision frequency correspond to experimental data. The axial distribution of the plasma electron density was assumed to be uniform and with measured gradients, while the radial distribution was assumed to be uniform in all studied cases.”

* It would be beneficial to perform additional numerical calculations for the effective electrical length and to present the corresponding radiation patterns.

REPLY: Numerical calculations for the effective electrical length and to present the corresponding radiation patterns have been added.

* The keywords include 'RF discharge', while the abstract mentions 'microwave discharge'. Since 445 MHz is rather in the microwave range, please use consistent terminology throughout the paper.

REPLY: The list of keywords in the current version of the manuscript has the following structure:

Keywords: low-temperature plasma, plasma antenna, gas discharge tubes, microwave discharge, plasma electron density, antenna electrical length, surface electromagnetic wave, microwave cavity, radiation pattern.

* The acronym PADA in the abstract is not explained.

REPLY: The acronym PADA has been removed from the abstract. All abbreviations used in the manuscript are listed and explained in the Abbreviations section on page 13.

* Page 2: Since the reader may not be familiar with antenna terminology, it would be helpful to briefly define the term 'effective electrical length'

REPLY: The text includes the following clarification: "The effective electrical length is determined by the current distribution that forms the antenna's far-field radiation at the resonant frequency."

* In Figure 1, the discharge tube appears green and opaque. Please specify the material of the tubes.

REPLY: All discharge tubes used in the experiments are made of quartz glass. The green color in Figure 1 was chosen solely for visual clarity, to distinguish the tube material from metallic and other structural components in the schematic. We have indicated the gas discharge tube material in the corrected version of the manuscript.
* Page 4, first line: the symbol inside the parentheses is not visible.

REPLY: In the current version, the manuscript looks like this :For the condition of weakly collisional plasma (ω≫ν).

* The text alternates between 'electron density' and 'electron concentration'. Please use consistent terminology. I also suggest replacing the term 'plasma density' with 'electron density' throughout the text, including in the title.

REPLY: The entire manuscript now uses "plasma electron density".

* Page 4, below Equation (3): define the quantity 'E'.

REPLY: In amended manuscript equation (3) is excluded.

* Page 4, line 130: please clarify that this electron density is typical for low-pressure discharges (at atmospheric pressure it exceeds 10¹⁵ cm⁻³).

REPLY: The typical plasma electron density is 10¹¹-10¹² cm^-3 for microwave surface wave low-pressure discharges, and the electron-electron collision frequency for plasma in both tubes is about 10⁷ s⁻¹, which allowed us to use a collisionless approach.

* Page 4, line 137: define S₂₁ here (it is currently defined on the next page). In the figures showing this coefficient the indices are written as subscripts, but in the text they appear in normal font. Please make the notation consistent.

REPLY: It has been corrected: “The cavity’s scattering parameter S₂₁(forward transmission coefficient between two ports) was measured over the 2 – 4 GHz frequency range using a Keysight N9912A vector network analyzer.”

* Figures 8 and 9: the radiation characteristics are not normalized. Please provide the units.

REPLY: Figures 8 and 9 have been normalized.

REPLY: The proposed article is consistent with this article and has been used in the updated manuscript.

Thank you for your attention to our manuscript and constructive comments.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a study on the effect that a non homogeneous plasma distribution in plasma antenna has on the radiation pattern. The authors experimentally estimated the plasma density contained inside 2 plasma antennas and fed the quantity to COMSOL in order to investigate the radiation pattern and compare it against the results given by a uniform distribution.
Overall, the study is well presented and addresses a key aspect in plasma antenna's performances.
My main concern is that, despite the experimental setup, the radiation simulation are not corroborated by any evidence (only a slight reference to [17]). I would suggest the authors to stress more such aspect if possible.
Therefore, I recommend to accept this manuscript after these minor revisions.

Minor comments:

- Page 4 Line 106: I cannot visualise the symbol between the two frequencies in bracket. I assume that it is a ">>". Please confirm.

- Reference style is not constant throughout the manuscript, please choose a single way to introduce references in the text.

- Figures font and size should be more consistent throughout the manuscript

Author Response

REPLIES for Reviewer 2

Minor comments:

- Page 4 Line 106: I cannot visualise the symbol between the two frequencies in bracket. I assume that it is a ">>". Please confirm.

REPLY: In the current version, the manuscript looks like this :For the condition of weakly collisional plasma (ω≫ν)

- Reference style is not constant throughout the manuscript, please choose a single way to introduce references in the text.

REPLY: It corrected in the latest version of the manuscript.

- Figures font and size should be more consistent throughout the manuscript

REPLY: It corrected in the latest version of the manuscript.

Thank you for your attention to our manuscript and constructive comments.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is well written and structured. The applied methods are simple but well supporting the results. A clear statement with respect to the main achievements and the novelty of the work should be given.

Minor remarks are mentioned in what follows:

1. Missing symbol in the frequency relation in line 106

2. Different subscript size in Eq. 3 and the text part mentioning the shape factor

3. The cut-off densities n_c for different frequencies are mentioned but not explained (lines 127-128)

4. The Drude model used is a low-level model. It is clear that for the purpose here it might be enough. However, the simplifications and the limitations of the model should be clearly given.

5. The Size of numbers and text in Figs. 5,6,8,9 should be increased (e.g., to match that in Fig. 7).

6. Misprint in the unit in line 236 (Wt).

Author Response

REPLIES for Reviewer 3

Minor remarks are mentioned in what follows:

Missing symbol in the frequency relation in line 106

REPLY: This has been fixed.

Different subscript size in Eq. 3 and the text part mentioning the shape factor

REPLY: In amended manuscript equation (3) is excluded.

The cut-off densities n_c for different frequencies are mentioned but not explained (lines 127-128)

REPLY: Explanation for term "critical plasma density" is added.

The Drude model used is a low-level model. It is clear that for the purpose here it might be enough. However, the simplifications and the limitations of the model should be clearly given.

REPLY: The Drude model is a classic and widely used approximation for describing the behavior of free electrons in plasmas and metals. The model's main advantages lie in its simplicity and clarity. It effectively describes electrical conductivity by taking into account the free motion of electrons between collisions with ions, which helps explain the electrodynamic properties of plasma. To describe plasma, the Drude model considers an electron gas in which electrons move in straight lines until random collisions with ions. The time between collisions is stable and described by memoryless statistics. This approach significantly simplifies calculations and yields solutions that are consistent with more complex and resource-intensive modeling methods, such as the PIC method. Because of this, the Drude model is often used to quickly estimate the dielectric properties of plasma and its electrical conductivity. The Drude model also has significant limitations. It does not take into account interactions between electrons and between electrons and ions, with the exception of simple collisions. This approach does not account for quantum effects, collective excitations, and nonlinear processes in plasma, which are important in some cases. The model also cannot describe processes associated with nonequilibrium states. Furthermore, the lack of consideration of real particle dynamics and interactions limits the model's accuracy for complex and inhomogeneous plasmas.

The Size of numbers and text in Figs. 5,6,8,9 should be increased (e.g., to match that in Fig. 7).