Fast Camera Analysis of Plasma Instabilities in Hall Effect Thrusters Using a POD Method under Different Operating Regimes

Round 1

Reviewer 1 Report

The paper is devoted to a very important issue – an experimental study of the instabilities in the Hall Effect Thruster plasma. The authors used a high-speed camera and obtained a significant amount of data to analyse different functioning regimes due to a modification of the cathode emissivity. The evolution of the plume shape in these regimes and the measurement of the extraction voltage might indicate that a strong electric field builds up inside the HET channel when the cathode emissivity is high enough. A low-frequency breathing mode and high-frequency rotating modes were observed by varying the cathode emissivity. In the under-emissive regime, the breathing mode disappears and only rotating modes are observed. The breathing mode develops axially and is related to the neutral gas dynamics, while the rotating modes propagate in the azimuthal direction and might be related to rotating spokes or gradient-induced instabilities. However, additional measurements of the gradients and electric field are needed for a deeper analysis of the instabilities and their proper identification.

Broad comments

From the experimental point of view one of the main weaknesses of this study is due to the front and side videos acquired separately. The reproducibility of the discharges is therefore questionable, for example in the case of the modes’ analysis with the front and side views.

The authors acknowledge that the light emission measured with the fast camera cannot be taken as a direct measurement of the local plasma density. This issue becomes important when the instabilities show the modification of their frequency in different areas of the discharge.

Although many papers on the HET plasma dynamics have been published, I believe that the present results will give additional information on the instabilities evolution during a current limited transition of the discharge regime. However, I think several questions and suggestions listed below should be taken into account by the authors before the publication.

Specific comments

• Fig. 1
  It would be beneficial for the clarity of the paper to mirror the left hand image in order to have the same plasma plume direction on both left and right figures. The potential difference between the anode and the plume U_S is not shown on the figure.
• p.3 line 91
  The sentences:
  “However, because of their lower mass, the electrons are strongly magnetized in the discharge channel so the magnetic field has a major impact on their dynamics.”
  and
  “Their Larmor radius is much smaller than the size of the channel and the electrons are thus forced to follow very tight helical trajectories along the field lines.”
  basically express the same idea, therefore one of them should be removed.
• p.5 line 152
  Concerning the history of the POD, it is misleading to claim that this method was first introduced by Lumley in fluid dynamics. The method has been known as Principle Components Analysis since early 1900s with the works of K. Pearson (On lines and planes of closest fit to systems of points in space, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2:11, 559-572). The term POD itself is also used in many works before Lumley by Kosambi (1943), Karhunen (1946), Pougachev (1953) and E N Lorenz (1965) (non-exhaustive list). When describing the POD method, authors provide unnecessary details on p.6 about the standard technique of SVD, lines 157-169. I would suggest to shorten this description and replace it by a suitable reference.
• p.10 line 276
  “Then, these neutrals are strongly ionized in the high magnetic field region which deplete  their density profile: the atom front moves towards the anode where the ionization is less efficient due to a higher electron mobility (lower magnetic field).”
  better
  “Then, these neutrals are strongly ionized in the high magnetic field region which depletes  their density profile: the front of neutrals density moves towards the anode where the ionization is less efficient due to a higher electron mobility (lower magnetic field).”
• p.12 line 305
  “These patterns come out only on the videos from the side because the level of light is too low compared to the camera sensitivity”
  What are the reasons for the light intensity to be low from the side and not from the front view?
• p.12 line 320
  “These instabilities can be compared to instabilities arising in tokamak scrape off layers usually called drift instabilities”. “In the tokamak edge plasma” would be more accurate.
• p.12
  Is there explanation why the observed frequency of m=1 is higher than the estimation for rotating spokes? Can it support the hypothesis of the gradient driven instabilities nature of this mode instead of the rotating spokes?
• Fig. 2, 3, 4, 5, 6, 7, 8 the axes are not readable

The style of the paper is satisfying with following minor corrections.

• p.3 line 103
  “it extends drastically the lifetime of the cathode” should be “it drastically extends”. Generally and for other sentences in this paper, adverbs should be placed before the verb in English in contrast to French.
• If the authors choose to use the British English spelling, following words should be changed:
  p.3 line 81 center – centre
  p.3 line 106 neutralize – neutralise
  p.6 line 156 vectorized - vectorised
  p.9 line 260 non homogeneous – non-homogeneous
  and so on.
• Some of the spelling mistakes:
  p.2 line 58 propagate instead of propagates
  p.4 line 124 as - has
  p.7 line 198 fueled – fuelled
  p.7 line 201 self sustained – self-sustained
  p.9 line 260 labeled – labelled
  p.10 line 276 deplete - depletes
  p.10 line 289 showed - shown
  p.13 line 350 doumented - documented

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Dear Editor,

I have read the manuscript by Désangles et al. with pleasure. It is a well-written report on the experimental study of the modes forming in a plasma thruster using POD. The modes are described in two regimes (nominal and under-emissive), and the transition between the two is also briefly studied. The result are interesting and the article deserves publication after my comments below are taken into account.

I have a few minor comments:

1. In the abstract: the consequences or need of removing the breathing mode should be stated.

2. Line 28: "orders of magnitude higher..." --> "orders of magnitude larger..."

3. Line 124, typo: "Each pixel as a 12 bit" ---> "Each pixel has a 12 bit"

4. Lines 285-286: "w0 oscillates at about 7 kHz", by the look of the plots (Fig 4) of w0 (I can count 5 peaks in about 0.2 ms) and its spectrum (approximate localization of the peak seems larger than 10 kHz), the oscillating frequency seems more around 10kHz. How was the value of 7Hz estimated?

5. Lines 321-322: The sentence "Both these types of instabilities does not actually have their typical oscillation frequencies set but the phase velocity of their wave" is not clear to me.

6. Lines 328-329: "They are typically composed of two POD modes that needs to be summed up to reconstruct a rotating mode": how do you know that and which POD modes have to be coupled to get one single rotation mode? How are the m modes determined, and how do you know which POD mode correspond to a particular m-mode?

7. Lines 390-391: "The voltage difference between the anode and the plume, referred as extraction voltage, is constant in both regimes but changes abruptly at the transition." I am not sure I understand how the authors determine the disappearing of the breathing mode. If its amplitude in the POD decomposition decreases enough, could it be that the mode is simply not captured by POD (being close to noise or too weak for being isolated as a mode) rather than disappearing? How can the author make sure this is not the case?

Besides that, the manuscript has some spelling errors and will need some moderate revision of the English.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 3 Report

The paper by V. Desangles et al. presents a characterization of two regimes (and the transition between them) of a low power Hall Effect Thruster (HET). The study is based on fast camera measurements, which are analysed with a Proper Orthogonal Decomposition (POD) method.

The subject of the study is well posed, the article is well written, well-constructed and pleasant to read. It clearly demonstrates that fast imaging diagnostics coupled with a POD method can improve the understanding of the operating regimes of HET. Figures are clear and convincing, and the results of the study are well related to the state of the art on the subject. There is no doubt that the type of analysis presented in this study paves the way for a better understanding of instabilities in HET. In summary, this is an excellent paper that I recommend for publication in Atmosphere.

However, I have a few remarks that I recommend to take into account to improve the paper:

• The authors write that light fluctuations are only a proxy for density fluctuations. In fact, light I is related to the density of neutrals n0, density of electrons ne and electron temperature Te by a law of the type I = n0 f(ne, Te) ~ n0*ne^alpha* Te ^beta (see for instance: Zweben et al., Rev. Sci. Instrum. 88, 041101 (2017)). For light fluctuations to be a good proxy for density fluctuations, it must therefore be ensured that electron temperature fluctuations are negligible, which is the case in the article cited in reference [50]. Is this indeed the case in HET? If the authors do not have clear indications on this point, this hypothesis should at least be mentioned.
• In section 3.2.2, the authors attribute the 15kHz oscillations observed in the front view to a possible breathing mode hidden behind the rotating modes. For the side view, however, the authors wonder about the nature of the low-frequency oscillations revealed by the POD analysis, even though their frequency is in the same range. Why not consider both cases with the same arguments? And why not considering the possibility for these fluctuations to be spokes? The frequency range corresponds, and in section 3.1.2 the authors do not exclude that they may be observed in the thruster plume.

A small remark: the acquisition rates of the fast camera are given in kHz. Even if this is not incorrect, it would be better to express them in fps (frames per second) to avoid possible confusion with the pixel read-out rate (in some articles, 900 kHz could mean 900 k pixels per second, whereas here it is 900 k frames per second).

Another small remark: in order to visualize the last file corresponding to the under-emissive regime (M2-M1) I had to rename it. So it might be necessary to rename it to allow other readers to view it.

In addition, here are a few typos I've noticed:

Line 45 tough > though

Line 49 utmost > outmost

Line 261 correspond > corresponds

Line 288 intermittence > intermittency

Line 325 it is not useful to indicate the decimals, given the width of the interval

Line 345 the authors write « u1 » instead of « u3 »

Line 350 doumented > documented

Lige 398 : more > mode

Author Response

Please see the attachment

Author Response File: Author Response.docx