M Mikikian
email: maxime.mikikian@univ-orleans.fr

H Tawidian

T Lecas

O Vall Ée

OCCURRENCE OF MIXED-MODE OSCILLATIONS IN A DUSTY PLASMA

Keywords: Dusty plasmas, Complex plasmas, Instabilities, Mixed-Mode Oscillations

Nonlinear instabilities can appear in laboratory plasmas containing dust particles. These unstable phenomena are easily observed during experiments and their analysis reveals that they correspond to mixed-mode oscillations (MMOs). In this paper, experimental results and their preliminary analyses are presented.

Introduction

The plasma state of matter is ubiquitous in nature and also quite common in our everyday life. Plasmas are gases that are partly or fully ionized, meaning that some (or all) the atoms have lost a part of (or all) their electrons. Classical plasmas are thus a mixture of still neutral atoms, free electrons and positive ions. This electrically conductive gas can be influenced by electromagnetic fields and is an energetic medium with thermal, reactive and radiative properties. It is the most encountered state in the universe as all stars are just plasma balls and is also present in comets or nebulae. On Earth, natural plasmas also exist, like aurora borealis and lightnings. In our houses, plasmas can also be found in fluorescent tubes, compact fluorescent lamps and plasma TVs. Most of the electronic devices like mobile phone or computers use processors that are fabricated partly thanks to plasmas. Plasmas are also used or considered for many other applications, like ion thrusters, plasma torches, medical applications, pollution control, fuel cells, solar cells, ... Plasmas are finally expected to be a solution for the mass production of energy thanks to thermonuclear fusion.

In many cases, another component can be found in addition to atoms, molecules, ions and electrons. Indeed, solid bodies with sizes ranging from a few nm to a few cm can be present in the plasma. These dust particles get electrically charged by attaching plasma free electrons. This new massive electrical species can strongly disturb the original plasma properties. It gave birth to a new field of research named dusty (or complex in analogy with complex fluids) plasmas. 1,2 Dusty plasmas are thus multi-component systems with similarities with colloidal suspensions or granular media. They are encountered in many environments such as astrophysics 3,4 (comet tails, planetary rings or atmospheres), industrial processes 5,6 (in microelectronics and nanotechnologies) and thermonuclear fusion. 7 These dust particles can come from regions surrounding the plasma or can be formed by the plasma itself. Indeed, in the plasma phase, some molecules can be at the origin of complex chemical and physical reactions leading to the formation of dust particles. 8 In laboratory plasmas, dust particles are usually formed by using reactive gases like for example silane or acetylene, or by ion sputtering of the surfaces exposed to the plasma. In this last case, either big parts (already formed dust particles) or molecules (acting as reactive gases) are removed from the surfaces. Dust particle formation has to be taken into account in many laboratory or industrial plasmas as these particles can be desired (for example for designing useful nanoparticles) or unwanted when cleanliness is required (in many microelectronics processes).

Instabilities in dusty plasmas

The presence of this additional charged species can strongly disturb the plasma equilibrium due to the important loss of free electrons captured by the dust particles. This effect is particularly important for high dust densities. In this case, self-excited instabilities can appear in the plasma. [START_REF] Mikikian | Selfexcited instabilities in plasmas containing dust particles (dusty or complex plasmas)[END_REF] Due to the high mass of the dust particles (relatively to ions and electrons), these unstable phenomena have typical frequencies ranging from a few Hz (for dust particle size in the µm range) to a few kHz (in the nm range). These instabilities can consist of quite regular oscillations or in more chaotic ones. In the present study, instabilities have been experimentally observed in the following conditions:

• During dust particle growth: the instability shape and frequency evolve as the dust particle size and density are changing. It has been observed in silane [START_REF] Cavarroc | [END_REF]11 and sputtering discharges [12][13][14] during the growth of the first dust particle generation. As long as molecular precursors are provided in the plasma discharge, the dust particle growth appears to be cyclic. A different type of instabilities is observed during these successive generations. [15][16][17] • Once the dust cloud is formed (when only one generation is grown), the central dust-free part of the plasma can oscillate. Indeed, it has been observed that dust particles are removed from the central part of the plasma. Thus, the dusty plasma consists of a mixture of dust particles and plasma except in a small central region where only plasma exists. This region, named the void, is characterized by an enhanced plasma emission. 2 It is sustained by the equilibrium between an outward ion drag force expelling dust particles (positive ions push away negatively charged dust particles) and an inward electric force induced by the plasma potential difference existing between the inner part and the outer part of the void (attracting dust particles toward the center 18 ). This equilibrium can be broken leading to complex void size oscillations: the heartbeat instability 19 (due to its apparent similarity with a beating heart).

• A recently discovered instability, consisting of small plasma spheroids rotating around the plasma. 20,21 Their origin is still misunderstood but seems to be related to dust particle growth.

In the following, we will focus on the heartbeat instability that appears to be strongly nonlinear. In particular, its behavior has been shown to be associated to mixed-mode oscillations 22 (MMOs). Indeed, the self-excited heartbeat instability can stop by its own through the occurrence of more and more failed contractions 23 similar to MMOs.

Mixed-Mode Oscillations

MMOs consist of an alternation of small and large (spikes) amplitude oscillations. The system relaxes through the spikes while it undergoes subthreshold oscillations in between the spikes. This dynamical behavior is encountered in many different fields, like in chemistry, 24,25 especially in the well-known Belousov-Zhabostinskii oscillating reaction, 26,27 or in natural sciences, [28][29][30] for example in the Hodgkin-Huxley model of neuronal activity. 30,31 In this last context, MMOs are strongly related to spiking and bursting activities in neurons. 32,33 They have also been discovered in electrical circuits 34,35 and in plasma physics in some dc glow discharges. 36,37 More recently, their existence has been revealed in dusty plasmas. 22,23 MMOs are characterized by using a notation based on the number of spikes and subthreshold oscillations: 24,27 the MMO state is identified by a pair of integers L S where L and S are respectively the number of spikes and subthreshold oscillations. For example, a pattern consisting of 1 spike and 4 subthreshold oscillations will be noted 1 4 (like the first three patterns in figure 1, while the last three patterns are in the 1 5 state).

To analyze and explain these characteristic oscillations appearing in so diverse scientific fields, the use of dynamical system theories is of high interest. These studies deal with well-defined behaviors like for example canards, 28,30,38 subcritical Hopf-homoclinic bifurcations 31,39 or Shilnikov homoclinic orbits. 40,41

Evidence of MMOs in dusty plasmas

The heartbeat instability appears to be strongly nonlinear as evidenced by the complex shape of the measured signals. One of the easiest and interesting signal to follow is the amplitude of the discharge current collected on the electrodes (see for example Ref. 19 for details on the experimental setup). A typical signal is presented in figure 1 recorded during the ending phase of the heartbeat instability. The signal shape clearly corresponds to typical MMOs and is remarkably similar to waveforms measured or modeled in chemical systems 24,25,27,41 or in neuronal dynamics. 28,30,33,42,43 During the fully-developed instability, only the main spikes exist. As the instability is about to stop, intermediate oscillations with a very small amplitude appear between the spikes. As the instability "looses energy", more and more small oscillations occur and the spike frequency decreases. In our case these subthreshold oscillations correspond to failed contractions of the void. 23 In figure 1 a transition between the 1 4 state and the 1 5 state is observed through the appearance of an additional subthreshold oscillation. It is interesting to observe that during the first patterns of the 1 5 state, the new subthreshold oscillation has a higher amplitude than the other ones. In a sense, it keeps partly the characteristics of the spike it was during the previous pattern. It can also be observed that the spike of the first 1 5 pattern has a higher amplitude than the last ones of the 1 4 state.

State transition

In order to better characterize the transition between a L S state and a L S+1 state, we superimposed successive 1 10 states up to the transition to the first 1 11 state. In figure 2, eight successive 1 10 patterns have been superimposed by using as a common reference the current minimum value preceding the first subthreshold oscillation (around 150 on the x-axis). Each subthreshold oscillation is indicated by its number. From the first, up to the 10 th subthreshold oscillation, each pattern appears to be similar to the pre- ceding one (excluding experimental noise). No clear difference in position or amplitude is observed during this part of the patterns. Nevertheless, a slight difference is localized on the abrupt increase of the spike. A zoom of this part is shown in figure 2 insert. It clearly appears that the occurrence time of the spike is slightly delayed from one pattern to the next one. This progressive shift during the 1 10 patterns partly creates the space for a new subthreshold oscillation to occur, as observed in figure 2 with the transition to the 1 11 state.

State alternation

In figures 1 and 2, progressive transitions from L S to L S+1 states have been evidenced: several patterns of the L S state are followed by several ones of the L S+1 , then L S+2 , etc ... In some conditions, the transition between a L S and a L S+1 state is not definitive and regular or irregular alternations of L S and L S+1 sates are observed.

In figure 3(a), the dominant pattern is the 1 0 with sporadic 1 1 states (indicated by arrows) appearing approximately each two 1 0 patterns. It indicates that the transition from the 1 0 state to the 1 1 state is not stable and the systems goes back to the previous state. Like in the transitions observed in figures 1 and 2, the amplitude of the transition spike is higher than the one of the two surrounding spikes. In figure 3(b), the 1 1 state appears more and more often and can exist during two consecutive patterns. This behavior means that the 1 1 state is becoming little by little the dominant state. Finally, in figure 3(c), the 1 1 state establishes itself as the only state with the disappearance of the 1 0 pattern. The progressive appearance of a given state during another one and its final establishment, is quite similar to the behavior of a devil's staircase. 22 In this structure, the number of steps is nearly infinite and in between two parent states, intermediate states exist that are related to the parent states by the Farey arithmetic. 24,27,44 This specific structure has been observed in chemistry in the framework of MMOs 24,25,27,44 but also in a wide range of other fields like in physiology 45 or in wave-particle interaction. 46 Thus, the structure obtained in figure 3 can be an incomplete devil's staircase with an unidentified control parameter evolving with time. It can be suggested that more intermediate states could be obtained with a system which vary slower, and that the staircase could be partly completed.

Conclusion

In this paper, we showed that mixed-mode oscillations can also be observed in the field of dusty plasmas and preliminary analyses of the obtained patterns have been performed. A particular attention has been paid on the transition between L S and L S+1 patterns. It has been shown that the transition occurs consecutively to an increasing delay in the spike appearance while subthreshold oscillations seem to be similar. Situations where the transition is not definitive have been presented. In these cases, the system cannot stay in the new L S+1 state and comes back to the previous L S state. The system oscillates between the two states with a progressive change of the dominant state. Indeed, while the L S state is the dominant one at the beginning, the L S+1 state little by little establishes itself as the dominant one. This step by step transition is quite similar to a devil's staircase. of DLR/BMBF under grants No.50WM9852.

This work was partly supported by the French National Research Agency (ANR), project INDIGO n • ANR-11-JS09-010-01.

Fig. 1 .

 1 Fig. 1. Part of the evolution of the discharge current during the ending phase of the heartbeat instability. Using the MMO notation, a transition between the 1 4 state and the 1 5 state is observed around 4.05 s.

Fig. 2 .

 2 Fig. 2. Superimposition of eight successive 1 10 patterns and the first consecutive 1 11 pattern. Each subthreshold oscillation is numbered. In the insert, zoom on the spike increase showing a slight shift from one pattern to the next one.

Fig. 3 .

 3 Fig. 3. Progressive occurrence of the 1 1 state during the 1 0 state. The 1 1 state appears (a) sporadically, (b) more regularly, (c) establishes itself as the dominant state.

Acknowledgments

The authors would like to thank S. Dozias and B. Dumax for electronic support and J. Mathias for optical support.

The PKE-Nefedov chamber has been made available by the Max-Planck-Institute for Extraterrestrial Physics, Germany, under the funding


Didier Torny

From paywall builders to data tracking moguls or… How the big publishers have put on a new super vilain costume

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

From paywall builders to data tracking moguls or…

Elsevier is a felon, that is a given. This company epitomizes all the crimes, misdemeanors and petty theft that can be accomplished by a publisher. Its wikipedia page is so full of affairs, scandals and raunchy stories that it would be enough to read it to give a talk to an academic congress. And yet Elsevier still find new ways to extract value from academic communities, which both produces new profits and new critiques. This communication is the story of the publisher becoming a data company.

An endless list of academic misdemeanors

In 1880, It all begin with a "borrowing" as we say in academic life, which may also be named an hommage, a plagiarism or a steal, depending on the point of view. When the company was founded, it took over a logo from an ancestral famous printing Dutch family, whose name was Elzevier (yes, with a Z).

As a Dutch publisher, they first put out journals in the language of the country, but the need to go into exile in England in 1940, and no doubt a rather specific vision of scholarly communication, led the company to launch English-language journals in the post-war period. Along with Pergamon, Elsevier is certainly the inventor of the concept of the 'international journal' and created a global market for scientific writings, with customers all over the world and, what is more, a profitable market. This led to cycles of development and acquisitions, which continue to this day. But as we know in the world of superheroes, "with great power comes great responsibilities". And indeed they are responsible. The list of "problems" attributed to Elsevier can be categorised into three different groups: firstly, a propensity to act in a "sloppy and dirty" manner, for example in copyediting failures, by selling closed articles for which authors have already paid an APC, or by not acting in front of legitimate requests for retracting articles, as in the very recent following example.

Secondly, its constant pursuit of profit leads it to bend academic rules. Above and beyond offering researchers Amazon vouchers to write reviews on products, one of the most famous examples is the publication of journals in Australia that were de facto advocacy media for Merck pharmaceutical products, through a subsidiary that is cited by Sergio Sismondo as an example of ghost management 2 . Third, its concern for protecting its intellectual property leads it to numerous actions opposing open access, unlimited text and data mining, or even metadata sharing. Elsevier thus funds numerous lobbying actions, and one aiming at the US Congress led to the "Cost of Knowledge" petition in 2010. This petition called for a boycott to write, review or make editorial work for the company. It was signed by tens of thousands of academics and led to some mocking of Elsevier logo.

From academic publisher to data company: a very public transition

In fact, Elsevier continued to thrive as a publisher despite the tens of thousands of petitioners. But the company has changed its core business and has significantly expanded its range of services until it no longer appears as a publisher. Take two exemplary acquisitions: in 2013, Elsevier purchased Mendeley, a library management service, and for some, it was as if the Empire had bought the rebels. This was me long ago when Mendeley sold off to Elsevier. They used to have the best desktop reference manager, but now it's clear that @zotero is miles ahead. https://t.co/8YvTVs1Y8A pic.twitter.com/TmmYMs3hgb -Timothée Poisot, Ph.D. (@tpoi) July 4, 2022

Elsevier had two objectives: on the one hand, to extend its information retrieval ecosystem, and on the other, to collect data on Mendeley users, potentially authors and reviewers. These same objectives were reflected in the acquisition two years later of SSRN, a preprint platform then specialising in the social sciences.

"Elsevier is now getting closer and closer to researchers with business models that don't involve libraries," says Joe Esposito, a publishing consultant in New York City. "The positioning is well thought out: lock up revenues to the legacy publishing business, move into areas where piracy is not much of an issue, create deeper relationships with researchers and become more and more essential to researchers even as librarians become less so." [START_REF] Tennant | RELX referral to EU competition authority[END_REF] .

The series of purchases aim to control the bricks directly used by researchers whose research projects, results, research data, texts read, cited, reviewed, tweeted, etc were linked and. Elsevier being able to identify them. But as the 2019 comprehensive diagram below shows, they are not the only target of the "new Elsevier". In a decade, Elsevier had become a data company, selling them to numerous clients, both academic and non-academic and defining itself in corporate documents as "a global leader in information and analytics, (which) helps researchers and healthcare professionals advance science and improve health outcomes for the benefit of society.", while making videos on the perfect world of information it designs with a product called PURE.

Naming a new supervilain : surveillance publishing

As of 2019, this transformation of Elsevier and, to a lesser degree, other big publishers, was a wake-up call for various institutions and authors. They started to formalise the list of new dangers that the construction of data tracking and information aggregation systems constituted, some of them specific to the academic world and others similar to those created by GAFAMlike companies. For example, a commission of the DFG published a briefing paper where they acted as alarm raisers for the following concerns 6 :

1. entail a violation of academic freedom and the freedom of research and teaching; 2. constitute a violation of the right to the protection of personal data; 3. pose a potential threat to scientists, as the data could also become accessible to foreign governments and authoritarian regimes; 4. constitute an encroachment of competition law, as new participants barely have a chance to enter the market; 5. favour a reduction in the value of public research investment, since data on research activity can be collected by commercial research competitors or made available to them in return for payment in connection with industrial espionage.

These fears may seem hypothetical, but the fact, for example, that Elsevier's parent company, RELX, has signed a huge contract to supply personal data to the US Immigration and Customs Enforcement agency has givn some weight to their warnings. But what data are we talking about? Two facetious colleagues used the provisions of the GDPR to ask Elsevier for their data and documented their findings on the traces of their stay in the Elsevier Hotel. It contains a number of directly personal data (phone numbers, bank details, addresses), but above all a great deal of usage data on the opening of e-mails sent by the company, the most basic operations on Mendeley and Science Direct or, more amusingly or worryingly, the trace of persons consents and non-consents:

Eiko I. Fried, Robin Niels Kok, Welcome to Hotel Elsevier: you can check-out any time you like … not, 2022

A new petition, twelve years after The Cost of knowledge, calls to "Stop Tracking Science", which actually means stop tracking academics. In the new configuration, libraries are still a passage point between the big publishers and the researchers though not exclusive anymore. But the data that goes for these exchanges is now considered in a different manner: "they are even attempting to persuade libraries to install trackers inside university networks: the research behavior of all of us is being recorded in real time." While identification has for long been presented as a necessary security to provide access to closed texts, it is now a source of concern, in a very similar manner as cell phone or internet tracking. To describe this phenomenon, several labels have been proposed, such as "platformization of science" 7 or "surveillance publishing" 8 The big publishers are trying through various legal actions to present Sci-hub and Libgen not only as IP offenders, but also as dangerous hackers for the security of research institutions., while it is the same accusation that is directed towards them. So, in the end, for you, which ones are the supervilains threatening academic communities?

  How the big publishers have put on a new super vilain costume. Didier Torny communication given at the 2022 EASST Conference in Madrid, July 2022.

  Michael Eisen, CC BY 3.0 https://creativecommons.org/licenses/by/3.0, via Wikimedia Commons To sum it up, If the kids of Bruno Latour had been STS PhD students in 2010, they would probably have authored a paper entitled "Portrait of a publisher as a wild capitalist". But that wouldn't have predicted what happened next.

  Chen, G., Posada, A., & Chan, L. 2019. Vertical Integration in Academic Publishing : Implications for Knowledge Inequality. In Chan, L., & Mounier, P. (Eds.), Connecting the Knowledge Commons -From Projects to Sustainable Infrastructure : The 22nd International Conference on Electronic Publishing -Revised Selected Papers. Marseille : OpenEdition Press. In fact, Elsevier's other target market is higher education and research institutions, and even governmental institutions. The enclosure of the Elsevier ecosystem has, for example, guaranteed the company a position as a subcontractor in the construction of the first European open access monitor, which has been deemed scandalous by open access activists 4 . When a consortium of Dutch universities signed a transformative agreement with the publisher in 2019, this included the joint development of projects involving all kinds of data, being a Faustus pact with Lucifer where open science becomes sustaining Elsevier data infrastructure in exchange for open access papers 5