Simon Flandin

Christine Vidal-Gomel

Raquel Becerril Ortega

Raquel Becerril

Raquel Becerril Ortega

Addressing

Becerril Ortega

An Introduction to Simulation Training Through the Lens of Experience and Activity Analysis

come

This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi. org/10.1007/978-3-030-89567-9_1 embodied and embedded experimentation, we are convinced that this type of training has much to offer. The research on simulation training to date has nevertheless mainly focused on understanding performance improvements in very compartmented domains of skills or professions. Educational approaches that focus on experience, activity, learning, development, and practice changes do not appear to be sufficiently integrated. A particular problem is that the research evidence often remains domain-related (medical healthcare, fire rescue, civil protection, police intervention, military missions, etc.) and offers simulation trainers very few robust inputs to build programs oriented by cross-cutting principles, even though these professional domains share very similar issues and challenges.

The aim of this book is to present a comprehensive account of the various ways in which the analysis of experience and activity in the context of simulation training (i) helps identify learning affordances and obstacles and provides a detailed description of the learning process and outcomes, (ii) points toward promising design orientations for simulationbased vocational education and training, and (iii) contributes to the overall understanding of practice-based professional learning. Accordingly, the objectives of the book are:

• to describe and discuss the theoretical, methodological, and/or practical issues related to trainees' experiences and activities in simulation training;

• to provide evidence of how the conditions under which lived experience in simulation can foster or hinder learning;

• to identify the conceptual bases and empirical applications and implications of this approach to learning through simulation-based experimentation;

• to contribute to both domain-related and generic orientations for simulation design.

Herein, we thus present the research on various simulation training programs in the domains of healthcare, victim rescue and population protection, involving healthcare workers (5 chapters), firemen (2 chapters), policemen (2 chapters), servicemen (2 chapters), and civil security leaders (1 chapter). This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi. org/10.1007/978-3-030-89567-9_1 This opening chapter offers an overview of the conditions under which experience and activity can be fruitful objects for examining what occurs in simulation training, understanding participants' learning and development processes, and deriving robust design principles. It is argued that this approach is particularly useful in the field of simulation training, especially when achieving high standards of operational performance is complicated by critical issues (health, safety, security, protection, etc.) and difficult working environments (dynamic, uncertain, high-risk, etc.). We show that this approach is able to integrate authentic, embodied, and embedded practice experiences with domainrelated or cross-cutting learning content. We also provide key concepts that can guide readers in understanding how simulation-enhanced learning and development processes are studied and how the different ways of enabling trainees to construct usable knowledge in verisimilar contexts are derived from these studies. The organization of the book sections and chapters are then presented. In sum, this opening chapter introduces the purpose of the book, explains why the research presented here fills an important knowledge gap, and suggests ways that readers might profitably engage with its contents.

THEORETICAL BACKGROUND: A FRANCOPHONE RESEARCH TRADITION IN COGNITIVE ERGONOMICS AND VOCATIONAL

EDUCATION AND TRAINING

COGNITIVE ERGONOMICS AND EDUCATIONAL RESEARCH TRADITIONS

IN SIMULATION TRAINING

The chapters of this book present studies at the interface of several research traditions, notably cognitive ergonomics and "the ergonomics of activity." Since the 1980s, cognitive ergonomics has focused on the design and improvement of "information technologies"and more recently on digital resources -by including training in its line of research questions, whereas the ergonomics of activity has been integrated into the sciences of education and training. Much of the research presented here has drawn on these two traditions in particular and sought to contribute to a deeper understanding of simulation as a support for the development of what Chernikova, Heitzmann, Stadler, Holzberger and This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1 Seidel (2020) call "complex skills": "Critical thinking, problem solving, communication, and collaboration seem to be the most relevant skills1 that […] should [be acquired], in addition to domain-specific knowledge and skills, to be able to make professional decisions and implement solutions" (op. cit., p. 501). However, unlike these authors, the researchers presented here are not necessarily concerned with initial training or higher education. The studies often focus on a set of professionals from different fields and with different levels of initial training who nevertheless all need to acquire and develop complex skills in order to perform quality work in everyday or more exceptional situations.

Simulation training experienced a real boom in the 20th century with the development of computing resources, computers and digital technology (Rosen, 2013). Cognitive ergonomics, which first emerged in the 1950s, has been interested in simulation since the 1960s, mainly conducting studies in the fields of the military, nuclear power plants and maintenance tasks (Patrick, 1992). In the 1980s, with the spread of new computing tools, simulation training expanded to other industrial and at-risk fields (Norros, 1989). During this period, the research focused on the design and improvement of simulators and simulations for teaching, certification, and training. The validity and reliability of the simulators and simulation situations in comparison to "real work" situations have been widely debated and these issues continue to receive attention (e.g., Drews & Bakdash, 2013;Persson, 2017). At the same time, the research carried out in the sciences of education and training in French-speaking countries since the mid-1990s has tended to focus on the professions of service relations (education and training, healthcare, etc.) in which the interventions relate to another human (particularly with education, development and health objectives). In these professional sectors, the contributions of digital technology are more recent than in industry, and some have touted digital resources for training as the means to achieve major improvements. These arguments recall those that Leplat (1989) and Patrick (1992) pointed to concerning other major contributions that were expected to improve the world of work, when in fact some indeed made real contributions and some were revealed to be limited and/or "naive."

This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced In the 1990s, the debates began to move in other directions. For example, some focused on the interest and limitations of microworlds designed for in vitro experiments (Brehmer & Dorner, 1993). These works underscored the complexity of fidelity: microworlds are artificial situations that are not faithful to "natural" situations, although they retain certain features. Two types of problems were thus raised: that of ecological validity, which can be defined as "the possibility to generalize the conclusion obtained by the study of an artificial situation to a class of natural situation" (Hoc, 2001, p. 284), and that of fidelity. Physical fidelity, or the resemblance to reality (Patrick, 1992), is differentiated from functional fidelity, or "the degree to which a simulator acts like the real equipment" (Grau, Doireau, Poisson, 1998, p. 370), and from "psychological fidelity," which refers to the determination of the psychological dimensions mobilized in the simulated situation that are hypothesized to be equivalent to those at work in a "natural" situation (Baker, Marshall, 1989;Patrick, 1992). Patrick reformulated it in these terms: "The simulation has to represent the task to the trainee in such a way that the psychological or skill requirements of the task are not changed significantly. The trainee should have to deploy the same cognitive activities in performing the simulated task as the actual task" (1992, p. 495). It has thus been well established that physical fidelity is not necessary when the objective of training is the acquisition of procedures or the mastery of tasks for which the cognitive dimensions of the activity are important. Rogalski (1995) suggested that these problems might be better understood and even resolved by analyzing the tasks to be performed at a cognitive and conceptual level and by modeling the development of professional skills 2 (the KEOPS model). This implies designing simulation situations while retaining or transforming "task functionalities" for a learning and development objective. "The term task functionality refers, on the one hand, to the properties of the deep structure of the task, involving cognitive requirements, and, on the other hand, to the properties of what is often seen as context which are in fact closely tied to the task and have strong effects on operators' behavior when performing a task" (op. cit., p. 127). From this perspective, the model takes into account the situational and This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1 organizational characteristics that affect activity and require the development of specific skills by individuals and groups in order to achieve mastery of these situations and obtain the desired results.

SIMULATION TRAINING THROUGH THE LENS OF EXPERIENCE AND ACTIVITY

The debates on validity and fidelity have continued with one example being in the health sector, which tends to favor high-fidelity simulations, thus creating confusion between fidelity and its many components and the "reproduction of the real." In the research world, authors like Persson (2017) and Hamstra, Brydges, Hatala et al. ( 2014) have suggested dropping the term "fidelity." Persson (op. cit.) pointed out that this term tends to center the debate on technological advances and a resemblance to "real" situations, rather than on the relevance of simulation for learning. Béguin and Pastré (2002) suggested going beyond questions of validity and fidelity in exploring the functions of the simulated situation by putting the focus on trainees' activity and the meanings that the simulation takes on for them. This viewpoint is quite close to that of Rogalski (op. cit.) in that it emphasizes the importance of how trainees interpret a situation, and it may be an important dimension of the skills that need to be acquired.

During this period, the issues surrounding simulations for professional training came to the attention of researchers working within the cognitive ergonomics framework (i) regarding the characterization of expertise and "skills" and the development and learning processes, as in Bainbridge and Ruiz Quintanilla's book (1989) This type of research has intensified in high-risk sectors. As studies have highlighted the importance of collective functioning to ensure the efficiency and safety of work systems, This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., this theme has also emerged in research on the use of simulation in training (Salas & Cannon-Bowers, 2001;Salas, Tannenbaum, Kraiger et al., 2012). In the 2000s, training simulations developed beyond these professional environments in response to societal demands, notably in healthcare environments where such rules as "never for the first time on a patient" are unquestioned. They also proliferated because the costs of simulation devices have decreased with technological advances (web 2.0, etc.). Yet, despite this growing body of research, it is regrettable that certain aspects of training simulations, such as the activity of trainers -who are crucial to training effectiveness -have been little explored, with few exceptions (Rogalski, Plat, & Antolin, 2002).

In the 1990s, the education and training sciences of the French-speaking world seized upon a set of theoretical frameworks that mobilized the concept of activity. Fillietaz and Billet (2015) gave a detailed account of this period. Thus, alongside the work in cognitive ergonomics, aspects of which we have noted because of their contributions to simulation training, other orientations developed. This particularly concerned the research carried out from the "ergonomics of activity"3 perspective, whose researchers have been critical of cognitive psychology, as have "course-of-action" researchers (Durant & Poizat, 2015).

These two approaches to "human factors," for example, can be distinguished from the traditional approaches by the place given to the concept of activity and the systemic point of view that is defended (Daniellou, 2005;Rabardel & Daniellou, 2005;Vidal-Gomel, Boccara, Delgoulet et al., 2019).

Thus, Durand and Poizat (op. cit., p. 223) specified the framework of the "course of action," which defines activity as "what a given actor does as a living, cultural and reflexive unit engaged in a social practice (in this case, work). A here-and-now activity refers to a time point or state in the history of dynamic exchanges between this living unit and its environment." This approach integrates contributions from Maturana (1988), particularly by taking into account "the living unit as autopoietic," which means that the unit of analysis is defined as a unit-environment coupling. The definition of coupling within this research This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., stream differs markedly from that of other approaches to activity: "Activity is, thus, taken to be the set of ongoing interactions of a living unit and its environment, and it is further assumed that these interactions produce the very structure of this unit and its environment and are in no way the mere response of a predetermined unit reacting to stimuli or adapting to constraints from a world that is itself predetermined. During these interactions, the unit and its environment are in a relationship of co-definition. They define each other. But, this co-definition is asymmetric in that only the living unit specifies what in the environment is meaningful for it (and not the reverse)" (op. cit., p. 226).

Other researchers working within the framework of the ergonomics of activity are closer to the community conducting research based on Russian psychology. The culturalhistorical activity theory (CHAT) of Leontiev (1978) and Vygotsky (1934Vygotsky ( /1978) ) presents some of the best-known ideas from Russian psychology. Engestrom's model (1987), which was built on an interpretation of CHAT, has been widely disseminated. However, other models, such as the model of Norros (2005,2014) was not yet called "the ergonomics of activity." He explained how the concept of activity was incorporated into research that mobilized "psychological analyses of work," replacing the concept of "conduct" that had been used up to that point. In this regard, Daniellou quotes Leplat and Cuny (1977, in Daniellou, op. cit., p. 411): "the central object of psychological analysis is the worker's conduct or in other words, the human operator's conduct. We will sometimes use the word 'activity' as being synonymous with conduct. (...) When analyzing work, we must differentiate the analysis of conduct from the analysis of the requirements or conditions to which this conduct is subjected and to which it replies." This quotation is striking for underlining the reconciliation of the viewpoints of the two communities. This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., Daniellou and Rabardel (2005, p. 355) also recalled a set of viewpoints shared by the ergonomics of activity and Russian psychology-based research on the subject of activity, which we recall here very schematically:

• "Activity is finalized. Activity is object-oriented in order to attain one or more goals, which are not always evident, and which the analyst may have trouble identifying.

• The relation between the subject and object is mediated by technical devices, psychological schemes and organization […] These activity mediators are socially and culturally constructed as well as historically situated.

• Activity is always unique. It is specific to given subjects in a given context […].

• Activity bears traces of its past. Activity […] is affected by the subject's life experience and is, thus, constantly revised and reinvested […].

• Activity is not only a relationship between a subject and an object. It is also a relationship with other subjects, who may be physically present or present via instruments and tools, sign systems […].

• The analyst's approach to activity is intrinsic: he/she seeks to understand 'from within' how the subject constructs his/her activity to attain the object, given the resources and constraints at their disposal […].

• Activity is integrational. It is constructed at the crossroads of the subject's motives and goals […] and several determinants, which may be clearly connected to the workstation layout or apparently unrelated (the subject's history, the company's sales policy)."

One of the peculiarities of Francophone ergonomics is precisely its interest in these determinants from a systemic approach, that is, "the point of view that is adopted to jointly take into account a set of dimensions of human activity (biological, psychological, cognitive, social) and that also seeks to highlight a set of determinants of operators' activity, depending on the problem addressed" (Vidal-Gomel et al., 2019, p. 234). Leplat's model (1997), which is shared by many researchers in the ergonomics of activity (Daniellou, 2005), provides a framework for such an analysis. It differentiates:

This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., • the factors that determine activity (characteristics of workers, means of work and tasks);

• the characteristics of the activity in the situations being analyzed;

• the effects (in terms of health or skills development) and results (in terms of productive efficiency);

• last, given the dynamics of the situated action in the short, medium or longer term, the effects that transform the determining factors in a transitory or more lasting way. This approach has been widely used in the field of professional training, highlighting, for example, (i) the interest of not limiting the scope of activity analysis to the work activities to be trained for; (ii) the need to take into account the work activities of both trainers and trainees and, in some situations, colleagues that are not directly concerned but will have to help new entrants; (iii) the interest of an approach that seeks to understand work situations rather than only the tasks that must be mastered by the end of a training program; and (iv) the importance of subjective engagement at work (Vidal-Gomel et al., op. cit.).

Professional didactics is an heir to both cognitive ergonomics and the ergonomics of activity with regard to understanding work, as well as to a theory of adult cognitive development that considers "conceptualization in action" (Vergnaud, 2009) and seeks to develop a pedagogy of situations for training (Mayen, 2015;Tourmen et al., 2017). These currents of thought, all based on the concept of activity but sometimes approaching it from different angles, run through this book to varying degrees. We would like to point out that they also share a number of epistemological, theoretical and methodological orientations. We note the following points:

• The actual work (as it is performed in the situation) is differentiated from the work prescribed by those who order its execution orally or via job descriptions;

• The work expected and planned for by the work organization or the workers themselves is different from the actual work;

• Analyzing work cannot be reduced to analyzing the tasks that need to be done. The analysis must take into account the results of the work (results prescribed, expected, and recognized in the company or institution, as well as the various viewpoints on the results) This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced and the consequences for individuals, collectives, and the work organization. Also, the analysis takes on its full meaning only with the analysis of activity, which starts from the situated action of an individual or a group and is apprehended through its dynamics as the situation unfolds (action carried out or action prevented);

• The activity is understood to depend jointly on the characteristics of the situation and those of the individual;

• Primacy is given to the analysis of in vivo activity and the ecological validity of the results;

• Intervention is an important dimension of the research carried out using these approaches: the research aims to transform work and training environments with the objective of developing the actors.

Among the viewpoints shared by these schools of thought, some relate more specifically to professional training. In particular, it is acknowledged that scientific and technical knowledge is necessary but insufficient to perform work, and it must therefore be supplemented by knowledge about action based on professional experience to ensure optimal preparation for work: "the operator's knowledge comes from basic education, training, and direct experience in working with the system. Through basic education, the operator learns the physical laws underlying the process, the principles of functioning for the components, and the principles that govern the behavior of complex systems. It is, however, only through training and experience that the operator becomes acquainted with how the plant or the process conducts itself in normal and abnormal conditions" (Hoc, Cacciabue & Hollnagel, 1995, p. 13).

When the initial training involves many years devoted to knowledge acquisition (typically higher education), the confrontation with professional situations or simulation situations leads to a restructuring of this knowledge, as well as its articulation with the characteristics of the encountered situations and the knowledge acquired in the course of processing these situations. Thus, Boshuizen and Schmidt (Schmidt, Boshuizen & Hobus, 1988;Boshuizen, Schmidt, Custers & Van de Wiel, 1995;Van de Wiel, Boshuizen & Schmidt, 2000) focused on the initial training of doctors and showed that as doctors acquire experience with the This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1 situation of dealing with clinical cases, they develop concepts that encapsulate the theoretical knowledge that they have acquired thus far: "the networks of biomedical knowledge acquired in initial training are included in higher-level clinical concepts," which means that "the networks of knowledge about the pathophysiological mechanisms linking the causes and consequences of a disease are 'captured ' [i.e., encapsulated] by clinical concepts" drawn from situated action (Van de Wiel, Boshuizen, & Schmidt, 2000, p. 328). Biomedical knowledge is mobilized when the clinical knowledge is insufficient, and for students with little or no experience this is often the case, while for more experienced physicians it only occurs in rare or complex situations. Pastré (2005) made a similar observation by examining the activity of engineers learning to operate a nuclear power plant on a simulator after high-level scientific and technical training. He hypothesized that during training on simulators, a "semantics of action" is constituted in the confrontation with the situation. This semantics articulates the indices present in in the situation and the concepts (scientific and technical or resulting from action in a simulated situation and interactions with peers) that give them meaning and allow for an interpretation of the situation -and ultimately the categorization of situations. Thus, categories of problems and situations are developed in a process he calls "pragmatization," wherein theoretical concepts are transformed.

However, such processes do not take into account the sets of action knowledge necessary for the work, as part of this knowledge remains partly implicit and embedded and includes knowledge of particular cases and different types of experience of dealing with risk and the unforeseen events that punctuate the daily job or constitute exceptional situations -even "crisis situations." In fact, the types of training that interest us here are non-curricular.

APPLICATIONS TO HEALTHCARE, VICTIM RESCUE AND POPULATION

PROTECTION

Based on this common grounding, the book chapters focus on the use of simulation in training in several areas of activity, particularly the management of typical, deteriorating or even critical situations in contexts of health and safety. These are areas in which simulation is a necessity because it is impossible and/or unacceptable to learn on the job. It This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., is impossible because of the rarity of crises or disasters and unacceptable because of the risks involved for the professionals and those they serve.

These domains of intervention are all "dynamic environments: It is characteristic of a dynamic system that it may evolve without operator intervention. Thus, even if the operator does not interact with the system, for instance, when he is trying to diagnose or plan, the state of the system may change" (Hoc, Cacciabue & Hollnagel, 1995, p. 4). The situation variables may change at different tempos and their effects may intersect at possibly different moments. The sequences of reasoning required to understand what is happening and to act may thus progress through "several steps."

The characteristics of such work situations have consequences for the skills that need to be acquired: "Working with a dynamic system not only means that time may be limited, but it also means that the mental representation of the system must be continuously updated.

The choice of a specific action is based on the operator's understanding of the current state of the system and the expectations of what the action will accomplish. If the understanding is incomplete or incorrect, the actions may fail to achieve their purpose" (op. cit., p. 5).

Among these dynamic work situations, some can immediately be qualified as "crisis management" situations, whereas others drift toward crisis -that is, "an event, in general unexpected, whose consequences may develop with very rapid dynamics, producing significant risks that exceed the pre-existing resources in terms of action procedures" (Rogalski, 2004, p. 531). We might underline that crises have serious consequences. They create "significant and widespread human, material, economic and or environmental losses that exceed the ability of the affected community or society to cope within its own resources

[…] The development of events following the sudden onset is so rapid that it exceeds the ability to respond […] Events often develop in unexpected directions, thus challenging the readiness and resources of the responding organizations" (Hollnagel, 2012 4 ).

Crises thus pose recurring problems, but the shift into crisis cannot be analyzed in the same way across these fields of activity: "disasters are 'normal' in the activity of firefighters, which is not the case for most other systems. Therefore, a variety of resources are already This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced associated with different types of disasters, the organization of which (actors and resources) has been extensively planned for […] The difference in disaster management by emergency service actors is the relocation of system functions and the overwhelming of pre-existing resources" (Rogalski, 2004, p. 531).

Yet, there are also substantial points in common for these areas of intervention that justify our choice to have brought them together in this book: all these professionals have to deal with risky situations that are not always predictable, despite the planning efforts of their respective professional communities. Thus, in disaster management or at another scale of crisis management, the appropriate response to the situation rarely comes from the application of standardized procedures. They must be at the very least adjusted to the situation, which requires the operators to have a detailed understanding of the situation and the procedures in question. In the field of healthcare with relationships with patients and caregiving, "care" itself cannot be reduced to techniques and procedures that can be applied systematically. Thus, training is not merely a matter of imitation or reproduction. These are, of course, usable training methods, but they must lead to understanding, the construction of meaning, and conceptualization on individual and collective levels.

Moreover, these areas are all affected by uncertainty and surprise, which are therefore important characteristics that operators must be prepared for through training.

These are interesting areas for professional training because learning in these contexts is difficult: it is difficult to relate an action that has been carried out to its effects on the situation, especially with the rapidly changes dynamics and entangled variables; it is impossible to go back and learn by repetition; and it is necessary to anticipate (which constitutes one of the difficulties of beginners) in a situation that is uncertain, poses multiple risks, cannot be fully understood, and presents phenomena that may never before been encountered … Indeed, we do not have sufficient scientific models for these contexts, which also underlines the importance of experiential knowledge even though these fields can be very codified, standardized, and procedural, sometimes leaving little room for the actor's experience.

Focusing attention on "fields of activity" can contribute to the construction of knowledge about the characteristics of situations and of the activity in these situations, which can This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., facilitate the identification of relevant training situations. Fields of activity in fact call upon sets of activities, objects and tasks which, at a certain level, can be defined as characteristics, as having common traits (Rabardel & Samurçay, 2004). Thus, we know that the control of dynamic environments, which are characteristic of these situations, requires anticipation, a characteristic of activity. Activity cannot be reduced to this trait, but it encompasses it. Therefore, characterizing fields of activity can help guide the design of simulation situations.

From this perspective, the jobs of firefighters, police officers and healthcare professionals fall within fields of activity that differ in terms of the objectives they pursue, the resources they can access, the organization of the work and value systems.

In these fields, however, although scientific and technical knowledge is necessary, it is insufficient to produce quality work. Knowledge is not always well stabilized and the knowledge that professionals acquire over the course of their experience often remains implicit, poorly understood, and little disseminated and discussed. The contributions of the professional community can therefore be important, although they often need to be discussed and debated to identify their limits. The contributions for training can then be distributed among peers and trainers who may differ in their opinions, particularly because there is rarely a single good response to a situation but rather a set of acceptable solutions, which need to be evaluated according to different types of criteria. In the field of healthcare and crisis management, it may be a question of stabilizing the situation by limiting the consequences of risks according to the resources that are available at time "t." A debriefing can then provide opportunities for debate to examine the chosen solutions and identify their advantages and limitations (Mollo & Nascimento, 2014). Last, in these fields, the experience acquired by the professionals is not always sufficient as they may need to be prepared for new situations: the interest of simulation is precisely that it offers "the possibility of extrapolating and creating a knowledge base starting from bounded experience" (Hoc, Cacciabue & Hollnagel, 1995, p. 13).

In any case, trainees are not considered as having "received" knowledge transmitted by trainers. Simulation situations are designed to give trainees experience, letting them live an experience that can then be analyzed individually and collectively after the fact. This kind This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1 of a posteriori analysis, removed from the heat of the moment, is an opportunity for professional development.

The training simulations presented in this book also suggest a set of ethical questions: Is it acceptable to put professionals in difficulty in front of their colleagues? How far can they be pushed to confront difficult and stressful situations? What are the consequences for them?

SIMULATION TRAINING AS A CONTROLLED SPACE FOR EXPERIMENTATION IN PRACTICE-BASED LEARNING

Simulations grew out of the demand from work organizations to take real activity into account in training situations (Ughetto et al., 2018) by giving individuals the possibility of experiencing or reliving past or current situations (realized or not) and future situations in order to think or rethink more productively about them and better act in them (Bobillier Chaumon et al., 2018). Simulations can be understood as putting activity into perspective, leading to a form of detachment from reality. In this book, simulation is considered a pedagogical and didactic approach to promote experimentation in training that can be configured in different ways, depending on the objectives noted in the research presented in each chapter.

Simulation, an educational process

The history of simulation as a method of acquiring professional skills (Singh et al., 2013) sheds light on this educational issue. Simulation training drew inspiration from simulations in avionics safety systems and military training, which were then transposed to other professional systems, such as healthcare (Rosen, 2013) or civil security. Simulations in avionics focus on error and action and prevention strategies, with a pedagogical corollary being to "do the experiment without causing damage": without physical damage to self and others, without material damage, and thus without ecological damage. In the military, the simulation tradition aims to make the combat experience more up-close and intimate in

  titled "Developing skills with information technology", and (ii) from a training perspective, as in Patrick's (1992) work: "Training: Research and practice." Along the same lines, Hoc, Cacciabue and Hollnagel's book (1995) included a section of four chapters that focused on characterizing expertise and its consequences for training, skills development through simulation, and the limits of operational knowledge acquired on the job and by transmission within a group of peers, as well as how it can be completed through training.

  , are less well-known, as are a range of other studies based on Russian psychology (Daniellou & Rabardel, 2005). It is notable that the ergonomics of activity community and the community that has drawn on Russian psychology and its developments continue to interact in events organized regularly for the triennial Congress of the International Ergonomics Association. They are identified under the title "Activity theory for work analysis and design." In a historical analysis of the development of activity ergonomics, Daniellou (2005) noted how the translation of Leontiev's work into French in 1975 influenced researchers in what

  An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

  An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

The notion of skill is used here to highlight the characteristics of the tasks to be performed, and this usage is different from that found later in this introduction.

The notion of professional competence used in French, which is often translated by the term "skill" in English, refers to the dimensions of activity mobilized to carry out tasks, to accomplish a mission. Bainbridge and Ruiz Quintanilla (1989) discussed the different meanings of the term skill in English and French cognitive ergonomics.

Many authors use the term "French-speaking ergonomists" to designate this line of research. In order to avoid overlooking a large part of our colleagues who contribute and enrich this approach, we prefer the term "ergonomics of activity."

This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1

order to build the military experience needed for success in theaters of operation (Hill & Tolk, 2017). Here, simulations are used to develop and test action protocols and train soldiers to implement them. Thus, this educational approach places the person "in a situation" to experiment in order to learn or question practices. It is based on experimentation with ordinary, complex and even critical situations. Different educational configurations can be used, depending on the knowledge targeted, the type of trainees, the objectives to be achieved (learning, assessment, certification), the technologies available, etc.

On the assumption that experimentation is a continuous elaboration of experience, two cognitive dispositions can be mobilized according to different temporalities. First, regarding the immediacy of action, experimentation is understood as a reworking of the experience in situ. This occurs, for example, when a professional in the situation constructs guiding and corrective hypotheses related to action strategies, depending on the context. Second, with regard to long-term experience as a reservoir of available actions inscribed in the biographical or life story, actions are geared toward the success of a project.

Experimentation, here understood as a sifting through of experience, is activated to face new situations, thereby contributing to the anticipation and management of future problems.

Simulation, a didactic approach

The history of simulation also teaches us that its development goes hand in hand with the new possibilities offered by simulators (Rosen, 2013), which are the technical support for simulations (Vadcard, 2019). In the military field, for example, board games were used to develop strategies, then life-size simulations were used to train soldiers (Hill & Tolk, 2017).

In the field of medicine, simulation methods can be supported by biological equipment, as in animal experimentation, cadaver use, standardized patients, role plays, etc.; synthetic equipment, like patient or procedural simulators; and electronic equipment, like virtual or augmented reality, 3D environments, and so on (Betz et al., 2014). Thus, beyond the representativeness and fidelity of the simulation to the situation it represents, the didactic approach is concerned with the design of the training situation. This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced Simulators support preconceived simulation situations, most of which are designed from real field situations (military, aviation, clinical cases, etc.). These simulation situations are part of the training system or meet a specific training need. An epistemological vigilance that is specific to this didactic approach consists in identifying the technical constraints that the simulator imposes on the simulation -for example, by limiting the possible actionsand by doing so, it identifies the possibilities of developing new knowledge and skills. This epistemological vigilance also consists in controlling the epistemic network mobilized during the simulation, and not only that of the representation provided by the simulator from the start. Thus, the technical constraints and possibilities of simulations constitute one dimension among others, largely influenced, moreover, by the knowledge and skills brought into play by the trainees and trainers.

Simulation as a didactic approach offers a space for experimentation to elaborate or reelaborate knowledge. It assumes the elaboration of knowledge from action -on the assumption that this elaboration results in novelty compared to the state of knowledge previously available -and the gradual stabilization of a repertoire of action structures to act effectively and deal with the unforeseen -which presupposes adaptation to the context.

Simulation, a controlled experimentation space

In this book, simulation is seen as part of a constructivist perspective on learning, heir to major trends in the psychology of learning and development (Piaget, 1947). It has been grouped by some under the term experiential learning (Yardley et al., 2012), which also includes Vygotsky's socioconstructivist perspective. Dewey, for example, argued that experience implies a connection between the action and its consequence for the subject: if the active phase, action, is separated from the passive phase of experience, the reflection carried on about this action, real meaning is destroyed (Dewey, 1934, p. 298). For Piaget (1947), on the other hand, experience is not a primary fact: it must be organized by the subject and presupposes an activity. It is therefore quite different from a system of exogenous associations. Any experience is an experiment in the sense of the subject's organization of a question posed to nature or a situation in which he or she is engaged, which must respond with yes or no. Experimentation is active and cannot be reduced to This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., An Introduction to Simulation Training through the Lens of Experience and Activity Analysis, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_1 experience in the ordinary sense of everyday experience -that is, simple perceptual contact with events taking place in the external environment.

Simulation, as an educational and didactic process, is constituted as a controlled space for experimentation: experimentation with risks, unforeseen events, or the vagaries of new or known situations, in the aim of elaborating or re-elaborating knowledge. Simulation helps to define the dimensions of a context of anticipation and freedom, so that this context can be assumed by professionals during training.

INTRODUCING THE CONTRIBUTIONS TO SIMULATION TRAINING

The contributors to this book have empirically or conceptually analyzed the characteristics and effects of simulation training programs, mainly in the dimensions of the activity deployed and/or the experience lived by the trainees, as explained above. Doing so has enabled them to evaluate the design principles that might fruitfully be generalized and/or to improve their effectiveness for both trainers and trainees. These simulation systems involve one or more categories of professionals in the fields of healthcare, victim rescue or civil protection, and are all finalized by the improvement of performance, defined through a wide spectrum of generic factors (e.g., crisis management) or factors specific to the field of practice (e.g., a technical nursing act).

The contributions bring together:

• Empirical reports based on the study of programs either designed by the researchers or identified in the field as having characteristics of particular interest (innovative goals, original principles, unprecedented attempts, etc.); The book is structured into three sections.

Experience and activity-based conceptualizations of simulation design and outcomes

This first section examines activity as unfolding and experience as meaningful lived episodes during contrasted simulation training situations. It contributes to a deeper understanding of simulation design (objectives, format, tasks, animation, perturbations, facilitation, etc.) and outcomes (from very specific technical gestures to wide and multidimensional dispositions).

Conceptual contributions for the design of activity-led simulation training

The chapters of this subsection (2-3-4) provide insights from empirical and conceptual research about simulation training outcomes and design principles in the domains of healthcare and interprofessional management of civil safety. This ambition to contribute to a conceptual renewal in the field of simulation training is shared by Zoya Horcik, who explains how a (re-)consideration of the situated cognition approach could prove fruitful for simulation in the medical field. Specifically, she defines three "missed appointments" between medical simulation and situated cognition. Chapter 4 thus aims to encourage global reflection on the relationships between theoretical frameworks and design principles by analyzing the links between how learning is conceptualized and how simulationbased training programs are implemented.

Insights from design-based research in simulation training

The chapters of the next subsection (5-6-7) provide design-based research accounts regarding three simulation programs: care gestures in healthcare, patient management in geriatrics, and "mass casualty event" management.

Chapter 5, authored by Christine Vidal-Gomel, addresses the notion of psychological validity by reflecting on the dimensions of work activity that are brought into play in simulation. In this chapter, she analyzes the activity of healthcare professionals in a simulation co-designed by the researcher and a trainer, finalized by the acquisition of a technical gesture: the gesture of "relational-touch." In doing so, Vidal-Gomel contributes to our understanding of the conditions under which simulation promotes the learning of "professional" gestures through practice, here seen (i) as the "transformation of schemas" and (ii) through the lens of the subjective engagement of actors in situation and with their relationship to the profession. train medical leaders as they acquire and develop the skills needed to cope with a mass casualty event (attack, external operation, etc.).

Empirical lessons from experience and activity-based approaches to simulation training

The second section is devoted to empirical accounts of the activity and experience of professionals through the study of work-as-done in simulation training programs. It informs the field of simulation with original and acute findings on professional engagement and performance in simulation training and offers relevant guidelines for simulation design.

Empirical lessons from the analysis of trainees' activity in simulation training

The chapters of this subsection (8-9-10) present activity studies of professionals' actions, decisions, communications, interactions, and configurations as they deal with urgent and/or critical events (firemen and policemen).

Chapter 8, authored by Laurie-Anna Dubois, Sylvie Vandestrate, and Agnès Van Daele, presents a study on how firefighters belonging to a "Casualty Extraction Team" manage and learn to manage high risks in a simulated exceptional crisis situation (post-attack crisis). In this chapter, they analyze the activity of both the trainees and trainers in simulation from audiovideo recordings. The relevance of the simulation training under study vis-à-vis the skills targeted for acquisition is assessed through the study of transformations in the trainees' activity.

The results contribute to the state of knowledge on preparing for the management of high-risk relief situations.

The second chapter in this subsection also analyzes the activity of firefighters during full-scale simulated rescue situations. Cyril Bossard, Yohann Cardin, Magali Prost, and Gilles Kermarrec studied the construction of collective meaning in intervention during an urban fire simulation.

Using subjective video data and resituating interviews, the analysis presented in Chapter 9 allowed them to model six typical collective configurations. This contribution informs both the work of firefighters in this type of intervention and the design of simulation training likely to favor the processes of collective meaning construction, which is a crucial dimension of performance in this type of rescue.

This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., The methods that use subjective video data and resituating interviews are particularly suited to very fine-grained analysis of the activity of professionals, particularly when they are engaged in very intense interventions. Sophie Le Bellu, Saadi Lahlou, Joshua M. Phelps, and Jan Aandal also used these methods in their documentation of the decision-making processes of police officers during training simulations. In Chapter 10, they propose a method that can be used for both research purposes and training: subjective evidence-based ethnography. This method uses contextualized, constructed, and guided debriefings to make better use of the simulation situation, with benefits to learning and reflexivity for the trainees.

Empirical lessons from the analysis of trainees' lived experience in simulation training

The chapters of this subsection (11-12-13) present fine-grained explorations of the lived experience, concerns, sensemaking and situational dispositions of individual policemen, servicemen, and healthcare workers facing complex and potentially -physically and mentally -intense simulated occupational configurations.

Chapter 11, authored by Rachel Boembeke, Laurane De Carvalho, and Germain Poizat, examines the full-scale simulation training of police officers in intervention techniques and tactics. In this chapter, they document the lived experience of the trainees, particularly (i) their typical concerns, (ii) the nature of their involvement in the situation, and (iii) their methods of knowledge building. The analyses contribute to a better understanding of the optimal conditions for ensuring the effectiveness of high-fidelity simulations and point to the design principles to be favored.

Full-scale high-fidelity simulations offer particularly interesting training opportunities for trainers aiming for a high degree of ecological validity. In the following chapter, Hervé de Bisschop and Serge Leblanc show how simulated situations that are physically and mentally "overly demanding" are able to transform the way in which army officer cadets mobilize, maintain and preserve the resources and capacities needed to fulfill their mission. In Chapter 12, they thus point out the need for disruptive and long-lasting simulations so that the trainees develop "conservatory" arrangements allowing them to "hold on" in the face of critical adversity.

This is a post-print of the following chapter: Flandin, S., Vidal-Gomel, C. and Becerril Ortega, R., Critical situations are not always at the heart of professional activity. Elodie Ciccone, Lucie Cuvelier, Anne Bationo-Tillon, and Françoise Decortis were interested in simulation preparation for healthcare professionals who need to communicate with the families of patients, particularly when bad news is announced. In Chapter 13, they examine the role of the sensitive dimensions of experience in the simulation training process. In an original and fertile approach, these authors trace the development of highly specific caring skills that are often reduced in the scientific literature to "relational" or "nontechnical" dimensions.

Promising avenues for simulation training design and research

The third and last section is a prospective discussion and extension to the preceding chapters.

Scholars having broad international expertise in simulation and vocational learning have been invited to react to the preceding chapters, present complementary views, and/or establish the connections between the evidence provided in each chapter and its implications for simulation training design.

In the first chapter, Janine Rogalski considers the book from two perspectives: Frenchlanguage ergonomics and professional didactics. She first presents her reflections on the studies -particularly French-language -which seem to her to have a structuring role in the field of simulation training for professionals. She then focuses particularly on the examples in the health field to present several promising avenues for future research to both expand our current understanding and enhance effective simulation design.

In the second chapter, Eliana Escudero suggests taking a step back and reflecting both retrospectively and prospectively on the challenges and progress related to the use of simulation for healthcare training. She develops her expert point of view on simulation as a means of improving healthcare performance and patient safety by including an analysis concerning a crisis unprecedented in modern history: the Covid-19 pandemic.


T M Burinskaya

J L Rauch

THIN PLASMA CAVITIES AS A SOURCE OF THE AURORAL KILOMETRIC RADIATION

The investigation of the cyclotron maser instability in sources of finite perpendicular extension separated from the denser and cold surrounding plasma by sharp density gradients is made within the waveguide approximation. The general dispersion equation of wave propagation and amplification is obtained and solved numerically for different regimes. It is found that the growth rate of oblique eigenmode increases with the increasing of the perpendicular component of the wave vector directed along cavity boundaries. The structure of electromagnetic fields inside the source region is studied and changes of the wave polarization are discussed.

Introduction

Experimental data obtained during the modern spacecraft missions strongly suggest that Auroral Kilometric Radiation (AKR) sources have a small extension (usually not more than one hundred km) in the direction perpendicular to the geomagnetic field. AKR sources are observed as plasma cavities, filled by hot and tenuous plasma, and separated from the denser and colder surrounding plasma by sharp density gradient with typical scale length of the order or below 1 km. The electron population in these regions is dominated by particles with low parallel velocities and the energy of the order of several keV [Louarn and Le Quéau, 1996a]. During the last years it was established that the most likely mechanism for the generation of AKR, as well as to its analogs at other magnetized planets (Jupiter, Saturn and Uranus), is the electron cyclotron maser instability (CMI) [START_REF] Wu | A theory of terrestrial kilometric radiation[END_REF][START_REF] Pritchett | Relativistic dispersion, the cyclotron maser instability and auroral kilometric radiation[END_REF]. Louarn and Le Quéau [1996b] were the first who suggested a waveguide model for the AKR source, on the basis that a source boundary thickness is less than a typical wave length, whereas a source width is far in excess. They derived a dispersion equation for the waveguide eigenmode frequencies and solved it for different parameter regimes. However their results are correct for waves propagating along the magnetic field only. Since a waveguide model of the AKR source seems to us very promising in the light of the experimental data,we have found a dispersion equation of wave excitation and amplification in sources of finite extension in the general case.

Model and basic equations

The model of the AKR source region is chosen similar to [Louarn and Le Quéau, 1996b]. It is a slab structure limited in the x direction with width L = 2l and unlimited in the y and z directions (z is along the background magnetic field in the opposite direction to it) (Fig. 1). The source region is separated from the denser and cold surrounding plasma by infinitely density gradients. Inside the source the electron population consist of energetic particles with a ring-like distribution: is idealized, it takes into account relativistic effects and does not significantly modify the results obtained with the use of more realistic distributions as shown in [START_REF] Pritchett | Relativistic dispersion, the cyclotron maser instability and auroral kilometric radiation[END_REF]]. Assuming that changes of plasma parameters have a characteristic scale larger than a source width, the plasma inside and outside the source region may be considered as homogeneous. Writing the Maxwell equations with a appropriate dielectric tensor for each of the three homogeneous regions in the Fourier space, we perform a Fourier transform in the y and z directions:

(f (v z , v ⊥ ) = (2πv ⊥0 ) -1 δ(v ⊥ -v ⊥0 )δ(v z -v 0 ),
∇ × H = -i ω c (ε E), ∇ × E = i ω c H, (1)
where c is a speed of light, ε is the dielectric tensor and ∇ = (∇ x , ik y , ik z ). Since in the region of the AKR generation the electron plasma frequency (ω p ) is much less than the electron gyrofrequency (ω c ) and AKR wavelengths are much larger than the electron Larmor radius, it can be shown that for the ring-distribution the dielectric tensor components are the next:

ε xx = ε yy ≡ ε 1 , ε zz = 1, ε xy = -ε yx ≡ ε 2 , ε xz = ε yz = ε zx = ε zy = 0, (2)
where ε 1 = ε i 1 , ε 2 = ε i 2 for the plasma inside a source region and ε 1 = ε 0 1 , ε 2 = ε 0 2 for the outside plasma.

ε i 1 = 1 - α i 2ω 2 (F 1 + F 2 ), ε i 2 = α i 2ω 2 (F 1 -F 2 ) F 1 = ω -N z u 0 ω -1 + δ Σ -N z u 0 + v 2 ⊥ 2c 2 N 2 z -ω (ω -1 + δ Σ -N z u 0 ) 2 , F 2 = ω -N z u 0 ω + 1 -δ Σ -N z u 0 + v 2 ⊥ 2c 2 N 2 z -ω (ω + 1 -δ Σ -N z u 0 ) 2 , ε 0 1 = 1 - α 0 2ω 1 ω -1 + 1 ω+1 , ε 0 2 = α 0 2ω 1 ω -1 + 1 ω+1 , (3)
where normalized parameters and variables are used:

α i = ω 2 pi /ω 2 c , α 0 = ω 2 p0 /ω 2 c (ω pi
, ω p0 are electron plasma frequencies inside and outside the source respectively), 1), (2) all the components of the electromagnetic field can be written as functions of the parallel electric and magnetic field components only:

ω = ω/ω c , N z = k z c/ω c , u 0 = v 0 /c, δ Σ = (v 2 ⊥0 + v 2 0 )/2c 2 . From equations (
H x = N y E z -N z E y ω , H y = i ω ∂E z ∂x + N z ω E x , (4)
E x = 1 D iN z ε 1 - N 2 z ω 2 ∂E z ∂x + ε 2 N y E z -ω ε 2 ∂H z ∂x + N y ε 1 - N 2 z ω 2 H z , E y = - 1 D N z ǫ 2 ∂E z ∂x + ε 1 - N 2 z ω 2 N y E z + iω - N 2 z ω 2 -ε 1 ∂H z ∂x + ε 2 N y H z , D = ω 2 ε 1 - N 2 z ω 2 2 -ε 2 2 ,
(5) where N y = k y c/ω c , x = xω c /c. The parallel components of the electric and magnetic field are related by the equations:

∂ 2 E z ∂x 2 - N 2 y ω 2 E z + 1 - N 2 z ε 1 ω 2 E z = i N z ω ε 2 ε 1 H z , ∂ 2 H z ∂x 2 - N 2 y ω 2 H z + ε 2 1 -ε 2 2 ε 1 - N 2 z ω 2 H z = -i N z ω ε 2 ε 1 E z (6)
For the case of a perpendicular propagation (N z = 0) the upper equation ( 6) describes the ordinary (O) mode and the bottom corresponds to the extraordinary (X) mode when

N 2 ⊥ = (N 2 x + N 2 y ) < 1 (ω 2 /ω 2 c ≈ 1
). The general solution of equations ( 6) inside the AKR source is a superposition of two extraordinary and two ordinary mode waves. Thus for -L/2 ≤ x ≤ L/2

H i z = (a 1 cos(N 1 x) + b 1 sin(N 1 x) + a 2 cos(N 2 x) + b 2 sin(N 2 x)) exp(i(N y y + N z z -ωt)) (7) Outside the source the solution is f or x > L/2 H + z = (A 1 exp(iN 3 (x -L/2)) + A 2 exp(iN 4 (x -L/2))) exp(i(N y y + N z z -ωt)), f or x < -L/2 H - z = (B 1 exp(-iN 3 (x + L/2)) + B 2 exp(-iN 4 (x + L/2))) exp(i(N y y + N z z -ωt)). (8)
In expressions (7,8) N 1 , N 3 are the transverse wave numbers for the X mode and N 2 , N 4 for the O mode. For each of the three homogeneous regions transverse wave numbers are found from the dispersion equation with corresponding ε 1 and ε 2 :

1 - N 2 z ε 1 ω 2 - N 2 ⊥ ω 2 ε 2 1 -ε 2 2 ε 1 - N 2 z + N 2 ⊥ ω 2 = N 2 z ε 2 2 ω 2 ε 2 1 (9)
The dispersion equation for the waveguide eigenmodes is found from the continuity of H z , E z , H y and E y .

3 Study of dispersion equation

Eigenmodes for the wave transverse propagation

First we consider the equation of wave propagation and amplification for N z = 0. In this case the parallel electric and magnetic fields are decoupled and the electromagnetic field can be decomposed into waves corresponding to X (E z = 0) or O (H z = 0) modes. Thus in the general solution (7,8) we take into consideration only the terms attributing to X mode (a 2 = b 2 = A 2 = B 2 = 0). Substituting (7,8) into the expression for E y (5) and using the conditions of continuity:

H i z = H + z , E i y = E + y for x = L/2 and H i z = H - z , E i y = - y for x = -L/2
, the system of four linear equations is obtained. The compatibility conditions of this system gives the dispersion equation:

1 D i [ε i 1 N 1 sin(N 1 l) -ε i 2 N y cos(N 1 l)] + cos(N 1 l) D 0 [iN 3 ε 0 1 + ε 0 2 N y ] × 1 D i [ε i 1 N 1 cos(N 1 l) -ε i 2 N y sin(N 1 l)] - sin(N 1 l) D 0 [iN 3 ε 0 1 -ε 0 2 N y ] = - 1 D i [ε i 1 N 1 sin(N 1 l) + ε i 2 N y cos(N 1 l)] + cos(N 1 l) D 0 [iN 3 ε 0 1 -ε 0 2 N y ] × 1 D i [ε i 1 N 1 cos(N 1 l) + ε i 2 N y sin(N 1 l)] - sin(N 1 l) D 0 [iN 3 ε 0 1 + ε 2 N y ] (10)
Here D i and D 0 are found with the use of ( 5) by substituting ε i 1 , ε i 2 and ε 0 1 , ε 0 2 respectively. Equation (10) depends on N 2 y as it must be, because there is no difference for wave propagation in the positive or negative y direction. Contrary to this the dispersion equation (15) obtained in [Louarn and Le Quéau, 1996b] depends on N y , because symmetric functions were chosen as solutions and the use of them is correct only for the case N y = 0. The reason is that although the equation ( 6) for H z may have symmetric (b 1 = 0) and antisymmetric (a 1 = 0) solutions, it is impossible for any of them to satisfy the boundary conditions for x = -L/2 and x = L/2 simultaneously, when N y = 0. It follows from the fact that expression (5) for E y , have terms with H z and ∂H z /∂x simultaneously.

Solutions of the dispersion equation for N y = 0 were studied by Louarn and Le Quéau [1996b] in details and it was shown that each of the solutions can be labeled by an integer n. In this paper we determine n ≈ 1 + N 1 * L/π (here L is a normalized width L = ω c L/c)indicating the number of maximums of |H z | inside the source. We have studied the numerical solutions of equation ( 10) depending on the value of N y for different eigenmodes denoted by n. The normalized parameters used for calculations are similar to [Louarn and Le Quéau, 1996b]: α i = 0.002, α 0 = 0.01, u 0 = 0., δ Σ = 0.0075, l = ω c l/c = 60. At an altitude where f c = 200kHz the width corresponds to ≈ 30km, the internal density to ≈ 1cm -3 , the external density to ≈ 5cm -3 and the electron energy ≈ 4KeV . Solutions of (10) are plotted in Fig. 2 from numerical results the greater is the eigenmode number n, the less is an interval of N y where the wave amplification is possible. Obviously it is a consequence of the X mode condition N 2 1 + N 2 y < 1, because n ≈ 1 + N 1 * L/π. It worth to note that the growth rate has the greater value for oblique eigenmodes with small number n. Taking into account the ratio between coefficients in the solution (7), following from the system of linear equations obtained for the derivation of dispersion equation ( 10),

b 1 a 1 = 1 D i [ε i 1 N 1 sin(N 1 l) -ε i 2 N y cos(N 1 l)] + cos(N 1 l) D 0 [iN 3 ε 0 1 + ε 0 2 N y ] 1 D i [ε i 1 N 1 cos(N 1 l) + ε i 2 N y sin(N 1 l)] - sin(N 1 l) D 0 [iN 3 ε 0 1 + ε 2 N y ] , (11)
it is possible to illustrate the modification of the eigenmode in dimensionless units versus N y . In Fig. 3 3.2 Eigenmodes for the wave propagation at an arbitrary angle to the magnetic field

In the waveguide approximation the dispersion equation for the wave propagation at an arbitrary angle to the background magnetic field is found by a routine way with a use of a general solution (7,8) and the continuity of H z , E z , H y and E y for x = L/2 and x = -L/2. Since this equation has a huge size, we do not reproduce it here but present some results obtained by numerical calculations.In [Louarn and Le Quéau, 1996b] the dependence of the dispersion equation upon N z was obtained for N z ≪ N 1 but in our calculations we use the general dispersion equation for an arbitrary value of N z without limitations.

In Fig. 5 the normalized frequency δω = (ω -ω c )/ω c and the growth rate γ = γ/ω c are shown versus N z for different n. A contraction of N z range with the increasing of the eigenmode number is clearly seen. However the larger is the eigenmode number n, the greater is a value of the growth rate. Fig. 6 displays the N z -dependence of the normalized frequency and growth rate for the eigenmode n = 12 for different N y . As might be expected, there is a decreasing of N z range with the increasing of N y . Results of our investigation, when electrons velocity u 0 directed along the magnetic field inside the source region is taken into consideration, are plotted in Fig. 7 for the eigenmode n = 29 and different u 0 . For u 0 = 0 the N z -dependence of the frequency is changed in such way that in the Earth magnetic field the waves generated with N z = 0 or even having a rather small N z < 0 directed from the Earth at first would propagate down to the Earth, because their group velocity V gr > 0. After wave passing through the reflection point (V gr = 0), waves propagate upward until they reach an altitude where the external X mode cut-off becomes equal to the wave frequency. Thus, although the N z -dependence of the growth rate is practically the same (see Fig. 7) the wave amplification factor may increase due to the enhancement of wave duration inside the cavity.

Conclusion

The results of our investigation of the development of the CMI in sources of finite perpendicular extension in the waveguide approximation have shown that the growth rate of oblique eigenmode increases with the increasing of the perpendicular component of the wave vector directed along cavity boundaries. In general a structure of electromagnetic fields inside the source is asymmetric. E y dominates for N y = 0 and |E x |/|E y | is not -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,009

Figure 1 :

 1 Figure 1: The model of the source region

Figure 2 :

 2 Figure 2: N y -dependence of δω and γ for different eigenmodes, N z = 0

Figure 3 :Figure 4 :

 34 Figure 3: Structure of the |H z | for the eigenmode n = 12 for N y = 0 and N y = 0.5

Figure 5 :Figure 6 :

 56 Figure 5: N z -dependence of δω and γ for different eigenmodes, N y = 0

Figure 7 :

 7 Figure 7: N z -dependence of δω and γ for the eigenmode n = 29 for different u 0

Acknowledgments. This investigation was partially supported by grant of President RF HIII -1739.2003.2 and RFBR grant 05-02-17566.


P M E Décréau

E Le Guirriec

J L Rauch

J G Trotignon

P Canu

F Darrouzet

J Lemaire

A Masson

F Sedgemore

M André

Density irregularities in the plasmasphere boundary layer: Cluster observations in the dusk sector

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

One of the main objectives of the multi-spacecraft CLUSTER mission is the study of small-scale plasma structures. The grounds for using four measurement points is to overcome the limitations of a single spacecraft, or even of a pair, in resolving the spatio-temporal evolution of plasma structures; indeed such information is crucial for understanding the underlying physical mechanisms, involved in the formation of new plasmapause density gradients. We present here case studies of density irregularities observed by CLUSTER in the plasmapause region. We show how a comparison of the four measured density profiles can improve our in-situ perception and knowledge of this key magnetospheric region.

Recognizing that a four spacecraft formation is not able to fully resolve the evolution of a plasma structure in the general case, we follow here two main approaches. The first one considers the simple problem of a rigid planar structure drifting at constant velocity during the time interval when it is crossed successively by the four spacecraft. Under such circumstances, the speed V along boundary normal, and corresponding direction n, can be determined from the so called timing analysis method. The method relies on the equation r n • n = V t n , where r n and t n are the differential positions and times of crossing by three spacecraft relative to position and time of crossing by the fourth spacecraft chosen as reference. This method has proven to be successful in a number of studies carried on by CLUSTER (see for instance [START_REF] Dunlop | Four-point Cluster application of magnetic field analysis tools: The discontinuity analyzer[END_REF]. The second approach compares simply the shape of the four density profiles and identifies similar features in those profiles as signature of a structure coherent in time and/or space. This is facilitated by plotting density variations as a function of the L parameter. Relative spatio-temporal positions of identified features can further be used to derive useful characteristic dimensions.

The paper is divided in two main parts. The first part presents the general context: density measurements, orbital properties, general features observed in the Plasmasphere Boundary Layer (PBL, [START_REF] Carpenter | Remote sensing the Earth's Plasmasphere[END_REF]. The second part presents detailed observations of two density structures, and some discussions about the physical processes implied.

GENERAL CONTEXT

Measurement techniques

The density observations discussed in this paper are obtained by combining two instruments of CLUSTER: EFW (Gustafsson et al., 1997) and WHISPER [START_REF] Décréau | Whisper investigators, Whisper, a resonance sounder and wave analyser: performances and perspectives for the Cluster mission[END_REF]. Spacecraft potential values SC V derived at a high time resolution by EFW follow the electron density N e variations in a given plasma regime (Laakso and Pedersen, 1998). They can be calibrated by WHISPER measurements [START_REF] Moullard | Density modulated whistler mode emissions observed near the plasmapause[END_REF]. Plasma frequency variations discussed in this paper are obtained from measured values of Vsc and the empirical parametric relationship:

B SC e V A N - * =
. The constant A and B are obtained by fitting data subsets of Vsc measurements and of N e values derived by the WHISPER sounder at a lower time resolution [START_REF] Trotignon | How to determine the thermal electron density and the magnetic field strength from ,the CLUSTER/WHISPER observations around the Earth[END_REF].

Orbitography

CLUSTER travels on a polar orbit of large eccentricity (4 and 19.5 Earth radii respectively at perigee and apogee). During main manoeuvres (activated at least once a year), the spacecraft orbits are adjusted in order for the constellation to form a perfect tetrahedron of prescribed dimension usually in the cusp or close to the magnetopause. This results in an elongated constellation shape at perigee, where the plasmasphere region is encountered. In figure 1 each panel displays, for a given perigee pass, colour coded density values measured at successive spacecraft positions along the four orbit tracks. The orbit tracks are plotted in a meridian plane of the solar magnetic (SM) coordinate system [START_REF] Russell | Geophysical Coordinate Transformations[END_REF], where the abscissa r measures the distance of the spacecraft to the dipole axis and the ordinate z measures the distance of the spacecraft to the magnetic dipole equator. Such a presentation erases the local time differences at the various spacecraft positions, and only three orbit tracks appear as being distinct

General topology

Several interesting features appear clearly on figure 1, illustrating a general behaviour: 1) the major density structures are globally field aligned. This is particularly true for the rather sharp density gradients typical of the plasmapause knee ('yellow' density levels in the 13 th June 2001 plots). It is also the case for density features separated from the main plasmasphere body as viewed on an orbit cut, which does not mean that the feature is necessarily detached (see example at L= 6, in the 5 th June 2001 plot, northern hemisphere), 2) a large number of density irregularities (10 to 200 cm -3 N e levels, typical density variations observed at plasmapause) are observed on some orbits (5 th and 24 th June 2001). The region encompassing those irregularities appears as rather large (entire orbit segment below L ~ 5), roughly centred on the magnetic equator. This region has recently been called the Plasmasphere Boundary Layer [START_REF] Carpenter | Remote sensing the Earth's Plasmasphere[END_REF]). The solid lines highlight two positions of the cylindrically symmetric Roche limit surface, or Zero Parallel Force (ZPF) surface if the angular velocity of the plasma would be 3 times larger than the corotation velocity (inner curve) and 1.5 times the corotation velocity (outer curve). According to the theory outlined by [START_REF] Lemaire | Hydrostatic equilibrium and convective stability in the plasmasphere[END_REF][START_REF] Lemaire | The formation of the light-ion-trough and peeling off the plasmasphere[END_REF] the part of the plasmasphere outside this limit is convectively unstable, leading to the formation of quasiinterchange modes (see [START_REF] Ferrière | Quasi-interchange modes and interchange instability in rotating magnetospheres[END_REF] with a non-zero component of the k-vector parallel to the magnetic field lines. This produces small-scale density irregularities and leads to plasmapause formation via erosion in the post-midnight MLT sector, where the plasma angular velocity is the largest and the ZPF surface closest to Earth. André (2004) has calculated that the characteristic time for this type of instability is of the order of 10 minutes.

It happens that the Cluster orbit below L ~ 5 is roughly aligned with a Roche limit surface, such that a large orbit segment will encounter similar unstable conditions if the surface happens to meet the orbit position, i.e. at plasma angular velocities about twice that of co-rotation. The presence of irregularities along large orbit segments is compatible with the hydrodynamic instability (HI) theory proposed by Lemaire. Let's hope that future studies will enable us: (i) to follow the formation of irregularities in the post-midnight sector and during magnetic substorms, where and when they are supposed to form; (ii) to identify how these density irregularities are convected away from the unperturbed co-rotating inner part of the plasmasphere, to be found later in the dusk sector.

DETAILED OBSERVATIONS

Observations of the plasmapause region when spacecraft are widely separated

Large separations are linked to large time intervals between spacecraft when crossing the same region of space. In June 2001, three spacecraft (C1, C2, C4) were within 2000 km of each other (sketch of Figure 1); C3 was significantly farther (at a distance of about 10 000 km from the trio). The perigee is then at 17.3 MLT. Such an elongated configuration can be used for testing the stability of large scale boundaries. Using the timing analysis method described in the introduction, we have analyzed the motion of the plasmapause (PP) crossed around 00:05 UT by the C124 trio and 40 minutes later by C3 (as shown in Figure 2). This requires three conditions to be met: planarity, rigidity and velocity constancy. The four crossing points form a tetrahedron of reasonable characteristics, leading to a satisfying precision (~ 5%) both on orientation and magnitude of drift velocity. This tetrahedron is inscribed within a sphere of ~ 1000 km radius, such that the requirement of planarity of the travelling boundary needs to be satisfied only at that scale. The position of the crossings are shown in figure 1 (middle panel) by the yellow region at L ~ 8, southern hemisphere. There, the magnetic shell curvature radius is large enough (about 5 R E ) for planarity to be satisfied locally. Concerning the rigidity, we note a striking similarity between the four density profiles displayed in Figure 2 (discarding small scale features). The thickness of the overall boundary layer and density distribution within, which are not varying significantly from one pass to the other, can qualify both as 'rigid' and travelling at a roughly constant velocity. The timing analysis indicates that the plasmapause velocity is low: 0.33 km s -1 in the GSE system (the total displacement over the large time interval studied is only 910 km, ~ 0.15 R E ). The respective components of the boundary unit normal are 0.78, 0.26 and 0.56. This vector is not oriented parallel to the local meridian plane (the X component is not small), as could be expected from an axisymmetric plasmapause. Considering that the boundary is encountered at a large L value (L = 8) in the dusk sector, the likely explanation is that the plasmasphere expands in a bulge along the Y axis. The bulge is crossed by Cluster on its night-side flank, aligned with a magnetic shell oriented roughly along the 18 MLT meridian plane. We have tested the likeness of our interpretation and assumptions against independent information: the DC magnetic field vectors measured by the FGM instrument at the four crossing points. The four vectors have the same orientation within ± 2° (confirming planarity). They are all perpendicular to the estimated boundary normal (within ± 2°), confirming the view of a plasmapause locally aligned with a magnetic shell.

After 00:30 UT, small scale structures (S) with large density indentations show up in the electron density versus time profiles of Figure 2 (density scales are shifted). In order to facilitate the comparison of the four profiles, we can plot the N e values measured at various positions as a function of the L parameter. Such an approach is directly relevant to in-situ observations when they are obtained by quasi equatorial missions, like ISEE 1. In the case of Cluster, we make use of a magnetic field model, combining IGRF95 and Tsyganenko-96 [START_REF] Tsyganenko | Modeling the global magnetic field of the large-scale Birkeland current systems[END_REF]. We follow the magnetic field line provided by the model from the spacecraft position to the equator (identified by a minimal magnetic field strength value), using the Unilib library (see reference list). The geocentric distance of this equatorial point, which we call R eq and which we express in Earth radii, plays the same role as the L value. As this paper deals mainly with small structures, we ignore the density variation with altitude in a magnetic tube of constant flux. All density values presented are raw in-situ measurements. The details of the indentation crossed around 00:30 UT by the C1, C2, C4 trio, are displayed in Figure 3. They point out the same density signature, referred to below as H 1 H 2 : a pair of density holes separated by roughly 0.2 R E along the R eq parameter. In Figure 3, time runs from right to left and from bottom to up: C2 crosses the structure the first, C1 13 s later (H 1 , the first encountered density hole, is chosen as marker), C4 127 s after that, and finally C3, roughly 40 minute after the trio. The orbit elements crossed by C1, C2 and C4 between the density holes H 1 H 2 are located in almost the same meridian plane of the SM coordinate system (differences in longitude are less than one degree), which happens to be close to the YZ plane. In figure 4, those elements are plotted as line segments of the YZ plane. The three DC magnetic field vectors measured by the FGM instrument, plotted at the H 1 markers, are quasi parallel to this plane (at an angle below 3°). In this particular configuration, figure 4 shows that the three spacecraft, which are less than 350 km apart in the third dimension (along the X axis) are roughly aligned along a direction roughly parallel to the magnetic field direction. They recognize the same cross-field structure, within a short time interval.

We can now discuss the dimension of the double indentation structure. In the plane of figure 4 (YZ plane of the SM coordinate system), its overall size along the field direction is 2000 km or more, whereas the distance between the field lines respectively along H 1 holes and H 2 holes is about 800 km. The field line distance of smaller irregularities is below 100 km. In the third dimension -in longitude -we can only state that the structure is larger than the maximal spacecraft separation, i.e. about 350 km.

Another interesting piece of information derived from the multipoint measurements is the time life of the well defined density holes observed. A detailed inter-comparison of the three similar density profiles show actually slight differences between them, indicating either that there are differences over even smaller dimensions, or that the structure has evolved in time, over less than one minute time interval. Note that the profile measured by C3 is different, displaying shallower indentations (see figure 3). This could be a temporal effect, due to refilling (both magnetic feet are illuminated at ionospheric altitude), or to cross-field interchange motion. Alternatively, it could be a longitude effect (C2, C4, C1 and C3 are placed at increasing respective longitudes, within one degree total).

Observations of the plasmapause region when the spacecraft are close to each other

For a duration of about 4 months in 2002, the CLUSTER configuration has been adjusted to small separations, while the perigee was located in the midnight to dusk local time sector. Preliminary analysis confirms here also the presence of frequent small scale density irregularities in the vicinity of the plasmapause and inside the plasmasphere [START_REF] Darrouzet | Density structures inside the plasmashere,: Cluster observations[END_REF]; some of them can clearly be identified as the same entities on all four density profiles. We can in such cases apply the timing analysis, as done above.

Figure 5 displays detailed electron density profiles as a function of R eq at the plasmapause discontinuity observed the 9 th of May 2002 on the inbound leg near L = 6, around 19 MLT. There, the orbit track and the magnetic field lines make an angle of about 60°, hence successive field lines at decreasing R eq are crossed rapidly: 1 R E range in about 10 minutes. The four profiles show density values fluctuating between two smooth levels reached respectively in the high and low R eq range, a typical situation in the outer plasmasphere region (as illustrated in Lemaire and Gringauz, 1998, chapter 2). These density fluctuations are well correlated, except near the foot of the plasmapause region (R eq ~ 6), where it is clear that the four spacecraft do not sweep through a stagnant rigid 1D structure, like that detected below Req = 5.8. Various explanations can be proposed and considered: this can be a density structure of complex 3D shape which is standing still, or else a 1D double peak which varies in shape with time, or even more elaborated behaviours that will have to be examined in more comprehensive studies.

Focusing on the plasma blob of higher density observed between R eq = 6.0 and R eq = 6.5 R E , we have conducted an analysis in the SM coordinate system (not to fully describe in this short paper). The exercise indicates that either the blob moves rapidly (at about 5 km s -1 ) from a higher to a lower L shell, or that a discontinuity surface almost parallel to a local meridian plane separates C1 and C4 on one hand (earlier local times), from C2 and C3 on the other hand (later local times). This thin layer would be ~ 20 km wide. Across this thin layer, a rigid 3D blob could change position in L shell.

We have analysed the motion of the density dip observed at R eq = 5.7 to 5.8 via timing analysis. In this case of a small constellation (largest separation of 350 km at traversal points in the moving plane), the assumption of a planar boundary seems justified. The exercise yields velocity components of respectively -2, 0.7, 0.5 km s -1 in the GSE co-ordinate system, indicating that co-rotation (~ 2 km s -1 at this position) is the major mechanism involved in the plasma motion. On the other hand, the local orientation of magnetic field is measured at an angle of ~ 30° with the boundary. If the conditions for applying timing analysis are met, part of the motion is parallel to field line. This opens the possibility of hydrodynamic instability (HI) with a parallel component of centrifugal force. The plasma interchange velocity value according to the HI model can be evaluated from the formula listed in Lemaire and Gringauz, 1998, p. 263. For the density irregularities shown in Figure 5 above Req = 5.5 (dip and blob with ∆n ~ 50 cm -3 ) it amounts to a value of about 0.2 km s -1 . If interchange is indeed at work, the corresponding motion of irregularities is too slow to be distinguished from co-rotation in this case, and we cannot conclude.

SUMMARY AND DISCUSSION

The configuration of CLUSTER orbits allows the four platforms to cross the outer region of the plasmapause, and has revealed large and small-scale patchiness of the plasma distribution in this transition region. The small separation (from 100 km up to 12 000 km) between the four spacecraft, combined with the very high time resolution (less than 3 s) of the WHISPER and EFW observations, offer unprecedented opportunities to study in greatest details the small-scale irregularities in the narrow region of the plasmapause boundary layer.

In this study, it has been shown that the plasma irregularities observed at the plasmasphere boundary have dimensions along magnetic field larger than 2000 km (at least in the case event analysed), cross-field dimensions ranging from less than 20 km to more than 350 km, and a wide range of lifetimes (from 10 seconds to several tens of minutes). Drift velocities have been derived from timing analysis, demonstrating -if simple assumptions are met -the slow motion of both a small and a large-scale density discontinuity. The results presented above constitute a first step toward further studies of plasma irregularities at the plasmapause boundary layer. In particular toward testing if plasmapause density gradients are forming due to plasma interchange instability [START_REF] Lemaire | Hydrostatic equilibrium and convective stability in the plasmasphere[END_REF][START_REF] Lemaire | The formation of the light-ion-trough and peeling off the plasmasphere[END_REF].

Fig. 1 .

 1 Fig.1. Colour coded density values measured at three perigee passes in the dusk sector, plotted along the spacecraft orbits in the SM coordinate system. C4 travels at the lowest altitudes, C1 at the highest ones. At intermediate altitudes, the track of C3 hides that of C2, taken about 45 minutes earlier. Dotted curves are dipole field lines (from L=3 to L=8). Solid curves are cuts of Roche limit surfaces. Constellation configurations close to perigee are sketched on the right (C1 in black, C2 in red, C3 in green and C4 in purple), respectively for the June 2001 epoch and for the May 2002 epoch (event of figure 5).

  . The shape of Cluster configuration is sketched on the right of the figure, respectively top right for large average separation (June 2001) and bottom right for small separation (May 2002). In both cases, the largest separation (~ 10000 km in June 2001, ~ 300 km in May 2002) is aligned roughly along the orbit, tangent to the magnetic field direction at the equator. Across the orbit, the average separation is ~ 2000 km in June 2001, ~ 60 km in May 2002. The shape is less regular at large separation, three spacecraft, C1, C2 and C4, being grouped as a trio, than at small separation. Dipole field lines are plotted from L=3 to 8 (dotted lines), where the McIlwain parameter L (McIlwain, 1961) identifies a surface of cylindrical symmetry with respect to the dipole axis. Real field line orientations measured onboard by the FGM instrument (Balogh et al., 1997) deviate from this representation, which nevertheless guides the eye to recognize global features. It takes about 1 hour 40 minutes for a spacecraft to travel from South to North between the two orbit positions located at L=6. MLT values at perigee are listed at the top of each orbit plot. They are decreasing from South to North, of about 1.8 hours between the two orbit positions located at L=6.

Fig. 2 .

 2 Fig.2. Compared density time profiles obtained on spacecraft C1 (solid line), C2 (dotted line), C3 (dashed line) and C4 (dash-dotted line), at the inbound leg of the 13 June 2001 pass. The analysed features, PP and S, are pointed.

Fig. 3 .

 3 Fig.3. Details of the structure S: density versus R eq parameter. Density values have been multiplied by 10 for C1, 100 for C4 and 1000 for C3. Time runs from right to left. UT values are given at pointed H 1 dips.

Fig. 4 .

 4 Fig. 4. Case event of 13 June 2001. Position of the density structure H 1 H 2 (line style as in Figure 2) in a meridian plane of the SM coordinate system. The arrows indicate the respective magnitudes (350 nT for C1) and orientation of the measured magnetic field vectors.

Fig. 5 .

 5 Fig. 5. Details of the electron density profiles versus R eq parameter measured on 9 th May 2002. Line code as in figure 2. The two thin lines are R eq -4 profiles fitting observations respectively at low and high R eq values. Arrows point to structures discussed in text.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the ESA teams at ESOC, Germany, and JSOC, UK, and the WEC operation team (University of Sheffield, UK), for their efficient work in operating the four spacecraft and four sets of WEC instruments. The Whisper team thanks CNRS and CNES, France, for their continuous support of the experiment. J. Lemaire and F. Darrouzet acknowledge the support by the Belgian Federal Science Policy Office through the ESA/PRODEX-7 CLUSTER project.