Etienne Papegnies

Vincent Labatut

Richard Dufour

Georges Linarès

Graph-based Features for Automatic Online Abuse Detection

Keywords: Text categorization, Abuse detection, Online communities, moderation

While online communities have become increasingly important over the years, the moderation of user-generated content is still performed mostly manually. Automating this task is an important step in reducing the financial cost associated with moderation, but the majority of automated approaches strictly based on message content are highly vulnerable to intentional obfuscation. In this paper, we discuss methods for extracting conversational networks based on raw multi-participant chat logs, and we study the contribution of graph features to a classification system that aims to determine if a given message is abusive. The conversational graph-based system yields unexpectedly high performance, with results comparable to those previously obtained with a content-based approach.

Introduction

The widespread availability of Internet access allows users from around the world to congregate into online communities. With the ever-increasing number of users, online communities have become important places to trade ideas, and have acquired a great socio-economical importance.

However, because of the anonymity provided by the medium, an online community is often confronted with users that display abusive behaviors. For community maintainers, it can be important to act on this issue through the use of moderation, because failure to do so can poison the community, trigger user exodus, and expose the administrators to legal jeopardy. Moderation is the application of sanctions when users are judged to violate the community rules. When done by humans, this work is expensive and companies have a vested interest in automating the process. One can distinguish two types of automated systems assisting in moderation: 1) an automated flagging system that raises some messages to the attention of moderators; and 2) a fully automated system that detects abusive messages and executes sanctions on users that are breaking the community rules.

In this work, we consider the classification problem of automatically determining if a message from a user is abusive or not. For this purpose, we propose an original approach aiming at exploring a range of graph-based features extracted from online textual conversations. We first extract various types of conversational networks, i.e. graphs where vertices represent users and where edges correspond to supposed message-based interactions between them. We then process a number of graph-theoretical measures that characterize these networks in different ways. A classifier is then trained and tested on a corpus of chat logs originating from the community of the French massively multiplayer on-line game SpaceOrigin1 . We finally conduct a qualitative study to analyze the impact of each graph-based feature on the automatic abusive message classification performance.

The rest of this paper is organized as follows. In Section 2, we review related work on abuse detection and network extraction from raw conversation logs. In Section 3, we describe the method proposed to extract conversational networks, and the topological features that we compute for the resulting graphs. In Section 4, our dataset is presented as well as the overall experimental setup for the classification task. A discussion and a qualitative study of our results is also provided. Finally, we summarize our contributions in Section 5 and present some perspectives.

Related Work

This section is a brief review of the literature focusing on the most relevant works relating to two aspects of the problem at hand. First, in Subsection 2.1, we review general works regarding the detection of online abuse. Second, in Subsection 2.2, we explore previously used techniques to extract network structures from raw conversation data.

Abuse Detection

One can distinguish two main categories of works related to abuse detection: those using the content of the exchanged messages and those focusing on their context. Some works also propose to combine both categories.

From the content-based point-of-view, the work initiated by Spertus in [START_REF] Spertus | Smokey: Automatic recognition of hostile messages[END_REF] was a first attempt to create a classifier for hostile messages. This is relevant to us, because abusive messages often contain hostility. They use static rules to extract linguistic markers for each message: Imperative Statement, Profanity, Condescension, Insult, Politeness and Praise. These are then used as features in a binary classifier. They obtain good results, except in specific cases like hostility through sarcasm. However, the limitation of this approach is that its application to another language is a difficult task, requiring to transpose it to other grammar rules and idioms.

Cheng et al. [START_REF] Chen | Detecting offensive language in social media to protect adolescent online safety[END_REF] note that a word tagged as offensive in a message is not a definite indication that the message is offensive, i.e. while "You are stupid." is clearly offensive, "This is stupid. xD" is not. Lack of context can be somewhat mitigated by looking at word n-grams instead of unigrams (i.e. single words).

Dinakar et al. [START_REF] Dinakar | Modeling the detection of textual cyberbullying[END_REF] use tf -idf features, a static list of badwords and of widely used sentences containing verbal abuse to detect cyberbullying in Youtube comments. Again, their model showed good results, except when sarcasm was used.

In [START_REF] Chavan | Machine learning approach for detection of cyberaggressive comments by peers on social media network[END_REF], Chavan et al. review machine learning approaches to detect aggressive messages in on-line social networks. They show that Pronoun Occurrence, usually neglected in text classification, is important, and use Skip-Gram features to mitigate the context issues.

Content-based text classification usually makes for a good baseline. Content features are inexpensive to compute. However, such methods have severe limitations: for instance, abuse can be spread over a succession of messages. Some messages can reference a shared history between two users. Even more common are users that are voluntarily obfuscating message content to work around badwords detection. Indeed, abusers can bypass automatic systems by making the abusive content difficult to detect [START_REF] Hosseini | Deceiving google's perspective api built for detecting toxic comments[END_REF]: for instance, they can intentionally modify the spelling of a forbidden word.

Because the reactions of other users to an abuse case are completely beyond the control of the abuser, some works consider the content of messages around the targeted message.

For instance, Yin et al. [START_REF] Yin | Detection of harassment on web 2.0[END_REF] use features derived from the neighboring phrases of a given message to detect harassment on the Web. Their goal is to spot conversations going off-topic, and use that as an indicator. Their approach shows good results when used against multi-participant chat logs, and they note that sentiment features seem to constitute mostly noise due to the high misspelling rate.

In [START_REF] Cheng | Antisocial behavior in online discussion communities[END_REF], Cheng et al. propose to focus on building user behavior models. For this purpose, they perform a comprehensive study of antisocial behavior in online discussion communities. Their work provides insight into the devolution of abusive users over time in a community, regarding both the quality of their contributions and their reactions towards other members of the community. A critical result of the analysis is that instances of antisocial messages usually generate a bigger response from the community, compared to normal messages.

Balci et al. [START_REF] Balci | Automatic analysis and identification of verbal aggression and abusive behaviors for online social games[END_REF] make use of user features to detect abuse in the community of an online game. These features include information such as gender, number of friends, financial investment, avatars, and general rankings. The goal is to help human moderators dealing with abuse reports, and the approach yields sufficiently good results to achieve it. However, in our case the user data necessary to replicate this approach is not available.

In our own previous work [START_REF] Papegnies | Impact of content features for automatic online abuse detection[END_REF], we propose to detect abusive messages from chat messages using a wide array of language features (bag-of-words, tf -idf scores, sentiment scores, etc.) as well as context features derived from the language models of other users. We also try advanced preprocessing approaches. This method allowed us to reach a performance of 72.1% in terms of F -measure on an abusive message detection task.

Network Extraction from Raw Data

Although a major part of the solutions focus on content features of exchanged messages to address the abuse problem, it appears that a user with previous exposure to automatic moderation techniques can easily circumvent them [START_REF] Hosseini | Deceiving google's perspective api built for detecting toxic comments[END_REF].

To avoid this problem, a solution would be to not focus only on the direct content exchanged but on the interactions between the users through these messages.

The number of respondents to a given message appears frequently in the literature, as a classification feature, e.g. [START_REF] Cheng | Antisocial behavior in online discussion communities[END_REF]. However, there are not many works dealing with the extraction of conversational networks. This may be due to the fact that the task can be far from trivial, depending on the nature of the available raw data: the task is much harder for chat logs than for structured messages board or Web forums, for instance. These networks have the advantage of including the mentioned feature, but also much more information regarding the way users interact.

In [START_REF] Mutton | Inferring and visualizing social networks on internet relay chat[END_REF], Mutton proposes a strategy to extract such a network from IRC chat logs. The goal is to build a tool to visualize user interactions in an IRC chat room over time. The author uses a simple set of rules based on direct referencing (when a user addresses another one by using his nickname), temporal proximity of messages, and temporal density of messages. In this paper, we will adapt and expend on those rules. Specifically, while in a regular IRC channel timestamps are indeed useful to determine intended recipients of a message, in our case they are basically irrelevant, so this approach cannot be adapted as is.

Travassoli et al. [START_REF] Tavassoli | Constructing social networks from semistructured chat-log data[END_REF] explore different methods to extract representative networks from group psychotherapy chat logs. One method includes fuzzy referencing to mitigate effects of misspelled nicknames, and rules for representing one-to-all messages. The bulk of the methods uses static patterns of exchanges to predict a receiver. Their system shows a good agreement score with a human annotator.

Sinha et al. [START_REF] Sinha | Investigating substructures in goal oriented online communities: Case study of ubuntu irc[END_REF] use only direct referencing, but with the same fuzzy matching strategy, in order to extract a network representing the activity in the #ubuntu IRC support channel. This method manages to expose high level components of the Ubuntu social network, which in turn allows for the qualification of user behaviors into specific classes. This method of building user models can be very interesting when the data describing the users are scarce, as is the case on IRC where everyone can join and there is no requirement to register.

Methods

In this section, we describe our proposed original approach to detect abusive messages. It basically consists in training a classifier on features corresponding to topological measures processed on conversational networks. The classifier is standard, so we focus on the processing of the features. Thereby, Subsection 3.1 presents how we extract conversational networks from conversation logs, while Subsection 3.2 describes the topological measures computed for these conversational networks, and later used as classification features.

Network Extraction

We extract networks representing conversations between users, through a textual discussion channel. They take the form of weighted undirected graphs, in which the vertices and edges represent the users and the communication between them, respectively. The edge weights are a score which is an estimation of the intensity of the communication between the two connected users. Note that each network is defined relatively to a targeted message, since the goal of this operation is to provide features used to classify the said message.

The first step consists in determining which messages are used to extract the network. For this purpose, we define a context period, which is centered on the targeted message, and spans symmetrically before and after its occurrence. We arbitrarily use a width of 200 messages in our experiments. The graph extracted from this context period contains only the vertices representing the users which posted at least once on this channel, during this period.

The second step is to add the appropriate edges to the network, and to process their weight. We use a method based on a sliding window, a choice that is justified by two properties of the user interface of the considered discussion channel: 1) when a user joins a channel, the server sends him only the last 20 messages posted on the channel; and 2) it is impossible for a user to scroll back the history further than 20 lines. In our experiments, we arbitrarily use a window of 10 messages. We apply an iterative process, consisting in sliding the window over the whole context one message at a time. We call current message the last message of the window taken at a given time. Our assumption is that this message is destined to the authors of the other messages present in the window at this time. Furthermore, we suppose it is more likely that the message concerns the users who posted the most recently. These hypotheses can be justified by another property of the user interface: by default, users do not know who is in the channel at a given time, in particular the join / part events are not shown to them.

Based on these hypotheses, we update the edges and weights in the following way. First, we list the authors of the messages currently present in the window, order them by last message posted, and discard the author of the current message (since it is possible that several of his messages appear in this window): this results in what we call the neighbor list. However, the user interface allows to explicitly mention users in a message by their name, and the game prevents the users from changing their name: we need to take this property into account. For this purpose, we move the users directly referenced in the current message at the top of our list. If a user was not even in the window, it is simply inserted at the top of the list. Each user in the neighbor list is assigned by a score, which is a decreasing function of both his position in the list and of the length of the neighbor list. We can then update the graph: we create an edge between each user in the neighbor list and the author of the current message, with a weight corresponding to the user's score. If this edge already exists, we increase its current weight by the user's score.

Our choice to create or update edges towards all users in the window even in case of direct referencing is based on several considerations. First, directly referencing a user does not imply that he is part of the conversation or that the message is directed towards him: for instance, his name could just be mentioned as an object of the sentence. Second, there can be multiple direct references in a single message. Third, when in online public discourse, directly addressing someone does not mean he is the sole intended recipient of the message. For instance when discussing politics, a question directed towards someone can have as a secondary objective to have the target expose his stance on an issue to the other participants.

Once the iterative process has been applied for the whole context period, we get what we call the Full network. For testing matters, we also process 2 lesser networks based on the same context: the Before and After networks are extracted using only the 100 messages preceding and following the targeted message, respectively, as well as the targeted message itself. Figure 1 shows an example of the three networks associated with an abusive comment.

Features

The classification features we consider in this work are all topological measures, allowing to characterize graphs in various ways. We adopt an exploratory approach and consider a wide range of such measures, focusing on the most widespread in the literature. In the following, we describe them briefly, distinguishing between local ones, which characterize individual vertices, and global ones, which describe the whole graph at once. We process all the features for each of the 3 types of networks (Before, After, Full) described in the previous subsection.

Local Topological Measures. These measures are computed for the Vertex corresponding to the author of the targeted message.

The Degree centrality is a normalized version of the standard degree, which corresponds itself to the number of direct neighbors of the considered vertex. The Eigenvector Centrality [START_REF] Bonacich | Power and centrality: A family of measures[END_REF] can be considered as a generalization of the degree, in which instead of just counting the neighbors, one also takes into account their centrality: a central neighbor increases the centrality of the vertex of interest more than a peripheral one.

The PageRank Centrality [START_REF] Brin | The anatomy of a large-scale hypertextual web search engine[END_REF] is also spectral (like the Eigenvector Centrality), but it is based on very different rationales. It models a random walk occurring on the network, and noticeably includes the possibility for the walker to teleport anywhere in the network at any step. The Hub and Authority Scores [START_REF] Kleinberg | Authoritative sources in a hyperlinked environment[END_REF] are two complementary measures also based on random walks.

The Betweenness Centrality [START_REF] Freeman | Centrality in social networks i: Conceptual clarification[END_REF] is based on the number of shortest paths going through the considered vertex.

In communication networks, it is sometimes interpreted as the level of control the vertex of interest has over information transmission in the network. The Closeness Centrality [START_REF] Freeman | Centrality in social networks i: Conceptual clarification[END_REF] is the reciprocal of the total geodesic distance (i.e. the length of the shortest path) between the vertex of interest and the other vertices. It is generally considered it measures the efficiency of the vertex to spread a message over the graph, and its independence from the other vertices in terms of communication. The Eccentricity [START_REF] Harary | Graph Theory[END_REF] is also distance-based, but to the contrary of the other selected measures, it quantifies how peripheral the vertex of interest is, by considering the distance to its farthest vertex.

Finally, the Coreness Score [START_REF] Seidman | Network structure and minimum degree[END_REF] is based on the notion of k-core, which is a maximal induced subgraph whose all vertices have a degree of at least k. The coreness of a vertex is the k of the k-core of maximal degree to which it belongs.

Global Topological Measures. First, we use very classic statistics describing the graph size, the Vertex and Edge Counts. We also select the Density, which corresponds to the ratio of the number of existing edges to the number of edges in a complete graph containing the same number of vertices. In other words, the density corresponds to the proportion of existing edges, compared to the maximal possible number for the considered graph.

We also use two distance-related measures. The first is the Diameter, which corresponds to the highest distance found in the graph, i.e. the length of the longest shortest path. The second is the Average Distance, which is the average length of the shortest path processed over all pairs of vertices.

We process the total Clique Count in the network, where a clique is a complete induced subgraph. The Degree Assortativity [START_REF] Newman | Assortative mixing in networks[END_REF] is also potentially interesting. It corresponds to the correlation processed between the series constituted of all connected vertices, and measures the statistical dependence between the degrees of two vertices and the presence of an edge connecting them. Finally, for each one of the 10 previously described local measures, we process the average over the whole graph.

Experiments

In this section, we first briefly present our corpus and our experimental setup (Subsection 4.1), before describing and discussing our classification results (Subsection 4.2).

Experimental Setup

We have access to a database of 4, 029, 343 messages that were exchanged by the users of a browser-based multi-player game. In the database, 779 messages have been flagged by one or more users as being abusive and subsequently confirmed as abusive by the game moderators. Each message belongs to a unique communication channel.

We further extract 2, 000 messages at random from the messages not confirmed as abusive to constitute the non-abuse class. We previously experimented with this dataset in [START_REF] Papegnies | Impact of content features for automatic online abuse detection[END_REF].

Because of the relatively small dataset, our experiment is set up for 10-Fold cross validation. We use a 70%-train / 30%-test split.

We use Python-iGraph [START_REF] Csardi | The igraph software package for complex network research[END_REF] to create the network and process the graph-based features for each message. As a classifier, we use an SVM, implemented in Sklearn under the name SVC (C-Support Vector Classification) [START_REF] Pedregosa | Scikit-learn: Machine learning in python[END_REF] toolkit.

Results

Table 1 displays the results obtained for our random baseline, the content-and context-based classifier we previously presented in [START_REF] Papegnies | Impact of content features for automatic online abuse detection[END_REF], and the graph-based classifier proposed in this article. The baseline uses the same classifier and architecture but the feature extraction step is replaced by a dummy function that yields two random values in [0, 1]. Our previous approach takes advantage of morphological, language and user behavior-based features, such as: message length, number of words, compressibility, bag of words with tf -idf scores and probability of n-gram emission. In the present experiment, the training and testing sets were resampled, which explains why the values displayed for the content/contextbased classifier are slightly different form the ones shown in [START_REF] Papegnies | Impact of content features for automatic online abuse detection[END_REF].

With the graph-based approach, the performance is improved according to all 3 considered measures, compared to our previous effort. The overall performance is unexpectedly high for an approach that completely ignores the content of the messages. We suppose that this is mainly due to the fact that two thirds of the features include information regarding to the part of the conversations happening after the classified message, whereas this was the case for only two features (out of 67) in our content/context-based approach. Independently from this point, the fact that both approaches reach relatively high performance levels is a very promising result: given that both classifiers are built on completely different features, combining them should even improve the overall performance.

Table 1. Classification results (in %) of the 3 abusive message classifiers: a random baseline, our previous approach [START_REF] Papegnies | Impact of content features for automatic online abuse detection[END_REF], and the one presented in this article. All measures are computed for the Abuse class. Since our classifier is an SVM, we can use the Platt Scalling implementation of Sklearn to vary the decision threshold and therefore tune the system towards either high precision or high recall. The left plot of Figure 2 shows the Precision-Recall curves of each of the 10 classifiers created for our experiment. One can see that by lowering the post probability threshold a little, it is possible to gain better coverage of the abuse class without losing too much precision. Therefore, we would argue that this system shows better promise as an alert system than as an automated moderation system. In order to estimate the importance of our features with regards to this classification task, we use the meta estimator ExtraTreesClassifier provided by the Sklearn toolkit. While the process is stochastic, it allows to give features a score indicating their contribution to the decisions of the classifier. We run further ablation runs, ordering the features by increasing impact of their removal on the classifier performance. This allows obtaining a smoother curve, with a performance drop on the right-side, corresponding to the removal of the most discriminant features (right plot of Figure 2). Table 2 shows the 10 most discriminant features: using only these features, one can train a classifier obtaining a F -Measure score of 75.8%. Overall, these features are quite heterogeneous, topologically speaking, in the sense they correspond to very different ways of characterizing graph structures. The Degree Centrality, Edge Count, and Density features are based on a microscopic view of the graph (vertices and edges are considered individually, or only with respect to their direct neighborhood). On the contrary, the Betweenness Centrality, Hub Score and Eccentricity are macroscopic, because they take advantage of paths spanning the whole graph. Finally, the Coreness Score is mesoscopic, in the sense it is based on an intermediate view and considers subgraphs. This is consistent with the assumption that redundant features should not appear amongst the most discriminant ones.

Experiment

At first sight, finding both Edge Count and Density can be surprising: given that the latter is a normalized version of the former, one could suppose they are redundant. However, this normalization is based on the number of vertices in the graph. Thus, in the present case, this simply means that the number of edges in our networks does not increase as a square function of number of vertices. On the contrary, certain features present in the table are part of some very correlated groups of features, which can be considered as almost inter-exchangeable. For instance, the Average Eigenvector Centrality and Average Hub Score for the Before graph have a 0.73 correlation.

All 3 considered types of graphs (Before, After, Full ) are represented in these top features, which means they convey different information and are all of some help regarding the classification problem at hand. Moreover, it appears that certain related features appear together for several versions of the graph. This is the case for the Edge Count (Before vs. After ), and of the Hub Score and Eigenvector Centrality (Full vs. Before). We assume that this reflects the fact abuses significantly modify the graph structure, according to these topological measures. In other words, they reflect strong changes in the conversation dynamics. When a measure appears only for the Before or After version of the graph, we conclude it allows characterizing only the pre-or post-state of the conversation, relatively to the abuse.

It is interesting that both the individual and average Eccentricity features are present in this table. A closer look reveals that their values are lower for graphs belonging to the Abuse class. This means that the maximal distance between the author of the targeted message and the rest of the graph decreases in case of abuse. More concretely, this user becomes less peripheral (or more central), and the same goes for the other users of the graph (in average). This fits in quite well with assumptions about how abuse impacts a discussion: an abuser would tend not to be peripheral in a conversation, while we can reasonably assume that the other participants will be piling on and therefore be less peripheral themselves. This may also explain why those features are, by far, the most discriminant ones.

Conclusion

In this article, we have presented an approach purely based on graph features to tackle the problem of automatically detecting online abuse. The method, while simple, yields reasonable results, besting the score obtained with our previous effort, which was content-and context-based.

However it is important to note a couple of important limitations. First, the amount of necessary computation is quite high if it is to be applied each time a new message is posted to the channel, compared to a pure content-based approach. Second, the method can only be applied after a delay when the necessary number of messages have been posted in response to the target message -this is not a method that can help prevent the 5 th message in a torrent of insults from reaching the channel. Rather, it could be used to perform some a posteriori moderation.

The next step in our study will be to assess the impact of different network construction strategies on the performance of the classifier. This will include experimenting with other weight distribution strategies, and different sizes for the context period and the sliding window. We will then aim to combine this system with our content-based classifier: in theory, they are both based on completely different types of information, so we can assume they are complementary and could lead to improved classification performance.

Fig. 1 .

 1 Fig.1. Example of the 3 types of conversational networks extracted for a given context period: Before (left), After (center), and Full (right). The abusive user is represented in red.

Fig. 2 .

 2 Fig. 2. Left: Precision-Recall curves of the 10 SVM classifiers. Right: Feature ablation curves of one classifier (200 runs). In both plots, the red curve represents the average.

Table 2 .

 2 Most useful features of the graph-based classification approach.

	Network	Feature name	F -Measure before ablation
	Full	Average Betweenness Centrality	75.8
	Before	Average Coreness Score	75.4
	After	Edge Count	74.5
	After	Density	73.1
	Full	Hub Score	72.9
	After	Degree Centrality	67.7
	Before	Edge Count	67.2
	Full	Average Eccentricity	58.4
	Before	Average Eigenvector Centrality	56.6
	Full	Eccentricity	35.0

https://play.spaceorigin.fr/

Acknowledgments.

This work was financed by a grant from the Provence Alpes Côte d'Azur region (France) and the Nectar de Code company.


Nicolò Riva
email: nicolo.riva@epfl.ch

Francesco Grilli
email: francesco.grilli@kit.edu

Bertrand Dutoit
email: bertand.dutoit@epfl.ch

AURORA: Learning Superconductivity Through Apps

Keywords: App, teaching, web application, COMSOL, superconductivity, AURORA, open access

The growing interest in modeling superconductors has led to the development of increasingly effective numerical methods and software. Alongside this interest, the question of how to teach and to explain the operation of superconductors to students has arisen. EPFL and KIT have created a series of web applications based on COMSOL Multiphysics that are accessible through an open access web server called AURORA. This project allows users to dynamically change the parameters of the apps and observe their influence on the results, creating a vivid learning experience. The project is particularly directed to students. If, as Richard Feynman used to say "the questions of the students are often the source of new research," why not stimulate students to ask questions on superconductivity?

I. INTRODUCTION AND LEARNING APPROACH

In confronting the growing necessity of innovative teaching methods, it is necessary to consider students' audience and today's educational system. Modern education is partially online, which open new paths for the learning process.

In Roman mythology, Aurora was a goddess who flew across the sky at dawn, opening the path to the Sun and a new day1 [START_REF] Aeneid | Book IV Verses[END_REF]. Similarly, the server AURORA aims at opening the path to a new generation of brilliant students and 'initiate' them by leArning sUpeRcOnductivity thRough Apps. The possibility of using apps for educational purposes allows demonstrating complex phenomena with a userfriendly interface. It also leverages a straightforward and visual teaching method to raise interest in students and convey the importance that superconductivity has on the world.

II. APPLICATION EXAMPLES

In this contribution, we present three apps currently available on the AURORA server [START_REF]AURORA -leArning sUpeRcOnductivity thRough Apps[END_REF].

A. Time-Dependent Ginzburg-Landau Equation for Type-I and Type-II Superconductors

Superconductors have the property of excluding magnetic fields up to a certain strength. When the field exceeds this strength, the field penetrates the material. This process is modeled by a set of equations, proposed by Ginzburg V. and Landau L. in 1950 [START_REF] Ginzburg | [END_REF]. The app helps visualize the magnetic field penetration in type-I and type-II superconductors (in the latter case, in the form of quantized current vortices). It is possible to modify parameters such as the applied magnetic field, the radius of the sample and the Ginzburg-Landau parameter k, which determines whether a superconductor is type-I (0

< k < 1/ √ 2) or type-II (k > 1/ √ 2).

B. Critical State Model

This applications simulates the electromagnetic response of an infinitely long superconducting wire of elliptical crosssection to a sinusoidal external field applied in transverse direction (perpendicular to the wire's length). The app is based on A. M. Campbell's implementation [4] of Bean's critical state model [5], [6]. Users can change the magnitude of the applied field and the aspect ratio of the wire and calculate the resulting magnetization cycle.

C. Resistive Superconducting Fault Current Limiters

In a power-system the fault currents occurring during a short-circuit can exceed the nominal current by more than ten times. Superconducting fault current limiters (SFCL) can limit the fault current and protect the power system without interruptions. With this app users can investigate the electric and thermal response of a resistive SFCL under AC fault conditions using a 1-D thermal model coupled with circuit. It is possible to evaluate figures of merit such as the limited current, the prospective current and the maximum temperature reached within the tape during the fault and modify the superconducting properties and the geometric parameters of the device.

  (a) AURORA server appearance. (b) Time-Dependent Ginzburg-Landau Model App. (c) Critical State Model App.

Fig. 1 :

 1 Fig.1:The website is open access and does not require a VPN (https://aurora.epfl.ch/app-lib).

"Aurora now had left her saffron bed, and beams of early light the heav'ns o'erspread" Aeneid Book IV, Verses 585-586.


So Noguchi
email: noguchi@ssi.ist.hokudai.ac.jp

Seungyong Hahn
email: hahnsy@snu.ac.kr

Comparison of screening current simulation modellings of REBCO pancake coils

Keywords: numerical simulation, REBCO magnet, screening current, screening current-induced field

An irregular magnetic field generated by screening current in rare-earth barium copper oxide (REBCO) coated conductor is undesired, when REBCO magnets are applied to magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), particle accelerators. The screening current-induced fields (SCIF) have been evaluated in not only experiments but simulations. A few numerical methods have been proposed for screening current simulation. Since these methods have different characteristics, they are compared. Furthermore, a new screening current simulation model, named "ladder equivalent circuit model," is proposed.

I. INTRODUCTION

Rare-earth barium copper oxide (REBCO) coated conductors (CC) are promising for high magnetic field applications; magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), particle accelerator, and fusion. Especially for devices requiring an accurate magnetic field, the screening current-induced field is undesired. Many kinds of researches on screening current are underway [START_REF] Lee | A field-shaking system to reduce the screening-currentinduced field in the 800-MHz HTS insert of the MIT 1.3-GHz LTS/HTS NMR magnet: a small-model study[END_REF]. To simulate the screening current, a few simulation methods have been proposed; simple equivalent circuit model [START_REF] Noguchi | A simple screening current-induced magnetic field estimation method for REBCO pancake coils[END_REF], axisymmetric FEM [START_REF] Wang | Electromagnetic modeling using T-A formulation for high temperature superconductor (RE)Ba2Cu3Ox high field magnets[END_REF], quasi 3D FEM with thin plate approximation [START_REF] Ueda | Spatial and temporal behavior of magnetic field distribution due to shielding current in HTS coil for cyclotron application[END_REF].

As these methods have different characteristics, their superiority and drawbacks must be clarified. In this paper, the characteristics of these simulation methods are discussed. Furthermore, to overcome the drawbacks of these previously proposed method, a new screening current simulation method is proposed. The proposed method employs an equivalent electric circuit consisting of distributed inductances and resistances.

II. SCREENING CURRENT SIMULATION (SEC) MODELS

A. Simple Equivalent Circuit Model

The simple equivalent circuit model [START_REF] Noguchi | A simple screening current-induced magnetic field estimation method for REBCO pancake coils[END_REF] is the simplest among the screening current simulation models. The equivalent screening current circuit is represented with the resistive and inductive components, as shown in Fig. 1. It is magnetically coupled with the equivalent circuit of a pancake coil. To make an equivalent circuit, the following rough assumption is introduced: the screening currents flow along only the top and bottom surface of pancake coil, like Fig. 1. This model takes a short computation time, however the accuracy of screening current-induced field (SCIF) is the worst.

It Li Rcti Icti Iθi Rsti Rrei Lsci Rsci Lj Ictj Rstj Rrej Lscj Rscj Rctj Iθj M scj,θj M sci,θi

B. Axisymmetric FEM (A-FEM)

This method is based on 2D axisymmetric finite element method [START_REF] Wang | Electromagnetic modeling using T-A formulation for high temperature superconductor (RE)Ba2Cu3Ox high field magnets[END_REF] (Fig. 2(a)). It produces a sufficiently accurate solution, though mesh-making is a labor task. The major drawback of this model is that each turn is considered as a single turn, as shown in Fig. 2(b). Moreover, it is impossible to represent an axial current. Therefore, there is a possibility that the screening current is overestimated.

C. Quasi 3D FEM (Q3D-FEM) with thin plate approximation

In this model, a current distribution is computed based on 2D FEM [START_REF] Ueda | Spatial and temporal behavior of magnetic field distribution due to shielding current in HTS coil for cyclotron application[END_REF], as shown in Fig. 3. Each element is supposed to be thin plate, and the thickness of REBCO is approximated using a thin plate approximation technique. In order to compute the magnetic flux density on every element, all the elements are allocated in 3D space, as shown in Fig. 3. This method needs a long computation time. A heavy computation task is also required to compute the magnetic flux density on every element. Hence, a special simulation technique, e.g., a fast multipole method [START_REF] Ueda | Spatial and temporal behavior of magnetic field distribution due to shielding current in HTS coil for cyclotron application[END_REF], is often used.

The phenomenological drawback of this model is to neglect the thickness of REBCO layer. Since the current screening is simulated on 2D plane, the transport current is slowly penetrating into the middle of REBCO layer [START_REF] Noguchi | An extended thin approximation method to simulate screening current induced in REBCO coils[END_REF]. According to [START_REF] Norris | Calculation of hysteresis losses in hard superconductors carrying ac: isolated conductors and edges of thin sheets[END_REF], the transport current should flow on not only the edge but the middle of REBCO layer.

D. Comparison Summary

Table I lists the phenomenological features of models.

TABLE I PHENOMENOLOGICAL FEATURES OF MODELS

Features SEC A-FEM Q3D-FEM Spatial resolution of current × ⃝ ⃝ Current in axial direction × × ⃝ Winding structure of coil × × ⃝ Thickness of REBCO CC × ⃝ × ⃝: good, ×: not good

III. LADDER EQUIVALENT CIRCUIT (LEC) MODEL

In the proposed LEC method, a REBCO CC is represented with distributed inductances and resistances, as shown in Fig. 4. The REBCO CC is divided into many short circuits in the longitudinal and transverse directions. The inductances are computed considering the winding configuration, and the resistances are obtained according to n-value power model. Fig. 5 shows an example of simulation result. In the simulation, the current distribution of single pancake coil was obtained under the conditions of 10-A transport current and external radial magnetic field time transient dB r /dt = 0.01 T/s. The proposed method can take into account the phenomena of axial currents, winding structure, and REBCO layer thickness effect.

IV. SUMMARY

The screening currents in REBCO CC generate an undesired irregular magnetic field. A center magnetic field can be sufficiently evaluated by the previously proposed methods, even though the simulated screening current distributions are a little different. Recently, plastic deformation due to screening currents attracts attention [START_REF] Hahn | 45.5-tesla direct-current magnetic field generated with a high-temperature superconducting magnet[END_REF]. The accurate and precise current distribution is required to compute an accurate stress/strain map for magnet protection. The proposed LEC model does not have the drawbacks that the previously proposed methods have. The comparison between the screening current distributions obtained by every models will be shown and discussed.

MFig. 1 .

 1 Fig. 1. Conceptual illustration of simple equivalent circuit (SEC) model.

Fig. 2 .

 2 Fig. 2. (a) Simulation region on rz-plane (A-FEM). (b) Conceptual drawing of axisymmetric simulation.

Fig. 3 .

 3 Fig. 3. Conceptual image of quasi 3D FEM (Q3D-FEM) with thin plate approximation.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Conceptual illustration of ladder equivalent circuit (LEC) model.