ASSOCIATION EURATOM - HELLENIC REPUBLIC ΕΝΩΣΗ EURATOM - ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ BOOK OF ABSTRACTS 8TH SCHOOL OF FUSION PHYSICS & TECHNOLOGY

Transcript

1 ASSOCIATION EURATOM - HELLENIC REPUBLIC ΕΝΩΣΗ EURATOM - ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ 8 Ο ΣΧΟΛΕΙΟ ΦΥΣΙΚΗΣ & ΤΕΧΝΟΛΟΓΙΑΣ ΣΥΝΤΗΞΗΣ BOOK OF ABSTRACTS 8TH SCHOOL OF FUSION PHYSICS & TECHNOLOGY Volos 6-11 April 2009 UNIVERSITY OF THESSALY DEPARTMENT OF MECHANICAL ENGINEERING Auditoria: Mechanical & Planning Engineering Athens Avenue & Sekeri Str Volos Greece (Info: Tel or Tel/Fax ) Website: We look forward to your active participation in the 8 th School on Fusion Physics & Technology The Programme & Organizing Committees

2 The editor wishes to thank all authors for contributing timely to the preparation of this Book of Abstracts. The financial support of the European Commission, of the General Secretariat for R & T of the Greek Ministry of Development and of the University of Thessaly is gratefully acknowledged (NSV April 2009) ii

3 FOREWORD The 8 th School of Fusion Science & Technology brings together students who have heard little about plasma and fusion, doctoral candidates who are working on problems related to fusion, researchers working on fusion topics for some years and academics staff from universities in Greece who are coordinating research. Also, distinguished researchers from Europe and the USA will give invited talks. The joint attendance of such a school by all the above is creating additional needs and going beyond traditional schools. Thus, the programme committee developed a multi-level series of lectures with the aim to satisfy as many of the audience needs. The programme is divided in four units: School Classes, Invited Lectures, Workshops/Advanced Seminars, and Research Seminars. The School starts Monday morning in the Auditorium of Planning Engineering of the University of Thessaly with the invited lectures on topics of interest to all. In the afternoon there will be a first workshop on Stochastic Modeling and Transport in the Auditorium of Mechanical Engineering. The School classes start on Tuesday morning introductory classes on electrodynamics, plasma and charged particle dynamics, while the second workshop on Viscous MHD Flow, Heat Transfer & Turbulence takes place in the afternoon. The School classes continue on Wednesday morning with kinetic theory and waves, while α plenary session of the National Programme of Controlled Thermonuclear Fusion will be held in the afternoon. This afternoon will be free for students and in the evening the School Dinner will be held. All Thursday will be devoted to School classes such as MHD theory, CFD, Plasma transport, MHD instability and gyrotrons. At the end of the afternoon session, there will be a Teachers/Students interaction with general and specific questions posed by students to be answered by their teachers. Friday morning will be the last session of School classes on plasma turbulence, vacuum flows and computational MHD followed by the invited research seminars. In mid afternoon, the floor will be given to the young researchers participating in the National and European Fusion programme, who will present findings of their current research, all relating to advanced subjects of physics and technology of fusion, in a series of 20-minutes talks. This will continue until Saturday afternoon when the 8th School of Fusion will come to a close and the Certificates of (good) Attendance will be delivered to all participants. In this manner the School of Fusion serves as a multi-disciplinary forum covering the interest of all. We hope that you will find this programme structure rewarding, and we look forward to your active participation, which will warranty its success. In concluding, the organizers of the Fusion Schools in Volos would like to express their sincere thanks to the European Commission for the continuous support, which makes possible this productive science and technology meeting. Volos 6 April The Organizing Committee iii

4 ΠΡΟΛΟΓΟΣ Το 8 ο Σχολείο Φυσικής & Τεχνολογίας Σύντηξης φέρνει μαζί φοιτητές που έχουν ακούσει ελάχιστα για πλάσμα και σύντηξη, υποψήφιους διδάκτορες που εργάζονται σε προβλήματα συνδεόμενα με σύντηξη, ερευνητές που ασχολούνται με θέματα σύντηξης αρκετά χρόνια, και ακαδημαϊκό προσωπικό ελληνικών πανεπιστημίων που διευθύνουν έρευνες. Επίσης, θα κάνουν προσκεκλημένες ομιλίες διακεκριμένοι ερευνητές από την Ευρώπη και ΗΠΑ Η κοινή παρακολούθηση ενός τέτοιου σχολείου από όλους τους παραπάνω είναι φυσικό να δημιουργεί πρόσθετες ανάγκες και να ξεφεύγει από τα παραδοσιακά σχολεία. Έτσι, η επιτροπή προγράμματος δημιούργησε μία πολυ-επίπεδη σειρά διαλέξεων με στόχο να ικανοποιήσει όσο το δυνατόν τις ανάγκες του ακροατηρίου. Το πρόγραμμα χωρίζεται σε τέσσερις ενότητες: Μαθήματα Σχολείου, Προσκεκλημένες Ομιλίες, Σεμινάρια Εμβάθυνσης, Ερευνητικές Εργασίες. Το Σχολείο ξεκινά την Δευτέρα το πρωί στο Αμφιθέατρο Χωροταξίας του Πανεπιστημίου Θεσσαλίας με τις προσκεκλημένες ομιλίες σε θέματα που ενδιαφέρουν όλους. Το απόγευμα θα γίνουν τα πρώτα σεμινάρια εμβάθυνσης σε Στοχαστικά Μοντέλα και Μεταφορά στο Αμφιθέατρο των Μηχανολόγων Τα μαθήματα του Σχολείου αρχίζουν την Τρίτη το πρωί με εισαγωγικά θέματα ηλεκτροδυναμικής, πλάσματος και φορτισμένων σωματιδίων ενώ το απόγευμα θα διεξαχθούν τα δεύτερα σεμινάρια εμβάθυνσης σε Ιξώδεις ΜΥΔ Ροές, Μεταφορά Θερμότητας & Τύρβη. Τα μαθήματα του Σχολείου συνεχίζονται την Τετάρτη το πρωί με κινητική θεωρία και κύματα, ενώ το απόγευμα θα συνεδριάσει η oλομέλεια του Εθνικού Προγράμματος Ελεγχόμενης Θερμοπυρηνικής Σύντηξης. Το απόγευμα αυτό θα είναι ελεύθερο για του φοιτητές/ριες και το βράδυ θα παρατεθεί το Δείπνο του Σχολείου. Όλη η Πέμπτη είναι αφιερωμένη σε μαθήματα του Σχολείου όπως θεωρία ΜΥΔ, CFD, μεταφορά σε πλάσμα, ΜΥΔ αστάθεια και γυροτρόνια. Στο τέλος της απογευματινής συνεδρίας, θα υπάρξει μία αλληλεπίδραση Καθηγητών/Φοιτητών με γενικές και ειδικές ερωτήσεις από φοιτητές που θα απαντηθούν από τους καθηγητές. Την Παρασκευή το πρωί θα γίνουν τα τελευταία μαθήματα του Σχολείου πάνω σε τύρβη πλάσματος, ροές κενού, και υπολογιστική ΜΥΔ και θα ακολουθήσουν τα ερευνητικά σεμινάρια. Μετά το μεσημέρι, το βήμα θα δοθεί στους νέους ερευνητές και ερευνήτριες που συμμετέχουν στο Εθνικό και Ευρωπαϊκό πρόγραμμα Σύντηξης, οι οποίοι θα παρουσιάσουν αποτελέσματα από την τρέχουσα έρευνά τους, όλα σχετιζόμενα με προχωρημένα θέματα φυσικής και τεχνολογίας της σύντηξης, σε μία σειρά από 20-λεπτες ομιλίες. Αυτό θα συνεχισθεί μέχρι το Σάββατο το απόγευμα όπου το 8 ο Σχολείο Σύντηξης θα κλείσει και θα διανεμηθούν τα Πιστοποιητικά (καλής) Παρακολούθησης στους συμμετέχοντες. Με τον τρόπο αυτό το Σχολείο Σύντηξης λειτουργεί ως ένας πολύ-επιστημονικός χώρος που καλύπτει τα ενδιαφέροντα όλων. Ελπίζουμε ότι θα βρείτε ενδιαφέρουσα αυτή την δομή του προγράμματος και προσδοκούμε στην ενεργή συμμετοχή σας που θα εξασφαλίσει την επιτυχία του. Κλείνοντας, οι οργανωτές των Σχολείων Σύντηξης στο Βόλο επιθυμούν να εκφράσουν τις θερμές ευχαριστίες τους στην Ευρωπαϊκή Επιτροπή για την συνεχή υποστήριξη, η καθιστά δυνατή αυτή την παραγωγική επιστημονική και τεχνολογική συνάντηση. Βόλος 6 Απριλίου Η Οργανωτική Επιτροπή iv

5 CONTENTS INVITED LECTURES Page A. Ram: Thermonuclear Fusion Nourishing the Energy Addiction 01 D. Bartlett: The European Fusion Programme 01 B. Weyssow: Activities of European Fusion Development Agency 01 M. Watkins/M. Tsalas: Overview of JET 2008 Experimental Program 02 WORKSHOPS-1: STOCHASTIC MODELING AND TRANSPORT WS1A M. Negrea, B. Weyssow: Aspects related to the magnetic field lines diffusion in tokamak plasm 03 WS1B A. Yannacopoulos: Transport, diffusion and chaos: a homogenization approach 03 WS1C A. Anastasiadis: Charged particle dynamics in non-linear fields 03 WS1D A. Ram: Chaotic magnetic fields and charged particle transport 04 WS1E Y. Kominis: Generalized Fokker Planck equation 04 WS1F H. Isliker: Anomalous transport modeled by continuous time random walk and fractional diffusion equations 04 WS1G S. Varoutis, D. Valougeorgis: Investigation of vacuum flows through tubes of finite length using the direct simulation Monte Carlo method 04 WORKSHOP-2: VISCOUS MHD FLOW, HEAT TRANSFER & TURBULENCE WS2A I. Petrisor, B. Weyssow: Zonal flow generation in weak electrostatic turbulence 05 WS2B A. Lazaros: Magnetic islands - The cancer of magnetically confined plasmas 05 WS2C I. Sarris, D. Carati: Turbulent MHD flow driven by electromagnetic forces 05 WS2D C. Dritselis, N. Vlachos: Near-wall coherent structures in MHD turbulent flows 06 WS2E S. Kakarantzas, D. Fidaros, I. Sarris, A. Grecos, N. Vlachos: CFD modelling of viscous MHD flow and heat transfer 06 SCHOOL CLASSES (Given mainly in Greek, with some slides in English) SC1A M. Tsalas: Introduction to Electrodynamics and Plasma 07 SC1B Y. Kominis: Charged particle dynamics-i 07 SC1C Y. Kominis: Charged particle dynamics-ii 07 SC2A J. Vomvoridis: Kinetic theory-i 07 SC2B J. Vomvoridis: Kinetic theory-ii 07 SC2C A Ram: Heating and current drive by radio frequency waves in fusion plasmas-i 08 SC2D A Ram: Heating and current drive by radio frequency waves in fusion plasmas-ii 08 SC3A L Vlahos: Introduction to Magnetohydrodynamics theory 08 SC3B P. Lalousis: Compressible MHD with electric resistance 08 SC3C K Hizanidis: Introduction to Plasma Transport 08 SC3D N. Pelekasis: Introduction to hydrodynamic and MHD stability 09 SC3E J.-P. Hogge: A Gyrotron Overview 09 SC3F K. Avramidis: Gyrotron Components I Cavity 09 SC3G I. Pagonakis: Gyrotron Components II - Gun & Collector 09 SC4A A.G. Peeters: Micro instabilities and turbulence 10 SC4B D. Valougeorgis: Simulation of fusion vacuum flows via kinetic theory 10 SC4C N. Vlachos: Non-linear phenomena in viscous MHD flows- Mathematical models and CMHD code architecture 10 v

6 RESEARCH SEMINARS (Given in Greek, with slides in English and vice versa) Page Invited J. Ekaterinaris: A high order accurate numerical method for viscous compressible MHD flows 11 Invited P. Svarnas, M. Bacal: Experimental study of H-ion production/extraction from ECR-driven negative ion source 11 Review S. Moustaizis: Neutron sources and applications 12 RS01 C. Dritselis, I. Sarris, N. Vlachos: Numerical investigation of MHD turbulent particle-laden flows using DNS/LES methods 12 RS02 S. Misdanitis, D. Valougeorgis: Vacuum gas flow through a long tube of variable radius 12 RS03 J-P Hogge: Results of the EU 2 MW coaxial gyrotron 13 RS04 I. Pagonakis: Gun parameterization technique 13 RS05 D. Strintzi: Gyrokinetic simulations of JET experiments 13 RS06 I. Sandberg: On the scaling between skewness and kurtosis in plasma edge turbulence 14 RS07 S.A. Mallios, I.G. Tigelis, G.P. Latsas, S. Alberti: Characteristics of electromagnetic waves in complex electrodynamic devices 14 RS08 G.P. Latsas, J.L. Vomvoridis, I.G. Tigelis: Numerical results for parasitic rates in the beam channel of a conventional gyrotron 14 RS09 M. Moraitou, G.P. Latsas, I.G. Tigelis: Mathematical formulation and numerical results for TE and TM waves in the beam channel of a coaxial gyrotron 15 RS10 D. Dimopoulos, N. Pelekasis: Magnetic field effects on 3D stability of natural convection flows in differentially heated cavities 15 RS11 S. Kakarantzas, I. Sarris, A. Grecos, N. Vlachos: Modelling viscous MHD flow and heat transfer in cylindrical domains 16 RS12 A. Iatridis, I. Sarris, C. Dritselis, N. Vlachos: MHD natural convection cooling in cylindrical domains 16 RS13 S. Pantazis, D. Valougeorgis, A. Grecos: Implementation of a generalized approach to simulate the stochastic motion of a charged particle in a magnetic field 17 RS14 K. Avramidis: A new self-consistent code for gyrotron interaction RS15 G. Anastasiou, J.L. Vomvoridis: Amplification of the gaussian output beam from a gyrotron by its interaction with a sheet electron beam 17 RS16 I. Kominis: Explicit near-symplectic mappings of Hamiltonian systems relevant to fusion physics 19 RS17 H. Isliker, L. Vlahos: An MHD compatible model for self-organized criticality in the reversed field pinch 19 RS18 C. Tsironis A.R. Peeters, H. Isliker, D. Strintzi, L. Vlahos: On the effect of edge density fluctuations on the EC wave propagation in ITER 20 RS19 Y. Chatziantonaki, L. Vlahos, C. Tsironis: Perturbed magnetic topology due to NTM instability and ECRH 20 RS20 A. Lazaros: The advantage of early ECCD in the suppression of NTMs with an assessment for the ASDEX upgrade 21 RS21 H. Isliker, Th. Pisokas, D. Strintzi, L. Vlahos: A self-organized criticality model for ion temperature gradient (ITG) mode driven turbulence 21 RS22 D. Vavougios, A. Grecos: Lagrange expansion and time evolution of density distribution functions of particles 21 Poster: M. Vlachomitrou, N. Pelekasis: Numerical analysis of MHD stability of Taylor-Couette flow 22 vi

7 INVITED LECTURES IL01 - Abhay Ram: Thermonuclear Fusion Nourishing the Energy Addiction Massachusetts Institute of Technology, USA The fundamental issue of global energy supply and demand is briefly discussed from the perspective of societal development and world prosperity. The basic aspects and mathematical models of plasma physics and of fusion technology are presented and discussed. The challenge of developing energy from fusion is also critically reviewed. (Abstract not available at time of print The above text was compiled by the editor) IL02 Douglas Bartlett: The European Fusion Programme European Commission, EU The current status of the European Fusion Research Programme is briefly reviewed. The unresolved issues of the physics of fusion are also presented and discussed. The many technological problems arising in the construction of the International Thermonuclear Experimental Reactor (ITER) in Cadarache-France, especially plasma instabilities and reactor materials, are briefly reviewed. (Abstract not available at time of print Text was compiled by the editor) IL03 - Boris Weyssow: EFDA activities from the perspective of Tokamak Fuelling European Fusion Development Agreement, EU Université Libre de Bruxelles, Belgium In 1999, the European Fusion Development Agreement (EFDA) was created to provide a framework between European fusion research institutions and the European Commission to strengthen their coordination and collaboration, and to participate in collective activities. Between 1999 and 2007 EFDA was responsible for the exploitation of the Joint European Torus, the coordination and support of fusion-related research & development activities carried out by the Associations and by European Industry and coordination of the European contribution to large-scale international collaborations, such as the ITER-project. The year 2008 has brought a significant change to the structure of the European Fusion Programme triggered by the signature of the ITER agreement at the end of The ITER parties had agreed to provide contributions to ITER through legal entities referred to as "Domestic Agencies". Europe has fulfilled its obligation by launching the European Domestic Agency called "Fusion for Energy", also called F4E, in March Following the appearance of F4E, a revised European Fusion Development Agreement (EFDA) entered into force on 1 January 2008 focusing on research coordination with two main objectives: to prepare for the operation and exploitation of ITER and to further develop and consolidate the knowledge base needed for overall fusion development and in particular for DEMO, the first electricity producing experimental fusion power plant being built after ITER. EFDA has the following group of activities: - Collective use of JET, the world s largest fusion experiment, which is located near Oxford (United Kingdom). - Reinforced coordination of fusion physics and technology research and development in EU laboratories - Training and carrier development of researchers, promoting links to universities and carrying out support actions for the benefit of the fusion programme - EU contributions to international collaborations outside F4E 1

8 The implementation of these activities benefit from old structures such as the European Task Forces on Plasma Wall Interaction (PWI) and the one on Integrated Tokamak Modelling (ITM) set up respectively in 2002 and 2003 and new structures such as the Topical Groups. Up to now, five Topical Groups have been set up: on Fusion Materials Development, Diagnostics, Heating and Current Drive, Transport and MHD. The role of these newly formed Topical Groups is to develop well-informed and synthetic scientific views on their subject. The Topical Groups assist the EFDA Leader in the elaboration of the EFDA work programme, providing focus on subjects of particular importance, identifying specific issues and high priority research objectives which need to be addressed and proposing ways to address these issues. The Topical Groups naturally serve as forums to compare the results obtained in various conditions, assess the relative merits of different approaches and promote new developments. Some of the Topical Group activities will be reviewed considering a wellidentified physics based problem: the Tokamak fuelling. IL04 - M. Tsalas, M. Watkins: Overview of JET 2008 Experimental Program EFDA/JET, Culham, Oxofordshire. UK The Joint European Torus (JET) thermonuclear fusion machine is briefly described and past experimental successes are reviewed. The recent series of experiments undertaken in preparation for the ITER construction are presented in some detail and are discussed critically. (Abstract not available at time of print Text was compiled by the editor) 2

9 WORKSHOP-1: STOCHASTIC MODELING AND TRANSPORT WS1A - M. Negrea, B. Weyssow: Aspects related to the magnetic field lines diffusion in tokamak plasma University of Craiova, Romania Université Libre de Bruxelles, Belgium The magnetic turbulence appears as a plausible candidate for determining the anomalous transport properties of hot magnetized plasma (see e.g. Bickerton 1997, Plasma Phys. Controlled Fusion 39, 339). We consider, for the magnetic field, the simplified model in the slab approximation including the magnetic shear. These stochastic transports are induced by two random components which are added to the confining magnetic field B0ez, namely, the dimensionless in-homogenous Gaussian random processes bi(x; Z), i = (x, y) which depend on the coordinates X and Z. Ls is the shear length The diffusion of field lines in a stochastic anisotropic sheared slab representation of the magnetic field in a tokamak is analyzed using the DCT method. In contradistinction with the Corrsin approximation, this method handles the trapping effect of the turbulent field (Vlad, etal.1998 Phys. Rev. E ).The space variation of the magnetic field, i.e. the magnetic shear, creates the average poloidal velocity even in absence of an initial velocity of the field lines. Thus the inhomogeneity of the magnetic field determines a directed transport because the magnetic potential depends on the z coordinate, which plays here the role of time. In absence of the magnetic shear, for relatively small magnetic turbulence and different values of the stochastic anisotropy, the average poloidal velocity is zero. (Abstract not available at time of print Compiled by the editor) WS1B - A.N. Yannacopoulos: Transport, diffusion and chaos: a homogenization approach Athens University of Economics, Greece We will present aspects of the theory of averaging and homogenization in stochastic differential equations and how this can be used in order to derive effective descriptions of the evolution of probability densities (rigorous derivation of transport equations). In the second part of the talk, we will show how similar results apply to the derivation of transport coefficients for deterministic but highly unstable systems (chaotic systems) and discuss the theory of transport in chaotic systems. WS1C - A. Anastasiadis: Charged particle dynamics in non-linear fields: The case of current sheets National Observatory of Athens, Greece The interaction of charged particles (electrons and protons) with single of multiple reconnecting current sheets is analyzed by dynamical systems methods. The orbits of the particles are studied analytically and numerically. Two types of local reconnecting topologies are studied: the Harris-type and the X-point. Regular and chaotic orbits are identified. The particle acceleration is modelled as a stochastic process taking place by the interaction of the particles with local magnetic reconnection sites via multiple steps. In the case of the multiple interactions, in both topologies, the particles' kinetic energy distribution is found to acquire a practically invariant form after a small number of steps. This tendency is interpreted theoretically. Finally, selected results of PIC numerical simulations are presented for the case of the Harris-type configuration. 3

10 WS1D - A. Ram: Chaotic magnetic fields and charged particle transport Massachusetts Institute of Technology, USA (Abstract not available at time of print) WS1E - Y. Kominis: Generalized Fokker-Planck equation National Technical University of Athens, Greece (Abstract not available at time of print) WS1F - H. Isliker: Anomalous transport modeled by continuous time random walk and fractional diffusion equations Aristotle University of Thessaloniki, Greece First, we present the Continuous Time Random Walk (CTRW) as a model for anomalous transport. The CTRW equations are in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain position as a function of time. The CTRW equations are non-local in position-space and in time (non-markovian), and they thus represent a basic and very general description of transport. The kind of transport they describe is determined by the probability distributions of random walk steps (in position and time). We then introduce the combined Continuous Time Random Walk (CTRW) in position and momentum space. It is shown that the resulting extended integral equations can be solved numerically with a pseudo-spectral method that is based on the expansion of the unknown functions in terms of Chebyshev polynomials. Alternatively, Monte-Carlo simulations can be performed to solve the equations. Through the inclusion of momentum space, the combined CTRW is able to yield results on the evolution of particle densities and kinetic energy distributions, and, in confined plasmas, on density profiles, as well as on particle fluxes and diffusivities. Last, the CTRW is considered in the asymptotic fluid limit, and it is shown that the CTRW equations can very naturally be transformed into fractional diffusion equations (FDE), including as one particular limit-case also the classical, Fokker-Planck type of equation. The order of the fractional derivatives is determined by the probability distributions of the random walk steps at the microscopic level. In case of the combined CTRW, the resulting FDE is fractional also in momentum direction. In general, FDEs have power-law distributions as asymptotic solutions and they exhibit anomalous scaling of the mean square displacement with time, they thus represent a natural description of anomalous transport. WS1G - S. Varoutis, D. Valougeorgis: Investigation of vacuum flows through tubes of finite length using the direct simulation Monte Carlo method Forschungszentrum Karlsruhe, Germany University of Thessaly, Greece The gas flow through circular tubes of finite length has been investigated computationally in the whole range of the Knudsen number, by the Direct Simulation Monte Carlo (DSMC) method. The DSMC technique uses model particles that move and collide in physical space to perform a direct simulation of the molecular gas dynamics, while intermolecular collisions are modelled using a statistical approach. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-radius ratio and the pressure ratio along the tube. It has been found that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure drop, while the length-to-radius ratio has a rather modest impact. Several interesting findings have been reported including the behaviour of the flow rate and other macroscopic quantities in terms of these three parameters. In addition, the effect of gas rarefaction on the choked flow and on the Mach discs at large pressure drops is discussed. Comparison of some of the present numerical results with available experimental data has shown good agreement. 4

11 WORKSHOP-2: VISCOUS MHD FLOW, HEAT TRANSFER AND TURBULENCE WS2A - I. Petrisor, B. Weyssow: Zonal flow generation in weak electrostatic turbulence University of Craiova, Romania Université Libre de Bruxelles, Belgium The influence of the diamagnetic Kubo number, which is proportional to the diamagnetic drift velocity, on the zonal flow generation by an anisotropic stochastic electrostatic potential is considered from a semi-analytic point of view. The analysis is performed in the weak turbulence limit and as an analytical tool the decorrelation trajectory method is used. It is shown that the fragmentation of the drift wave structures (a signature of the zonal flow generation) is influenced not only by the anisotropy parameter and the electrostatic Kubo number as expected, but also by the diamagnetic Kubo number. Global Lagrangian averages of characteristic quantities are calculated and interpreted. (Abstract not available at time of print Compiled by the editor) WS2B - A. Lazaros: Magnetic islands - The cancer of magnetically confined plasmas National Technical University of Athens, Greece Here we present an outline of the very serious problem of magnetic islands in magnetically confined plasmas. More specifically, the following issues are addressed: - Definition of the magnetic island in magnetically confined plasmas - Disruptions of magnetically confined plasmas, due to the formation of magnetic islands - The classical theory of magnetic islands and the Rutherford equation - The neoclassical theory of magnetic islands - Control of Neoclassical Tearing Modes (NTMs) by electron cyclotron current drive (ECCD) - The design of Upper Launcher for NTM control by ECCD in ITER - Control of magnetic islands by in-vessel coils WS2C - I. Sarris, D. Carati: Turbulent MHD flow driven by electromagnetic forces University of Thessaly, Volos, Greece - Université Libre de Bruxelles, Belgium Almost ten years were past when Professor Alkis Grecos brought the two contributed authors together, the first as a graduate student and the second as a teacher, working on MHD turbulent flows at UTH and ULB. At that time, a project of common interest was defined with the help of Alkis, namely Numerical study of electromagnetically driven homogeneous turbulence. Taking advantage of this workshop which is dedicated to him, the physics and the numerical approach of this particular type of MHD turbulence is reviewed. In particular, the flow considered here is driven by the combination of an electric potential and an external magnetic field suitably arranged in order to avoid the formation of narrow Hartmann layers and to produce a motion-assisting Lorentz force. Old and especially new results are presented and analyzed. The focus of the new results is given to wall-bounded flows, where sophisticated numerical techniques, like large-eddy simulations, for the study of turbulence are discussed for this problem where intermittency and inverse-cascades exist. 5

12 WS2D - C. Dritselis, N. Vlachos: Near-wall coherent structures in MHD turbulent flows University of Thessaly, Volos, Greece The purpose of the present study is to investigate in some detail the modifications induced by the magnetic field on the turbulent coherent structures in the near-wall region of a rectangular channel. It is widely known that vortices are elongated in the direction of the applied magnetic field that is usually attributed to the minimization of Joule dissipation in order to conserve the momentum. Vortical structures elongated in the streamwise direction are identified by using the λ 2 -cretirion of Jeong & Hussain [JFM, 285, 69, (1995)]. Additionally, a conditional sampling scheme is used to extract the entire extent of the vortical structures and to educe an ensemble-averaged coherent structure for the flow cases with and without the external uniform magnetic fields at the same Reynolds number. The velocity and vorticity fields around each mean coherent structure are analyzed and compared. The present work provides further original results for the effect of Lorentz force in the turbulent characteristics of fully developed magnetohydrodynamic channel flows. WS2E - S. Kakarantzas, D. Fidaros, I. Sarris, A. Grecos, N. Vlachos: CFD modelling of viscous MHD flow and heat transfer Laboratory of Fluid Mechanics & Turbomachines, University of Thessaly, Volos, Greece Almost ten years have passed since professor Alkis P. Grecos suggested that the young University of Thessaly be involved in a new research effort on fusion science and technology, together with other university and national research Labs. Indeed, this was a risk for the newly established Fluid Mechanics & Turbomachines Lab, and a great challenge for its faculty and students. In honoring a matured researcher, a dedicated scientist and a good natured colleague, this presentation will review our main scientific research achievements in the past decade, as well as our many efforts in confronting successfully the technological and educational issues that were arisen in the course of executing of the various research tasks in the framework of the National Fusion programme.more specifically, we started from some simple CFD simulations of the Hartmann flow between parallel plates and compared successfully our results to the existing analytic solutions. This may sound very simple to many, but to us mechanical engineers without an electrical engineering background and a School of Engineering without a department of electrical engineering was not an easy task. However, it was made possible, thanks to Dr Grecos, who was always available to answer simple and complex questions in plasma physics, MHD, fusion and of course his beloved mathematics. We then developed CFD models and codes to handle complex flows of conductive fluids in the presence of magnetic fields. Being mechanical engineers, we have a strong interest in heat transfer because of the many practical applications relating to this field, such as, for example, efficient design of fusion reactor blankets. A number of young researchers, graduate students of our Department (co-authors in this presentation) undertook enthusiastically these tasks, developing efficient CFD model for complex MHD flow and heat transfer applications relating to fusion physics and technology. Representative results of these computational magnet-hydro-dynamic (CMHD) models are presented and their scientific and technological merit will be discussed. In particular, results of the CFD simulation of MHD natural convection flows in orthogonal and cylindrical cavities will be presented as well as the effects of magnetic fields on the rotating electrically conductive fluids. 6

13 SCHOOL CLASSES (Mainly in Greek, with some slides in English) SC1A - M. Tsalas: Introduction to Electrodynamics and Plasma (Στοιχεία Ηλεκτροδυναμικής και Εισαγωγή στο Πλάσμα) EFDA/JET, Culham, Oxfordshire. UK 1. Τι είναι η πυρηνική σύντηξη: Αντιδράσεις σύντηξης, Ηλιακές και στη Γη (ενεργός διατομή κτλ), Κριτήριο Lawson Πλάσμα 2. Τι είναι πλάσμα: Πλάσμα στη φύση, Παράμετροι πλάσματος (πυκνότητες, θερμοκρασίες κτλ), Η εξίσωση Saha, Μέθοδοι περιγραφής πλάσματος (μικρο vs μακροσκοπικές, κίνηση σωματιδίων, κινητική θεωρία, μαγνητοϋδροδυναμική, εξισώσεις Maxwell) 3. Δημιουργία πλάσματος στο εργαστήριο: Θερμικές μέθοδοι, Ηλεκτρικές μέθοδοι, Με ηλεκτρομαγνητικά κύματα, Με επιτάχυνση σωματιδίων 4. Βασικές παράμετροι πλάσματος: Μήκος και σφαίρα Debye - plasma parameter, Ηλεκτροστατικό δυναμικό-θωράκιση, Οιονεί ουδετερότητα, Συχνότητα πλάσματος, Μαγνητισμένο πλάσμα πλάσμα Beta 5. Συγκρούσεις Coulomb: Συχνότητα συγκρούσεων, Συγκρούσεις με ουδέτερα σωματίδια, Ηλεκτρική αντίσταση πλάσματος 6. Εισαγωγή στη μαγνητική συγκράτηση τοροειδή συστήματα SC1B &1C - Y. Kominis: Charged particle dynamics - I & II (Δυναμική των τροχιών φορτισμένων σωματιδίων) National Technical University of Athens, Greece 1. Τροχιές φορτισμένων σωματιδίων σε στατικά πεδία: Κίνηση σε στατικό ομογενές ηλεκτρικό πεδίο, Κίνηση σε στατικό ομογενές μαγνητικό πεδίο, Ολίσθηση E B, Κίνηση σε μη ομογενές στατικό ηλεκτρικό πεδίο, Κίνηση σε μη ομογενές στατικό μαγνητικό πεδίο (διαμήκης ανομοιογένεια, εγκάρσια ανομοιογένεια, καμπυλότητα πεδιακών γραμμών), Αδιαβατικές σταθερές 2. Αλληλεπίδραση φορτισμένων σωματιδίων με κύματα: Ομαλή και χαοτική κίνηση φορτισμένου σωματιδίου σε ομογενές στατικό μαγνητικό πεδίο υπό την επίδραση ηλεκτροστατικών κυμάτων (Χαμιλτονιανή περιγραφή της κίνησης φορτισμένου σωματιδίου, Κανονική θεωρία διαταραχών και υπολογισμός προσεγγιστικών σταθερών της κίνησης, Ο ρόλος των συντονισμών και το πρόβλημα των μικρών παρονομαστών, Επικάλυψη των συντονισμών και μετάβαση στο χάος), Περιπτώσεις (Διάδοση κύματος υπό διαφορετικές γωνίες ως προς το μαγνητικό πεδίο, Κυμάτων διακριτού και συνεχούς φάσματος) SC2A & 2B - J.L. Vomvoridis: Kinetic theory I & II (Κινητική Θεωρία I & II) National Technical University of Athens, Greece 1. Η συνάρτηση κατανομής: Ροπές της συνάρτησης κατανομής, Βασικές συναρτήσεις 2. Οι κινητικές εξισώσεις 3. Εφαρμογές κινητικής θεωρίας (Στατικές καταστάσεις ισορροπίας, Διάδοση κυμάτων (μικρού πλάτους) σε πλάσμα 4. Κύματα Langmuir σε μη μαγνητισμένο πλάσμα 5. Απόσβεση Landau 7

14 SC2C & 2D - A. Ram: Heating and current drive by radio frequency waves in fusion plasmas-i & II Massachusetts Institute of Technology, USA (Abstract not available at time of print) SC3A - L Vlahos: Introduction to Magnetohydrodynamics theory (Εισαγωγή στη Μαγνητοϋδροδυναμική) Aristotle University of Thessaloniki, Greece 1. Βασικές έννοιες: Υδροδυναμική, Ιδανική Μαγνητοϋδροδυναμική, ΜΥΔ με ηλεκτρική απόσβεση (resistive) 2. Ισορροπία: Σφιγκτήρας-z (z-pinch), Εξίσωση Grad-Shafranov, Λύση Solovev, Ισορροπία με εσωτερικά φράγματα (internal barrier) 3. Ευστάθεια: Ενεργειακή αρχή των Bernstein, Frieman, Kruscal και Kulsrud., Ανάλυση ιδιοσυχνοτήτων, Αστάθεια σφιγκτήρα-z, Κατηγορίες ασταθειών (αστάθειες λόγω ρεύματος και πίεσης, τρόποι ταλάντωσης στα πλαίσια της ιδανικής ΜΥΔ και ΜΥΔ με ηλεκτρική απόσβεση, παραδείγματα) Basic components of plasma confinement in fusion devices, e.g. tokamak, are equilibrium and stability. In equilibrium the pressure-gradient force acting on a plasma element is balanced by the magnetic force. Good confinement additionally requires stability for perturbations around an equilibrium state. The simplest model to study plasma confinement is magnetohydrodynamics (MHD). In the framework of MHD the plasma is described as a single fluid the physics of which is governed by electromagnetic interactions. In this talk the basic elements of the MHD model is first reviewed, then certain MHD equilibrium and linear stability issues of magnetically confined plasmas are presented. Finally, some current research problems in connection with the ITER project are briefly outlined. SC3B - P. Lalousis: Compressible MHD with electric resistance (Συμπιεστή ΜΥΔ με ηλεκτρική αντίσταση) Foundation of Research & Technology Hellas (ITE), Greece Εισαγωγή στις εξισώσεις της ιδανικής, με ηλεκτρική αντίσταση, Hall, και δυο-ρευστών Μαγνητο-υδροδυναμικής, με χρονική εξέλιξη και σε πολλές διαστάσεις. Περιγραφή της αριθμητικής επίλυση αυτών των εξισώσεων, και αριθμητικά πειράματα για την καλύτερη κατανόηση του περιορισμού του πλάσματος. Ιntroduction to the equations of ideal, resistive, Hall, and two-fluid Magnetohydrodynamics, with time evolution and in multi-dimensions. Description of how to solve these equations numerically and numerical experiments for the understanding of magnetic confinement. SC3C - K Hizanidis: Introduction to transport theory National Technical University of Athens, Greece Particles interacting in various confining magnetic field configurations (illustrative) Collisional scattering (simplistic picture) Collisional Vlasov equation (brief introduction) Landau collision operator Action angle formulation of the collisional Vlasov equation Derivation of transport equations 8

15 SC3D - N. Pelekasis: Introduction to hydrodynamic and MHD stability (Εισαγωγή στην υδροδυναμική και Μαγνητοϋδροδυναμική ευστάθεια) University of Thessaly, Volos, Greece 1. Στοιχειώδης θεωρία ευστάθειας και θεωρία διακλαδώσεων: Γραμμική και ελαφρώς μη γραμμική ανάλυση, Παραδείγματα από κλασσική υδροδυναμική ευστάθεια, Υπολογιστική κατασκευή διαγραμμάτων διακλάδωσης 2. Δυναμική σε χαμηλούς μαγνητικούς αριθμούς Reynolds: Μαγνητική απόσβεση Δημιουργία κίνησης, Οριακά στρώματα (Στρώματα Hartmann και πλαϊνά) 3. Ευστάθεια μαγνητοϋδροδυναμικών ροών: Ευστάθεια στρωμάτων Hartmann και πλαϊνών στρωμάτων, Ροή υγρών μετάλλων σε σωλήνες Εξαναγκασμένη και ελεύθερη αγωγή, Εφαρμογές στο σχεδιασμό αντιδραστήρων πλάσματος SC3E - J.-P. Hogge: A Gyrotron Overview Ecole Polytechnique Federale de Lausanne, Switzerland Gyrotrons are microwave sources able to deliver power ranging from a few watts up to the megawatt level, at frequencies extending from a few GHz up to hundreds of GHz, with an efficiency which can be as high as 50% Their simplicity makes them very robust. They find their main application in fusion devices such as tokamaks or stellarators, where they can be used to perform bulk heating of the plasma, generate current in a noninductive way, control instabilities, among others. The basic principles of the gyrotron interaction theory will be reviewed, and a description of some important components will be given. SC3F - K. Avramidis: Gyrotron Components I Cavity National Technical University of Athens, Greece (Abstract not available at time of print) SC3G - I. Pagonakis: Gyrotron Components II - Gun & Collector Ecole Polytechnique Fédéral de Lausanne, Switzerland The electron beam plays an important role in the gyrotron operation. Two main components of the gyrotron, the electron gun and the collector, are related to the generation and the collection of the electron beam. An accurate design of these components is essential for the efficient operation of the device. In particular, the operation of the gyrotron is based on the transformation of the electron beam kinetic energy to the RF field. The wave-particle interaction takes place at the resonant cavity (see the previous presentation by K. Avramides). The characteristics of the electron beam at the cavity entrance determine the excited RF mode of the cavity and the efficiency of the electron cyclotron interaction. In order to generate the appropriate electron beam, the magnetron injection gun arrangement is used. Several subjects related to the magnetron injection gun will be presented, such as, the electron emission, the electron dynamics in a converging magnetic field, the simulation codes and some basic design aspects. On the other hand, the electron trajectories are ended on the collector walls. There are several issues which are related to the collector design, such as, (i) the cooling system, (ii) the sweeping techniques, (iii) the single and multiple stage depression, etc. The above and many other subjects related to the collector design will also be presented. 9

16 SC4A A.G. Peeters: Micro instabilities and turbulence University of Warwick, Coventry, UK Introduction to the basic mechanisms that govern the physics of small-scale instabilities and turbulence in tokamak plasmas. These instabilities are thought to be responsible for the large observed loss rate of particles and energy from the plasma. For an economic fusion reactor it is of vital importance to confine the particles and heat for a sufficient long time, such that enough fusion reactions can occur. The study and explanation of the particle and energy loss rates, therefore, has a high priority in the fusion program. Several phenomena connected with the turbulence will be discussed: Why do the instabilities have a small scale? What limits them in having the wavelength go to zero? What drives the instabilities? What is the main dynamics involved? What types of modes exist? Etc. After an introduction that is focussed on linear dynamics, the nonlinear state will be briefly discussed, with particular emphasis on the self-generated flows that characterize much of the turbulence in a tokamak. SC4B - D. Valougeorgis: Simulation of fusion vacuum flows via kinetic theory University of Thessaly, Volos, Greece All large fusion devices, in particular DT fusion machines, such as ITER and DEMO, require the existence and smooth operation of advanced and demanding vacuum pumping systems, which are needed for the generation, evacuation and maintenance of the specified pressure levels in the torus, the NBI and the cryostat. The flow conditions in the pumping systems cover the whole range of the Knudsen number. The accurate design of such systems (pumps and piping) is still a challenge. One of the main approaches capable of handling such flows is kinetic theory. Here, based on kinetic theory some specific flow configurations are examined. Suitable kinetic model equations coupled with appropriate boundary conditions are presented and solved numerically both in a deterministic and probabilistic manner. The deterministic scheme is based on the discretization of the applied kinetic equations in the physical and molecular velocity spaces, while the probabilistic scheme on the direct simulation of a sample of model molecules, which statistically mimics the behavior of real molecules. Results for the flow rates and the pressure drop are presented for flows through basic elements of vacuum systems such as channels of infinite and finite length and various cross sections. Comparisons with available experimental work are included. The numerical modeling of cryogenic and other vacuum pumps as well as of integrated vacuum pumping systems is also discussed. SC4C - N. Vlachos: Non-linear phenomena in viscous MHD flows- Mathematical models and CMHD code architecture (Μη γραμμικά φαινόμενα ιξωδών ΜΥΔ ροών-μαθηματικά μοντέλα & αρχιτεκτονική κωδίκων ΥΜΥΔ) University of Thessaly, Volos, Greece Revisiting the hydrodynamic and magnetohydrodynamic flow equations - Comments on the dimensionless form of the Navier-Stokes equations - The non-linear terms and their implications to the nature of flows - Implications of non-linearity of the flow equations to CFD simulations - The SIMPLE algorithm for decoupling velocities from pressure - Integration of the Navier-Stokes equations with finite volumes - Numerical counterparts for a boundary layer. Application to MHD flows - Numerical counterparts of the N-S equations for recirculating flows - Turbulence models, buoyancy effects and particle dynamics. Επανεξετάζοντας τις εξισώσεις υδροδυναμικής και μαγνητο-υδροδυναμικής - Σχόλια επί της αδιάστατης μορφής των εξισώσεων Navier-Stokes - Μη-γραμμικοί όροι και επιπτώσεις τους στην μορφή των ροών - Επιπτώσεις της μη-γραμμικότητας των εξισώσεων ροής στην προσομοίωση με ΥΡΔ - Ολοκλήρωση των εξισώσεων Navier-Stokes με πεπερασμένους όγκους - Ο αλγόριθμος SIMPLE για αποσύζευξη ταχυτήτων από πίεση - Αριθμητική μορφή των εξισώσεων για οριακό στρώμα. Εφαρμογές σε απλές ΜΥΔ ροές - Αριθμητική μορφή των εξισώσεων N-S για ροές με ανακυκλοφορία - Μοντελοποίηση τύρβης, επίδραση άνωσης και δυναμική σωματιδίων 10

17 RESEARCH SEMINARS (Given in Greek, with slides in English and vice-versa) Invited - J. Ekaterinaris: A high order accurate numerical method for viscous compressible MHD flows University of Patras, Patras, Greece Imposed magnetic fields could significantly affect the flow structure of ionized gases and may be exploited for the control of transition and turbulence. The wave structure of ionized high speed gas flows under the influence of magnetic fields is more involved than the waves of ordinary gas dynamics and high resolution is required to accurately compute the complex wave interactions of flows with discontinuities. Numerical solutions of the nonlinear ideal and viscous magnetohydrodynamic (MHD) equations are obtained with high order accurate WENO schemes. The numerical method for MHD is tested for flows containing strong discontinuities and smooth flow features to ensure that it maintains high-order accuracy for the smooth parts of the flow, it preserves numerical stability, and eliminates non-physical features that result from the violation of the divergence-free conditions for the magnetic field. Results for model flow problems of ideal and viscous MHD flows with strong shocks are presented. The accuracy of the numerical method is validated by comparing numerical results with existing analytic solutions. Examples of flows with strong MHD interactions are computed to demonstrate the robustness of the proposed numerical scheme. Finally results for wall bounded flows under the influence of magnetic fields are shown. These flows are the key ingredients for the computation of transition and turbulence in MHD. Invited - P. Svarnas, M. Bacal: Experimental study of H-ion production/extraction from ECR-driven negative ion source Laboratoire de Physique et Technologie des Plasmas, École Polytechnique, France In order to start a nuclear fusion reactor, one has to heat the plasma to many millions of degrees. There are a few ways to invest the necessary energy into the plasma state, i.e. ohmic heating, magnetic compression, electromagnetic wave irradiation, and energetic neutral particle injection [1]. The latter is done in an indirect way since neutral particles cannot be accelerated to high velocities in a direct way. First, positive (or negative) ions are produced and accelerated to the desired energies. Then, before entering the tokamak, these ions pass through a chamber containing neutral gas. The energetic positive ions strip electrons from the neutral atoms of the gas and in this way become neutral (charge exchange). In the case of negative ions, the excess electrons are attached on neutral atoms and the ions are again neutralized. Consequently, a stream of high-energy neutrals is formed and enters the tokamak to heat the plasma. Thus, the production of reliable ion beams following strict standards is of great importance for the nuclear fusion reactor operation. In this invited seminar, the physical mechanisms for negative ion volume-production in hydrogen plasma are discussed. The dissociative low energy (<1 ev) electron attachment to highly vibrationally excited molecules is emphasized as a principal H - production process, while the need of high energy electrons (>20 ev) for the creation of these excited molecules is underlined. Those two requirements can be fulfilled by the use of a tandem source, like the H - negative ion source Camembert III [2,3] installed in École Polytechnique (France). This source is a multi-cusp one driven by seven elementary ECR (2.45 GHz) modules. The source is studied by electrical measurements, electrostatic probes, and photo-detachment technique [4]. A similar source is furthermore studied by Laser-induced fluorescence [5]. Experimental results are presented, and the above mechanisms proposed for H - production are supported. Eventually, the H - extraction process in the above source is discussed using experimental and numerical results. The extraction system combines a biased plasma 11

18 electrode and a magnetic field close to the extraction orifice. It is shown that the depletion of the electron population by the positive bias of the plasma electrode, disturbs the local plasma neutrality, and new negatively charged particles should replace the electrons collected by the plasma electrode. In a collisionless situation, the electrons present in the bulk plasma are unable to cross the transverse magnetic field in front of the plasma electrode. Therefore, negative ions from the main extraction region replace the depleted electrons in the magnetized region near the positively biased plasma electrode and enhanced extraction takes place. Finally, the present status of the H - negative ion sources prepared for the International Thermonuclear Experimental Reactor (ITER) and a new approach for H - surface-production are mentioned. [1] S. Eliezer et al., The Fourth State of Matter, Institute of Physics Publishing (2001) [2] A.A. Ivanov Jr. et al., Review of Scientific Instruments 75(5) (2004) 1750 [3] P. Svarnas et al., IEEE Transactions on Plasma Science 35(4) (2007) 1156 Review - S. Moustaizis: Neutron sources and applications University of Crete, Herakleion, Crete, Greece (Abstract not available at time of print) RS01 - C. Dritselis, I. Sarris, N. Vlachos: Numerical investigation of MHD turbulent particle-laden flows using DNS/LES methods University of Thessaly, Volos, Greece The feasibility of Direct Numerical Simulation and Large Eddy Simulation to predict wallbounded turbulent magnetohydrodynamic flows is investigated in the present study. For this reason several subgrid scale turbulence models have been tested in fully developed turbulent flows in a rectangular channel and in a circular pipe. These numerical techniques are then used to study turbulent dispersion and deposition of nonmetallic impurities in magnetodydrodynamic channel flow of liquid metals at low magnetic Reynolds number. The simplified magnetohydrodynamic equations for an electrically conducting and incompressible fluid in the limit of a low magnetic Reynolds number are adopted. The particle trajectories are controlled by the drag, pressure gradient, added mass and gravity forces. Binary, elastic interparticle collisions are also considered. Finally, the effect a small to moderate magnetic field applied in either the streamwise, wallnormal or spanwise direction on the spatial distribution and deposition of particles is examined. RS02 - S. Misdanitis, D. Valougeorgis: Vacuum gas flow through a long tube of variable radius University of Thessaly, Volos, Greece The flow of a gas through a long tube of constant cross section, under low, medium and high vaccum conditions has been extensively investigated on the basis of kinetic theory. However, in many vacuum applications, including the divertor vacuum system in fusion reactors the cross section varies along the flow. In this context a study has been initiated to estimate the flow characteristis through a cylindrical tube with variable radius. The flow may be due to pressure and temperature gradients. A certain methodology recently introduced has been applied successfully and the first results, presented here, include the flow rate and the pressure drop for a long conical tube. Since the approach is based on kinetic theory the solution is valid in the whole range of the Knudsen number. This study will be generalized to channels of any type of variable cross section. 12