CurriculumVitae

Natalia Tronko 13 September 1984, Saint-Petersburg, Russian Post Doctoral Research Assistant Center for Fusion Space and Astrophysics Physics Department, University of Warwick Gibbet Hill road CV 4 7AL Coventry, United Kingdom Tel: (+44|0) 7 944 908 728) (+33|0)6 13 58 12 88 email: [email protected]

Academic and Research positions • November 2010-October 2011 Postdoctoral research Assistant, Centre for Fusion Space and Astrophysics, Department of Physics, University of Warwick • September 2007-October 2010 Tutor in Physics, Aix-Marseille II University, France Academic degrees • September 2007-October 2010 : PhD Thesis, Center for Theoretical Physics of Marseille (Luminy) and Aix-Marseille-II University (Universit´e de la M´editerran´ee) ”Hamiltonian Perturbation Methods for Magnetically Confined Fusion Plasmas ”, Scientific advisor Michel Vittot (CNRS), defended 15 October 2010 with mention tr` es honorable, Financial support: CNRS grant • September 2006-June 2007 : Master 2 Research : Mathematical Physics, Theoretical Physics and Physics of Elementary Particles, Aix-Marseille II University (Universit´e de la M´editerran´ee) and Center for Theoretical Physics of Marseille (Luminy), French Government Grant, Master’s Degree Diploma ”Hamiltonian Perturbation Theory and its application to Physics of Plasma”, Scientific advisor Michel Vittot (CNRS), rate (3/18) • 2005-2007 : Saint-Petersbourg State University : Physics Faculty, Department of Mathematical Physics, Master 1 • May 2005 : Bachelor’s degree diploma with excellence ” About proprieties of spectra of Dirac’s operator”, Scientific advisor : Professor Suslina Tatyana Alexandrovna. Foreign Languages • French - DALF ( Diplˆ ome Approfondi de Langue Fran¸caise ), after 4 years of university studies and one years of intensive scientific collaborations in France, bilingual • English- A1 Certificate, experience of work and live in the United Kingdom since one year Honors and awards • June 2011 Robert’s funding grant, Physics department of the University of Warwick, awarded for collaboration with Center for theoretical physics, Marseille, France • October 2010 PhD with mention very honorable • July 2007 3 years CNRS ( French National Center for Scientific Research) grant for PhD thesis

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• April 2006 French government grant for Master degree studies (won one of the 5 grants for Russian students in Science) • May 2005 Bachelor’s degree diploma with excellence (rate 3/200 students) • April 2001 Won the olympiad in Physics for high school students permitting admission at the Faculty of Physics at Saint-Petersburg State University • February 1998 French government grant for studying French at Alliance Fran¸caise of SaintPetersburg Publications • N.Tronko, M.Vittot, C.Chandre, Ph. Ghendrih, G. Ciraolo ”Barriers for the reduction of transport due to the E×B drift in magnetized plasmas”, Journal of Physics A (Mathematical and Theoretical), J. Phys. A: Math. Theor. 42 (2009) 085501. • A.J.Brizard, N.Tronko ”Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations”, Physics of Plasmas, 18, 082307 (2011) • O.Izacard, N.Tronko, G.Ciraolo, C.Chandre, Ph.Ghendrih, M.Vittot ” Transport barrier for the radial diffusion due to the E×B drift motion of guiding centers in cylindrical confinement geometry”, Plasma Phys. Control. Fusion 53 (2011) 125008. • A.J. Brizard, N.Tronko ”Higher-order guiding center perturbation theory”, in preparation • N.Tronko, E. Tassi and P.J. Morrison, ”Magneto-rotational instability and generalized energy principle”, in preparation • N.Tronko, S.V. Nazarenko and S. Galtier, ”Anisotropic turbulence of Pseudo Alfv`en waves in 2D”, in preparation Proceedings • N.Tronko, A.J. Brizard, ”Vlasov-Poisson momentum conservation law in axisymmetric tokamak geometry” European Physical Society Conference, July 2011 • N.Tronko, A.J. Brizard ”Gyrokinetic conservation law: electrostatic turbulence case”, ”URSI Scientific days Propagation and Plasmas”, 2010, in French • N.Tronko, M.Vittot ”Creation of a Transport Barrier for the E × B drift in magnetized plasmas”. ”International Conference on Fusion BFR (Belgium - France - Romania)”, in Craiova (Romania), October 2008. ”Physics AUC” (Annals of the University of Craiova), (2009). • N.Tronko, M.Vittot ”Localized Hamiltonian control and its application to the reduction of chaotic transport of test particles in a Tokamak’s plasma”, ”Theory of fusion plasma”, ”Joint Varenna Lausanne International Workshop: Theory of Fusion Plasmas”,Varenna (Italie) 2008. Editor X. Garbet. • N.Tronko ”Physics and progress 2005”, students conference proceedings, Saint-Petersbourg, Russia ”About absolute continuity of Dirac operator spectra” pages 186-188 (in Russian) Seminars • 9 December 2011 School of Mathematics and Statistics, St Andrews University,”Higher-order guiding-center theory”, 50 minutes talk • 1 December 2011 Culham Center for Fusion Studies, ”Higher-order guiding-center theory”, 50 minutes talk • 10 January 2011 Center for Fusion Space and Astrophysics ”Hamiltonian Perturbation Methods for Magnetically Confined Fusion Plasmas”, 50 minutes talk • 25 February 2010 Max-Planck-Institut f¨ ur Plasmaphysik, Greifswald ”Hamiltonian perturbation methods for non-linear dynamics study for fusion plasmas” 2

Talks at Conferences • 24-26 October 2011 ”DYCOEC conference”, Marseille, France, 30 minute talk, ”Anisotropic turbulence of pseudo Alfv`en waves in 2D” • 4 July-8 July 2011 ”Festivale de la th´eorie”, Aix-en Provence, France, round table intervention,”Momentum conservation law for gyrokinetic Vlasov-Poisson equations” • 28 March-1April 2011 ”Workshop on Vlasov-Maxwell kinetics: theory, simulations and observations in space plasmas”, Vienna, Austria, 30 minute talk ”Hamiltonian reduction of the Maxwell-Vlasov system: toward gyrokinetcs” • 28 February-11 March 2011 ”Les Houches Winter school: Dynamics and turbulent transport in plasmas aand conducting fluids”, Les Houches, France, 20 minutes talk, ”Barriers for the reduction of transport due to the E × B drift in magnetized plasmas” • 16-17 March 2010 ”URSI Scientific days: Propagation and plasmas”, Paris, France, 20 minute talk, ”Gyrokinetic Momentum Conservation law” • 13-16 December 2009 ”DYCOEC conference”, Rouen, France, 20 minute talk, ”Gyrokinetic Momentum Conservation law” • 10-11 December 2009 ”ANR EGYPT workshop”, CIRM, Marseille, 20 minute talk ”On intrinsic formulation of Gyrokinetics” • 2-6 November 2009 ”Maths ITER”, CIRM, Marseille, 40 minute talk, ”Gyrokinetic momentum conservation law” • 2-9 September 2009 ”Vlasovia 2009”, CIRM, Marseille, 30 minute talk ”Hamiltonian reduction of Maxwell-Vlasov equations toward gyrokinetics” • 6-24 July 2009 ”Festival de Th´eorie 2009: Rotation and Momentum Transport in Magnetized Plasmas”, Aix en Provence, France, 10 minute talk ”Toward new Hamiltonian gyrokinetics for Maxwell-Vlasov approach” • 2-6 February 2009 ”Kinetic equations and their applications”, CIRM, Marseille, 45 minute talk, ”Hamiltonian reduction of Maxwell-Vlasov equations toward gyrokinetics” • 5-8 October 2008 ”Second Workshop in Plasma Physics for PhD Students”, Pont `a Mousson, France, 20 minute talk: ”Barriers for the reduction of transport due to the E ×B drift in magnetized plasmas” • 3 June 2008 ”Nonlinear Dynamics Day”, Center for Theoretical Physics, Marseille, France, 20 minute talk : ”Barriers for the reduction of transport due to the E ×B drift in magnetized plasmas” • November 2005 ”Progress and Physics”, student’s conference, Saint-Petersburg State University, Russia, 15 minute talk : ”About absolute continuity of Dirac operator spectra” Posters presentations • 14-17 November 2011 ”American Physical Society Conference: Division of Plasmas Physics”, Salt Lake City, USA,”Magneto-rotational instability and generalized energy principle” • 14-17 November 2011 ”American Physical Society Conference: Division of Plasmas Physics”, Salt Lake City, USA,”Momentum conservation law for the gyrokinetic Vlasov-Poisson equations” • 11-22 July 2011 ”48-th Culham Summer School”, Culham, Oxfordshire, UK,”Momentum conservation law for the gyrokinetic Vlasov-Poisson equations” • 27 June-1 July 2011 ”European Physical Society conference”, Strasbourg, France,”Momentum conservation law for the gyrokinetic Vlasov-Poisson equations” • 4-8 April 2011 ”Institute of Physics Annual Plasma Physics Conference”, North Berwick, UK, ”Momentum conservation law for the gyrokinetic Vlasov-Poisson equations” 3

• 15-17 April 2009 ”11th Easter Meeting on Reconnection and Turbulence in Magnetically Confined Plasmas”, Turin, Italy, ”Toward gyrokinetics of charged particles in a non-uniform external magnetic field” • 24-30 August 2008 ”Theory of Fusion Plasma”, International Center for promotion of Science ”Piero Caldirola”, Varenna, Italy, ”Barriers for the reduction of transport due to the E × B drift in magnetized plasmas” • March 2008 ”11-th nonlinear meeting”, Poincare Institute, Paris, France ”Barriers for the reduction of transport due to the E × B drift in magnetized plasmas” Computer skills Mathematica, Matlab, Origin; C, ForTran; Word processor: LaTex, MS Word Pedagogical skills September 2007-September 2010 Mediterranean University (Aix-Marseille II) Tutor in physics (192 hours) (electrokinetics(145 hours), optics(27 hours), Lagrangian and Hamiltonian mechanics (20 hours)) Scientific Popularization and Diffusion • May 2008, Institute for research on the methods for teaching mathematics, Marseille, Luminy Training for High School students ”Differential equations and all around it”. The purpose of this training was to show how differential equations appear in different domains of physics from mechanics to electrokinetics and thermodynamics with experimental illustrations. Scientific Interests • Interests Mathematical Physics, Plasma Physics: kinetic and fluid approaches, Gyrokinetics, Hamiltonian Systems, Turbulence, Wave-kinetic formalism, KAM Theory and Control Theory.

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Scientific collaborations • February 2011-Nowadays: University of Warwick, Department of Mathematics, UK, Collaborator: prof. S.V.Nazarenko I have started to work with Pr.S. Nazarenko after my arriving at the Warwick University for a postdoctoral position in Physics department. Due to my rather mathematical background I was extremely interested by the wave-kinetic approach to turbulence that was developed by Pr. Nazarenko since years. We are currently applying this formalism to the investigation of the two dimensional anisotropic MHD turbulence. In our work we can show that the two dimensional case is very different from the three dimensional case. The latter one was previously explored in 2000 by Pr. Nazarenko in collaboration with Sebastien Galtier (former post doc in Warwick Mathematics department, currently: Maitre des conferences at Paris XI). The main difference can be resumed in the absence of the universality and Kolmogorov like solutions for the two dimensional case. The article is in preparation on this subject in collaboration with Sebastien Galtier. The example of two dimensional MHD turbulence gave me an opportunity to discover this powerful wave-kinetic formalism. In our further work we would like to extend its application to case of other systems with relevant physical properties, for example for investigation of the instabilities in plasmas : Magneto-rotational Instability, Ion Temperature Gradient Instability etc. • October 2009-Nowadays: Saint Michael’s College USA (Vermont), Collaborator: Dr. A.J.Brizard The formalism, developed by Pr.A.J. Brizard has strongly influenced modern gyrokinetics formulation. During visits of Pr. Brizard at the Center for Theoretical Physics in Marseille I started to collaborate with him. I was strongly interested in studying his gyrokinetic approach. The purpose of my visit to Saint Michael’s College was to broaden my theoretical knowledge in plasma physics. At the beginning of my visit, we worked on the variational principle for gyrokinetics. As a result of our collaboration, a gyrokinetic momentum conservation law was derived for an arbitrary magnetic configuration. This result has an important physical meaning: momentum conservation equation can be interpreted as a momentum transport equation and helps understanding intrinsic plasma rotation influencing fusion device performance. This work was presented in several international conferences as ”Math ITER” in 2009, ”IOP” and ”EPS” in 2011 and finally became a subject of the article publication in August of 2011 in ”Physics of Plasmas”. Further, we plan to extend our investigation to a relevant magnetic configuration for fusion devices. The results of this work gave us a possibility to initiate the next part of our collaboration that we have led in 2011. The new topic is related to investigation of foundation of the gyrokinetic theory. This work has already attracted interest of plasma physicists and mathematicians who have invited me to give talks last December in Culham center for Fusion Studies and in School of Mathematics and Statistics of St Andrews University. The publication of results of this work is in preparation. There are potentially interesting subjects to investigate, we are currently looking for the financial support in order to reinforce our scientific exchange. • September 2006: Center for Theoretical Physics Marseille, Non-linear dynamics team My contact with the Center for Theoretical Physics at Marseille have started when I was looking for the opportunity to pursue my Master degree studies abroad, just after my graduation at St. Petersbourg State University. I am very grateful to the non-linear dynamics team for helping me with French Governement Grant application that allowed me to pursue my master degree studies in France and then with helping me to apply for CNRS Grant that allowed me to pursue my PhD thesis inside the team. Nowadays I continue to have a regular contact with team members and I am visiting the Center for Theoretical Physics regularly. This place also plays an important role for me in entertaining my collaborations with US professors A.J. Brizard and P.J. Morisson, whom visit CPT regularly as well. I have a current project with E. Tassi (CNRS team member) and Pr. P.J. Morisson from the University of Texas at Austin.In our work we consider the Compressible Reduced MHD system which was derived for the fusion plasmas description and we compare this system to the Magneto Rotational Instability system which appears into the astrophysical contexte, in particularly in accretion disc formation process. We transfer the information about the Hamiltonian structure and Casimirs from one system to another and then we are studying its stability by using the Generalized Energy principle. Our goal here is to obtain the information about the sources of the saturation for the Magneto Rotational Instability. This work is a currently running project. 5

• September 2007-September 2010: Cadarache CEA, France, Collaborator: Dr. Ph. Ghendrih My PhD thesis work was started in collaboration with theoretical team of the Institute of Magnetic Fusion Research from the Commissariat of Atomic Energy ( IRFM CEA Cadarache). One of the principal subject of this collaboration is Hamiltonian gyrokinetics. Stages • February 2006 - September 2006 : Corning Scientific Center ( CSC ) Saint Petersbourg. Stage subject: ”Evaluation of stress and strains in 3D periodic structure of anisotropic cubic domains by energy minimization”. The results have been published in the internal Corning report. Summary: The analytical model for ceramics with anisotropy has been developed. The validity of this model has been proved by comparison with stress and strains distributions (calculated analytically with Mathematica package) with the same distributions obtained numerically (with finite element method).

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