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In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

Superthermal energetic particles may alter the kinetic and resonant nature of zonal flows by leading to new types of instabilities. Here, we study the effects induced by superthermal energetic ions on trapped-ion modes (TIM) by using a reduced Hamiltonian gyrokinetic model, where both fast scales (cyclotron and bounce or transit motions) are gyro-averaged. In particular, we analyze the enhancement of resonant processes induced by energetic ions associated with nonlinear phase synchronization, in an extended version of the TIM model including circulating ions. Once an energetic particle mode is driven unstable, a rich nonlinear dynamics is observed, which encompasses a frequency chirping associated with a synchronization process driven by TIM and a transition scenario. An equivalence with the classic Kuramoto model—the paradigm describing the synchronization of a system of coupled oscillators—explains much of this phenomenology.

International audience; We address the study of reconnecting instabilities in magnetized plasmas, a highly multiscale process, using an innovative adaptive scheme based on Adaptive Mesh Refinement (AMR) and Multigrid Algorithms. The reduced model we exploit is very sensitive to numerical errors and demands high order solvers which we develop for this purpose. We validate our approach with two numerical experiments of physical interest.

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. The EP bounce frequency is calculated as a function of the EGAM frequency, and shown not to depend on the value of the bulk temperature. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e., the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

International audience; The Weibel instability, driven by a temperature anisotropy, is investigated within different kinetic descriptions based on the semi-Lagrangian full kinetic and rela-tivistic Vlasov-Maxwell model, on the multi-stream approach, which is based on a Hamiltonian reduction technique, and finally, with the full pressure tensor fluid-type description. Dispersion relations of the Weibel instability are derived using the three different models. A qualitatively different regime is observed in Vlasov numerical experiments depending on the excitation of a longitudinal plasma electric field driven initially by the combined action of the stream symmetry breaking and weak relativistic effects, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The multistream model offers an alternate way to simulate easily the coupling with the longitudinal electric field and particularly the nonlinear regime of saturation, making numerical experiments more tractable, when only a few moments of the distribution are considered. Thus a numerical comparison between the reduced Hamiltonian model (the multi-stream model) and full kinetic (relativistic) Vlasov simulations has been investigated in that regime. Although nonlinear simulations of the fluid model , including the dynamics of the pressure tensor, have not been carried out here, the model is strongly relevant even in the three dimensional case.

Global gyrokinetic Vlasov simulations for trapped ion modes indicate that the ion temperature gradient (ITG) instability saturates via nonlinear toroidal coupling. Trapped Ion modes were studied by solving a Vlasov equation averaged over the cyclotron and bounce motion of trapped ions. The distribution function, for trapped ions, is then calculated in a two-dimensional phase space, parametrized by two adiabatic invariants, the longitudinal action and the magnetic moment, in presence of a magnetic shear. Our model can be viewed as a kinetic version of the standard one-field Hasegawa-Mima-type and a broad frequency spectrum can originate from model for trapped-ion driven turbulence. Some interesting new features, which appear in the nonlinear regime of the instability, are then discussed.

In this paper we study the scaling relations for the triggering of the fast, or "ideal", tearing instability starting from equilibrium configurations relevant to astrophysical as well as laboratory plasmas that differ from the simple Harris current sheet configuration. We present the linear tearing instability analysis for equilibrium magnetic fields which a) go to zero at the boundary of the domain and b) contain a double current sheet system (the latter previously studied as a cartesian proxy for the m=1 kink mode in cylindrical plasmas). More generally, we discuss the critical aspect ratio scalings at which the growth rates become independent of the Lundquist number $S$, in terms of the dependence of the $\Delta'$ parameter on the wavenumber $k$ of unstable modes. The scaling $\Delta'(k)$ with $k$ at small $k$ is found to categorize different equilibria broadly: the critical aspect ratios may be even smaller than $L/a \sim S^{\alpha}$ with $\alpha=1/3$ originally found for the Harris current sheet, but there exists a general lower bound $\alpha\ge1/4$., Comment: 7 pages, 5 figures

Relativistic Vlasov–Maxwell model was developed to address the particle trapping or particle acceleration in phase space, including situation relevant to Stimulated Raman Scattering and plasma beatwave acceleration. In particular the case of realistically high ratio of driver frequency to plasma wave frequency ( ω 0 / ω p ∼ 30 ) was also considered using a hybrid version called Vlasov–Hilbert model. Some of the more striking features that have emerged from the Vlasov simulations are discussed in this paper, with particular emphasis on time-dependent matching relations in frequency and wavevector allowing the maintenance of the parametric resonance over a long time, particle dynamics in phase space and action transfer results obtained from the derivation of the integrated Manley–Rowe relations derived for a finite causal system.

International audience; The Letter explores the parametric excitation of low-frequency zonal flow induced by the beating of collisionless trapped ion and trapped electrons modes (CTIMs and CTEMs) and its feedback on the formation of transport barrier (TB). The zonal flow generation and the associated intermittent transport are investigated using a semi-Lagrangian gyrokinetic Vlasov simulations based on a Hamiltonian reduction technique, where both the fastest scales (cyclotron and bounce motions) are gyro-averaged. The model confirms the possibility to trigger TB by means of polarization effects, recently observed in global gyrokinetic simulations by A. Strugarek et al, Phys. Rev. Lett. 111 (2013) 145001.

Fast relativistic particles generated by an ultra strong laser pulse interacting with an overdense plasma, are the source of strong quasi‐static magnetic fields. The physical mechanism underlying this process is known as the current filamentation (Weibel) instability which is an electromagnetic instability driven by the electron momentum anisotropy. Here we investigate the development of this instability in the fluid, relativistic, collisionless regime in the case of beams with a finite transverse size. We show that the development of a spatially resonant mode plays a key role in determining the kind of magnetic structure generated during the evolution of the instability.

The role of the “generalized connections” in the development of collisionless magnetic field line reconnection and in the formation of current and vorticity layers is discussed in a two dimensional plasma configuration with a strong guide magnetic field. Secondary instabilities can modify how magnetic connections are advected in the plasma and lead to turbulent redistribution of the current layers and to the formation of long lived fluid vortices inside magnetic islands.

International audience; We present a multi-stream model obtained from the Vlasov-Maxwell system of equations based on the invariance of the canonical momentum in the perpendicular direction in a 1D-2V phase space. The model is conceived for the study of the Weibel and current filamentation instability in the relativistic regime, but turns out to be of more general importance. It can be used numerically for the study of the non-linear, kinetic dynamics with a drastic reduction of the computational cost with respect to the integration of the corresponding Vlasov-Maxwell system.

International audience; Global gyrokinetic Vlasov simulations for trapped ion modes are performed by solving a Vlasov equation averaged over the cyclotron and bounce motions of trapped ions. The distribution function, for trapped ions, is then calculated in a two-dimensional phase space, parametrized by the longitudinal action (energy) and the magnetic moment in presence of magnetic shear. The physical mechanism of the saturation processes between streamerlike structures and zonal flows in relation to the suppression of turbulent transport is discussed. The magnetic shear is identified to play a key role in the dominant streamer-induced transport regime, which exhibits a Bohm-like scaling. The interaction of streamerlike structures with plasma turbulence is shown to produce the inverse cascade that condenses onto long-wavelength trapped ion structures, on the basis on wave triad interactions.

The nonlinear phase of a magnetic field line reconnection instability in a collisionless two-dimensional cold plasma is investigated in the Hall dominated regime, described by the electron-magnetohydrodynamic equations, which corresponds to the frequency range of whistler waves. It is found that the regular pattern of current density layers that forms in the initial nonlinear phase of the reconnection instability is destroyed by the onset of a Kelvin–Helmholtz-type instability and the formation of current jets that develop into vortex rings. These processes can be interpreted in terms of a Hasegawa–Mima-type regime inside the magnetic island and lead to the creation of magnetic vortices. It is shown that electron compressibility, which is related to charge separation, tends to stabilize these processes.

The JET 2019–2020 scientific and technological programme exploited the results of years of concerted scientific and engineering work, including the ITER-like wall (ILW: Be wall and W divertor) installed in 2010, improved diagnostic capabilities now fully available, a major neutral beam injection upgrade providing record power in 2019–2020, and tested the technical and procedural preparation for safe operation with tritium. Research along three complementary axes yielded a wealth of new results. Firstly, the JET plasma programme delivered scenarios suitable for high fusion power and alpha particle (a) physics in the coming D–T campaign (DTE2), with record sustained neutron rates, as well as plasmas for clarifying the impact of isotope mass on plasma core, edge and plasma-wall interactions, and for ITER pre-fusion power operation. The efficacy of the newly installed shattered pellet injector for mitigating disruption forces and runaway electrons was demonstrated. Secondly, research on the consequences of long-term exposure to JET-ILW plasma was completed, with emphasis on wall damage and fuel retention, and with analyses of wall materials and dust particles that will help validate assumptions and codes for design and operation of ITER and DEMO. Thirdly, the nuclear technology programme aiming to deliver maximum technological return from operations in D, T and D–T benefited from the highest D–D neutron yield in years, securing results for validating radiation transport and activation codes, and nuclear data for ITER. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under Grant Agreement No. 633053. Peer Reviewed Article signat per 1223 autors/autores: J. Mailloux1, N. Abid1, K. Abraham1, P. Abreu2, O. Adabonyan1, P. Adrich3, V. Afanasev4, M. Afzal1, T. Ahlgren5, L. Aho-Mantila6, N. Aiba7, M. Airila6, M. Akhtar1, R. Albanese8, M. Alderson-Martin1, D. Alegre9, S. Aleiferis10, A. Aleksa1, A.G. Alekseev11, E. Alessi12, P. Aleynikov13, J. Algualcil14, M. Ali1, M. Allinson1, B. Alper1, E. Alves2, G. Ambrosino8, R. Ambrosino8, V. Amosov15, E.Andersson Sunden16, P. Andrew13, B.M. Angelini17, C. Angioni18, I. Antoniou1, L.C. Appel1, C. Appelbee1, S. Aria1, M. Ariola8, G. Artaserse17, W. Arter1, V. Artigues18, N. Asakura7, A. Ash1, N. Ashikawa19, V. Aslanyan20, M. Astrain21, O. Asztalos22, D. Auld1, F. Auriemma23, Y. Austin1, L. Avotina24, E. Aymerich25, A. Baciero9, F. Bairaktaris26, J. Balbin27, L. Balbinot23, I. Balboa1, M. Balden18, C. Balshaw1, N. Balshaw1, V.K. Bandaru18, J. Banks1, Yu.F. Baranov1, C. Barcellona28, A. Barnard1, M. Barnard1, R. Barnsley13, A. Barth1, M. Baruzzo17, S. Barwell1, M. Bassan13, A. Batista2, P. Batistoni17, L. Baumane24, B. Bauvir13, L. Baylor29, P.S. Beaumont1, D. Beckett1, A. Begolli1, M. Beidler29, N. Bekris30,31, M. Beldishevski1, E. Belli32, F. Belli17, É. Belonohy1, M. Ben Yaala33, J. Benayas1, J. Bentley1, H. Bergsåker34, J. Bernardo2, M. Bernert18, M. Berry1, L. Bertalot13, H. Betar35, M. Beurskens36, S. Bickerton1, B. Bieg37, J. Bielecki38, A. Bierwage7, T. Biewer29, R. Bilato18, P. Bílková39, G. Birkenmeier18, H. Bishop1, J.P.S. Bizarro2, J. Blackburn1, P. Blanchard40, P. Blatchford1, V. Bobkov18, A. Boboc1, P. Bohm39, T. Bohm41, I. Bolshakova42, T. Bolzonella23, N. Bonanomi18, D. Bonfiglio23, X. Bonnin13, P. Bonofiglo43, S. Boocock1, A. Booth1, J. Booth1, D. Borba2,30, D. Borodin44, I. Borodkina39,44, C. Boulbe45, C. Bourdelle27, M. Bowden1, K. Boyd1, I.Bozicevic Mihalic46, S.C. Bradnam1, V. Braic47, L. Brandt48, R. Bravanec49, B. Breizman50, A. Brett1, S. Brezinsek44, M. Brix1, K. Bromley1, B. Brown1, D. Brunetti1,12, R. Buckingham1, M. Buckley1, R. Budny, J. Buermans51, H. Bufferand27, P. Buratti17, A. Burgess1, A. Buscarino28, A. Busse1, D. Butcher1, E.de la Cal9, G. Calabrò52, L. Calacci53, R. Calado2, Y. Camenen54, G. Canal55, B. Cannas25, M. Cappelli17, S. Carcangiu25, P. Card1, A. Cardinali17, P. Carman1, D. Carnevale53, M. Carr1, D. Carralero9, L. Carraro23, I.S. Carvalho2, P. Carvalho2, I. Casiraghi56, F.J. Casson1, C. Castaldo17, J.P. Catalan14, N. Catarino2, F. Causa12, M. Cavedon18, M. Cecconello16, C.D. Challis1, B. Chamberlain1, C.S. Chang43, A. Chankin18, B. Chapman1,57, M. Chernyshova58, A. Chiariello8, P. Chmielewski58, A. Chomiczewska58, L. Chone59, G. Ciraolo27, D. Ciric1, J. Citrin60, Ł. Ciupinski61, M. Clark1, R. Clarkson1, C. Clements1, M. Cleverly1, J.P. Coad1, P. Coates1, A. Cobalt1, V. Coccorese8, R. Coelho2, J.W. Coenen44, I.H. Coffey62, A. Colangeli17, L. Colas27, C. Collins29, J. Collins1, S. Collins1, D. Conka24, S. Conroy16, B. Conway1, N.J. Conway1, D. Coombs1, P. Cooper1, S. Cooper1, C. Corradino28, G. Corrigan1, D. Coster18, P. Cox1, T. Craciunescu63, S. Cramp1, C. Crapper1, D. Craven1, R. Craven1, M.Crialesi Esposito48, G. Croci56, D. Croft1, A. Croitoru63, K. Crombe51,64, T. Cronin1, N. Cruz2, C. Crystal32, G. Cseh22, A. Cufar65, A. Cullen1, M. Curuia66, T. Czarski58, H. Dabirikhah1, A.Dal Molin56, E. Dale1, P. Dalgliesh1, S. Dalley1, J. Dankowski38, P. David18, A. Davies1, S. Davies1, G. Davis1, K. Dawson1, S. Dawson1, I.E. Day1, M. De Bock13, G. De Temmerman13, G. De Tommasi8, K. Deakin1, J. Deane1, R. Dejarnac39, D. Del Sarto35, E. Delabie29, D. Del-Castillo-Negrete29, A. Dempsey67, R.O. Dendy1,57, P. Devynck27, A. Di Siena18, C. Di Troia17, T. Dickson1, P. Dinca63, T. Dittmar44, J. Dobrashian1, R.P. Doerner68, A.J.H. Donne´69, S. Dorling1, S. Dormido-Canto70, D. Douai27, S. Dowson1, R. Doyle67, M. Dreval71, P. Drewelow36, P. Drews44, G. Drummond1, Ph. Duckworth13, H. Dudding1,72, R. Dumont27, P. Dumortier51, D. Dunai22, T. Dunatov46, M. Dunne18, I. Duran39, F. Durodie51, R. Dux18, A. Dvornova27, R. Eastham1, J. Edwards1, Th. Eich18, A. Eichorn1, N. Eidietis32, A. Eksaeva44, H. El Haroun1, G. Ellwood13, C. Elsmore1, O. Embreus73, S. Emery1, G. Ericsson16, B. Eriksson16, F. Eriksson74, J. Eriksson16, L.G. Eriksson75, S. Ertmer44, S. Esquembri21, A.L. Esquisabel76, T. Estrada9, G. Evans1, S. Evans1, E. Fable18, D. Fagan1, M. Faitsch18, M. Falessi17, A. Fanni25, A. Farahani1, I. Farquhar1, A. Fasoli40, B. Faugeras45, S. Fazinic46, F. Felici40, R. Felton1, A. Fernandes2, H. Fernandes2, J. Ferrand1, D.R. Ferreira2, J. Ferreira2, G. Ferrò53, J. Fessey1, O. Ficker39, A.R. Field1, A. Figueiredo2, J. Figueiredo2,30, A. Fil1, N. Fil1,20, P. Finburg1, D. Fiorucci23, U. Fischer31, G. Fishpool1, L. Fittill1, M. Fitzgerald1, D. Flammini17, J. Flanagan1, K. Flinders1, S. Foley1, N. Fonnesu17, M. Fontana40, J.M. Fontdecaba9, S. Forbes1, A. Formisano8, T. Fornal58, L. Fortuna28, E. Fortuna-Zalesna61, M. Fortune1, C. Fowler1, E. Fransson74, L. Frassinetti34, M. Freisinger44, R. Fresa8, R. Fridström34, D. Frigione53, T. Fülöp73, M. Furseman1, V. Fusco24, S. Futatani17, D. Gadariya77, K. Gál69, D. Galassi40, K. Gałazka58, S. Galeani53, D. Gallart78, R. Galvao55, Y. Gao44, J. Garcia27, M. García-Muñoz79, M. Gardener1, L. Garzotti1, J. Gaspar80, R. Gatto81, P. Gaudio53, D. Gear1, T. Gebhart29, S. Gee1, M. Gelfusa53, R. George1, S.N. Gerasimov1, G. Gervasini12, M. Gethins1, Z. Ghani1, M. Gherendi63, F. Ghezzi12, J.C. Giacalone27, L. Giacomelli12, G. Giacometti54, C. Gibson1, K.J. Gibson72, L. Gil2, A. Gillgren74, D. Gin4, E. Giovannozzi17, C. Giroud1, R. Glen1, S. Glöggler18, J. Goff1, P. Gohil32, V. Goloborodko82, R. Gomes2, B. Gonçalves2, M. Goniche27, A. Goodyear1, S. Gore1, G. Gorini56, T. Görler18, N. Gotts1, R. Goulding43, E. Gow1, B. Graham1, J.P. Graves40, H. Greuner18, B. Grierson43, J. Griffiths1, S. Griph1, D. Grist1, W. Gromelski58, M. Groth59, R. Grove29, M. Gruca58, D. Guard1, N. Gupta1, C. Gurl1, A. Gusarov83, L. Hackett1, S. Hacquin27,30, R. Hager43, L. Hägg16, A. Hakola6, M. Halitovs24, S. Hall1, S.A. Hall1, S. Hallworth-Cook1, C.J. Ham1, D. Hamaguchi7, M. Hamed27, C. Hamlyn-Harris1, K. Hammond1, E. Harford1, J.R. Harrison1, D. Harting1, Y. Hatano84, D.R. Hatch50, T. Haupt1, J. Hawes1, N.C. Hawkes1, J. Hawkins1, T. Hayashi7, S. Hazael1, S. Hazel1, P. Heesterman1, B. Heidbrink85, W. Helou13, O. Hemming1, S.S. Henderson1, R.B. Henriques2, D. Hepple1, J. Herfindal29, G. Hermon1, J. Hill1, J.C. Hillesheim1, K. Hizanidis26, A. Hjalmarsson16, A. Ho60, J. Hobirk18, O. Hoenen13, C. Hogben1, A. Hollingsworth1, S. Hollis1, E. Hollmann68, M. Hölzl18, B. Homan45, M. Hook1, D. Hopley1, J. Horácek39, D. Horsley1, N. Horsten59, A. Horton1, L.D. Horton30,40, L. Horvath1,72, S. Hotchin1, R. Howell1, Z. Hu56, A. Huber44, V. Huber44, T. Huddleston1, G.T.A. Huijsmans13, P. Huynh27, A. Hynes1, M. Iliasova4, D. Imrie1, M. Imrísek39, J. Ingleby1, P. Innocente23, K. Insulander Björk73, N. Isernia8, I. Ivanova-Stanik58, E. Ivings1, S. Jablonski58, S. Jachmich13,30,51, T. Jackson1, P. Jacquet1, H. Järleblad86, F. Jaulmes39, J.Jenaro Rodriguez1, I. Jepu63, E. Joffrin27, R. Johnson1, T. Johnson34, J. Johnston1, C. Jones1, G. Jones1, L. Jones1, N. Jones1, T. Jones1, A. Joyce1, R. Juarez14, M. Juvonen1, P. Kalnin¸ a24, T. Kaltiaisenaho6, J. Kaniewski1, A. Kantor1, A. Kappatou18, J. Karhunen5, D. Karkinsky1, Yu Kashchuk87, M. Kaufman29, G. Kaveney1, Ye.O. Kazakov51, V. Kazantzidis26, D.L. Keeling1, R. Kelly1, M. Kempenaars13, C. Kennedy1, D. Kennedy1, J. Kent1, K. Khan1, E. Khilkevich4, C. Kiefer18, J. Kilpeläinen59, C. Kim32, Hyun-Tae Kim1,30, S.H. Kim13, D.B. King1, R. King1, D. Kinna1, V.G. Kiptily1, A. Kirjasuo6, K.K. Kirov1, A. Kirschner44, T. kiviniemi59, G. Kizane24, M. Klas88, C. Klepper29, A. Klix31, G. Kneale1, M. Knight1, P. Knight1, R. Knights1, S. Knipe1, M. Knolker32, S. Knott89, M. Kocan13, F. Köchl1, I. Kodeli65, Y. Kolesnichenko82, Y. Kominis26, M. Kong1, V. Korovin71, B. Kos65, D. Kos1, H.R. Koslowski44, M. Kotschenreuther50, M. Koubiti54, E. Kowalska-Strzeciwilk ˛ 58, K. Koziol3, A. Krasilnikov87, V. Krasilnikov13,15, M. Kresina1,27, K. Krieger18, N. Krishnan1, A. Krivska51, U. Kruezi13, I. Ksia˛zek ˙ 90, A.B. Kukushkin11, H. Kumpulainen59, T. Kurki-Suonio59, H. Kurotaki7, S. Kwak36, O.J. Kwon91, L. Laguardia12, E. Lagzdina24, A. Lahtinen5, A. Laing1, N. Lam1, H.T. Lambertz44, B. Lane1, C. Lane1, E.Lascas Neto40, E. Łaszynska58, K.D. Lawson1, A. Lazaros26, E. Lazzaro12, G. Learoyd1, Chanyoung Lee92, S.E. Lee84, S. Leerink59, T. Leeson1, X. Lefebvre1, H.J. Leggate67, J. Lehmann1, M. Lehnen13, D. Leichtle31,93, F. Leipold13, I. Lengar65, M. Lennholm1,75, E. Leon Gutierrez9, B. Lepiavko82, J. Leppänen6, E. Lerche51, A. Lescinskis24, J. Lewis1, W. Leysen83, L. Li44, Y. Li44, J. Likonen6, Ch. Linsmeier44, B. Lipschultz72, X. Litaudon27,30, E. Litherland-Smith1, F. Liu27,30, T. Loarer27, A. Loarte13, R. Lobel1, B. Lomanowski29, P.J. Lomas1, J.M. Lopez21, R. Lorenzini23, S. Loreti17, U. Losada9, V.P. Loschiavo8, M. Loughlin13, Z. Louka1, J. Lovell29, T. Lowe1, C. Lowry1,75, S. Lubbad1, T. Luce13, R. Lucock1, A. Lukin94, C. Luna95, E.de la Luna9, M. Lungaroni53, C.P. Lungu63, T. Lunt18, V. Lutsenko82, B. Lyons32, A. Lyssoivan51, M. Machielsen40, E. Macusova39, R. Mäenpää59, C.F. Maggi1, R. Maggiora96, M. Magness1, S. Mahesan1, H. Maier18, R. Maingi43, K. Malinowski58, P. Manas18,54, P. Mantica12, M.J. Mantsinen97, J. Manyer78, A. Manzanares98, Ph. Maquet13, G. Marceca40, N. Marcenko87, C. Marchetto99, O. Marchuk44, A. Mariani12, G. Mariano17, M. Marin60, M. Marinelli53, T. Markovicˇ39, D. Marocco17, L. Marot33, S. Marsden1, J. Marsh1, R. Marshall1, L. Martellucci53, A. Martin1, A.J. Martin1, R. Martone8, S. Maruyama13, M. Maslov1, S. Masuzaki19, S. Matejcik88, M. Mattei8, G.F. Matthews1, D. Matveev44, E. Matveeva39, A. Mauriya2, F. Maviglia8, M. Mayer18, M.-L. Mayoral1,69, S. Mazzi54, C. Mazzotta17, R. McAdams1, P.J. McCarthy89 K.G. McClements1, J. McClenaghan32, P. McCullen1, D.C. McDonald1, D. McGuckin1, D. McHugh1, G. McIntyre1, R. McKean1, J. McKehon1, B. McMillan57, L. McNamee1, A. McShee1, A. Meakins1, S. Medley1, C.J. Meekes60,100, K. Meghani1, A.G. Meigs1, G. Meisl18, S. Meitner29, S. Menmuir1, K. Mergia10, S. Merriman1, Ph. Mertens44, S. Meshchaninov15, A. Messiaen51, R. Michling57, P. Middleton1, D. Middleton-Gear1, J. Mietelski38, D. Milanesio96, E. Milani53, F. Militello1, A.Militello Asp1, J. Milnes1, A. Milocco56, G. Miloshevsky101, C. Minghao1, S. Minucci52, I. Miron63, M. Miyamoto102, J. Mlynár39,103, V. Moiseenko71, P. Monaghan1, I. Monakhov1, T. Moody1, S. Moon34, R. Mooney1, S. Moradi51, J. Morales27, R.B. Morales1, S. Mordijck104, L. Moreira1, L. Morgan1, F. Moro17, J. Morris1, K.-M. Morrison1, L. Msero13,33, D. Moulton1, T. Mrowetz1, T. Mundy1, M. Muraglia54, A. Murari23,30, A. Muraro12, N. Muthusonai1, B. N’Konga45, Yong-Su Na92, F. Nabais2, M. Naden1, J. Naish1, R. Naish1, F. Napoli17, E. Nardon27, V. Naulin86, M.F.F. Nave2, I. Nedzelskiy3, G. Nemtsev15, V. Nesenevich4, I. Nestoras1, R. Neu18, V.S. Neverov11, S. Ng1, M. Nicassio1, A.H. Nielsen86, D. Nina2, D. Nishijima105, C. Noble1, C.R. Nobs1, M. Nocente56, D. Nodwell1, K. Nordlund5, H. Nordman13, R. Normanton1, J.M. Noterdaeme18, S. Nowak12, E. Nunn1, H. Nyström34, M. Oberparleiter74, B. Obryk38, J. O’Callaghan1, T. Odupitan1, H.J.C. Oliver1,50, R. Olney1, M. O’Mullane106, J. Ongena51, E. Organ1, F. Orsitto8, J. Orszagh88, T. Osborne32, R. Otin1, T. Otsuka107, A. Owen1, Y. Oya108, M. Oyaizu7, R. Paccagnella23, N. Pace1, L.W. Packer1, S. Paige1, E. Pajuste24, D. Palade63, S.J.P. Pamela1, N. Panadero9, E. Panontin56, A. Papadopoulos26, G. Papp18, P. Papp88, V.V. Parail1, C. Pardanaud54, J. Parisi1,109, F.Parra Diaz109, A. Parsloe1, M. Parsons29, N. Parsons1, M. Passeri53, A. Patel1, A. Pau40, G. Pautasso18, R. Pavlichenko71, A. Pavone36, E. Pawelec90, C.Paz Soldan110, A. Peacock1,75, M. Pearce1, E. Peluso53, C. Penot13, K. Pepperell1, R. Pereira2, T. Pereira2, E.Perelli Cippo12, P. Pereslavtsev107, C. Perez von Thun58, V. Pericoli58, D. Perry1, M. Peterka39, P. Petersson34, G. Petravich22, N. Petrella1, M. Peyman1, M. Pillon17, S. Pinches13, G. Pintsuk44, W. Pires de Sá55, A. Pires dos Reis55, C. Piron17, L. Pionr23,111, A. Pironti8, R. Pitts13, K.L. van de Plassche60, N. Platt1, V. Plyusnin2, M. Podesta43, G. Pokol22, F.M. Poli43, O.G. Pompilian63, S. Popovichev1, M. Poradzinski58, M.T. Porfiri17, M. Porkolab20, C. Porosnicu63, M. Porton1, G. Poulipoulis112, I. Predebon23, G. Prestopino53, C. Price1, D. Price1, M. Price1, D. Primetzhofer16, P. Prior1, G. Provatas46, G. Pucella17, P. Puglia40, K. Purahoo1, I. Pusztai73, O. Putignano56, T. Pütterich18, A. Quercia8, E. Rachlew73, G. Radulescu29, V. Radulovic65, M. Rainford1, P. Raj31, G. Ralph1, G. Ramogida17, D. Rasmussen29, J.J. Rasmussen86, G. Rattá9, S. Ratynskaia113, M. Rebai12, D. Refy22, R. Reichle13, M. Reinke29, D. Reiser44, C. Reux27, S. Reynolds1, M.L. Richiusa1, S. Richyal1, D. Rigamonti12, F.G. Rimini1, J. Risner29, M. Riva17, J. Rivero-Rodriguez79, C.M. Roach1, R. Robins1, S. Robinson1, D. Robson1, R. Rodionov87, P. Rodrigues2, M.Rodriguez Ramos109, P. Rodriguez-Fernandez3, F. Romanelli74, M. Romanelli1, S. Romanelli1, J. Romazanov44, R. Rossi53, S. Rowe1, D. Rowlands1,30, M. Rubel34, G. Rubinacci8, G. Rubino52, L. Ruchko55, M. Ruiz21, J.Ruiz Ruiz109, C. Ruset63, J. Rzadkiewicz3, S. Saarelma1, E. Safi5, A. Sahlberg16, M. Salewski86, A. Salmi6, R. Salmon1, F. Salzedas2,114, I. Sanders1, D. Sandiford1, B. Santos2, A. Santucci17, K. Särkimäki73, R. Sarwar1, I. Sarychev1, O. Sauter40, P. Sauwan14, N. Scapin48, F. Schluck44, K. Schmid18, S. Schmuck12, M. Schneider13, P.A. Schneider18, D. Schwörer67, G. Scott1, M. Scott1, D. Scraggs1, S. Scully1, M. Segato1, Jaemin Seo92, G. Sergienko44, M. Sertoli1, S.E. Sharapov1, A. Shaw1, H. Sheikh1, U. Sheikh40, A. Shepherd1, A. Shevelev4, P. Shigin13, K. Shinohara115, S. Shiraiwa43, D. Shiraki29, M. Short1, G. Sias25, S.A. Silburn1, A. Silva2, C. Silva2, J. Silva1, D. Silvagni18, D. Simfukwe1, J. Simpson1,59, D. Sinclair1, S.K. Sipilä59, A.C.C. Sips75, P. Siren5, A. Sirinelli13, H. Sjöstrand16, N. Skinner1, J. Slater1, N. Smith1, P. Smith1, J. Snell1, G. Snoep60, L. Snoj65, P. Snyder32, S. Soare63, E.R. Solano9, V. Solokha59, A. Somers67, C. Sommariva40, K. Soni33, E. Sorokovoy71, M. Sos39, J. Sousa2, C. Sozzi12, S. Spagnolo23, T. Spelzini1, F. Spineanu63, D. Spong29, D. Sprada1, S. Sridhar27, C. Srinivasan1, G. Stables1, G. Staebler32, I. Stamatelatos10, Z. Stancar65, P. Staniec1, G. Stankunas116, M. Stead1, E. Stefanikova34, A. Stephen1, J. Stephens1, P. Stevenson1, M. Stojanov1, P. Strand74, H.R. Strauss117, S. Strikwerda1, P. Ström34, C.I. Stuart1, W. Studholme1, M. Subramani1, E. Suchkov88, S. Sumida7, H.J. Sun1, T.E. Susts24, J. Svensson36, J. Svoboda39, R. Sweeney20, D. Sytnykov71, T. Szabolics22, G. Szepesi1, B. Tabia1, T. Tadic´46, B. Tál18, T. Tala6, A. Tallargio1, P. Tamain27, H. Tan1, K. Tanaka19, W. Tang43, M. Tardocchi12, D. Taylor1, A.S. Teimane24, G. Telesca58, N. Teplova4, A. Teplukhina43, D. Terentyev83, A. Terra44, D. Terranova23, N. Terranova17, D. Testa40, E. Tholerus1,34, J. Thomas1, E. Thoren113, A. Thorman1, W. Tierens18, R.A. Tinguely20, A. Tipton1, H. Todd1, M. Tokitani19, P. Tolias113, M. Tomes39, A. Tookey1, Y. Torikai118, U. von Toussaint18, P. Tsavalas10, D. Tskhakaya39,119, I. Turner1, M. Turner1, M.M. Turner67, M. Turnyanskiy1,69, G. Tvalashvili1, S. Tyrrell1, M. Tyshchenko82, A. Uccello12, V. Udintsev13, G. Urbanczyk27, A. Vadgama1, D. Valcarcel1, M. Valisa23, P.Vallejos Olivares34, O. Vallhagen73, M. Valovicˇ1, D. Van Eester51, J. Varje59, S. Vartanian27, T. Vasilopoulou10, G. Vayakis13, M. Vecsei22, J. Vega9, S. Ventre8, G. Verdoolaege64, C. Verona53, G.Verona Rinati53, E. Veshchev13, N. Vianello23, E. Viezzer79, L. Vignitchouk113, R. Vila9, R. Villari17, F. Villone8, P. Vincenzi23, I. Vinyar94, B. Viola17, A.J. Virtanen59, A. Vitins24, Z. Vizvary1, G. Vlad17, M. Vlad63, P. Vondrácek39, P.de Vries13, B. Wakeling1, N.R. Walkden1, M. Walker1, R. Walker1, M. Walsh13, E. Wang44, N. Wang1, S. Warder1, R. Warren1, J. Waterhouse1, C. Watts13, T. Wauters51, A. Weckmann34, H.Wedderburn Maxwell1, M. Weiland18, H. Weisen40, M. Weiszflog16, P. Welch1, N. Wendler58, A. West1, M. Wheatley1, S. Wheeler1, A. Whitehead1, D. Whittaker1, A. Widdowson1, S. Wiesen44, J. Wilkinson1, J.C. Williams1, D. Willoughby1, I. Wilson1, J. Wilson1, T. Wilson1, M. Wischmeier18, P. Wise1, G. Withenshaw1, A. Withycombe1, D. Witts1, A. Wojcik-Gargula38, E. Wolfrum18, R. Wood1, C. Woodley1, R. Woodley1, B. Woods1, J. Wright1, J.C. Wright20, T. Xu1, D. Yadikin74, M. Yajima19, Y. Yakovenko82, Y. Yang13, W. Yanling44, V. Yanovskiy39, I. Young1, R. Young1, R.J. Zabolockis24, J. Zacks1, R. Zagorski3, F.S. Zaitsev88, L. Zakharov5, A. Zarins24, D. Zarzoso Fernandez54, K.-D. Zastrow1, Y. Zayachuk1, M. Zerbini17, W. Zhang18, Y. Zhou34, M. Zlobinski44, A. Zocco36, A. Zohar65, V. Zoita63, S. Zoletnik22, V.K. Zotta81, I. Zoulias1, W. Zwingmann2 and I. Zychor3 // 1 United Kingdom Atomic Energy Authority, Culham Science Centre, Abingdon, Oxon, OX14 3DB, United Kingdom of Great Britain and Northern Ireland 2 Instituto de Plasmas e Fusao Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal 3 National Centre for Nuclear Research (NCBJ), 05-400 Otwock-Swierk, Poland 4 Ioffe Physico-Technical Institute, 26 Politekhnicheskaya, St Petersburg 194021, Russia 5 University of Helsinki, PO Box 43, FI-00014 University of Helsinki, Finland 6 VTT Technical Research Centre of Finland, PO Box 1000, FIN-02044 VTT, Finland 7 National Institutes for Quantum and Radiological Science and Technology, Naka, Ibaraki 311-0193, Japan 8 Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy 9 Laboratorio Nacional de Fusión, CIEMAT, Madrid, Spain 10 NCSR ‘Demokritos’ 153 10, Agia Paraskevi Attikis, Greece 11 NRC Kurchatov Institute, 1 Kurchatov Square, Moscow 123182, Russia 12 Institute for Plasma Science and Technology, CNR, via R. Cozzi 53, 20125 Milano, Italy 13 ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 Saint Paul Lez Durance Cedex, France 14 Universidad Nacional de Educacion a Distancia, Dept Ingn Energet, Calle Juan del Rosal 12, E-28040 Madrid, Spain 15 Troitsk Insitute of Innovating and Thermonuclear Research (TRINITI), Troitsk 142190, Moscow Region, Russia 16 Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden 17 Dip.to Fusione e Tecnologie per la Sicurezza Nucleare, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Roma), Italy 18 Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany 19 National Institute for Fusion Science, Oroshi, Toki, Gifu 509-5292, Japan 20 MIT Plasma Science and Fusion Center, Cambridge, MA 02139, United States of America 21 Universidad Politécnica de Madrid, Grupo I2A2, Madrid, Spain 22 Centre for Energy Research, POB 49, H-1525 Budapest, Hungary 23 Consorzio RFX, Corso Stati Uniti 4, 35127 Padova, Italy 24 University of Latvia, 19 Raina Blvd., Riga, LV 1586, Latvia 25 Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d’Armi 09123 Cagliari, Italy 26 National Technical University of Athens, Iroon Politechniou 9, 157 73 Zografou, Athens, Greece 27 CEA, IRFM, F-13108 Saint Paul Lez Durance, France 28 Dipartimento di Ingegneria Elettrica Elettronica e Informatica, Università degli Studi di Catania, 95125 Catania, Italy 29 Oak Ridge National Laboratory, Oak Ridge, TN 37831, TN, United States of America 30 EUROfusion Programme Management Unit, Culham Science Centre, Culham, OX14 3DB, United Kingdom of Great Britain and Northern Ireland 31 Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany 32 General Atomics, PO Box 85608, San Diego, CA 92186-5608, United States of America 33 Department of Physics, University of Basel, Switzerland 34 Fusion Plasma Physics, EECS, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden 35 Institut Jean Lamour, UMR 7198, CNRS-Université de Lorraine, 54500 Vandoeuvre-lès-Nancy, France 36 Max-Planck-Institut für Plasmaphysik, Teilinsitut Greifswald, D-17491 Greifswald, Germany 37 Maritime University of Szczecin Faculty of Marine Engineering, Waly Chrobrego 1-2, 70-500 Szczecin, Poland 38 Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Kraków, Poland 39 Institute of Plasma Physics of the CAS, Za Slovankou 1782/3, 182 00 Praha 8, Czech Republic 40 Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland 41 University of Wisconsin-Madison, Madison, WI 53706, United States of America 42 Magnetic Sensor Laboratory, Lviv Polytechnic National University, Lviv, Ukraine 43 Princeton Plasma Physics Laboratory, James Forrestal Campus, Princeton, NJ 08543, NJ, United States of America 44 Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung, Plasmaphysik, 52425 Jülich, Germany 45 Université Cote d’Azur, CNRS, Inria, LJAD, Parc Valrose, 06108 Nice Cedex 02, France 46 Ruder Boskovic Institute, Bijenicka 54, 10000 Zagreb, Croatia 47 The National Institute for Optoelectronics, Magurele-Bucharest, Romania 48 Mechanics, SCI, KTH SE-100 44 Stockholm, Sweden 49 Fourth State Research, 503 Lockhart Dr, Austin, TX, United States of America 50 University of Texas at Austin, Institute for Fusion Studies, Austin, TX 78712, United States of America 51 Laboratory for Plasma Physics LPP-ERM/KMS, B-1000 Brussels, Belgium 52 University of Tuscia, DEIM, Via del Paradiso 47, 01100 Viterbo, Italy 53 Università di Roma Tor Vergata, Via del Politecnico 1, Roma, Italy 54 Aix-Marseille University, CNRS, PIIM, UMR 7345, 13013 Marseille, France 55 Instituto de Física, Universidade de Sao Paulo, Rua do Mat˜ao Travessa R Nr.187, CEP 05508-090 Cidade Universitária, Sao Paulo, Brasil 56 University of Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy 57 Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, United Kingdom of Great Britain and Northern Ireland 58 Institute of Plasma Physics and Laser Microfusion, Hery 23, 01-497 Warsaw, Poland 59 Aalto University, PO Box 14100, FIN-00076 Aalto, Finland 60 FOM Institute DIFFER, Eindhoven, The Netherlands 61 Warsaw University of Technology, 02-507 Warsaw, Poland 62 Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University, Belfast, BT7 1NN, United Kingdom of Great Britain and Northern Ireland 63 The National Institute for Laser, Plasma and Radiation Physics, Magurele-Bucharest, Romania 64 Department of Applied Physics, Ghent University, 9000 Ghent, Belgium 65 Slovenian Fusion Association (SFA), Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia 66 The National Institute for Cryogenics and Isotopic Technology, Ramnicu Valcea, Romania 67 Dublin City University (DCU), Dublin, Ireland 68 University of California at San Diego, La Jolla, CA 92093, United States of America 69 EUROfusion Programme Management Unit, Boltzmannstr. 2, 85748 Garching, Germany 70 UNED, Dpto. Informática y Automática, Madrid, Spain 71 National Science Center ‘Kharkov Institute of Physics and Technology’, Akademichna 1, Kharkiv 61108, Ukraine 72 York Plasma Institute, Department of Physics, University of York, York, YO10 5DD, United Kingdom of Great Britain and Northern Ireland 73 Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden 74 Department of Space, Earth and Environment, Chalmers University of Technology, SE-41296 Gothenburg, Sweden 75 European Commission, B-1049 Brussels, Belgium 76 University of Tennessee, Knoxville, TN 37996, TN, United States of America 77 Universitat Politècnica de Catalunya, Barcelona, Spain 78 Barcelona Supercomputing Center, Barcelona, Spain 79 Universidad de Sevilla, Sevilla, Spain 80 Aix-Marseille University, CNRS, IUSTI, UMR 7343, 13013 Marseille, France 81 Dipartimento di Ingegneria Astronautica, Elettrica ed Energetica, SAPIENZA Università di Roma, Via Eudossiana 18, 00184 Roma, Italy 82 Institute for Nuclear Research, Prospekt Nauky 47, Kyiv 03680, Ukraine 83 Studiecentrum voor Kernenergie—Centre d’Etude de l’Energie Nucléaire, Boeretang 200, 2400 Mol, Belgium 84 University of Toyama, Toyama, 930-8555, Japan 85 University of California, Irvine, Irvine, California 92697, United States of America 86 Department of Physics, Technical University of Denmark, Bldg 309, DK-2800 Kgs Lyngby, Denmark 87 Institution ‘Project Center ITER’, Moscow, 123182, Russia 88 Faculty of Mathematics, Department of Experimental Physics, Physics and Informatics Comenius University Mlynska dolina F2, 84248 Bratislava, Slovakia 89 University College Cork (UCC), Cork, Ireland 90 Institute of Physics, Opole University, Oleska 48, 45-052 Opole, Poland 91 Daegu University, Jillyang, Gyeongsan, Gyeongbuk 712-174, Republic of Korea 92 Department of Nuclear Engineering, Seoul National University, Seoul, Republic of Korea 93 Fusion for Energy Joint Undertaking, Josep Pl. 2, Torres Diagonal Litoral B3, 08019, Barcelona, Spain 94 PELIN LLC, 27a, Gzhatskaya Ulitsa, Saint Petersburg, 195220, Russia 95 Arizona State University, Tempe, AZ, United States of America 96 Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy 97 ICREA and Barcelona Supercomputing Center, Barcelona, Spain 98 Universidad Complutense de Madrid, Madrid, Spain 99 Istituto dei Sistemi Complessi—CNR and Dipartimento di Energia—Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy 100 Eindhoven University of Technology, The Netherlands 101 Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, United States of America 102 Department of Material Science, Shimane University, 1060 Nishikawatsu, Matsue, 690-8504, Japan 103 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehová 78/7, 115 19 Praha 1, Czech Republic 104 College of William and Mary, Williamsburg, VA 23185, United States of America 105 University of California, 1111 Franklin St., Oakland, CA 94607, United States of America 106 University of Strathclyde, Glasgow, G4 0NG, United Kingdom of Great Britain and Northern Ireland 107 Kindai University, Higashi-Osaka, 577-8502, Japan 108 Shizuoka University, Shizuoka, 422-8529, Japan 109 Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom of Great Britain and Northern Ireland 110 Columbia University, New York, NY 10027, United States of America 111 Dipartimento di Fisica ‘G. Galilei’, Universita’ degli Studi di Padova, Padova, Italy 112 Space and Plasma Physics, EECS, KTH SE-100 44 Stockholm, Sweden 113 University of Ioannina, Panepistimioupoli Ioanninon, PO Box 1186, 45110 Ioannina, Greece 114 Universidade do Porto, Faculdade de Engenharia, 4200-465 Porto, Portugal 115 The University of Tokyo, Kashiwa, Chiba, 277-0882, Japan 116 Lithuanian Energy Institute, Breslaujos g. 3, LT-44403, Kaunas, Lithuania 117 HRS Fusion, West Orange, NJ, United States of America 118 Ibaraki University Graduate School of Science and Engineering, Mito, Ibaraki 310-8512, Japan 119 Technische Universität Wien, Fusion@ÖAW Österreichische Akademie der Wissenschaften (ÖAW), Austria

We review some recent results that have been obtained in the investigation of collisionless reconnection in two dimensional magnetic configurations with a strong guide field in regimes of interest for laboratory plasmas. First we adopt a two-fluid dissipationless plasma model where the plasma evolution is described by the advection of two Lagrangian invariant fields. Then, we show that an analogous formulation in terms of Lagrangian invariants applies to the case where the electron response is obtained from a drift-kinetic model.