Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T13:04:15.799Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulation as a tool to improve wave heating in fusion plasmas

Part of: Focus on Fusion ITER International School 2014

Published online by Cambridge University Press:  07 August 2015

S. Heuraux ,
F. da Silva ,
T. Ribeiro ,
B. Despres ,
M. Campos Pinto ,
J. Jacquot ,
E. Faudot ,
S. Wengerowsky ,
L. Colas  and
L. Lu
S. Heuraux*
Affiliation:
Institut Jean Lamour, UMR 7198, CNRS–Université de Lorraine, BP 70239, 54506 Vandoeuvre, France
F. da Silva
Affiliation:
Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
T. Ribeiro
Affiliation:
Max-Planck-Institut für Plasmaphysik, 85748 Garching, Germany
B. Despres
Affiliation:
Laboratory Jacques Louis Lions, University Pierre et Marie Curie, BP 187, 75252 Paris CEDEX 05, France
M. Campos Pinto
Affiliation:
Laboratory Jacques Louis Lions, University Pierre et Marie Curie, BP 187, 75252 Paris CEDEX 05, France
J. Jacquot
Affiliation:
CEA, IRFM, 13108 St Paul Lez Durance, France
E. Faudot
Affiliation:
Institut Jean Lamour, UMR 7198, CNRS–Université de Lorraine, BP 70239, 54506 Vandoeuvre, France
S. Wengerowsky
Affiliation:
Institut Jean Lamour, UMR 7198, CNRS–Université de Lorraine, BP 70239, 54506 Vandoeuvre, France
L. Colas
Affiliation:
CEA, IRFM, 13108 St Paul Lez Durance, France
L. Lu
Affiliation:
Institut Jean Lamour, UMR 7198, CNRS–Université de Lorraine, BP 70239, 54506 Vandoeuvre, France CEA, IRFM, 13108 St Paul Lez Durance, France
*
†Email address for correspondence: stephane.heuraux@univ-lorraine.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Firstly, a brief overview will be given on different models that are able to describe the behaviour of wave propagation as a function of specific frequency ranges. Each range corresponds to different heating systems, namely, 20–100 MHz for the ion cyclotron resonant heating, 2–20 GHz for lower-hybrid heating or current drive, and 100–250 GHz for electron cyclotron resonant heating or current drive systems. The specification of every system will be explained in detail, including the typical set of equations and the assumptions needed to describe the properties of these heating or current drive systems, as well as their specific domains of validity. In these descriptions, special attention will be paid to the boundary conditions. A review of specific physical problems associated with the wave heating systems will also be provided. The review will detail the role of simulation in answering questions that arise from experiments on magnetized plasma devices devoted to fusion. A few examples that will be covered are the impact of edge turbulence on wave propagation and its consequences on heating system performance, the effects of fast particles and ponderomotive effects, among others. A study that is more focused on radio-frequency sheath effects will also be discussed. It shows that such simulations require very sophisticated tools to gain a partial understanding of the observations undertaken in dedicated experiments. To conclude this review, an overview will be given about the requirements and progress necessary to obtain relevant predictive simulation tools able to describe the wave heating systems used in fusion devices.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 435810503
Copyright
© Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Artaud, J. F., Basiuk, V., Imbeaux, F., Schneider, M., Garcia, J., Giruzzi, G., Huynh, P., Aniel, T., Albajar, F., Ané, J. M., Bécoulet, A., Bourdelle, C., Casati, A., Colas, L., Decker, J., Dumont, R., Eriksson, L. G., Garbet, X., Guirlet, R., Hertout, P., Hoang, G. T., Houlberg, W., Huysmans, G., Joffrin, E., Kim, S. H., Kochl, F., Lister, J., Litaudon, X., Maget, P., Masset, R., Pégourié, B., Peysson, Y., Thomas, P., Tsitrone, E. & Turco, F. 2010 The CRONOS suite of codes for integrated tokamak modelling. Nucl. Fusion 50, 043001.CrossRefGoogle Scholar
Bai, B., Li, X., Liu, Y., Xu, J., Shi, L. & Xie, K. 2014 Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves. IEEE Trans. Plasma Sci. 42, 3365–3372.Google Scholar
Batanov, G. M., Borzosekov, V. D., Kovrizhnykh, L. M., Kolik, L. V., Konchekov, E. M., Malakhov, D. V., Petrov, A. E., Sarksyan, K. A., Skvortsova, N. N., Stepakhin, V. D. & Kharchev, N. K. 2013 Backscattering of gyrotron radiation and short-wavelength turbulence during electron cyclotron resonance plasma heating in the L-2M stellarator. Plasma Phys. Rep. 39, 444–455.CrossRefGoogle Scholar
Bérenger, J.-P. 1994 Numerical modeling of the coupling of an ICRH antenna with a plasma with self-consistent antenna current in the ion cyclotron range of frequencies. J. Comput. Phys. 114, 185–200.Google Scholar
Bertelli, N., Maj, O., Poli, E., Harvey, R., Wright, J. C., Bonoli, P. T., Phillips, C. K., Smirnov, A. P., Valeo, E. & Wilson, J. R. 2012 Paraxial Wentzel–Kramers–Brillouin method applied to the lower hybrid wave propagation. Phys. Plasmas 19, 082510.Google Scholar
Bindslev, H. 1991 Dielectric effects on Thomson scattering in a relativistic magnetized plasma. Plasma Phys. Control Fusion 33, 1775–1804.Google Scholar
Bobkov, V., Braun, F., Dux, R., Herrmann, A., Giannone, L., Kallenbach, A., Rohde, V., Schweinzer, J., Sips, A., Zammuto, I. & ASDEX Upgrade Team 2010 Assessment of compatibility of ICRF antenna operation with full W wall in ASDEX upgrade. Nucl. Fusion 50, 035004.Google Scholar
Bonoli, P. 1985 Linear theory of lower-hybrid wave in tokamak plasmas. In Wave Heating and Current Drive in Plasmas, pp. 175–218. Gordon and Breach.Google Scholar
Bonoli, P. T. 2014 Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters. AIP Conf. Proc. 1580, 15–24.Google Scholar
Bornatici, M., Cano, R., de Barbeiri, O. & Englemann, F. 1983 Electron cyclotron emission and absoprtion in fusion plasmas. Nucl. Fusion 23, 1153–1257.Google Scholar
Brambilla, M. 1999 Numerical simulation of ion cyclotron waves in tokamak plasmas. Plasma Phys. Control. Fusion 41, 1–34.CrossRefGoogle Scholar
Brambilla, M. & Bilato, R. 2009 Advances in numerical simulations of ion cyclotron heating of non-Maxwellian plasmas. Nucl. Fusion 49, 085004.CrossRefGoogle Scholar
Budny, R. V., Berry, L., Bilato, R., Bonoli, P., Brambilla, M., Dumont, R. J., Fukuyama, A., Harvey, R., Jaeger, E. F., Indireshkumar, K., Lerche, E., McCune, D., Phillips, C. K., Vdovin, V. & Wright, J. 2012 Benchmarking ICRF full-wave solvers for ITER. Nucl. Fusion 52, 023023.Google Scholar
Cairns, R. A. 1991 Radiofrequency Heating of Plasmas. chap. 3–5, Adam Hilger.Google Scholar
Campos Pinto, M., Sonnendrücker, E., Friedman, A., Grote, D. P. & Lund, S. P. 2014 Noiseless Vlasov–Poisson simulations with linearly transformed particles. J. Comput. Phys. 275, 236–256.Google Scholar
Casati, A., Grangirard, V., Bourdelle, C., Hennequin, P., Gerbaud, T., Heuraux, S., Vermare, L., Aniel, T., Clairet, F., Garbet, X., Imbeaux, F., Candy, J. & Waltz, R. 2009 Turbulence in the Tore Supra tokamak measurements and validation of nonlinear simulations. Phys. Rev. Lett. 102, 165005.CrossRefGoogle ScholarPubMed
Clairet, F., Colas, L., Heuraux, S. & Lombard, G. 2004 ICRF coupling and edge density profile on Tore Supra. Plasma Phys. Control. Fusion 46, 1567–1581.Google Scholar
Coelho, R., Äkäslompolo, S., Dinklage, A., Kus, A., Sundén, E., Blanco, E., Conway, G., Hacquin, S., Heuraux, S., Lechte, C., Silva, F. & Sirinelli, A. 2013 Synthetic diagnostics in the EU-ITM simulation platform. Fusion Sci. Technol. 63, 1–9.Google Scholar
Colas, L., Jacquot, J., Heuraux, S., Faudot, E., Crombé, K., Kyrytsya, V., Hillairet, J. & Goniche, M. 2012 Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: simplified three dimensional non-linear treatment in the wide sheath asymptotic regime. Phys. Plasmas 19, 092505.Google Scholar
Colas, L., Zou, X. L., Paume, M., Chareau, J. M., Guiziou, L., Hoang, G. T., Michelot, Y. & Gresillon, D. 1998 Internal magnetic fluctuations and electron heat transport in Tore Supra. Nucl. Fusion 38, 903–918.CrossRefGoogle Scholar
Comisso, L. & Lazzaro, E. 2010 Two-dimensional effects in the problem of tearing modes control by electron cyclotron current drive. Nucl. Fusion 50, 125002.Google Scholar
Courant, R., Friedrichs, K. & Lewy, H. 1928 Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100, 32–74.Google Scholar
Crouseilles, N., Lemou, M. & Méhats, F. 2013 Asymptotic preserving schemes for highly oscillatory Vlasov–Poisson equations. J. Comput. Phys. 248, 287–308.Google Scholar
Decker, J., Peysson, Y. & Coda, S. 2012 Effect of density fluctuations on ECCD in ITER and TCV. Eur. Phys. J. 32, 01016.Google Scholar
Després, B., Imbert-Gérard, L.-M. & Weder, R. 2014 Hybrid resonance of Maxwell’s equations in slab geometry. J. Math. Pure Appl. 101, 623–659.Google Scholar
D’Ippolito, D. A. & Myra, J. R. 2006 A radio-frequency sheath boundary condition and its effect on slow wave propagation. Phys. Plasmas 13, 102508.Google Scholar
Dumont, R. J. & Zarzoso, D. 2013 Heating and current drive by ion cyclotron waves in the activated phase of ITER. Nucl. Fusion 53, 013002.Google Scholar
van Eester, D. 2012 Modeling particle and current drive in fusion machines: brief review of adopted techniques. Trans. Fusion Sci. Technol. 61, 347–354.Google Scholar
van Eester, D. & Koch, R. 2001 Integrating the finite-temperature wave equation across the plasma/vacuum interface. Plasma Phys. Control. Fusion 43, 779–794.Google Scholar
Falchetto, G. L., Coster, D., Coelho, R., Scott, B. D., Figini, L., Kalupin, D., Nardon, E., Nowak, S., Alves, L. L., Artaud, J. F., Basiuk, V., Bizarro, J. P. S., Boulbe, C., Dinklage, A., Farina, D., Faugeras, B., Ferreira, J., Figueiredo, A., Huynh, Ph., Imbeaux, F., Ivanova-Stanik, I., Jonsson, T., Klingshirn, H.-J., Konz, C., Kus, A., Marushchenko, N. B., Pereverzev, G., Owsiak, M., Poli, E., Peysson, Y., Reimer, R., Signoret, J., Sauter, O., Stankiewicz, R., Strand, P., Voitsekhovitch, I., Westerhof, E., Zok, T. & Zwingmann, W. 2014 The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results. Nucl. Fusion 54, 043018.Google Scholar
Fanack, C., Boucher, I., Heuraux, S., Leclert, G., Clairet, F. & Zou, X. L. 1996 Ordinary mode reflectometry: modifications of the backscattering and cut-off responses due to shape of localized density fluctuations. Plasma Phys. Control. Fusion 40, 1915–1930.Google Scholar
Faudot, E., Heuraux, S. & Colas, L. 2006 Peaking criterion for rectified potential in front of ICRF antennas in fusion plasma. Phys. Plasmas 13, 042512.Google Scholar
Faudot, E., Heuraux, S., Colas, L. & Gunn, J. P. 2010 Broadening of rectified potential structures induced by RF currents in a magnetized plasma application to ITER scrape-off layer. Phys. Plasmas 17, 042503.Google Scholar
Faudot, E., Heuraux, S., Kubic, M., Gunn, J. & Colas, L. 2013 Fluid modeling of RF and DC currents in a biased magnetized plasma. Phys. Plasmas 20, 043514.Google Scholar
Figini, L., Decker, J., Farina, D., Marushchenko, N. B., Peysson, Y., Poli, E., Westerhof, E. & ITM-TF contributors 2012 Benchmarking of electron cyclotron heating and current drive codes on ITER scenarios within the European Integrated Tokamak Modelling framework. Eur. Phys. J. 32, 01011.Google Scholar
Fuchs, V., Ram, A. K., Schultz, S. D., Bers, A. & Lashmore-Davies, C. N. 1995 Mode conversion and electron damping of the fast Alfvén wave in a tokamak at ion–ion hybrid frequency. Phys. Plasmas 2, 1637–1647.Google Scholar
Gerbaud, T., Clairet, F., Sirinelli, A., Sabot, R., Heuraux, S., Vermare, L. & Leclert, G. 2006 Comparison of density fluctuation measurements between O-mode and X-mode reflectometry on Tore Supra. Rev. Sci. Instrum. 77, 10E928.Google Scholar
Gnesin, S.2011 Electron cyclotron heating and suprathermal electron dynamics in the TCV tokamak. PhD thesis, EPFL Laussane.Google Scholar
Gusakov, E. Z., Heuraux, S., Irzak, M. & Popov, A. Yu. 2011 Possibility of giant scattering enhancement due to wave trapping in a reflectometry experiment. Phys. Scr. 84, 04504.Google Scholar
Gusakov, E. Z., Heuraux, S. & Popov, A. Yu. 2009 Nonlinear regime of Bragg backscattering leading to probing wave trapping and time delay jumps in fast frequency sweep reflectometry. Plasma Phys. Control. Fusion 51, 065018.Google Scholar
Gusakov, E. Z., Popov, A. Yu. & Saveliev, A. N. 2014 Trapping of electron Bernstein waves in drift-wave eddies and parametric decay instability at second harmonic ECRH in toroidal devices. Plasma Phys. Control. Fusion 56, 015010.CrossRefGoogle Scholar
Heuraux, S. & da Silva, F. 2012 Simulations on wave propagation in fluctuating fusion plasmas for reflectometry applications and new developments. Discrete Continuous Dyn. Syst. S 5, 307–328.Google Scholar
Heuraux, S., Faudot, E., da Silva, F., Jacquot, J., Colas, L., Hacquin, S., Teplova, N., Sysoeva, E. V. & Gusakov, E. Z. 2014 Study of wave propagation in various kinds of plasmas using adapted simulation methods, with illustrations on possible future applications. C. R. Phys. 15, 421–429.Google Scholar
Heuraux, S., Gusakov, E. Z., Popov, A. Yu., da Silva, F. & Irzak, M. 2010 Simulations on the role of the resonance of the probing wave on reflectometry measurements in fluctuating plasmas. IEEE Trans. Plasma Sci. 38, 2150–2158.Google Scholar
Heuraux, S., Leclert, G. & Hadjoudj, Y. 1994 Low-frequency responses of a plasma to a large amplitude high-frequency wave polarized on the extraordinary mode. J. Phys. III 4, 839–848.Google Scholar
Hillairet, J., Voyer, D., Ekedahl, A., Goniche, M., Kazda, M., Meneghini, O., Milanesio, D. & Preynas, M. 2010 ALOHA: an Advanced LOwer Hybrid Antenna coupling code. Nucl. Fusion 50, 125010.Google Scholar
Irzak, M. A. & Popov, A. Yu. 2008 2D modeling of the O-X conversion in toroidal plasmas. Plasma Phys. Control. Fusion 50, 025003.Google Scholar
Jackson, J. D. 1999 Classical Electrodynamics, pp. 19–22. Wiley.Google Scholar
Jacquet, P., Colas, L., Mayoral, M.-L. & Arnoux, G. et al. 2011 Heat-loads on jet plasma facing components from ICRF and LH wave absorption in the sol. Nucl. Fusion 51, 103018.Google Scholar
Jacquot, J., Colas, L., Clairet, F., Goniche, M., Heuraux, S., Hillairet, J., Lombard, G. & Milanesio, D. 2013 2D and 3D modeling of wave propagation in cold magnetized plasma near the Tore Supra ICRH antenna relying on the perfectly matched layer technique. Plasma Phys. Control. Fusion 55, 115004.Google Scholar
Jacquet, P., Colas, L., Mayoral, M.-L., Arnoux, G., Bobkov, V., Brix, M., Coad, P., Czarnecka, A., Dodt, D., Durodie, F., Ekedahl, A., Frigione, D., Fursdon, M., Gauthier, E., Goniche, M., Graham, M., Joffrin, E., Korotkov, A., Lerche, E., Mailloux, J., Monakhov, I., Noble, C., Ongena, J., Petrzilka, V., Portafaix, C., Rimini, F., Sirinelli, A., Riccardo, V., Vizvary, Z., Widdowson, A., Zastrow, K.-D. & JET EFDA Contributors 2014 Radio-frequency sheath physics: experimental characterization on Tore Supra and related self-consistent modeling. Phys. Plasmas 21, 061509.Google Scholar
Jaeger, E. F., Batchelor, D. B. & Stallings, D. C. 1993 Influence of various physics phenomena on fast wave current drive in tokamaks. Nucl. Fusion 33, 179–195.Google Scholar
Jandieri, G. V., Ishimaru, A., Jandieri, V. G. & Zhukova, N. N. 2011 Depolarization of metric radio signals and the spatial spectrum of scattered radiation by magnetized turbulent plasma slab. Prog. Electromag. Res. 112, 63–75.Google Scholar
Javan, N. S. & Adli, F. 2013 Polarization effect on the relativistic nonlinear dynamics of an intense laser beam propagating in a hot magnetoactive plasma. Phys. Rev. E 88, 043102.Google Scholar
Jucker, M., Graves, J. P., Cooper, W. A., Mellet, N., Johnson, T. & Brunner, S. 2011 Integrated modeling for ion cyclotron resonant heating in toroidal systems. Comput. Phys. Commun. 182, 912–925.Google Scholar
Kohno, H., Myra, J. R. & D’ipolitto, D. A. 2012 Numerical modeling of the coupling of an ICRH antenna with a plasma with self-consistent antenna current in the ion cyclotron range of frequencies. Comput. Phys. Commun. 183, 2116–2127.Google Scholar
Kuhn, S., Tskhakaya, D. D. & Tskhakaya, D. Jr. 2007 The magnetized plasma–wall transition (PWT) and its relation to fluid boundary conditions. Comput. Phys. Commun. 177, 80–83.Google Scholar
Kuley, A., Wang, Z. X., Lin, Z. & Wessel, F. 2013 Verification of particle simulation of radio frequency waves in fusion plasmas. Phys. Plasmas 20, 102515.Google Scholar
Lancellotti, V., Milanesio, D., Maggiora, R., Vecchi, G. & Kyrytsya, V. 2006 TOPICA: an accurate and efficient numerical tool for analysis and design of IRRF antennas. Nucl. Fusion 46, S476–S499.Google Scholar
Laqua, H. P., Erckmann, V., Hartfuss, H. J. & Laqua, H. 1997 Resonant and nonresonant electron cyclotron heating at densities above the plasma cutoff by O-X-B mode conversion at the W7-AS stellarator. Phys. Rev. Lett. 78, 3467–3470.Google Scholar
Ledenev, V. G., Tirsky, V. V., Tomozov, V. M. & Zlobec, P. 2002 Polarization changes in solar radio emission caused by scattering from high-frequency plasma turbulence. Astron. Astrophys. 392, 1089–1094.Google Scholar
Marushchenko, N. B., Turkin, Y. & Maassberg, H. 2014 Ray-tracing code TRAVIS for ECR heating, EC current drive and ECE diagnostic. Comput. Phys. Commun. 185, 165–176.Google Scholar
Mazzucato, E. 1998 Microwave reflectometry for magnetically confined plasmas. Rev. Sci. Instrum. 69, 2201–2217.CrossRefGoogle Scholar
Milanesio, D., Meneghini, O., Maggiora, R., Guadamuz, S., Hillairet, J., Lancellotti, V. & Vecchi, G. 2012 TOPLHA: an accurate and efficient numerical tool for analysis and design of LH antennas. Nucl. Fusion 52, 013008.Google Scholar
Mirnov, V. V., Brower, D. L., Hartog, D. J. & Ding, W. X. et al. 2014 Electron kinetic effects on interferometry, polarimetry and Thomson scattering measurements in burning plasmas. Rev. Sci. Instrum. 85, 11D302.Google Scholar
Noterdaeme, J.-M. & van Oost, G. 1993 The interaction between waves in the ion cyclotron range of frequencies and the plasma boundary. Plasma Phys. Control. Fusion 35, 1481–1511.Google Scholar
Pécoul, S., Heuraux, S., Koch, R. & Leclert, G. 2002 Numerical modeling of the coupling of an ICRH antenna with a plasma with self-consistent antenna current. Comput. Phys. Commun. 146, 166–187.Google Scholar
Perkins, W. 1989 Radiofrequency sheaths and impurity generation by ICRF antennas. Nucl. Fusion 29, 583–592.Google Scholar
Peysson, Y. & Decker, J. 2014 Numerical simulations of the radio-frequency-driven toroidal current in tokamaks. Fusion Sci. Technol. 65, 22–42.Google Scholar
Peysson, Y., Decker, J. & Morini, L. 2012 A versatile ray-tracing code for studying RF wave propagation in toroidal magnetized plasmas. Plasma Phys. Control. Fusion 54, 045003.Google Scholar
Poli, F. M., Kessel, C. E., Bonoli, P. T., Batchelor, D. B., Harvey, R. W. & Snyder, P. B. 2014 External heating and current drive source requirements towards steady-state operation in ITER. Nucl. Fusion 54, 073007.Google Scholar
Popov, A. Yu. 2015 Anomalous reflection of electromagnetic waves at O–X mode conversion in 2D inhomogeneous turbulent plasma. Plasma Phys. Control. Fusion 57, 025010.Google Scholar
Prater, R., Farina, D., Gribov, Yu., Harvey, R. W., Ram, A. K., Lin-Liu, Y.-R., Poli, E., Smirnov, A. P., Volpe, F., Westerhof, E. & Zvonkov, A. 2008 Benchmarking of codes for electron cyclotron heating and electron cyclotron current drive under ITER conditions. Nucl. Fusion 48, 035006.Google Scholar
Shiraiwa, S., Meneghini, O., Parker, R. & Bonoli, P. et al. 2010 Plasma wave simulation based on a versatile finite element method solver. Phys. Plasmas 17, 056119.Google Scholar
Smithe, D. N. 2007 Finite-difference time-domain simulation of fusion plasmas at radiofrequency time scales. Phys. Plasmas 14, 056104.Google Scholar
Smithe, D., Myra, J. R. & D’Ippolito, D. A. 2014 Quantitative modeling of ICRF antennas with integrated time domain RF sheath and plasma physics. AIP Conf. Proc. 1580, 89–96.Google Scholar
Stangeby, P. C. 2012 The chodura sheath for angles of a few degrees between the magnetic field and the surface of divertor targets and limiters. Nucl. Fusion 52, 083012.Google Scholar
Stix, T. H. 1992 Waves in Plasmas. American Institute of Physics.Google Scholar
Swanson, A. 2003 Plasma Waves, 2nd edn. IOP Publishing.Google Scholar
Sysoeva, E. V., da Silva, F., Gusakov, E. Z., Heuraux, S. & Popov, A. Yu. 2014 ECRH microwave beam broadening in the edge turbulent plasma. AIP Conf. Proc. 1522, 522–525.Google Scholar
Sysoeva, E. V., da Silva, F., Gusakov, E. Z., Heuraux, S. & Popov, A. Yu. 2015 ECRH beam broadening in the edge turbulent plasma of fusion machines. Nucl. Fusion 55, 033016.Google Scholar
da Silva, F., Campos Pinto, M., Després, B. & Heuraux, S. 2015 Stable coupling of the Yee scheme with a linear current model. J. Comput. Phys. 295, 24–45.Google Scholar
da Silva, F., Heuraux, S., Gusakov, E. Z. & Popov, A. Yu. 2010 A numerical study of forward- and back-scattering signatures on Doppler reflectometry signals. IEEE Trans. Plasma Sci. 38, 2144–2149.Google Scholar
da Silva, F., Heuraux, S., Hacquin, S. & Manso, M. 2005 Unidirectional transparent signal injection in finite-difference time-domain electromagnetic codes. J. Comput. Phys. 203, 467–492.Google Scholar
da Silva, F., Heuraux, S. & Manso, M. 2006a Developments on reflectometry simulations for fusion plasmas: applications to ITER position reflectometry. J. Plasma Phys. 72, 1205–1211.Google Scholar
da Silva, F., Heuraux, S. & Manso, M. 2006b Studies on O-mode reflectometry spectra simulations with velocity shear layer. Nucl. Fusion 46, S816–S823.Google Scholar
da Silva, F., Heuraux, S., Manso, M. E. & Varela, P. 2003 A 2D FDTD full-wave code for simulating the diagnostic of fusion plasmas with microwave reflectometry. In Computational Methods in Engineering and Science, pp. 233–238. A. A. Balkema.Google Scholar
Taflove, A. & Hagness, S. C. 2000 Computational Electrodynamics: the Finite-Difference Time-Domain Method. pp. 175–235. Artech House.Google Scholar
Tenouxa, T. & Lostanlen, Y. 2012 ECRH beam broadening in the edge turbulent plasma of fusion machines. Phys. Commun. 5, 338–351.Google Scholar
Ticos, C. M., Stoica, D. S. & Delzanno, G. L. 2012 Generation of dust projectiles passing over an obstacle in the plasma sheath. Phys. Plasmas 19, 083701.CrossRefGoogle Scholar
Tierens, W. & de Zutter, D. 2012 Finite-temperature corrections to the time-domain equations of motion for perpendicular propagation in nonuniform magnetized plasmas. Phys. Plasmas 19, 112110.Google Scholar
Tsironis, C., Peteers, A. G., Isliker, H., Strinzi, D. & Chatziantonaki, I. 2009 Electron cyclotron wave scattering by edge density fluctuations in ITER. Phys. Plasmas 16, 112510.Google Scholar
Wilson, J. R. & Bonoli, P. 2015 Progress on ion cyclotron range of frequencies heating physics and technology in support of the International Tokamak Experimental Reactor. Phys. Plasmas 22, 021801.Google Scholar
Wright, J. C., Valeo, E. J., Phillips, C. K., Bonoli, P. T. & Brambilla, M. 2008 Full wave simulations of lower hybrid waves in toroidal geometry with non-Maxwellian electrons. Commun. Comput. Phys. 4, 545–555.Google Scholar
Wukitch, S. J., LaBombard, B., Lin, Y., Lipschultz, B., Marmar, E. & Reinke, M. L. 2009 ICRF specific impurity sources and plasma sheaths in Alcator C-Mod. J. Nucl. Mater. 390–391, 951–954.Google Scholar