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Physics of ultimate detachment of a tokamak divertor plasma

  • S. I. Krasheninnikov (a1) and A. S. Kukushkin (a2) (a3)

The basic physics of the processes playing the most important role in divertor plasma detachment is reviewed. The models used in the two-dimensional edge plasma transport codes that are widely used to address different issues of the edge plasma physics and to simulate the experimental data, as well as the numerical schemes and convergence issues, are described. The processes leading to ultimate divertor plasma detachment, the transition to and the stability of the detached regime, as well as the impact of the magnetic configuration and divertor geometry on detachment, are considered. A consistent, integral physical picture of ultimate detachment of a tokamak divertor plasma is developed.

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Adams, M. L., Scott, H. A., Lee, R. W., Terry, J. L., Marmar, E. S., Lipschultz, B., Pigarov, A. Yu. & Freidberg, J. P. 2001 Application of magnetically-broadened hydrogenic line profiles to computational modeling of a plasma experiment. J. Quant. Spectrosc. Radiat. Transfer. 71, 117128.
Aho-Mantila, L. et al. 2013 L-mode radiative plasma edge studies for model validation in ASDEX Upgrade and JET. J. Nucl. Mater. 438, S321S325.
Aho-Mantila, L., Bonnin, X., Coster, D. P., Lowry, C., Wischmeier, M., Brezinsek, S., Federici, G., the ASDEX Upgrade Team & The JET-EFDA Contributors 2015 Model-based radiation scalings for the ITER-like divertors of JET and ASDEX Upgrade. J. Nucl. Mater. 463, 546550.
Aho-Mantila, L., Wischmeier, M., Müller, H. W., Potzel, S., Coster, D. P., Bonnin, X., Conway, G. D.& The ASDEX Upgrade Team 2012 Outer divertor of ASDEX Upgrade in low-density L-mode discharges in forward and reversed magnetic field: I. Comparison between measured plasma conditions and SOLPS 5.0 code calculations. Nucl. Fusion 52, 103006.
Aho-Mantila, L. et al. 2017 Assessment of SOLPS 5.0 divertor solutions with drifts & currents against L-mode experiments in ASDEX Upgrade & JET. Plasma Phys. Control. Fusion 59, 035003.
Albritton, J. R., Williams, E. A., Bernstein, I. B. & Swartz, K. P. 1986 Nonlocal electron heat transport by not quite Maxwell–Boltzmann distributions. Phys. Rev. Lett. 57, 18871890.
Allen, J. E. 1976 A note on the generalized sheath criterion. J. Phys. D 9, 23312332.
Allen, J. E. 2009 The plasma–sheath boundary: its history and Langmuir’s definition of the sheath edge. Plasma Sources Sci. Technol. 18, 014004.
Angus, J. R. & Krasheninnikov, S. I. 2012 Drift wave dispersion relation for arbitrarily collisional plasma. Phys. Plasmas 19, 052504.
Aoki, K., Sone, Y. & Yamada, T. 1990 Numerical analysis of gas flows condensing on its plane condensation phase on the basis of kinetic theory. Phys. Fluids A 2, 18671878.
Artsimovich, L. A. & Shafranov, V. D. 1972 Tokamak with non-round section of the plasma loop. JETP Lett. 15, 5153.
Asakura, N., Hosogane, H., Tsuji-Iio, S., Itami, K., Shimizu, K. & Shimada, M. 1996 Field reversal effects on divertor plasmas under radiative & detached conditions in JT-60U. Nucl. Fusion 36, 795813.
Asakura, N. et al. 2016 Physics and engineering design studies on power exhaust and divertor for a 1.5 GW fusion power DEMO. In 26th IAEA Fusion Energy Conference, Kyoto, Japan, 17–22 October 2016, FIP/P7-22-CN-234.
Batishchev, O. V. et al. 1997 Kinetic effects in tokamak scrape-off layer plasmas. Phys. Plasmas 4, 16721680.
Berk, H. L., Cohen, R. H., Ryutov, D. D., Tsidulko, Yu. A. & Xu, X. Q. 1993 Electron temperature gradient induced instability in tokamak scrape-off layers. Nucl. Fusion 33, 263282.
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511525.
Boedo, J. A., Schaffer, M. J., Maingi, R. & Lasnier, C. J. 2000 Electric field-induced plasma convection in tokamak divertors. Phys. Plasmas 7, 10751078.
Borrass, K., Coster, D., Reiter, D. & Schneider, R. 1997a Study of recombining gas targets. J. Nucl. Mater. 241–243, 250254.
Borrass, K., Schneider, R. & Farengo, R. 1997b A scrape-off layer based model for Hugill-Greenwald type density limit. Nucl. Fusion 37, 523537.
Brezinsek, S.& JET-EFDA Contributors 2015 Plasma-surface interaction in the Be/W environment: Conclusions drawn from the JET-ILW for ITER. J. Nucl. Mater. 463, 1121.
Brezinsek, S. et al. 2016 Characterisation of the deuterium recycling at the W divertor target plates in JET during steady-state plasma conditions and ELMs. Phys. Scr. T167, 014076.
Bufferand, H., Ciraolo, G., Isoardi, L., Chiavassa, G., Schwander, F., Serre, E., Fedorczak, N., Ghendrih, Ph. & Tamain, P. 2011 Applications of SOLEDGE-2D code to complex SOL configurations and analysis of Mach probe measurements. J. Nucl. Mater. 415, S589S592.
Burnett, C. R., Grove, D. J., Palladino, R. W., Stix, T. H. & Wakefield, K. E. 1958 The divertor, a device for reducing the impurity level in a stellarator. Phys. Fluids 1, 438.
Carralero, D. et al. 2014 An experimental investigation of the high density transition of the scrape-off layer transport in ASDEX Upgrade. Nucl. Fusion 54, 123005.
Carreras, B. A., Gaffney, P. W., Hicks, H. R. & Callen, J. D. 1982 Rippling modes in the edge of a tokamak plasma. Phys. Fluids 25, 12311240.
Catto, P. J., Knoll, D. A. & Krasheninnikov, S. I. 1996b Two-body similarity and its violation in tokamak edge plasmas. Phys. Plasmas 3, 31913193.
Catto, P. J., Krasheninnikov, S. I. & Connor, J. W. 1996a Scaling laws for two-dimensional divertor modeling. Phys. Plasmas 3, 927938.
Chang, C. S., Ku, S., Maingi, R., Loarte, A., Parail, V., Romanelli, M. & Köchl, F.2016 Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER. In 26th IAEA Fusion Energy Conference, Kyoto, Japan, 17–22 October 2016, TH/2-1-CN-234.
Chankin, A. V. 1997 Classical drifts in the tokamak SOL and divertor: models and experiment. J. Nucl. Mater. 241–243, 199213.
Chankin, A. V. et al. 1996 Toroidal field reversal effects on divertor asymmetries in JET. Plasma Phys. Control. Fusion 38, 1579.
Chankin, A. V. & Coster, D. P. 2015 On the locality of parallel transport of heat carrying electrons in the SOL. J. Nucl. Mater. 463, 498501.
Chankin, A. V., Coster, D. P.& The ASDEX Upgrade Team 2009 Comparison of 2D models for the plasma edge with experimental measurements and assessment of deficiencies. J. Nucl. Mater. 390–391, 319324.
Chankin, A. V. & Stangeby, P. C. 1994 The effect of diamagnetic drift on the boundary conditions in tokamak scrape-off layers & the distribution of plasma fluxes near the target. Plasma Phys. Control. Fusion 36, 1485.
Chodura, R. 1982 Plasma–wall transition in an oblique magnetic field. Phys. Fluids 25, 16281633.
Coenen, J. W. et al. 2015 ELM induced tungsten melting and its impact on tokamak operation. J. Nucl. Mater. 463, 7884.
Cohen, R. H. & Ryutov, D. D. 1996 Phenomenology of flute-like perturbations in the divertor region. Contrib. Plasma Phys. 36, 161165.
Cohen, R. H. & Ryutov, D. D. 2003 Sheath physics and boundary conditions for edge plasmas. Contrib. Plasma Phys. 44, 111125.
Cohen, S. A. et al. 1992 The status of ITER divertor design concepts. J. Nucl. Mater. 196–198, 5058.
Connor, J. W., Counsell, G. F., Erents, S. K., Fielding, S. J., LaBombard, B. & Morel, K. 1999 Comparison of theoretical models for scrape-off layer widths with data from COMPASS-D, JET and Alcator C-Mod. Nucl. Fusion 39, 169188.
Connor, J. W., Hastie, R. J. & Wilson, H. R. 1998 Magnetohydrodynamic stability of tokamak edge plasma. Phys. Plasmas 5, 26872700.
Connor, J. W. & Taylor, J. B. 1977 Scaling laws for plasma confinement. Nucl. Fusion 17, 10471055.
Cordey, J. G. et al. 1996 A review of the dimensionless parameter scaling studies. Plasma. Phys. Control. Fusion 58, A67A75.
Coster, D. P., Bonnin, X. & Warrier, M. 2006 Extensions to the SOLPS edge plasma simulation code to include additional surface interaction possibilities. Phys. Scr. T124, 912.
Coster, D. P., Chankin, A. V., Klingshirn, H.-J., Dux, R., Fable, E., Bonnin, X., Kukushkin, A. & Loarte, A. 2015 SOLPS modelling of W arising from repetitive mitigated ELMs in ITER. J. Nucl. Mater. 463, 620623.
Counsell, G. F., Kirk, A., Ahn, J.-W., Tabasso, A. & Yang, Y. 2002 Boundary plasma and divertor phenomena in MAST. Plasma Phys. Control. Fusion 44, 827843.
Dekeyser, W., Baelmans, M., Reiter, D., Börner, P. & Kotov, V. 2011 2D edge plasma modeling extended up to the main chamber. J. Nucl. Mater. 415, S584S588.
Den Harder, N., Brezinsek, S., Puẗterich, T., Fedorczak, N., Matthews, G. F., Meigs, A., Stamp, M. F., van de Sanden, M. C. M., Van Rooij, G. J.& JET Contributors 2016 ELM-resolved divertor erosion in the JET ITER-Like Wall. Nucl. Fusion 56, 026014.
D’Ippolito, D. A., Myra, J. R. & Zweben, S. J. 2011 Convective transport by intermittent blob-filaments: comparison of theory and experiment. Phys. Plasmas 18, 060501.
Drake, J. F. 1987 Marfes: thermal condensation in tokamak edge plasmas. Phys. Fluids 30, 24292433.
Dux, R., Janzer, A., Puẗterich, T.& ASDEX Upgrade Team 2011 Main chamber sources and edge transport of tungsten in H-mode plasmas at ASDEX Upgrade. Nucl. Fusion 51, 053002.
Eich, T. et al. 2013 Scaling of the tokamak near the scrape-off layer H-mode power width and implications for ITER. Nucl. Fusion 53, 093031.
Fantz, U., Reiter, D., Heger, B. & Coster, D. 2001 Hydrogen molecules in the divertor of ASDEX Upgrade. J. Nucl. Mater. 290–293, 367373.
Farina, D., Pozzoli, R. & Ryutov, D. D. 1993 Effect of the magnetic field geometry on the flute-like perturbations near the divertor X point. Nucl. Fusion 33, 13151317.
Federici, G., Skinner, C. H., Brooks, J. N., Coad, J. P., Grisolia, C., Haasz, A. A., Hassanein, A., Philipps, V., Pitcher, C. S. & Roth, J. 2001 Plasma-material interactions in current tokamaks and their implications for next step fusion reactors. Nucl. Fusion 41, 19672137.
Fiksel, G., Kishinevsky, M. & Hershkowitz, N. 1990 Experimental simulation of a gaseous plasma collector. Phys. Fluids B 2, 837841.
Geraldini, A., Parra, F. I. & Militello, F. 2017 Gyrokinetic treatment of a grazing angle magnetic presheath. Plasma Phys. Control. Fusion 59, 025015.
Ghoos, K., Dekeyser, W., Samaey, G. & Baelmans, M. 2016 Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors. J. Comp. Phys. 322, 162182.
Goetz, J. et al. 1999 High confinement dissipative divertor operation on Alcator C-Mod. Phys. Plasmas 6, 18991906.
Goldston, R. J. 2012 Heuristic drift-based model of the power scrape-off width in low-gas-puff H-mode tokamaks. Nucl. Fusion 52, 013009.
Goldston, R. J., Hakim, A., Hammett, G. W., Jaworski, M. A. & Schwartz, J. 2017 Recent advances towards a lithium vapor box divertor. Nucl. Mater. Energy; doi:10.1016/j.nme.2017.03.020.
Grad, H. 1949 On the kinetic theory of rarefied gases. Commun. Pure Appl. Maths 2, 331407.
Gray, D. R. & Kilkenny, J. D. 1980 The measurement of ion acoustic turbulence and reduced thermal conductivity caused by a large temperature gradient in a laser heated plasma. Phys. Plasma 22, 81111.
Greenwald, M. 2002 Density limits in toroidal plasmas. Plasma Phys. Control. Fusion 44, R27R80.
Groth, M. et al. 2011 Influence of cross-field drifts and chemical sputtering on simulations of divertor particlwe and heat loads in ohmic and L-mode plasmas in DIII-D, AUG and JET using UEDGE. J. Nucl. Mater. 415, S530S534.
Groth, M. et al. 2013 Impact of carbon and tungsten as divertor materials on the scrape-off layer conditions in JET. Nucl. Fusion 53, 093016.
Grulke, O., Terry, J. L., Cziegler, I., LaBombard, B. & Garcia, O. E. 2014 Experimental investigation of the parallel structure of fluctuations in the scrape-off layer of Alcator C-Mod. Nucl. Fusion 54, 043012.
Guillemaut, et al. 2014 Influence of atomic physics on EDGE2D-EIRENE simulations of JET divertor detachment with carbon and beryllium/tungsten plasma-facing components. Nucl. Fusion 54, 093012.
Gunn, J. 2012 Evidence for strong secondary electron emission in the tokamak scrape-off layer. Plasma Phys. Control. Fusion 54, 086007.
Guo, H. Y. et al. 2016 Developing and validating advanced divertor solutions on DIII-D for next-step fusion devices. Nucl. Fusion 56, 126010.
Guo, H. Y., Sang, C. F., Stangeby, P. C., Lao, L. L., Taylor, T. S. & Thomas, D. M. 2017 Small angle slot divertor concept for long pulse advanced tokamaks. Nucl. Fusion 57, 044001.
Gurevich, A. V. & Istomin, Ya. N. 1979 Thermal runaway and convective heat transport by fast electrons in a plasma. Sov. Phys. JETP 50, 470475.
Halpern, F. D. et al. 2013 Theory-based scaling of the SOL width in circular limited tokamak plasmas. Nucl. Fusion 53, 122001.
Halpern, F. D. & Ricci, P. 2017 Velocity shear, turbulent saturation, and steep plasma gradients in the scrape-off layer of inner-wall limited tokamaks. Nucl. Fusion 57, 034001.
Harbour, P. J. 1988 Current flow parallel to the field in a scrape-off layer. Contrib. Plasma Phys. 28, 417419.
Harrison, E. R. & Thompson, W. B. 1959 The low pressure plane symmetric discharge. Proc. Phys. Soc. 74, 145152.
Havlíčková, E., Wischmeier, M., Lipschultz, B. & Fishpool, G. 2015 The effect of the Super-X divertor of MAST Upgrade on impurity radiation as modelled by SOLPS. J. Nucl. Mater. 463, 12091213.
Hayashi, Y., Ohno, N., Kajita, S. & Tanaka, H. 2016 Plasma flow in peripheral region of detached plasma in linear plasma device. Phys. Plasmas 23, 012511.
Heifetz, D., Post, D., Petravic, M., Weisheit, J. & Bateman, G. 1982 A Monte–Carlo model of neutral-particle transport in diverted plasmas. J. Comp. Phys. 46, 309327.
Helander, P., Krasheninnikov, S. I. & Catto, P. J. 1994 Fluid equations for a partially ionized plasma. Phys. Plasmas 1, 31743180.
Hill, D. N., Rensink, M. E., Futch, A., Buchenauer, D., Petrie, T. W., Mahdavi, M. A. & Matthews, G. 1990 Measurements & modeling of the DIII-D divertor plasma. J. Nucl. Mater. 176–177, 158164.
Hirshman, S. P. & Sigmar, D. J. 1981 Neoclassical transport of impurities in tokamak plasmas. Nucl. Fusion 21, 10791201.
Hobbs, G. D. & Wesson, J. A. 1967 Heat flow through a Langmuir sheath in the presence of electron emission. Plasma Phys. 9, 8587.
Hsu, W. L., Yamada, M. & Barret, P. J. 1982 Experimental simulation of the gaseous tokamak divertor. Phys. Rev. Lett. 49, 10011004.
Huber, A. et al. 2005 The effect of field reversal on the JET MkIIGB-SRP divertor performance in L-mode density limit discharges. J. Nucl. Mater. 337–339, 241245.
Huber, A. et al. 2013 Impact of the ITER-like wall on divertor detachment and on the density limit in the JET tokamak. J. Nucl. Mater. 438, S139S147.
Hutchinson, I. H. 1994 Thermal front analysis of detached divertor and MARFE. Nucl. Fusion 34, 13371348.
Hutchinson, I. H. 1996 The magnetic presheath boundary condition with E B drifts. Phys. Plasmas 3, 67.
Hutchinson, I. H., LaBombard, B., Goetz, J. A., Lipschultz, B., McCracken, G. M., Snipes, J. A. & Terry, J. L. 1995 The effects of field reversal on the Alcator C-Mod divertor. Plasma Phys. Control. Fusion 37, 13891406.
Hutchinson, I. H. & Vlases, G. C. 1996 Similarity in divertor studies. Nucl. Fusion 36, 783794.
Isler, R. C., McKee, G. R., Brooks, N. H., West, W. P., Fenstermacher, M. E. & Wood, R. D. 1997 Signatures of deuterium recombination in the DIII-D divertor. Phys. Plasmas 4, 29892996.
Igitkhanov, Yu. L., Kukushkin, A. S., Pigarov, A. Yu. & Pistunovich, V. I. 1986 Plasma near the wall in a tokamak with a poloidal magnetic divertor. Sov. J. Plasma Phys. 12, 19.
INTOR Group 1988 International tokamak-reactor phase two A Part III. Nucl. Fusion 28, 711743.
ITER Physics Basis 1999 Chapter 4: power and particle control. Nucl. Fusion 39, 23912469.
Janeschitz, G., Borrass, K., Federici, G., Igitkhanov, Y., Kukushkin, A., Pacher, H. D., Pacher, G. W. & Sugihara, M. 1995 The ITER divertor concept. J. Nucl. Mater. 220–222, 7388.
Janev, R. K.(Ed.) 1995 Atomic and Molecular Processes in Fusion Edge Plasmas. Plenum.
Janev, R. K., Kato, T. & Wang, J. G. 2000 Catalytic mechanism of divertor plasma recombination provided by hydrocarbon impurities. Phys. Plasmas 7, 43644367.
Janev, R. K., Post, D. E., Langer, W. D., Evans, K., Heifetz, D. B. & Weisheit, J. C. 1984 Survey of atomic processes in edge plasmas. J. Nucl. Mater. 121, 1016.
Kadomtsev, B. B. 1961 Turbulent convection of plasma in a magnetic field. Nucl. Fusion 1, 286308.
Kadomtsev, B. B. 1975 Tokamaks and analysis of scale dimensions. Sov. J. Plasma Phys. 1, 295.
Kajita, S., Sakaguchi, W., Ohno, N., Yoshida, N. & Saeki, T. 2009 Formation process of tungsten nanostructure by the exposure to helium plasma under fusion relevant plasma conditions. Nucl. Fusion 49, 095005.
Kallenbach, A. et al. 1999 Closed divertor operation in ASDEX Upgrade and JET. Plasma Phys. Control. Fusion 41, B177B189.
Kallenbach, A., Asakura, N., Kirk, A., Korotkov, A., Mahdavi, M. A., Mossessian, D. & Porter, G. D. 2005 Multi-machine comparisons of H-mode separatrix densities and edge profile behaviour in the ITPA SOL and divertor physics topical group. J. Nucl. Mater. 337–339, 381385.
Kallenbach, A. et al. 2015 Partial detachment of high power discharges in ASDEX Upgrade. Nucl. Fusion 55, 053026.
Keilhacker, M., Lackner, K., Behringer, K., Murmann, H. & Niedermeyer, H. 1982 Plasma boundary layer in limiter and divertor tokamaks. Phys. Scr. T2/2, 443453.
Kirk, A. et al. 2005 Structure of ELMs in MAST and the implications for energy deposition. Plasma Phys. Control. Fusion 47, 315333.
Klafter, J. & Sokolov, I. M. 2011 First Steps in Random Walks, From Tools to Applications. Oxford University Press.
Klingshirn, H.-J., Coster, D. P. & Bonnin, X. 2013 Advanced spatial discretizations in the B2.5 plasma fluid code. J. Nucl. Mater. 438, S856S860.
Knoll, D. A., Catto, P. J. & Krasheninnikov, S. I. 1998 A computational investigation of divertor plasma scaling laws. Phys. Plasmas 5, 29122920.
Knoll, D. A., McHugh, P. R., Krasheninnikov, S. I. & Sigmar, D. J. 1996 Simulation of an ITER-like dissipative divertor plasma with a combined edge plasma Navier–Stokes neutral model. Contrib. Plasma Phys. 36, 328332.
Kotov, V. & Reiter, D. 2009 Two-point analysis of the numerical modelling of detached divertor plasmas. Plasma Phys. Control. Fusion 51, 115002.
Kotov, V. & Reiter, D. 2012 Formation of a natural X-point multifaceted asymmetric radiation from the edge in numerical simulations of divertor plasmas. Plasma Phys. Control. Fusion 54, 082003.
Kotov, V., Reiter, D., Kukushkin, A. S., Pacher, H. D., Börner, P. & Wiesen, S. 2006 Radiation absorption effects in B2-EIRENE divertor modelling. Contrib. Plasma Phys. 46, 635642.
Kotschenreuther, M.2004 Scrape off layer physics for burning plasmas and innovative divertor solutions. In 20th IAEA Fusion Energy Conference, Vilamoura, Portugal, 1–5 November 2004, CD-ROM file IC/P6-43.
Krall, N. A. & Trivelpiece, A. W. 1973 Principles of Plasma Physics, pp. 315323. McGraw-Hill.
Krasheninnikov, S. I. 1993 On nonlocal electron heat conduction. Phys. Fluids B 5, 7476.
Krasheninnikov, S. I. 1996 Divertor plasma detachment: present status of understanding. Contrib. Plasma Phys. 36, 293303.
Krasheninnikov, S. I. 1997 Two-dimensional effects in plasma radiation fronts and radiation front jumps in tokamak divertor plasmas. Phys. Plasmas 4, 37413743.
Krasheninnikov, S. I., Batishcheva, A. A. & Simakov, A. N. 1998 Radiation fronts in tokamak divertor plasmas. Phys. Plasmas 5, 22972304.
Krasheninnikov, S. I., D’Ippolito, D. A. & Myra, J. R. 2008 Recent theoretical progress in understanding coherent structures in edge and SOL turbulence. J. Plasma Phys. 74, 679717.
Krasheninnikov, S. I. & Knoll, D. A. 1996 Effect of perpendicular transport on edge plasma energy loss due to impurity radiation. Contrib. Plasma Phys. 36, 266270.
Krasheninnikov, S. I., Kukushkin, A. S., Pistunovich, V. I. & Pozharov, V. A. 1987 Self-sustained oscillations in the divertor plasma. Nucl. Fusion 27, 18051816.
Krasheninnikov, S. I., Kukushkin, A. S. & Pshenov, A. A. 2016 Divertor plasma detachment. Phys. Plasmas 23, 055602.
Krasheninnikov, S. I., Kukushkin, A. S. & Pshenov, A. A. 2017a Stability of divertor detachment. Nucl. Mater. Energy; doi:10.1016/j.nme.2017.01.022.
Krasheninnikov, S. I., Kukushkin, A. S., Wonjae, L., Phsenov, A. A., Smirnov, R. D., Smolyakov, A. I., Stepanenko, A. A. & Zhang, Y. 2017b Edge and divertor plasma: detachment, stability, and plasma–wall interactions. Nucl. Fusion 57, 102010.
Krasheninnikov, S. I. & Marenkov, E. D. 2014 On hydrogen transport in the first wall material of fusion devices in the presence of a broadband distribution of traps over the trapping energy. Phys. Lett. A 378, 15261530.
Krasheninnikov, S. I. & Pigarov, A. Yu. 1987 Super-dense regimes of the divertor in tokamak-reactor. Nucl. Fusion Supplement 3, 387394.
Krasheninnikov, S. I., Pigarov, A. Yu., Knoll, D. A., LaBombard, B., Lipschultz, B., Sigmar, D. J., Soboleva, T. K., Terry, J. L. & Wising, F. 1997 Plasma recombination and molecular effects in tokamak divertors and divertor simulators. Phys. Plasmas 4, 16381646.
Krasheninnikov, S. I., Pigarov, A. Yu. & Lee, W. 2014 Physics of the edge plasma and first wall in fusion devices: synergistic effects. Plasma Phys. Control. Fusion 57, 044009.
Krasheninnikov, S. I., Pigarov, A. Yu. & Sigmar, D. J. 1996 Plasma recombination and divertor detachment. Phys. Lett. A 214, 285291.
Krasheninnikov, S. I., Pigarov, A. Yu., Soboleva, T. K. & Rudakov, D. L. 2009 Strongly intermittent edge plasma transport: issues with modeling and interpretation of experimental data. Phys. Plasmas 16, 014501.
Krasheninnikov, S. I., Rensink, M., Rognlien, T. D., Kukushkin, A. S., Goetz, J. A., LaBombard, B., Lipschultz, B., Terry, J. L. & Umansky, M. 1999 Stability of the detachment front in a tokamak divertor. J. Nucl. Mater. 266–269, 251257.
Krasheninnikov, S. I., Sigmar, D. J. & Yushmanov, P. N. 1995 Effect of drift on divertor plasma flow. Phys. Plasmas 2, 19721975.
Krasheninnikov, S. I. & Smolyakov, A. I. 2016 Current convective instability in detached divertor plasma. Phys. Plasmas 23, 092505.
Krstic, P. S. & Schultz, D. R. 1999a Elastic scattering and charge transfer in slow collisions: isotopes of H and H colliding with isotopes of H and with He. J. Phys. B 32, 34853508.
Krstic, P. S. & Schultz, D. R. 1999b Elastic and vibrationally inelastic slow collisions: H H2, H H2. J. Phys. B 32, 24152431.
Kubo, H., Takenaga, H., Sawada, K., Nakano, T., Kobayashi, S., Higashijima, S., Asakura, N. & Shimizu, K. 2005 Spectroscopic study of hydrogen particle behavior in attached and detached divertor plasmas of JT-60U. J. Nucl. Mater. 337–339, 161165.
Kukushkin, A., Pacher, H. D., Baelmans, M., Coster, D., Janeschitz, G., Reiter, D. & Schneider, R. 1997 2D modelling of radiating divertor regime for ITER. J. Nucl. Mater. 241–243, 268272.
Kukushkin, A. S. 1994 Feasibility of ‘gas target’ mode of divertor operation in ITER. Contrib. Plasma Phys. 34, 282292.
Kukushkin, A. S., Krasheninnikov, S. I., Pshenov, A. A. & Reiter, D. 2017 Role of molecular effects in divertor plasma recombination. Nucl. Mater. Energy; doi:10.1016/j.nme.2016.12.030.
Kukushkin, A. S. & Pacher, H. D. 2002 Divertor modelling and extrapolation to reactor conditions. Plasma Phys. Control. Fusion 44, 931943.
Kukushkin, A. S. & Pacher, H. D. 2006 Critical evaluation of the determination of the SOL transport mechanism from a statistical examination of experimental data. Contrib. Plasma Phys. 46, 545550.
Kukushkin, A. S. & Pacher, H. D. 2016 Neutral recirculation-the key to control of divertor operation. Nucl. Fusion 56, 126012.
Kukushkin, A. S., Pacher, H. D., Coster, D., Pacher, G. W. & Reiter, D. 2005a ITER divertor performance in conditions of carbon re-erosion. J. Nucl. Mater. 337–339, 5054.
Kukushkin, A. S., Pacher, H. D., Kotov, V., Pacher, G. W. & Reiter, D. 2011 Finalizing the ITER divertor design: the key role of SOLPS modeling. Fusion Engng Des. 86, 28652873.
Kukushkin, A. S., Pacher, H. D., Kotov, V., Reiter, D., Coster, D. & Pacher, G. W. 2005b Effect of neutral transport on ITER divertor performance. Nucl. Fusion 45, 608616.
Kukushkin, A. S. & Runov, A. M. 1994 Implementation of non-local transport model into 2D fluid code. Contrib. Plasma Phys. 34, 204209.
LaBombard, B., Umansky, M. V., Boivin, R. L., Goetz, J. A., Hughes, J., Lipschultz, B., Mossessian, D., Pitcher, C. S., Terry, J. L.& Alcator Group 2000 Cross-field plasma transport and main-chamber recycling in diverted plasmas on Alcator C-Mod. Nucl. Fusion 40, 20412060.
LaBombard, et al. 2004 Transport-driven Scrape-Off-Layer flows and the boundary conditions imposed at the magnetic separatrix in a tokamak plasma. Nucl. Fusion 44, 10471066.
LaBombard, et al. 2015 ADX: a high field, high power density, advanced divertor and RF tokamak. Nucl. Fusion 55, 053020.
Lackner, K. 1994 Figures of merit for divertor similarity. Comments Plasma Phys. and Control. Fusion 18, 353359.
Lackner, K., Chodura, R., Kaufman, M., Neuhauser, J., Rauh, K. G. & Schneider, W. 1984 Control of particle and energy transport across the boundary of a tokamak plasma. Plasma Phys. Control. Fusion 26, 105115.
Lackner, K., Coster, D., Schneider, R.& The Asdex-Upgrade Team 1998 Consequences of core and edge similarity for experiments. Czech. J. Phys. 48, 167175.
Landau, L. D. & Lifshitz, E. M. 1986 Hydrodynamics. Pergamon.
Lehnert, B. 1968 Screening of a high-density plasma from neutral gas penetration. Nucl. Fusion 8, 173181.
Lieberman, M. A. & Lichtenberg, A. J. 1994 Principles of Plasma Discharges and Material Processing. John Wiley & Sons Inc.
Lipschultz, B., LaBombard, B., Marmar, E. S., Pickrell, M. M., Terry, J. L., Watterson, R. & Wolfe, S. M. 1984 Marfe: an edge plasma phenomenon. Nucl. Fusion 24, 977988.
Lipschultz, B. et al. 1997 Variation of the divertor geometry in Alcator C-Mod. In Proc. 16th International Conference on Fusion Energy. Montreal, Canada, 7–11 October 1996, vol. 1, p. 425.
Lipschultz, B. et al. 1999 The role of particle sinks and sources in Alcator C-Mod detached divertor discharges. Phys. Plasmas 6, 19071916.
Lipschultz, B., LaBombard, B., Terry, J. L., Boswell, C. & Hutchinson, I. 2007 Divertor physics research on Alcator C-Mod. Fusion Sci. Technol. 51, 369389.
Liu, S. C. et al. 2012 Divertor asymmetry and scrape-off layer flow in various divertor configurations in experimental advanced superconducting tokamak. Phys. Plasmas 19, 042505.
Loarte, A. 1997 Understanding the edge physics of divertor experiments by comparison of 2D edge code calculations and experimental measurements. J. Nucl. Mater. 241–243, 118134.
Loarte, A. 2001 Effects of divertor geometry on tokamak plasmas. Plasma Phys. Control. Fusion 43, R183R224.
Loarte, A. et al. 1998 Plasma detachment in jet mark I divertor experiments. Nucl. Fusion 38, 331371.
Loarte, A., Monk, R. D., Kukushkin, A. S., Righi, E., Campbell, D. J., Conway, G. D. & Maggi, C. F. 1999 Self-sustained divertor plasma oscillations in the JET tokamak. Phys. Rev. Lett. 83, 36573660.
Loarte, A. et al. 2007 Progress in ITER physics basis. Chapter 4: power and particle control. Nucl. Fusion 47, S203S263.
Loizu, J., Ricci, P., Halpern, F. D. & Jolliet, S. 2012 Boundary conditions for plasma fluid models at the magnetic presheath entrance. Phys. Plasmas 19, 122307.
Luciani, J. F., Mora, P. & Virmont, J. 1983 Nonlocal heat transport due to steep temperature gradients. Phys. Rev. Lett. 51, 16641667.
Lumma, D., Terry, J. L. & Lipschultz, B. 1997 Radiative and three-body recombination in the Alcator C-Mod divertor. Phys. Plasmas 4, 25552566.
Maddison, G. P., Reiter, D. & Hugil, J. 1997 Modelling of plasma momentum transference to side-walls by neutral particles. J. Nucl. Mater. 241–243, 353357.
Mahdavi, M. A., Deboo, J. C., Hsieh, C. L., Ohyabu, N., Stambaugh, R. D. & Wesley, J. C. 1981 Particle exhaust from plasma discharges with an expanded-boundary divertor. Phys. Rev. Lett. 47, 16021605.
Maingi, R., Mahdavi, M. A., Petrie, T. W., Baylor, L. R., Jernigan, T. C., La Haye, R. J., Hyatt, A. W., Wade, M. R., Watkins, J. G. & Whyte, D. G. 1999 Density limit studies on DIII-D. J. Nucl. Mater. 266–269, 598603.
Mandrekas, J. 2004 GTNEUT: a code for the calculation of neutral particle transport in plasmas based on the transmission and escape probability method. Comp. Phys. Commun. 161, 3664.
Manheimer, W., Colombant, D. & Goncharov, V. 2008 The development of a Krook model for nonlocal transport in laser produced plasmas. I. Basic theory. Phys. Plasmas 15, 083103.
Manz, P., Potzel, S., Reimold, F., Wischmeier, M.& ASDEX Upgrade Team 2017 Stability and propagation of the high field side high density front in the fluctuating state of detachment in ASDEX Upgrade. Nucl. Mater. Energy; doi:10.1016/j.nme.2016.10.002.
Maqueda, R. J., Stotler, D. P.& The NSTX Team 2010 Intermittent divertor filaments in the national spherical torus experiment and their relation to midplane blobs. Nucl. Fusion 50, 075002.
Marchand, R. & Lauzon, J. 1992 High recycling with multistep and resonance line absorption effects. Phys. Fluids B 4, 924933.
Matsubara, A., Watanabe, T., Sugimoto, T., Sudo, S. & Sato, K. 2006 Observations of macroscopic oscillations of the detachment front for injection of H2, He, and Ne into the simulated baffled divertor. J. Nucl. Mater. 337–339, 181185.
Matthews, G. F. 1995 Plasma detachment from divertor targets and limiters. J. Nucl. Mater. 220–222, 104116.
McCracken, G. M., Stamp, M. F., Monk, R. D., Meigs, A. G., Lingertat, J., Prentice, R., Starling, A., Smith, R. J. & Tabasso, A. 1998 Evidence for volume recombination in JET detached divertor plasmas. Nucl. Fusion 38, 619629.
McLean, A. G. et al. 2015 Electron pressure balance in the SOL through the transition to detachment. J. Nucl. Mater. 463, 533536.
McLean, A. G. et al. 2016 The role of drifts and radiating species in detached divertor operation at DIII-D. In 26th IAEA Fusion Energy Conference. Kyoto, Japan, 17–22 October 2016, EX/2-1-CN-234.
Mikhailovskii, A. B. 1974 Theory of Plasma Instabilities: Volume I, Instabilities in a Homogeneous Plasma. Consultants Bureau.
Miyamoto, M., Nishijima, D., Baldwin, M. J., Doerner, R. P., Ueda, Y., Yasunaga, K., Yoshida, N. & Ono, K. 2011 Microscopic damage of tungsten exposed to deuterium–helium mixture plasma in PISCES and its impacts on retention property. J. Nucl. Mater. 415, S657S660.
Morozov, D. Kh. & Herrera, J. J. E. 1996 Slow thermal waves in impurity seeded radiative plasmas. Phys. Rev. Lett. 76, 760763.
Moulton, D., Fundamenski, W., Wiesen, S., Corrigan, G., Belo, P., Maddison, G., Giroud, G.& JET-EFDA Contributors 2011 EDGE2D-EIRENE modelling of the inter-ELM phase of H-mode plasmas on JET. J. Nucl. Mater. 415, S509S512.
Myra, J. R., D’Ippolito, D. A. & Russel, D. A. 2015 Turbulent transport regimes and the scrape-off layer heat flux width. Phys. Plasmas 22, 042516.
Nakano, T., Asakura, N., Takenaga, H., Kubo, H., Miura, Y., Shimizu, K., Konoshima, S., Masaki, K., Higashijima, S.& The JT-60Team 2006 Impact of wall saturation on particle control in long and high-power-heated discharges in JT-60U. Nucl. Fusion 46, 626634.
Nedospasov, A. V. 1989 Turbulence near the wall in tokamaks. Sov. J. Plasma Phys. 15, 659665.
Neuhauser, L., Schneider, W. & Wunderlich, R. 1986 Thermal instabilities and poloidal asymmetries in the tokamak edge plasma. Nucl. Fusion 26, 16791692.
Ohno, N., Ezumi, N., Takamura, S., Krasheninnikov, S. I. & Pigarov, A. Yu. 1998 Experimental evidence of molecular activated recombination in detached recombining plasmas. Phys. Rev. Lett. 81, 818821.
Pacher, H. D., Kukushkin, A. S., Pacher, G. W., Kotov, V., Pitts, R. A. & Reiter, D. 2015 Impurity seeding in ITER DT plasmas in a carbon-free environment. J. Nucl. Mater. 463, 591595.
Pégourié, B. et al. 2013 Deuterium inventory in Tore Supra: coupled carbon–deuterium balance. J. Nucl. Mater. 438, S120S125.
Petravic, M., Bateman, G. & Post, D. 1994 Modeling of gaseous divertors with the PLANET code. Contrib. Plasma Phys. 34, 380385.
Petravic, M., Post, D. E., Heifez, D. & Schmidt, J. A. 1982 Cool, high-density regimefor poloidal divertors. Phys. Rev. Lett. 48, 326329.
Petrie, T. W. et al. 1992 Divertor heat flux reduction by D2 injection in DIII-D. J. Nucl. Mater. 196–198, 848853.
Petrie, T. W., Watkins, J. G., Lao, L. L. & Snyder, P. B. 2003 The role of magnetic geometry on the poloidal distribution of ELM-induced peak particle flux at the divertor targets in DIII-D. Nucl. Fusion 43, 910913.
Philipps, V., Loarer, T., Esse, H. G., Vartanian, S., Kruezi, U., Brezinsek, S. & Matthews, G. 2013 Dynamic fuel retention and release under ITER like wall conditions in JET. J. Nucl. Mater. 438, S1067S1071.
Pigarov, A. Yu. & Krasheninnikov, S. I. 1996 Application of the collisional-radiative, atomic-molecular model to the recombining divertor plasma. Phys. Lett. A 222, 251257.
Pigarov, A. Yu., Krasheninnikov, S. I., Hollmann, E. M. & Rognlien, T. D. 2016 Modeling of small-sized ELMs in detached divertor plasmas. Contrib. Plasma Phys. 56, 742747.
Pigarov, A. Yu., Krasheninnikov, S. I. & Rognlien, T. D. 2011 New approach in two-dimensional fluid modeling of edge plasma transport with high intermittency due to blobs and edge localized modes. Phys. Plasmas 18, 092503.
Pigarov, A. Yu., Krasheninnikov, S. I., Rognlien, T. D., Lasnier, C. J. & Unterberg, E. 2014 Multi-fluid transport code modeling of time-dependent recycling in ELMy H-mode. Phys. Plasmas 21, 062514.
Pigarov, A. Yu., Krasheninnikov, S. I., Rognlien, T. D., Lasnier, C. J. & Unterberg, E. 2015 Dynamic plasma–wall modeling of ELMy H-mode with UEDGE-MB-W. J. Nucl. Mater. 463, 705708.
Pigarov, A. Yu., Krstic, P., Krasheninnikov, S. I., Doerner, R. & Rognlien, T. D. 2012 Dynamic models for plasma-wall interactions. Contrib. Plasma Phys. 52, 465477.
Piras, F., Coda, S., Duval, B. P., Labit, B., Marki, J., Medvedev, S. Yu., Moret, J.-M., Pitzschke, A., Sauter, O.& The TCV Team 2010 Snowflake divertor experiments on TCV. Plasma Phys. Control. Fusion 52, 124010.
Pitcher, C. S. & Stangeby, P. C. 1997 Experimental divertor physics. Plasma Phys. Control. Fusion 39, 779930.
Pitts, R. A. et al. 2001 Divertor geometry effects on detachment in TCV. J. Nucl. Mater. 290–293, 940946.
Pitts, R. A. et al. 2005 Edge and divertor physics with reversed toroidal field in JET. J. Nucl. Mater. 337–339, 146153.
Post, D. E. 1995 A review of recent developments in atomic processes for divertor and edge plasmas. J. Nucl. Mater. 220–222, 143157.
Post, D., Putvinskaya, N., Perkins, F. W. & Nevins, W. 1995 Analytic criteria for power exhaust in divertors due to impurity radiation. J. Nucl. Mater. 220–223, 10141018.
Potzel, S., Wischmeier, M., Bernert, M., Dux, R., Mul̈ler, H. W., Scarabosio, A.& The ASDEX Upgrade Team 2013 Characterization of the fluctuating detachment state in ASDEX upgrade. J. Nucl. Mater. 438, S285S290.
Ralchenko, Yu.(Ed.) 2016 Modern Methods in Collisional-Radiative Modeling of Plasmas. Springer.
Rebut, P.-H., Boucher, D., Gambier, D. J., Keen, B. E. & Watkins, M. L. 1993 The ITER challenge. Fusion Engng Des. 22, 718.
Reimold, F. et al. 2015a Experimental studies and modeling of complete H-mode divertor detachment in ASDEX Upgrade. J. Nucl. Mater. 463, 128134.
Reimold, F., Wischmeier, M., Bernert, M., Potzel, S., Kallenbach, A., Mul̈ler, H. W., Sieglin, B., Stroth, U.& The ASDEX Upgrade Team 2015b Divertor studies in nitrogen induced completely detached H-modes in full tungsten ASDEX Upgrade. Nucl. Fusion 55, 033004.
Reimold, F., Wischmeier, M., Potzel, S., Guimarais, L., Reiter, D., Bernert, M., Dunne, M., Lunt, T.& The ASDEX Upgrade Team & EUROfusion MST1 Team 2017 The high field side high density region in SOLPS-modeling of nitrogen-seeded H-Modes in ASDEX upgrade. Nucl. Mater. Energy; doi:10.1016/j.nme.2017.01.010.
Reiter, D.2017 The EIRENE Code User Manual
Reiter, D., Baelmans, M. & Börner, P. 2005 The EIRENE and B2-EIRENE Codes. Fusion Sci. Technol. 47, 172186.
Reiter, D., Kever, H., Wolf, G. H., Baelmans, M., Behrisch, R. & Schneider, R. 1991 Helium removal from tokamaks. Plasma Phys. Control. Fusion 33, 15791600.
Reiter, D., Kotov, V., Börner, P., Sawada, K., Janev, R. K. & Küppers, B. 2007 Detailed atomic, molecular and radiation kinetics in current 2D and 3D edge plasma fluid codes. J. Nucl. Mater. 363–365, 649657.
Reiter, D., May, Chr., Baelmans, M. & Börner, P. 1997 Non-linear effects on neutral gas transport in divertors. J. Nucl. Mater. 241–243, 342348.
Reiter, D., Wiesen, S. & Born, M. 2002 Towards radiation transport modelling in divertors with the EIRENE code. Plasma Phys. Control. Fusion 44, 17231737.
Riemann, K.-U. 1989 The Bohm criterion and the field singularity at the sheath edge. Phys. Fluids B 1, 961963.
Riemann, K.-U. 1991 The Bohm criterion and sheath formation. J. Phys. D 24, 493518.
Rognlien, T. D., Braams, B. J. & Knoll, D. A. 1996 Progress in integrated 2D models for analysis of scrape-off layer transport physics. Contrib. Plasma Phys. 36, 105116.
Rognlien, T. D., Milovich, J. L., Rensink, M. E. & Porter, G. D. 1992 A fully implicit, time dependent 2-D fluid code for modeling tokamak edge plasmas. J. Nucl. Mater. 196–198, 347351.
Rognlien, T. D., Porter, G. D. & Ryutov, D. D. 1999 Influence of E B and B drift terms in 2-D edge/SOL transport simulations. J. Nucl. Mater. 266–269, 654659.
Roth, J. et al. 2008 Tritium inventory in ITER plasma-facing materials and tritium removal procedures. Plasma. Phys. Control. Fusion 50, 103101.
Rozhansky, V. et al. 2009 New B2SOLPS 5.2 transport code for H-mode regimes in tokamaks. Nucl. Fusion 49, 025007.
Rozhansky, V., Molchanov, P., Veselova, I., Voskoboynikov, S., Kirk, A. & Coster, D. 2013 Contribution of drifts and parallel currents to divertor asymmetries. J. Nucl. Mater. 438, S297S302.
Rozhansky, V. A. 2014 Drifts, currents, and radial electric field in the edge plasma with impact on pedestal, divertor asymmetry and RMP consequences. Contrib. Plasma Phys. 54, 508516.
Rudakov, D. L. et al. 2005 Far SOL transport and main wall plasma interaction in DIII-D. Nucl. Fusion 45, 15891599.
Ryutov, D. D. 1996 Kinetic theory analysis of sheaths and shocks. Contrib. Plasma Phys. 36, 207219.
Ryutov, D. D. 2007 Geometrical properties of a snowake divertor. Phys. Plasmas 14, 064502.
Ryutov, D. D. & Cohen, R. H. 2004 Instability driven by sheath boundary conditions and limited to divertor legs. Contrib. Plasma Phys. 44, 168175.
Sawada, K. & Fujimoto, T. 1995 Effective ionization and dissociation rate coefficients of molecular hydrogen in plasma. J. Appl. Phys. 78, 29132924.
Self, S. A. & Ewald, H. N. 1966 Static theory of a discharge column at intermediate pressures. Phys. Fluids 9, 24862492.
Schaffer, M. J. et al. 2001 E B circulation at the tokamak divertor X point. Phys. Plasmas 9, 21182124.
Schmid, K., Krieger, K., Lisgo, S. W., Meisl, G., Brezinsek, S.& JET Contributors 2015 WALLDYN simulations of global impurity migration in JET and extrapolations to ITER. Nucl. Fusion 55, 053015.
Schmid, K., Reinelt, M. & Krieger, K. 2011 An integrated model of impurity migration and wall composition dynamics for tokamaks. J. Nucl. Mater. 415, S284S288.
Schmitz, L., Lehmer, R., Chevalier, G., Tynan, G., Chia, P., Doerner, R. & Conn, R. W. 1990 Experimental simulation of the gaseous divertor concept in PISCES-A. J. Nucl. Mater. 176–177, 522527.
Schneider, R., Bonnin, X., Borrass, K., Coster, D. P., Kastelewicz, H., Reiter, D., Rozhansky, V. A. & Braams, B. J. 2006 Plasma edge physics with B2-Eirene. Contrib. Plasma Phys. 46, 3.
Schneider, R., Reiter, D., Coster, D., Neuhauser, J., Lackner, K. & Braams, B. 1995 Analysis of cold divertor concepts for ITER. J. Nucl. Mater. 220–222, 10761080.
Schneider, R. et al. 1999 Role of divertor geometry on detachment in ASDEX Upgrade. J. Nucl. Mater. 266–269, 175.
Schneider, R., Reiter, D., Zehrfeld, H.-P., Braams, B., Baelmans, M., Geiger, J., Kastelewicz, H., Neuhauser, J. & Wunderlich, R. 1992 B2-EIRENE simulation of ASDEX and ASDEX-Upgrade scrape-off layer plasmas. J. Nucl. Mater. 196–198, 810813.
Scott, H. A. 2001 Cretin—a radiative transfer capability for laboratory plasmas. J. Quant. Spectrosc. Radiat. Transfer. 71, 689701.
Shimizu, K., Takizuka, T., Ohya, K., Inai, K., Nakano, T., Takayama, A., Kawashima, H. & Hoshino, K. 2009 Kinetic modelling of impurity transport in detached plasma for integrated divertor simulation with SONIC (SOLDOR/NEUT2D/IMPMC/EDDY). Nucl. Fusion 49, 065028.
Shimomura, Y., Kaufman, M., Lackner, K. & Murman, H. 1983 Characteristics of the divertor plasma in neutral-beam-heated ASDEX discharges. Nucl. Fusion 23, 869879.
Simonini, R., Corrigan, G., Radford, G., Spence, J. & Taroni, A. 1994 Models and numerics in the multi-fluid 2-D edge plasma code EDGE2D/U. Contrib. Plasma Phys. 34, 368371.
Sizyuk, V. & Hassanein, A. 2015 Heat loads to divertor nearby components from secondary radiation evolved during plasma instabilities. Phys. Plasmas 22, 013301.
Smirnov, R. D., Krasheninnikov, S. I., Pigarov, A. Yu. & Rognlien, T. D. 2016a Tungsten dust impact on ITER-like plasma edge. Phys. Plasmas 22, 012506.
Smirnov, R. D., Kukushkin, A. S., Krasheninnikov, S. I., Pigarov, A. Yu. & Rognlien, T. D. 2016b Impurity-induced divertor plasma oscillations. Phys. Plasmas 23, 012503.
Soukhanovskii, V. A. et al. 2009 Divertor heat flux mitigation in high-performance H-mode discharges in the National Spherical Torus Experiment. Nucl. Fusion 49, 095025.
Soukhanovskii, V. A. et al. 2011 Taming the plasma–material interface with the ‘snowflake’ divertor in NSTX. Nucl. Fusion 51, 012001.
Spitzer, L. 1958 The stellarator concept. Phys. Fluids 1, 253264.
Spitzer, L. & Harm, R. 1953 Transport phenomena in a completely ionized gas. Phys. Rev. 89, 977981.
Staebler, G. M. & Hinton, F. L. 1989 Currents in the scrape-off layer of diverted tokamaks. Nucl. Fusion 29, 18201824.
Stangeby, P. C. 1993 Can detached divertor plasmas be explained as self-sustained gas targets? Nucl. Fusion 33, 16951705.
Stangeby, P. C. 2000 The Plasma Boundary of Magnetic Fusion Devices. Taylor and Francis.
Stepanenko, A. A. & Krasheninnikov, S. I. 2017 Numerical study of the current-convective instability driven by asymmetry of detachment in inner and outer divertors. Phys. Plasmas; (in press).
Stotler, D. P. & Karney, C. F. F. 1994 Neutral gas-transport modeling with DEGAS-2. Contrib. Plasma Phys. 34, 392397.
Summers, H. P., Dickson, W. J., O’Mullane, M. G., Badnell, N. R., Whiteford, A. D., Brooks, D. H., Lang, J., Loch, S. D. & Griffin, D. C. 2006 Ionization state, excited populations and emission of impurities in dynamic finite density plasmas: I. The generalized collisional–radiative model for light elements. Plasma. Phys. Control. Fusion 48, 263293.
Sun, H. J., Wolfrum, E., Eich, T., Kurzan, B., Potzel, S., Stroth, U.& The ASDEX Upgrade Team 2015 Study of near scrape-off layer (SOL) temperature and density gradient lengths with Thomson scattering. Plasma Phys. Control. Fusion 57, 125011.
Tabasso, A., Dowling, J., Ahn, J.-W., Cunningham, G., Kirk, A., Mcardle, G., Price, M.& The MAST Team 2003 Analysis of the progress to detachment in the divertor of the MAST tokamak. J. Nucl. Mater. 313–316, 936940.
Takamura, S., Ohno, N., Nishijima, D. & Kajita, S. 2006 Formation of nanostructured tungsten with arborescent shape due to helium plasma irradiation. Plasma Fusion Res. 1, 051.
Tamm, I. E. & Sakharov, A. D. 1961 Proceedings of the Second International Conference on the Peaceful Uses of Nuclear Energy (ed. Leontovich, M. A.), vol. 1, pp. 147. Pergamon.
Taroni, A., Corrigan, G., Radford, G., Simonini, R., Spence, J. & Weber, S. 1992 The multifluid codes EDGE1D and EDGE2D – models and results. Contrib. Plasma Phys. 32, 438441.
Taroni, A., Corrigan, G., Simonini, R., Spence, J. & Weber, S. 1995 A study with EDGE2D code of the power exhaust problem in IETR relevant divertor plasmas. J. Nucl. Mater. 220–222, 10861090.
Tendler, M. & Rozhansky, V. 1992 Analytical studies of multidimensional plasma transport in the scrape-off layer. J. Nucl. Mater. 196–198, 912917.
Tenney, F. H. 1974 Divertor operation in the princeton reference design model tokamak reactor. J. Nucl. Mater. 53, 4347.
Terry, J. L., Lipschultz, B., Pigarov, A. Yu., Krasheninnikov, S. I., LaBombard, B., Lumma, D., Ohkawa, H., Pappas, D. & Umansky, M. 1998 Volume recombination and opacity in Alcator C-Mod divertor plasmas. Phys. Plasmas 5, 17591766.
The JET Team 1994 JET divertor research in support of ITER. Plasma Phys. Control. Fusion 36, B241B251.
Tokar, M. Z. & Kelly, F. A. 2003 The role of plasma–wall interactions in thermal instabilities at the tokamak edge. Phys. Plasmas 10, 43784386.
Tskhakaya, D., Jachmich, S., Eich, T., Fundamenski, W.& JET EFDA Contributors 2011 Interpretation of divertor Langmuir probe measurements during the ELMs at JET. J. Nucl. Mater. 415, S860S864.
Umansky, M. V., Krasheninnikov, S. I., LaBombard, B. & Terry, J. L. 1998 Comments on particle and energy balance in the edge plasma of Alcator C-Mod. Phys. Plasmas 5, 33733376.
Umansky, M. V., LaBombard, B., Brunner, D., Rensink, M. E., Rognlien, T. D., Terry, J. L. & Whyte, D. G.2016 Attainment of a stable, fully detached plasma state in innovative divertor configurations. In 26th IAEA Fusion Energy Conference, Kyoto, Japan, 17–22 October 2016, TH/P6-32-CN-234.
Umansky, M. V., Rognlien, T. D. & Xu, X. Q. 2005 Simulation of turbulence in the divertor region of tokamak edge plasma. J. Nucl. Mater. 337–339, 266270.
Valanju, P., Kotschenreuther, M., Mahajan, S. & Canik, J. 2009 Super-X divertors and high power density fusion devices. Phys. Plasmas 70, 056110.
Valanju, P. M., Kotschenreuther, M. & Mahajan, S. M. 2010 Super X divertors for solving heat and neutron flux problems of fusion devices. Fusion Engng Des. 85, 4652.
Wagner, F. et al. 1982 Regime of improved confinement and high beta in neutral-beam-heated divertor discharges of the ASDEX tokamak. Phys. Rev. Lett. 49, 14081412.
Wang, D., Guo, H., Wang, H., Luo, G., Wu, Z., Wu, J., Gao, W., Wang, L., Li, Q.& East Team 2011 Active control of divertor asymmetry on EAST by localized D2 and Ar puffing. Phys. Plasmas 18, 032505.
Weber, S., Simonini, R. & Taroni, A. 1994 Numerical simulation of hydrogenic atomic losses in a divertor plasma. Contrib. Plasma Phys. 34, 374379.
Wenzel, U., Bachmann, P., Carlson, A., Laux, M., Napiontek, B. & Weinlich, M. 1997 Relaxation oscillations in the divertor of the ASDEX upgrade tokamak. Nucl. Fusion 37, 13431347.
Wenzel, U., Behringer, K., Carlson, A., Gafert, J., Napiontek, B. & Thoma, A. 1999 Volume recombination in divertor I of ASDEX Upgrade. Nucl. Fusion 39, 873882.
Wenzel, U., Coster, D. P., Kallenbach, A., Kastelewicz, H., Laux, M., Maier, H., Schneider, R.& ASDEX Upgrade Team 2001 In-out asymmetry of divertor temperatures in tokamaks. Nucl. Fusion 41, 16951701.
Whyte, D. G., Olynyk, G. M., Barnard, H. S., Bonoli, P. T., Bromberg, L., Garrett, M. L., Haakonsen, C. B., Hartwig, Z. S., Mumgaard, R. T. & Podpaly, Y. A. 2012 Reactor similarity for plasma–material interactions in scaled-down tokamaks as the basis for the Vulcan conceptual design. Fusion Engng Des. 87, 234247.
Wiesen, S., Brezinsek, S., Harting, D., Dittmar, T., de la Luna, E., Matveev, D., Schmid, K.& JET Contributors 2016 Effect of PFC recycling conditions on JET pedestal density. Contrib. Plasma Phys. 56, 754759.
Wiesen, S., Fundamenski, W., Wischmeier, M., Groth, M., Brezinsek, S., Naulin, V.& JET EFDA Contributors 2011 Relevance of collisionality in the transport model assumptions for divertor detachment multi-fluid modelling on JET. J. Nucl. Mater. 415, S535S539.
Wiesen, S. et al. 2015 The new SOLPS-ITER code package. J. Nucl. Mater. 463, 480484.
Wirth, B. D., Hammond, K. D., Krasheninnikov, S. I. & Maroudas, D. 2015 Challenges and opportunities of modeling plasma–surface interactions in tungsten using high-performance computing. J. Nucl. Mater. 463, 3038.
Wischmeier, M. et al. 2011 Assessment of edge modeling in support of ITER. J. Nucl. Mater. 415, S523S529.
Wischmeier, M.& The ASDEX Upgrade Team & JET EFDA Contributors 2015 High density operation for reactor-relevant power exhaust. J. Nucl. Mater. 463, 2229.
Wising, F., Knoll, D. A., Krasheninnikov, S. I., Rognlien, T. D. & Sigmar, D. J. 1996 Simulation of detachment in ITER-geometry using the UEDGE code and fluid neutral model. Contrib. Plasma Phys. 36, 309313.
Zibrov, M., Balden, M., Morgan, T. W. & Mayer, M. 2017 Deuterium trapping and surface modification of polycrystal tungsten exposed to a high-flux plasma at high fluence. Nucl. Fusion 57, 046004.
Zhdanov, V. M. 2002 Transport Processes in Multicomponent Plasma. CRC.
Zweben, S. J., Boedo, J. A., Grulke, O., Hidalgo, C., LaBombard, B., Maqueda, R. J., Scarin, P. & Terry, J. L. 2007 Edge turbulence measurements in toroidal fusion devices. Plasma Phys. Control. Fusion 49, S1S23.
Zweben, S. J. et al. 2016 Blob structure and motion in the edge and SOL of NSTX. Plasma Phys. Control. Fusion 58, 044007.
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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
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