Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T15:46:05.807Z Has data issue: false hasContentIssue false

Impurity transport and bulk ion flow in a mixed collisionality stellarator plasma

Published online by Cambridge University Press:  11 October 2017

S. L. Newton*
Affiliation:
Department of Physics, Chalmers University of Technology, Göteborg SE-412 96, Sweden CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK
P. Helander
Affiliation:
Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
A. Mollén
Affiliation:
Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
H. M. Smith
Affiliation:
Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
*
Email address for correspondence: [email protected]

Abstract

The accumulation of impurities in the core of magnetically confined plasmas, resulting from standard collisional transport mechanisms, is a known threat to their performance as fusion energy sources. Whilst the axisymmetric tokamak systems have been shown to benefit from the effect of temperature screening, that is an outward flux of impurities driven by the temperature gradient, impurity accumulation in stellarators was thought to be inevitable, driven robustly by the inward pointing electric field characteristic of hot fusion plasmas. We have shown in Helander et al. (Phys. Rev. Lett., vol. 118, 2017a, 155002) that such screening can in principle also appear in stellarators, in the experimentally relevant mixed collisionality regime, where a highly collisional impurity species is present in a low collisionality bulk plasma. Details of the analytic calculation are presented here, along with the effect of the impurity on the bulk ion flow, which will ultimately affect the bulk contribution to the bootstrap current.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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

Angioni, C. & Helander, P. 2014 Neoclassical transport of heavy impurities with poloidally asymmetric density distribution in tokamaks. Plasma Phys. Control. Fusion 56, 124001.Google Scholar
Beidler, C. D., Allmaier, K., Isaev, M. Y., Kasilov, S. V., Kernbichler, W., Leitold, G. O., Maaßberg, H., Mikkelsen, D. R., Murakami, S., Schmidt, M. et al. 2011 Benchmarking of the mono-energetic transport coefficients – results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS). Nucl. Fusion 51, 076001.Google Scholar
Boozer, A. H. 1980 Guiding center drift equations. Phys. Fluids 23, 904.Google Scholar
Braun, S. & Helander, P. 2010 Pfirsch–Schlüter impurity transport in stellarators. Phys. Plasmas 17, 072514.CrossRefGoogle Scholar
Burrell, K. H. & Wong, S. K. 1981 Transport of a trace impurity in a dirty plasma in the Pfirsch–Schlüter regime. Phys. Fluids 24, 284289.Google Scholar
Calvo, I., Parra, F. I., Alonso, J. A. & Velasco, J. L. 2014 Optimizing stellarators for large flows. Plasma Phys. Control. Fusion 56, 094003.CrossRefGoogle Scholar
Calvo, I., Parra, F. I., Velasco, J. L. & Alonso, J. A. 2015 Flow damping in stellarators close to quasisymmetry. Plasma Phys. Control. Fusion 57, 014014.CrossRefGoogle Scholar
Calvo, I., Parra, F. I., Velasco, J. L. & Alonso, J. A. 2017 The effect of tangential drifts on neoclassical transport in stellarators close to omnigenity. Plasma Phys. Control. Fusion 59, 055014.Google Scholar
Connor, J. W. 1973 The neo-classical transport theory of a plasma with multiple ion species. Plasma Phys. 15, 765782.Google Scholar
Dinklage, A., Sakamoto, R., Yokoyama, M., Ida, K., Baldzuhn, J., Beidler, C. D., Cats, S., McCarthy, K. J., Geiger, J., Kobayashi, M. et al. & The LHD Experiment Group 2017 The effect of transient density profile shaping on transport in large stellarators and heliotrons. Nucl. Fusion 57, 066016.Google Scholar
Field, A. R., McCone, J., Conway, N. J., Dunstan, M., Newton, S. & Wisse, M. 2009 Comparison of measured poloidal rotation in MAST spherical tokamak plasmas with neo-classical predictions. Plasma Phys. Control. Fusion 51, 105002.Google Scholar
García-Regaña, J. M., Beidler, C. D., Kleiber, R., Helander, P., Mollén, A., Alonso, J. A., Landreman, M., Maaßberg, H., Smith, H. M., Turkin, Y. et al. 2017 Electrostatic potential variation on the flux surface and its impact on impurity transport. Nucl. Fusion 57, 056004.Google Scholar
Geiger, J., Beidler, C. D., Feng, Y., Maaßberg, H., Marushchenko, N. B. & Turkin, Y. 2015 Physics in the magnetic configuration space of W7-X. Plasma Phys. Control. Fusion 57, 014004.Google Scholar
Hazeltine, R. D. & Meiss, J. D. 2003 Plasma Confinement. Dover Publications.Google Scholar
Helander, P. 2014 Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77, 087001.Google Scholar
Helander, P., D.Beidler, C., Bird, T. M., Drevlak, M., Feng, Y., Hatzky, R., Jenko, F., Kleiber, R., Proll, J. H. E., Turkin, Y. et al. 2012 Stellarator and tokamak plasmas: a comparison. Plasma Phys. Control. Fusion 54, 124009.CrossRefGoogle Scholar
Helander, P., Geiger, J. & Maaßberg, H. 2011 On the bootstrap current in stellarators and tokamaks. Phys. Plasmas 18, 092505.CrossRefGoogle Scholar
Helander, P., Newton, S. L., Mollén, A. & Smith, H. M. 2017a Impurity transport in a mixed collisionality stellarator plasma. Phys. Rev. Lett. 118, 155002.Google Scholar
Helander, P., Parra, F. I. & Newton, S. L. 2017b Stellarator bootstrap current and plasma flow velocity at low collisionality. J. Plasma Phys. 83, 905830206.Google Scholar
Helander, P. & Sigmar, D. J. 2002 Collisional Transport in Magnetized Plasmas. Cambridge University Press.Google Scholar
Hirsch, M., Baldzuhn, J., Beidler, C., Brakel, R., Burhenn, R., Dinklage, A., Ehmler, H., Endler, M., Erckmann, V., Feng, Y. et al. & the W7-AS Team 2008 Major results from the stellarator Wendelstein 7-AS. Plasma Phys. Control. Fusion 50, 053001.Google Scholar
Hirshman, S. P. 1976 Transport properties of a toroidal plasma in a mixed collisionality regime. Phys. Fluids 19, 155158.Google Scholar
Hirshman, S. P. 1977 Transport of a multiple-ion species plasma in the Pfirsch–Schlüter regime. Phys. Fluids 20, 589598.Google Scholar
Hirshman, S. P., Shaing, K. C., van Rij, W. I., Beasley, C. O. Jr. & Crume, E. C. Jr. 1986 Plasma transport coefficients for nonsymmetric toroidal confinement systems. Phys. Fluids 29, 2951.Google Scholar
Ho, D. D. & Kulsrud, R. M. 1987 Neoclassical transport in stellarators. Phys. Fluids 30, 442461.Google Scholar
Ida, K., Yoshinuma, M., Osakabe, M., Nagaoka, K., Yokoyama, M., Funaba, H., Suzuki, C., Ido, T., Shimzu, A., Tamura, N. et al. & LHD Experimental Group 2009 Observation of an impurity hole in a plasma with an ion internal tranport barrier in the Large Helical Device. Phys. Plasmas 16, 056111.Google Scholar
Igitkhanov, Y., Polunovsky, E. & Beidler, C. D. 2006 Impurity dynamics in nonaxisymmetric plasmas. Fusion Sci. Technol. 50, 268275.Google Scholar
Joffrin, E., Baruzzo, M., Beurskens, M., Bourdelle, C., Brezinsek, S., Bucalossi, J., Buratti, P., Calabro, G., Challis, C. D., Clever, M. et al. & JET-EFDA Contributors 2014 First scenario development with the JET new ITER-like wall. Nucl. Fusion 54, 013011.CrossRefGoogle Scholar
Klinger, T., Alonso, A., Bozhenkov, S., Burhenn, R., Dinklage, A., Fuchert, G., Geiger, J., Grulke, O., Langenberg, A., Hirsch, M. et al. & The Wendelstein 7-X Team 2017 Performance and properties of the first plasmas of Wendelstein 7-X. Plasma Phys. Control. Fusion 59, 014018.Google Scholar
Landreman, M. 2017 An improved current potential method for fast computation of stellarator coil shapes. Nucl. Fusion 57, 046003.Google Scholar
Landreman, M. & Catto, P. J. 2013 Conservation of energy and magnetic moment in neoclassical calculations for optimized stellarators. Plasma Phys. Control. Fusion 55, 095017.Google Scholar
Landreman, M., Smith, H. M., Mollén, A. & Helander, P. 2014 Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas. Phys. Plasmas 21, 042503.Google Scholar
Maaßberg, H., Beidler, C. D. & Turkin, Y. 2009 Momentum correction techniques for neoclassical transport in stellarators. Phys. Plasmas 16, 072504.Google Scholar
Mollén, A., Landreman, M., Smith, H. M., Braun, S. & Helander, P. 2015 Impurities in a non-axisymmetric plasma: tranport and effect on bootstrap current. Phys. Plasmas 22, 112508.Google Scholar
Morozov, A. I. & Solov’ev, L. S. 1966 Motion of charged particles in electromagnetic fields. In Reviews of Plasma Physics, vol. 2, pp. 201297. Consultants Bureau.Google Scholar
Nakajima, N., Okamoto, M., Todoroki, J., Nakamura, Y. & Wakatani, M. 1989 Optimization of the bootstrap current in a large helical system with $L=2$ . Nucl. Fusion 29, 605616.Google Scholar
Newton, S. & Helander, P. 2006 Neoclassical momentum transport in an impure rotating tokamak plasma. Phys. Plasmas 13, 012505.Google Scholar
Parra, F. I. & Catto, P. J. 2008 Limitations of gyrokinetics on transport time scales. Plasma Phys. Control. Fusion 50, 065014.Google Scholar
van Rij, W. I. & Hirshman, S. P. 1989 Variational bounds for transport coefficients in three-dimensional toroidal plasmas. Phys. Fluids B 1, 563.Google Scholar
Rosenbluth, M. N., Hazeltine, R. D. & Hinton, F. L. 1972 Plasma transport in toroidal confinement systems. Phys. Fluids 15, 116140.Google Scholar
Rutherford, P. H. 1974 Impurity transport in the Pfirsch–Schlüter regime. Phys. Fluids 17, 1782.CrossRefGoogle Scholar
Samain, A. & Werkoff, F. 1977 Diffusion in tokamaks with impurities in the Pfirsch–Schlüter regime. Nucl. Fusion 17, 5364.Google Scholar
Sugama, H. & Nishimura, S. 2002 How to calculate the neoclassical viscosity, diffusion, and current coefficients in general toroidal plasmas. Phys. Plasmas 9, 46374653.Google Scholar
Velasco, J. L., Calvo, I., Satake, S., Alonso, A., Nunami, M., Yokoyama, M., Sato, M., Estrada, T., Fontdecaba, J. M., Liniers, M. et al. & The LHD Experimental & Team The TJ-II Team 2017 Moderation of neoclassical impurity accumulation in high temperature plasmas of helical devices. Nucl. Fusion 57, 016016.Google Scholar
W VII-A Team & NI Group 1985 Impurity transport in the Wendelstein VII-A stellarator. Nucl. Fusion 25, 15931609.Google Scholar
Wade, M. R., Houlberg, W. A. & Baylor, L. R. 2000 Experimental confirmation of impurity convection driven by the ion-temperature gradient in toroidal plasmas. Phys. Rev. Lett. 84, 282285.Google Scholar