Hostname: page-component-7c8c6479df-995ml Total loading time: 0 Render date: 2024-03-29T13:56:10.044Z Has data issue: false hasContentIssue false

Validating modeling assumptions of alpha particles in electrostatic turbulence

Published online by Cambridge University Press:  21 January 2015

G. J. Wilkie*
Affiliation:
University of Maryland, College Park, MD 20742, USA
I. G. Abel
Affiliation:
Princeton University, Princeton, NJ 08544, USA
E. G. Highcock
Affiliation:
University of Oxford, Oxford OX1 3NP, UK
W. Dorland
Affiliation:
University of Maryland, College Park, MD 20742, USA
*
Email address for correspondence: gwilkie@umd.edu

Abstract

To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In this work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian, while previously shown to give an adequate order-of-magnitude estimate of the diffusion coefficient, gives incorrect estimates for the radial alpha particle flux, and a method of correcting it in general is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.

Type
Research Article
Copyright
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

REFERENCES

Abel, I., Barnes, M., Cowley, S. C., Dorland, W. and Schekochihin, A. 2008 Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory. Phys. Plasmas 15, 122 509.CrossRefGoogle Scholar
Abel, I., Plunk, G. G., Wang, E., Barnes, M., Cowley, S. C., Dorland, W. and Schekochihin, A. A. 2013 Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows. Rep. Prog. Phys. 76, 116 201.CrossRefGoogle ScholarPubMed
Abel, I. and Schekochihin, A. In preparation.Google Scholar
Albergante, M., Graves, J. P., Fasoli, A., Jenko, F. and Dannert, T. 2009 Anomalous transport of energetic particles in ITER relevant scenarios. Phys. Plasmas 16, 112 301.CrossRefGoogle Scholar
Angioni, C. and Peeters, A. G. 2008 Gyrokinetic calculations of diffusive and convective transport of α particles with a slowing-down distribution function. Phys. Plasmas 15, 052 307.CrossRefGoogle Scholar
Angioni, C., Peeters, A. G., Pereverzev, G. V., Bottino, A., Candy, J., Dux, R., Fable, E., Hein, T. and Waltz, R. E. 2009 Gyrokinetic simulations of impurity, He ash and α particle transport and consequences on ITER transport. Nucl. Fusion 49, 055 013.CrossRefGoogle Scholar
Barnes, M., Abel, I., Dorland, W., Ernst, D. R., Hammett, G. W., Ricci, Paolo, Rogers, B. N., Schekochihin, A. and Tatsuno, T. 2009 Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests. Phys. Plasmas 16, 072 107.CrossRefGoogle Scholar
Brizard, A. and Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79, 421.CrossRefGoogle Scholar
Budny, R. 2002 Fusion alpha parameters in tokamaks with high DT fusion rates. Nucl. Fusion 42, 1383.CrossRefGoogle Scholar
Campbell, D. J. 2001 The physics of the international thermonuclear experimental reactor FEAT. Phys. Plasmas 8, 2041.CrossRefGoogle Scholar
Candy, J., Holland, C., Waltz, R. E., Fahey, M. R. and Belli, E. 2009 Tokamak profile prediction using direct gyrokinetic and neoclassical simulation. Phys. Plasmas 16, 060 704.CrossRefGoogle Scholar
Candy, J. and Waltz, R. E. 2003 An Eulerian gyrokinetic-Maxwell solver. J. Comput. Phys. 186, 545.CrossRefGoogle Scholar
Citrin, J.et al. 2013 Nonlinear stabilization of tokamak microturbulence by fast ions. Phys. Rev. Lett. 111, 155 001.CrossRefGoogle ScholarPubMed
Cowley, S. C., Kulsrud, R. M. and Sudan, R. 1991 Considerations of ion-temperature-gradient-driven turbulence. Phys. Fluids B Plasma Phys. 3, 2767.CrossRefGoogle Scholar
Dannert, T., Gunter, S., Hauff, T., Jenko, F., Lapillonne, X. and Lauber, P. 2008 Turbulent transport of beam ions. Phys. Plasmas 15, 062 508.CrossRefGoogle Scholar
Dimits, A. M.et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7, 969.CrossRefGoogle Scholar
Dorland, W., Jenko, F., Kotschenreuther, M. and Rogers, B. N. 2000 Electron temperature gradient turbulence. Phys. Rev. Lett. 85, 5579.CrossRefGoogle ScholarPubMed
Estrada-Mila, C., Candy, J. and Waltz, R. E. 2006 Turbulent transport of alpha particles in reactor plasmas. Phys. Plasmas 13, 112 303.CrossRefGoogle Scholar
Frieman, E. A. and Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502.CrossRefGoogle Scholar
Gaffey, J. D. 1976 Energetic ion distribution resulting from neutral beam injection in tokamaks. J. Plasma Phys. 16, 149.CrossRefGoogle Scholar
Hauff, T., Pueschel, M. J., Dannert, T. and Jenko, F. 2009 Electrostatic and magnetic transport of energetic ions in turbulent plasmas. Phys. Rev. Lett. 102, 075 004.CrossRefGoogle ScholarPubMed
Helander, P. and Sigmar, D. 2002 Collisional Transport in Magnetized Plasmas. Cambridge University Press, Cambridge.Google Scholar
Holland, C., Petty, C. C., Schmitz, L., Burrell, K. H., McKee, G. R., Rhodes, T. L. and Candy, J. 2012 Progress in GYRO validation studies of DIII-D H-mode plasmas. Nucl. Fusion 52, 114 007.CrossRefGoogle Scholar
Jenko, F., Dorland, W., Kotschenreuther, M. and Rogers, B. N. 2000 Electron temperature gradient driven turbulence. Phys. Plasmas 7, 1904.CrossRefGoogle Scholar
Kotschenreuther, M., Rewoldt, G. and Tang, W. M. 1995 Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities. Comput. Phys. Commun. 88, 128.CrossRefGoogle Scholar
Li, B. and Ernst, D. R. 2011 Gyrokinetic Fokker-Planck collision operator. Phys. Rev. Lett. 106, 195 002.CrossRefGoogle ScholarPubMed
Mishchenko, A., Könies, A. and Hatzky, R. 2014 Gyrokinetic particle-in-cell simulations of Alfvén eigenmodes in presence of continuum effects. Phys. Plasmas 21, 052 114.CrossRefGoogle Scholar
Nave, M. F. F.et al. and Contributors to the JET-EFDA Workprogramme 2003 Role of sawtooth in avoiding impurity accumulation and maintaining good confinement in JET radiative mantle discharges. Nucl. Fusion 43, 1204.CrossRefGoogle Scholar
Nishimura, Y. 2009 Excitation of low-n toroidicity induced Alfven eigenmodes by energetic particles in global gyrokinetic tokamak plasmas. Phys. Plasmas 16, 030 702.CrossRefGoogle Scholar
Pace, D. C.et al. 2013 Energetic ion transport by microturbulence is insignificant in tokamaks. Phys. Plasmas 20, 056 108.CrossRefGoogle Scholar
Pueschel, M. J., Jenko, F., Schneller, M., Hauff, T., Gunter, S. and Tardini, G. 2012 Anomalous diffusion of energetic particles: connecting experiment and simulations. Nucl. Fusion 52, 103 018.CrossRefGoogle Scholar
Roach, C.et al. 2008 The 2008 public release of the international multi-tokamak confinement profile database. Nucl. Fusion 48, 125 001.CrossRefGoogle Scholar
Rosenbluth, M. N. and Rutherford, P. H. 1975 Excitation of alfven waves by high-energy ions in a tokamak. Phys. Rev. Lett. 34, 1428.CrossRefGoogle Scholar
Stix, T. 1973 Heating of toroidal plasmas by neutral injection. Plasma Physics 14, 367.CrossRefGoogle Scholar
Sugama, H. and Horton, W. 1998 Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows. Phys. Plasmas 5, 2560.CrossRefGoogle Scholar
Tardini, G.et al. 2007 Thermal ions dilution and ITG suppression in ASDEX Upgrade ion ITBs. Nucl. Fusion 47, 280.CrossRefGoogle Scholar
Waltz, R. E. and Bass, E. M. 2014 Prediction of the fusion alpha density profile in ITER from local marginal stability to Alfvén eigenmodes. Nucl. Fusion 54, 104 006.CrossRefGoogle Scholar
Zhang, W., Decyk, V., Holod, I., Xiao, Y., Lin, Z. and Chen, L. 2010 Scalings of energetic particle transport by ion temperature gradient microturbulence. Phys. Plasmas 17, 055 902.CrossRefGoogle Scholar