Appropriate References

Physics code

Topical Area

Required citation


gyrokinetic simulation



gyrokinetic simulation



neoclassical simulation

[BC08, BC12]


transport model

[SKW07, SK10]


profile evolution



C. Angioni, T. Gamot, G. Tardini, E. Fable, T. Luda, N. Bonanomi, C.K. Kiefer, G.M. Staebler, the ASDEX Upgrade Team, and the EUROfusion MST1 Team. Confinement properties of L-mode plasmas in ASDEX Upgrade and full-radius predictions of the TGLF transport model. Nucl. Fusion, 62:066015, 2022. doi:10.1088/1741-4326/ac592b.


C. Angioni, A.G. Peeters, G.V. Pereverzev, A. Bottino, J. Candy, R. Dux, E. Fable, T. Hein, and R.E. Waltz. Gyrokinetic simulations of impurity, He ash and α particle transport and consequences on ITER transport modelling. Nucl. Fusion, 49:055013, 2009.


R. Arbon, J. Candy, and E.A. Belli. Rapidly-convergent flux-surface shape parameterization. Plasma Phys. Control. Fusion, 63:012001, 2020. doi:10.1088/1361-6587/abc63b.


M.A. Beer and G.W. Hammett. Bounce averaged trapped electron fluid equations for plasma turbulence. Phys. Plasmas, 3:4018, 1996.


M.A. Beer and G.W. Hammett. Toroidal gyrofluid equations for simulations of tokamak turbulence. Phys. Plasmas, 3:4046, 1996.


E.A. Belli and J. Candy. Kinetic calculation of neoclassical transport including self-consistent electron and impurity dynamics. Plasma Phys. Control. Fusion, 50:095010, 2008. doi:10.1088/0741-3335/50/9/095010.


E.A. Belli and J. Candy. An Eulerian method for the solution of the multi-species drift-kinetic equation. Plasma Phys. Control. Fusion, 51:075018, 2009.


E.A. Belli and J. Candy. Full linearized Fokker-Planck collisions in neoclassical transport simulations. Plasma Phys. Control. Fusion, 54:015015, 2012.


E.A. Belli and J. Candy. Implications of advanced collision operators for gyrokinetic simulation. Plasma Phys. Control. Fusion, 59:045005, 2017.


E.A. Belli and J. Candy. Impact of centrifugal drifts on ion turbulent transport. Phys. Plasmas, 25:032301, 2018.


R.V. Bravenec, J. Candy, M. Barnes, and C. Holland. Linear and nonlinear verification of gyrokinetic microstability codes. Phys. Plasmas, 18:122505, 2011.


J. Candy. Beta scaling of transport in microturbulence simulations. Phys. Plasmas, 12:072307, 2005.


J. Candy and E. Belli. GYRO Technical Guide. General Atomics Technical Report, 2010.


J. Candy and E.A. Belli. Spectral treatment of gyrokinetic shear flow. J. Comput. Phys., 356:448, 2018. doi:10.1016/


J. Candy, E.A. Belli, and R.V. Bravenec. A high-accuracy Eulerian gyrokinetic solver for collisional plasmas. J. Comput. Phys., 324:73, 2016. doi:10.1016/


J. Candy, E.A. Belli, and G. Staebler. Spectral treatment of gyrokinetic profile curvature. Plasma Phys. Control. Fusion, 62:042001, 2020. doi:10.1088/1361-6587/ab759c.


J. Candy, C. Holland, R.E. Waltz, M.R. Fahey, and E. Belli. Tokamak profile prediction using direct gyrokinetic and neoclassical simulation. Phys. Plasmas, 16:060704, 2009.


J. Candy, I. Sfiligoi, E. Belli, K. Hallatschek, C. Holland, N. Howard, and E.D`Azevedo. Multiscale-optimized plasma turbulence simulation on petascale architechtures. Computers & Fluids, 188:125, 2019. doi:10.1016/j.compfluid.2019.04.016.


J. Candy and R.E. Waltz. Anomalous transport scaling in the DIII-D tokamak matched by supercomputer simulation. Phys. Rev. Lett., 91:045001, 2003. doi:10.1103/PhysRevLett.91.045001.


J. Candy and R.E. Waltz. An Eulerian gyrokinetic-Maxwell solver. J. Comput. Phys., 186:545, 2003. doi:10.1016/S0021-9991(03)00079-2.


J. Candy and R.E. Waltz. Velocity-space resolution, entropy production and upwind dissipation in Eulerian gyrokinetic simulations. Phys. Plasmas, 13:032310, 2006.


J. Candy, R.E. Waltz, and W. Dorland. The local limit of global gyrokinetic simulations. Phys. Plasmas, 11:L25, 2004. doi:10.1063/1.1695358.


J. Candy, R.E. Waltz, M.R. Fahey, and C. Holland. Plasma microturbulence simulation of instabilities at highly disparate scales. J. Phys: Conf. Series, 78:012008, 2007.


J. Candy, R.E. Waltz, M.R. Fahey, and C. Holland. The effect of ion-scale dynamics on electron-temperature-gradient turbulence. Plasma Phys. Control. Fusion, 49:1209, 2007.


J. Candy, R.E. Waltz, S.E. Parker, and Y. Chen. Relevance of the parallel nonlinearity in gyrokinetic simulations of tokamak plasmas. Phys. Plasmas, 13:074501, 2006.


J. Candy, R.E. Waltz, and M.N. Rosenbluth. Smooothness of turbulent transport across a minimum-$q$ surface. Phys. Plasmas, 11:1879, 2004.


Y. Chen, S.E. Parker, B.I. Cohen, A.M. Dimits, W.M. Nevins, D. Schumaker, V.K. Decyk, and J.N. Leboeuf. Simulations of turbulent transport with kinetic electrons and electromagnetic effects. Nucl. Fusion, 43:1121, 2003.


J. Chowdhury, W. Wan, Y. Chen, S.E. Parker, R.J. Groebner, C. Holland, and N.T. Howard. Study of the l-mode tokamak plasma “shortfall” with local and global nonlinear gyrokinetic $\delta f$ particle-in-cell simulation. Phys. Plasmas, 21:112503, 2014.


A.M. Dimits, T.J. Williams, J.A. Byers, and B.I. Cohen. Scalings of ion-temperature-gradient-driven anomalous transport in tokamaks. Phys. Rev. Lett., 77:71, 1996.


J.Q. Dong and W. Horton. Study of impurity mode and ion temperature gradient mode in toroidal plasmas. Phys. Plasmas, 2:3412, 1995.


W. Dorland and G.W. Hammett. Gyrofluid turbulence models with kinetic effects. Phys. Fluids B, 5:812, 1993.


W. Dorland, F. Jenko, M. Kotschenreuther, and B.N. Rogers. Electron temperature gradient turbulence. Phys. Rev. Lett., 85:5579, 2000.


H.G. Dudding, F.J. Casson, D. Dickinson, B.S. Patel, C.M. Roach, E.A. Belli, and G.M. Staebler. A new quasilinear saturation rule for tokamak turbulence with application to the isotope scaling of transport. Nuclear Fusion, 62(9):096005, 2022. doi:10.1088/1741-4326/ac7a4d.


Harry George Dudding. A new quasilinear saturation rule for tokamak turbulence. PhD thesis, University of York, October 2022. URL:


C. Estrada-Mila, J. Candy, and R.E. Waltz. Gyrokinetic simulations of ion and impurity transport. Phys. Plasmas, 12:022305, 2005.


C. Estrada-Mila, J. Candy, and R.E. Waltz. Density peaking and turbulent pinch in DIII-D discharges. Phys. Plasmas, 13:074505, 2006.


C. Estrada-Mila, J. Candy, and R.E. Waltz. Turbulent transport of alpha particles and helium ash in reactor plasmas. Phys. Plasmas, 13:112303, 2006.


M.R. Fahey and J. Candy. GYRO: A 5-D gyrokinetic-Maxwell solver. In ACM/IEEE Proceedings of SC2004: High Performance Computing, Networking and Storage (Pittsburgh, PA). 2004.


B.A. Grierson, G.M. Staebler, W.M. Solomon, G.R. McKee, C. Holland, M. Austin, A. Marinoni, L. Schmitz, R.I. Pinsker, and DIII-D Team. Multi-scale transport in the DIII-D ITER baseline scenario with direct electron heating and projection to ITER. Phys. Plasmas, 25(2):022509, 2018.


T. Görler, A.E. White, D. Told, F. Jenko, C. Holland, and T.L. Rhodes. A flux-matched gyrokinetic analysis of diii-d l-mode turbulence. Phys. Plasmas, 21:122307, 2014. doi:10.1063/1.4904301.


G.W. Hammett, M.A. Beer, J.C. Cummings, W. Dorland, W.W. Lee, H.E. Mynick, S.E. Parker, R.A. Santoro, M. Artun, H.P. Furth, T.S. Hahm, G. Rewoldt, W.M. Tang, R.E. Waltz, G.D. Kerbel, and J.L. Milovich. Advances in simulating tokamak turbulent transport. In Proceedings of the 15th IAEA Fusion Energy Conference, Seville, Spain, 1994, Vol III, p. 273. 1994.


F.L. Hinton and R.E. Waltz. Gyrokinetic turbulent heating. Phys. Plasmas, 13:102301, 2006.


F.L. Hinton, R.E. Waltz, and J. Candy. Effect of electromagnetic turbulence in the neoclassical Ohm's law. Phys. Plasmas, 11:2433, 2004.


F.L. Hinton and S.K. Wong. Neoclassical ion transport in rotating axisymmetric plasmas. Phys. Fluids, 28:3082, 1985. doi:10.1063/1.865350.


C. Holland. Validation metrics for turbulent plasma transport. Phys. Plasmas, 23:060901, 2016.


C. Holland, J. Candy, R.E Waltz, A.E. White, G.R. McKee, M.W. Shafer, L. Schmitz, and G.R Tynan. Validating simulations of core tokamak turbulence: current status and future directions. J. Phys: Conf. Series, 125:012043, 2008.


C. Holland, A.E. White, G.R. McKee, M.W. Shafer, J. Candy, R.E Waltz, L. Schmitz, and G.R Tynan. Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence. Phys. Plasmas, 16:052301, 2009.


N.T. Howard, C. Holland, A.E. White, M. Greenwald, and J. Candy. Multi-scale gyrokinetic simulation of tokamak plasmas: enhanced heat loss due to cross-scale coupling of plasma turbulence. Nucl. Fusion, 56(1):014004, 2016. doi:10.1088/0029-5515/56/1/014004.


S.M. Kaye and others. NSTX/NSTX-U theory, modeling and analysis results. Nucl. Fusion, 59:112007, 2019.


J. E. Kinsey, G. M. Staebler, and R. E. Waltz. The first transport code simulations using the trapped gyro-Landau-fluid model. Phys. Plasmas, 15(5):055908, 2008. doi:10.1063/1.2889008.


J.E. Kinsey, R.E. Waltz, and J. Candy. Nonlinear gyrokinetic turbulence simulations of E×B shear quenching of transport. Phys. Plasmas, 12:062302, 2005.


J.E. Kinsey, R.E. Waltz, and J. Candy. The effect of safety factor and magnetic shear on turbulent transport in nonlinear gyrokinetic simulations. Phys. Plasmas, 13:022305, 2006.


J.E. Kinsey, R.E. Waltz, and J. Candy. The effect of plasma shaping on turbulent transport and E×B shear quenching in nonlinear gyrokinetic simulations. Phys. Plasmas, 14:102306, 2007.


Y. Kishimoto, J.-Y. Kim, W. Horton, T. Tajima, M.J. LeBrun, S.A. Dettrick, J.Q. Li, and S. Shirai. Discontinuity model for internal transport formation in reversed magnetic shear plasmas. Nucl. Fusion, 40:667, 2000.


M. Kotschenreuther. Invited talk 9I4. Bull. Am. Phys. Soc., 33:2107, 1988.


M. Kotschenreuther, G. Rewoldt, and W.M. Tang. Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities. Comput. Phys. Commun., 88:128, 1995. doi:10.1016/0010-4655(95)00035-E.


J.A. Krommes. Thermostatted $\delta f$. Phys. Plasmas, 6:1477, 1999.


J.A. Krommes and G. Hu. The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox. Phys. Plasmas, 1:3211, 1994.


L. Lin, M. Porkolab, E.M. Edlund, J.C. Rost, C.L. Fiore, M. Greenwald, Y. Lin, D.R. Mikkelsen, N. Tsujii, and S J. Wukitch. Studies of turbulence and transport in Alcator C-Mod H-mode plasmas with phase contrast imaging and comparisons with GYRO. Phys. Plasmas, 16:012502, 2009.


Z. Lin, S. Ethier, T.S. Hahm, and W.M. Tang. Size scaling of turbulent transport in magnetically confined plasmas. Phys. Rev. Lett., 88:195004, 2002.


W.M. Nevins, J. Candy, S. Cowley, T. Dannert, A. Dimits, W. Dorland, C. Estrada-Mila, G.W. Hammett, F. Jenko, M.J. Pueschel, and D.E. Shumaker. Characterizing electron temperature gradient turbulence via numerical simulation. Phys. Plasmas, 13:122306, 2006.


W.M. Nevins, G.W. Hammett, A.M. Dimits, W. Dorland, and D.E. Shumaker. Discrete particle noise in particle-in-cell simulations of plasma microturbulence. Phys. Plasmas, 12:122305, 2005.


M.N. Rosenbluth and F.L. Hinton. Poloidal flow driven by ion-temperature-gradient turbulence in tokamaks. Phys. Rev. Lett., 80:724, 1998.


P.B. Snyder and G.W. Hammett. Electromagnetic effects on plasma microturbulence and transport. Phys. Plasmas, 8:744, 2001.


G M Staebler, J Candy, E A Belli, J E Kinsey, N Bonanomi, and B Patel. Geometry dependence of the fluctuation intensity in gyrokinetic turbulence. Plasma Physics and Controlled Fusion, 63(1):015013, 2020. doi:10.1088/1361-6587/abc861.


G. M. Staebler, J. Candy, N. T. Howard, and C. Holland. The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence. Phys. Plasmas, 23(6):062518, 2016. doi:10.1063/1.4954905.


G. M. Staebler, J. E. Kinsey, and R. E. Waltz. A theory-based transport model with comprehensive physics. Phys. Plasmas, 14(5):055909, 2007. doi:10.1063/1.2436852.


G. M. Staebler, R. E. Waltz, J. Candy, and J. E. Kinsey. New paradigm for suppression of gyrokinetic turbulence by velocity shear. Phys. Rev. Lett., 110:055003, 2013. doi:10.1103/PhysRevLett.110.055003.


G.M. Staebler, E. A. Belli, J. Candy, J.E. Kinsey, H. Dudding, and B. Patel. Verification of a quasi-linear model for gyrokinetic turbulent transport. Nuclear Fusion, 61(11):116007, 2021. doi:10.1088/1741-4326/ac243a.


G.M. Staebler, J. Candy, R.E. Waltz, J.E. Kinsey, and W.M. Solomon. A new paradigm for ExB velocity shear suppression of gyro-kinetic turbulence and the momentum pinch. Nuclear Fusion, 53(11):113017, 2013. doi:10.1088/0029-5515/53/11/113017.


G.M. Staebler and J.E. Kinsey. Electron collisions in the trapped gyro-landau fluid transport model. Phys. Plasmas, 17:122309, 2010.


G.M. Staebler, J.E. Kinsey, and R.E. Waltz. Gyro-Landau fluid equations for trapped and passing particles. Phys. Plasmas, 12:102508, 2005.


H. Sugama and W. Horton. Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows. Phys. Plasmas, 5:2560, 1998.


H. Sugama, T.-H. Watanabe, M. Nunami, and S. Nishimura. Momentum balance and radial electric fields in axisymmetric and nonaxisymmetric toroidal plasmas. Plasma Phys. Control. Fusion, 53:024004, 2011.


K.E. Thome, X.D. Du, B.A. Grierson, G.J. Kramer, C.C. Petty, C. Holland, M. Knolker, G.R. McKee, J. McClenaghan, D.C. Pace, T.L. Rhodes, S.P. Smith, C. Sung, F. Turco, M.A. Van Zeeland, L. Zeng, and Y.B. Zhu. Response of thermal and fast-ion transport to beam ion population, rotation and Te/Ti in the DIII-D steady state hybrid scenario. Nucl. Fusion, 61:036036, 2021.


J.S. Vetter, S. Alam, Jr. T.H. Dunigan, M.R. Fahey, P.C. Roth, and P. Worley. Early evaluation of the cray xt3 at ornl. In Proceedings of the 47th Cray User Group Conference, Knoxville, TN, May 16-19. 2005.


R.E. Waltz. Rho-star scaling and physically realistic gyrokinetic simulations of transport in DIII-D. Fus. Sci. Tech., 48:1051, 2005.


R.E. Waltz, M.E. Austin, K.H. Burrell, and J. Candy. Gyrokinetic simulations of off-axis minimum-q profile corrugations. Phys. Plasmas, 12:052301, 2006.


R.E. Waltz and J. Candy. Heuristic theory of nonlocally broken gyrobohm scaling. Phys. Plasmas, 12:072303, 2005.


R.E. Waltz, J. Candy, and M. Fahey. Coupled ion temperature gradient and trapped electron mode to electron temperature gradient mode gyrokinetic simulations. Phys. Plasmas, 14:056116, 2007.


R.E. Waltz, J. Candy, F.L. Hinton, C. Estrada-Mila, and J.E. Kinsey. Advances in comprehensive simulations of transport in tokamaks. Nucl. Fusion, 45:741, 2005.


R.E. Waltz, J. Candy, and C.C. Petty. Projected profile similarity in gyrokinetic simulations of Bohm and gyroBohm scaled DIII-D L and H modes. Phys. Plasmas, 13:072304, 2006.


R.E. Waltz, J. Candy, and M.N. Rosenbluth. Gyrokinetic turbulence simulation of profile shear stabilization and broken gyrobohm scaling. Phys. Plasmas, 9:1938, 2002.


R.E. Waltz and C. Holland. Numerical experiments on the drift wave-zonal flow paradigm for nonlinear saturation. Phys. Plasmas, 15:122503, 2008.


R.E. Waltz, G.R. Kerbel, and J. Milovich. Toroidal gyro-landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes. Phys. Plasmas, 1:2229, 1994.


R.E. Waltz, G.R. Kerbel, J. Milovich, and G.W. Hammett. Advances in the simulation of toroidal gyro-landau fluid model turbulence. Phys. Plasmas, 2:2408, 1995.


R.E. Waltz and G.M. Staebler. Gyrokinetic theory and simulation of turbulent energy exchange. Phys. Plasmas, 15:014505, 2008.


R.E. Waltz, G.M. Staebler, J. Candy, and F.L. Hinton. Gyrokinetic theory and simulation of angular momentum transport. Phys. Plasmas, 14:122507, 2007.


R.E. Waltz, G.M. Staebler, W. Dorland, G.W. Hammett, M. Kotschenreuther, and J.A. Konings. A gyro-landau fluid transport model. Phys. Plasmas, 4:2482, 1997.


A.E. White, L. Schmitz, G.R. McKee, C. Holland, W.A. Peebles, T.A. Carter, M.W. Shafer, M.E. Austin, K.H. Burrell, J. Candy, and others. Measurements of core electron temperature and density fluctuations in DIII-D and comparison to nonlinear gyrokinetic simulations. Phys. Plasmas, 15(5):056116, 2008.


P. Worley, S. Alam, Jr. T.H. Dunigan, M.R. Fahey, and J.S. Vetter. Comparative analysis of interprocess communication on the x1, xd1, and xt3. In Proceedings of the 47th Cray User Group Conference, Knoxville, TN, May 16-19. 2005.


P. Worley, J. Candy, L. Carrington, K. Huck, T. Kaiser, G. Mahinthakumar, A. Maloney, S. Moore, D. Reed, P. Roth, H. Shan, S. Shende, A. Snavely, S. Sreepathi, F. Wolf, and Y. Zhang. Performance analysis of gyro: a tool evaluation. In Proceedings of the 2005 SciDAC Conference, San Francisco, CA, June 26-30. 2005.