The nonlinear gyro-kinetic flux tube code GKW

Peeters, A. G.; Camenen, Y.; Casson, F. J.; Hornsby, W. A.; Snodin, A. P.; Strintzi, D.; Szepesi, G.

doi:10.1016/j.cpc.2009.07.001

Cited by 269 publications

(359 citation statements)

References 51 publications

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“…and the r.h.s. of (4.5) Candy and Waltz (2003a); Peeters et al (2009). If we do not integrate the second term of the l.h.s.…”

Section: Difficulties Of Electromagnetic Gyrokinetic Simulationsmentioning

confidence: 99%

“…In addition, the kinetic electron effect elongates the mode structure along the field line, and thus a large simulation domain along the field line is required. Large computational resources which meet the requirements are the reason why numerical simulations of turbulence based on the electromagnetic gyrokinetic model (Antonsen and Lane 1980;Frieman and Chen 1982;Hahm et al 1988;Hazeltine and Meiss 2003;Brizard and Hahm 2007) are mainly carried out in the flux-tube geometry (Kotschenreuther et al 1995;Jenko 2000;Jenko et al 2000;Jenko and Dorland 2001;Candy and Waltz 2003a,b;Candy 2005;Pueschel et al 2008;Peeters et al 2009;Pueschel and Jenko 2010;Waltz 2010;Hatch et al 2012;Pueschel et al 2013a,b) which is along a magnetic field line and is localized in the radial direction to reduce computational cost (Beer et al 1995). Although, there are some gyrokinetic simulations on electromagnetic turbulence in global domain covering a whole torus plasma and also some electromagnetic gyrokinetic studies on space plasmas (Schekochihin et al 2009), we focus on gyrokinetic simulations in local flux-tube domain in this review.…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

et al. 2015

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Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

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“…and the r.h.s. of (4.5) Candy and Waltz (2003a); Peeters et al (2009). If we do not integrate the second term of the l.h.s.…”

Section: Difficulties Of Electromagnetic Gyrokinetic Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

et al. 2015

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“…The most accurate solutions are obtained through nonlinear, initial value simulations of either the gyrokineticMaxwell equations or their fluid variants, analogous to direct numerical simulation (DNS) of neutral fluid turbulence. A variety of such codes have been developed, which can generally be divided between those taking a continuum approach [52][53][54][55][56] and those that use particle-in-cell methods. [57][58][59][60][61][62] As in neutral fluid DNS, both approaches initialize the simulation with some very small amplitude fluctuations, which first grow exponentially at the linear growth rate(s) of the instabilities being considered (the "linear" phase), and then saturate at a finite amplitude set by the balance of these linear drives and nonlinear couplings between different wavenumbers (the "saturated" phase).…”

Section: Basics Of Turbulence and Transport Modeling In Magneticmentioning

confidence: 99%

Validation metrics for turbulent plasma transport

Holland

2016

Physics of Plasmas

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Developing accurate models of plasma dynamics is essential for confident predictive modeling of current and future fusion devices. In modern computer science and engineering, formal verification and validation processes are used to assess model accuracy and establish confidence in the predictive capabilities of a given model. This paper provides an overview of the key guiding principles and best practices for the development of validation metrics, illustrated using examples from investigations of turbulent transport in magnetically confined plasmas. Particular emphasis is given to the importance of uncertainty quantification and its inclusion within the metrics, and the need for utilizing synthetic diagnostics to enable quantitatively meaningful comparisons between simulation and experiment. As a starting point, the structure of commonly used global transport model metrics and their limitations is reviewed. An alternate approach is then presented, which focuses upon comparisons of predicted local fluxes, fluctuations, and equilibrium gradients against observation. The utility of metrics based upon these comparisons is demonstrated by applying them to gyrokinetic predictions of turbulent transport in a variety of discharges performed on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], as part of a multi-year transport model validation activity.

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“…Linear calculations of the turbulent momentum flux were performed with the gyrokinetic fluxtube code GKW [26,27] at three radii, c ¼ 0:65, 0.75, and 0.85, for the plasmas described in Figs. 1 and 2 (simulation parameters in Table II).…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Experimental Evidence of Momentum Transport Induced by an Up-Down Asymmetric Magnetic Equilibrium in Toroidal Plasmas

et al. 2010

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The first experimental evidence of parallel momentum transport generated by the up-down asymmetry of a toroidal plasma is reported. The experiments, conducted in the Tokamak à Configuration Variable, were motivated by the recent theoretical discovery of ion-scale turbulent momentum transport induced by an up-down asymmetry in the magnetic equilibrium. The toroidal rotation gradient is observed to depend on the asymmetry in the outer part of the plasma leading to a variation of the central rotation by a factor of 1.5-2. The direction of the effect and its magnitude are in agreement with theoretical predictions for the eight possible combinations of plasma asymmetry, current, and magnetic field.

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The nonlinear gyro-kinetic flux tube code GKW

Cited by 269 publications

References 51 publications

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

Validation metrics for turbulent plasma transport

Experimental Evidence of Momentum Transport Induced by an Up-Down Asymmetric Magnetic Equilibrium in Toroidal Plasmas

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