# Publications by Felix Parra Diaz

## Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulations

PHYSICS OF PLASMAS **20** (2013) ARTN 056106

## Electron flow driven instability in finite beta plasmas

40th EPS Conference on Plasma Physics, EPS 2013 **2** (2013) 1098-1101

## Kinetic effects on a tokamak pedestal ion flow, ion heat transport and bootstrap current

Plasma Physics and Controlled Fusion **55** (2013)

We consider the effects of a finite radial electric field on ion orbits in a subsonic pedestal. Using a procedure that makes a clear distinction between a transit average and a flux surface average we are able to solve the kinetic equation to retain the modifications due to finite E→ × B→ drift orbit departures from flux surfaces. Our approach properly determines the velocity space localized, as well as the nonlocal, portion of the ion distribution function in the banana and plateau regimes in the small aspect ratio limit. The rapid variation of the poloidal ion flow coefficient and the electrostatic potential in the total energy modify previous banana regime evaluations of the ion flow, the bootstrap current, and the radial ion heat flux in a subsonic pedestal. In the plateau regime, the rapid variation of the poloidal flow coefficient alters earlier results for the ion flow and bootstrap current, while leaving the ion heat flux unchanged since the rapid poloidal variation of the total energy was properly retained. © 2013 IOP Publishing Ltd.

## Long-wavelength limit of second-order gyrokinetics and the intrinsic ambipolarity of the turbulent tokamak

39th EPS Conference on Plasma Physics 2012, EPS 2012 and the 16th International Congress on Plasma Physics **1** (2012) 433-436

## Sources of intrinsic rotation in the low-flow ordering

Nuclear Fusion **51** (2011)

A low flow, δf gyrokinetic formulation to obtain the intrinsic rotation profiles is presented. The momentum conservation equation in the low-flow ordering contains new terms, neglected in previous first-principles formulations, that may explain the intrinsic rotation observed in tokamaks in the absence of external sources of momentum. The intrinsic rotation profile depends on the density and temperature profiles and on the up-down asymmetry. © 2011 IAEA, Vienna.

## Critically balanced ion temperature gradient turbulence in fusion plasmas

Physical Review Letters **107** (2011)

Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three dimensional. © 2011 American Physical Society.

## Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

Physics of Plasmas **18** (2011)

First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear, because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the existence of modes, driven by the ion temperature gradient and the parallel velocity gradient, which grow transiently. Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. A parametric model is constructed which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in the reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical parallel-velocity-gradient-driven turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence (which cannot be modelled by the quasi-linear methods used in current transport codes) and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows. © 2011 American Institute of Physics.

## Turbulent transport in tokamak plasmas with rotational shear

Physical Review Letters **106** (2011)

Nonlinear gyrokinetic simulations are conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E×B shear value for plasma confinement. Local maxima in the momentum fluxes are observed, implying the possibility of bifurcations in the E×B shear. The critical temperature gradient for the onset of turbulence increases with flow shear at low flow shears; at higher flow shears, the dependence of heat flux on temperature gradient becomes less stiff. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity. © 2011 American Physical Society.

## Overview of toroidal momentum transport

Nuclear Fusion **51** (2011)

Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E × B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development. © 2011 IAEA, Vienna.

## Second-order electrostatic gyrokinetics in general magnetic geometry and its relevance for toroidal momentum transport in tokamaks

38th EPS Conference on Plasma Physics 2011, EPS 2011 - Europhysics Conference Abstracts **35 1** (2011) 561-564

## Asymptotic expansion for stellarator equilibria with a non-planar magnetic axis

38th EPS Conference on Plasma Physics 2011, EPS 2011 - Europhysics Conference Abstracts **35 1** (2011) 409-412

## Momentum injection in tokamak plasmas and transitions to reduced transport

Physical Review Letters **106** (2011)

The effect of momentum injection on the temperature gradient in tokamak plasmas is studied. A plausible scenario for transitions to reduced transport regimes is proposed. The transition happens when there is sufficient momentum input so that the velocity shear can suppress or reduce the turbulence. However, it is possible to drive too much velocity shear and rekindle the turbulent transport. The optimal level of momentum injection is determined. The reduction in transport is maximized in the regions of low or zero magnetic shear. © 2011 American Physical Society.

## Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

PHYSICS OF PLASMAS **18** (2011) ARTN 102304

## Transport bifurcation in a rotating tokamak plasma

Physical Review Letters **105** (2010)

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients. © 2010 The American Physical Society.

## Comment on "nonlinear gyrokinetic theory with polarization drift" [Phys. Plasmas 17, 082304 (2010)]

Physics of Plasmas **17** (2010)

In this comment, we show that by using the discrete particle distribution function the changes of the phase-space volume of gyrocenter coordinates due to the fluctuating E×B velocity do not explicitly appear in the Poisson equation and the [Sosenko, Phys. Scr. 64, 264 (2001)] result is recovered. It is demonstrated that there is no contradiction between the work presented by Sosenko and the work presented by [Wang, Phys. Plasmas 17, 082304 (2010)]. © 2010 American Institute of Physics.

## Fulfillment of the kinetic Bohm criterion in a quasineutral particle-in-cell model

Physics of Plasmas **17** (2010)

Quasineutral particle-in-cell models of ions must fulfill the kinetic Bohm criterion, in its inequality form, at the domain boundary in order to match correctly with solutions of the Debye sheaths tied to the walls. The simple, fluid form of the Bohm criterion is shown to be a bad approximation of the exact, kinetic form when the ion velocity distribution function has a significant dispersion and involves different charge numbers. The fulfillment of the Bohm criterion is measured by a weighting algorithm at the boundary, but linear weighting algorithms have difficulties to reproduce the nonlinear behavior around the sheath edge. A surface weighting algorithm with an extended temporal weighting is proposed and shown to behave better than the standard volumetric weighting. Still, this must be supplemented by a forcing algorithm of the kinetic Bohm criterion. This postulates a small potential fall in a supplementary, thin, transition layer. The electron-wall interaction is shown to be of little relevance in the fulfillment of the Bohm criterion. © 2010 American Institute of Physics.

## Non-physical momentum sources in slab geometry gyrokinetics

PLASMA PHYSICS AND CONTROLLED FUSION **52** (2010) ARTN 085011

## Transport of momentum in full f gyrokinetics

Physics of Plasmas **17** (2010)

Full f electrostatic gyrokinetic formulations employ two gyrokinetic equations, one for ions and the other for electrons, and quasineutrality to obtain the ion and electron distribution functions and the electrostatic potential. We demonstrate with several examples that the long wavelength radial electric field obtained with full f approaches is extremely sensitive to errors in the ion and electron density since small deviations in density give rise to large, nonphysical deviations in the conservation of toroidal angular momentum. For typical tokamak values, a relative error of 10-7 in the ion or electron densities is enough to obtain the incorrect toroidal rotation. Based on the insights gained with the examples considered, three simple tests to check transport of toroidal angular momentum in full f simulations are proposed. © 2010 American Institute of Physics.

## Turbulent transport of toroidal angular momentum in low flow gyrokinetics (vol 52, 045004, 2010)

PLASMA PHYSICS AND CONTROLLED FUSION **52** (2010) ARTN 059801