arXiv subjects

F. I. Parra

Publications and source records attributed to F. I. Parra.

At least 37 records · Page 2Linked to original sources

arXiv2021

Electrostatic gyrokinetic simulations in Wendelstein 7-X geometry: benchmark between the codes stella and GENE

The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, documented and verified set of gyrokinetic simulations in W7-X geometry against which new codes or upgrades of existing codes can be tested and benchmarked. This paper attemps to provide such a set of simulations in the form of a comprehensive benchmark between the recently developed code stella and the well-established code GENE. The benchmark consists of electrostatic gyrokinetic simulations in W7-X magnetic geometry and includes different flux tubes, linear ion-temperature-gradient (ITG) and trapped-electron-mode (TEM)} stability analyses, computation of linear zonal flow responses and calculation of ITG-driven heat fluxes.

physics.plasm-ph↗

arXiv2021

A model for the fast evaluation of prompt losses of energetic ions in stellarators

A good understanding of the confinement of energetic ions in non-axisymmetric magnetic fields is key for the design of reactors based on the stellarator concept. In this work, we develop a model that, based on the radially-local bounce-averaged drift-kinetic equation, classifies orbits and succeeds in predicting configuration-dependent aspects of the prompt losses of energetic ions in stellarators. Such a model could in turn be employed in the optimization stage of the design of new devices.

physics.plasm-ph↗

arXiv2021

Gyrokinetic simulations in stellarators using different computational domains

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube, full-flux-surface, and radially global domains. Two problems are studied: the linear relaxation of zonal flows and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The zonal flow relaxation properties obtained in different flux tubes are found to differ with each other and with the radially global result, except for sufficiently long flux tubes, in general. The flux tube length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different flux tubes provide different results, but the discrepancy between them diminishes with increasing flux tube length. Full-flux-surface and flux tube simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the flux tube and the full-flux-surface domains. Radially global simulations provide results close to the full-flux-surface ones. The radial scale of unstable ITG modes is studied in global and flux tube simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found.

physics.plasm-ph↗

arXiv2021

Fast simulations for large aspect ratio stellarators with the neoclassical code KNOSOS

In this work, a new version of KNOSOS is presented. KNOSOS is a low-collisionality radially-local, bounce-averaged neoclassical code that is extremely fast, and at the same time, includes physical effects often neglected by more standard codes: the component of the magnetic drift that is tangent to the flux-surface and the variation of the electrostatic potential on the flux-surface. An earlier version of the code could only describe configurations that were sufficiently optimized with respect to neoclassical transport. KNOSOS can now be applied to any large aspect ratio stellarator, and its performance is demonstrated by means of detailed simulations in the configuration space of Wendelstein 7-X.

physics.plasm-ph↗

arXiv2020

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ITG, TEM and ETG modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermo-diffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

physics.plasm-ph↗

arXiv2020

Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations. A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear. The break up of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system -- the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol{E}\times\boldsymbol{B}$ flow. By analysing the linear ITG modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

physics.plasm-ph↗

arXiv2020

KNOSOS: a fast orbit-averaging neoclassical code for stellarator geometry

KNOSOS (KiNetic Orbit-averaging SOlver for Stellarators) is a freely available, open-source code (\href{https://github.com/joseluisvelasco/KNOSOS}{https://github.com/joseluisvelasco/KNOSOS}) that calculates neoclassical transport in low-collisionality plasmas of three-dimensional magnetic confinement devices by solving the radially local drift-kinetic and quasineutrality equations. The main feature of KNOSOS is that it relies on orbit-averaging to solve the drift-kinetic equation very fast. KNOSOS treats rigorously the effect of the component of the magnetic drift that is tangent to magnetic surfaces, and of the component of the electrostatic potential that varies on the flux surface, φ_1. Furthermore, the equation solved is linear in φ_1, which permits an efficient solution of the quasineutrality equation. As long as the radially local approach is valid, KNOSOS can be applied to the calculation of neoclassical transport in stellarators (helias, heliotrons, heliacs, etc.) and tokamaks with broken axisymmetry. In this paper, we show several calculations for the stellarators W7-X, LHD, NCSX and TJ-II that provide benchmark with standard local codes and demonstrate the advantages of this approach.

physics.plasm-ph↗

arXiv2019

A Scale-Separated Approach for Studying Coupled Ion and Electron Scale Turbulence

Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio $(m_e/m_i)^{1/2}$ and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space-time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale separation between ion and electron scales,and expanding the gyrokinetic equations for the turbulence in $(m_e/m_i)^{1/2}$, we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The electron scale turbulence experiences a modified drive due to gradients in the ion scale distribution function, and is advected by the ion scale $E \times B$ drift, which varies in the direction parallel to the magnetic field line. The largest possible cross-scale term in the ion scale equations is sub-dominant in our $(m_e/m_i)^{1/2}$ expansion. Hence, in our model the ion scale turbulence evolves independently of the electron scale turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard "twist-and-shift" boundary condition. This approach allows one to simulate multi-scale turbulence using electron scale flux tubes nested within an ion scale flux tube.

physics.plasm-ph↗

arXiv2017

Large tangential electric fields in plasmas close to temperature screening

Low-collisionality stellarator plasmas usually display a large negative radial electric field that has been expected to cause accumulation of impurities due to their high charge number. In this paper, two combined effects that can potentially modify this scenario are discussed. First, it is shown that, in low collisionality plasmas, the kinetic contribution of the electrons to the radial electric field can make it negative but small, bringing the plasma close to impurity temperature screening (i.e., to a situation in which the ion temperature gradient is the main drive of impurity transport and causes outward flux); in plasmas of very low collisionality, such as those of the Large Helical Device displaying impurity hole, screening may actually occur. Second, the component of the electric field that is tangent to the flux surface (in other words, the variation of the electrostatic potential on the flux surface), although smaller than the radial component, has recently been suggested to be an additional relevant drive for radial impurity transport. Here, it is explained that, especially when the radial electric field is small, the tangential magnetic drift has to be kept in order to correctly compute the tangential electric field, that can be larger than previously expected. This can have a strong impact on impurity transport, as we illustrate by means of simulations using the newly-developed code KNOSOS (KiNetic Orbit-averaging-SOlver for Stellarators).

physics.plasm-ph↗

arXiv2017

Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements

We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose that the transition to subcritical turbulence occurs via an intermediate state dominated by low number of coherent long-lived structures, close to threshold, which increase in number as the system is taken away from the threshold into the more strongly turbulent regime, until they fill the domain and a more conventional turbulence emerges. We show that the properties of turbulence are effectively functions of the distance to threshold, as quantified by the ion heat flux. We make quantitative comparisons of correlation lengths, times, and amplitudes between our simulations and experimental measurements using the MAST BES diagnostic. We find reasonable agreement of the correlation properties, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence.

physics.plasm-ph↗

arXiv2017

Stellarator bootstrap current and plasma flow velocity at low collisionality

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/ν$-collisionality regime and need to be modified in the $\sqrtν$-regime. The correction due to finite collisionality is also discussed and is found to scale as $ν^{2/5}$.

physics.plasm-ph↗

arXiv2016

Symmetry breaking in MAST plasma turbulence due to toroidal flow shear

The flow shear associated with the differential toroidal rotation of tokamak plasmas breaks an underlying symmetry of the turbulent fluctuations imposed by the up-down symmetry of the magnetic equilibrium. Using experimental Beam-Emission-Spectroscopy (BES) measurements and gyrokinetic simulations, this symmetry breaking in ion-scale turbulence in MAST is shown to manifest itself as a tilt of the spatial correlation function and a finite skew in the distribution of the fluctuating density field. The tilt is a statistical expression of the "shearing" of the turbulent structures by the mean flow. The skewness of the distribution is related to the emergence of long-lived density structures in sheared, near-marginal plasma turbulence. The extent to which these effects are pronounced is argued (with the aid of the simulations) to depend on the distance from the nonlinear stability threshold. Away from the threshold, the symmetry is effectively restored.

physics.plasm-ph↗

arXiv2016

Observation of oscillatory radial electric field relaxation in a helical plasma

Measurements of the relaxation of a zonal electrostatic potential perturbation in a non-axisymmetric magnetically confined plasma are presented. A sudden perturbation of the plasma equilibrium is induced by the injection of a cryogenic hydrogen pellet in the TJ-II stellarator, which is observed to be followed by a damped oscillation in the electrostatic potential. The waveform of the relaxation is consistent with theoretical calculations of zonal potential relaxation in a non-axisymmetric magnetic geometry. The turbulent transport properties of a magnetic confinement configuration are expected to depend on the features of the collisionless damping of zonal flows, of which the present letter is the first direct observation.

physics.plasm-ph↗

arXiv2015

Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths

In the linear collisionless limit, a zonal potential perturbation in a toroidal plasma relaxes, in general, to a non-zero residual value. Expressions for the residual value in tokamak and stellarator geometries, and for arbitrary wavelengths, are derived. These expressions involve averages over the lowest order particle trajectories, that typically cannot be evaluated analytically. In this work, an efficient numerical method for the evaluation of such expressions is reported. It is shown that this method is faster than direct gyrokinetic simulations performed with the GENE and EUTERPE codes. Calculations of the residual value in stellarators are provided for much shorter wavelengths than previously available in the literature. Electrons must be treated kinetically in stellarators because, unlike in tokamaks, kinetic electrons modify the residual value even at long wavelengths. This effect, that had already been predicted theoretically, is confirmed by gyrokinetic simulations.

physics.plasm-ph↗

arXiv2015

Dependence of intrinsic rotation reversals on collisionality in MAST

Tokamak plasmas rotate even without external injection of momentum. A Doppler backscattering system installed at MAST has allowed this intrinsic rotation to be studied in Ohmic L-mode and H-mode plasmas, including the first observation of intrinsic rotation reversals in a spherical tokamak. Experimental results are compared to a novel 1D model, which captures the collisionality dependence of the radial transport of toroidal angular momentum due to the effect of neoclassical flows on turbulent fluctuations. The model is able to accurately reproduce the change in sign of core toroidal rotation, using experimental density and temperature profiles from shots with rotation reversals as inputs and no free parameters fit to experimental data.

physics.plasm-ph↗

arXiv2015

Equivalence of two independent calculations of the higher order guiding center Lagrangian

The difference between the guiding center phase-space Lagrangians derived in [J.W. Burby, J. Squire, and H. Qin, Phys. Plasmas {\bf 20}, 072105 (2013)] and [F.I. Parra, and I. Calvo, Plasma Phys. Control. Fusion {\bf 53}, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication the difference between the guiding center coordinates is calculated explicitly.

physics.plasm-ph↗

arXiv2013

Intrinsic rotation driven by non-Maxwellian equilibria in tokamak plasmas

The effect of small deviations from a Maxwellian equilibrium on turbulent momentum transport in tokamak plasmas is considered. These non-Maxwellian features, arising from diamagnetic effects, introduce a strong dependence of the radial flux of co-current toroidal angular momentum on collisionality: As the plasma goes from nearly collisionless to weakly collisional, the flux reverses direction from radially inward to outward. This indicates a collisionality-dependent transition from peaked to hollow rotation profiles, consistent with experimental observations of intrinsic rotation.

physics.plasm-ph↗

arXiv2012

Experimental Signatures of Critically Balanced Turbulence in MAST

Beam Emission Spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as $ν_{*i}^{-0.8\pm0.1}$, where $ν_{*i}=$ ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding the drift waves' by $\sim ν_{*i}^{-0.8}$.

physics.plasm-ph↗