arXiv subjects

Felix I. Parra

Publications and source records attributed to Felix I. Parra.

50 records · Page 3Linked to original sources

arXiv2014

Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry

Gyrokinetic theory is based on an asymptotic expansion in the small parameter $ε$, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this article, this ordering is strictly implemented to compute the electrostatic gyrokinetic phase-space Lagrangian in general magnetic geometry to order $ε^2$. In particular, a new expression for the complete second-order gyrokinetic Hamiltonian is provided, showing that in a rigorous treatment of gyrokinetic theory magnetic geometry and turbulence cannot be dealt with independently. The new phase-space gyrokinetic Lagrangian gives a Vlasov equation accurate to order $ε^2$ and a Poisson equation accurate to order $ε$. The final expressions are explicit and can be implemented into any simulation without further computations.

physics.plasm-ph↗

arXiv2014

Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity

Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates have been computed to order $ε^2$ in general magnetic geometry. Here $ε$ is the gyrokinetic expansion parameter, the gyroradius over the macroscopic scale length. Starting from these results, the long-wavelength limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken for tokamak geometry. Employing the set of equations derived in the present article, it is possible to calculate the long-wavelength components of the distribution functions and of the poloidal electric field to order $ε^2$. These higher-order pieces contain both neoclassical and turbulent contributions, and constitute one of the necessary ingredients (the other is given by the short-wavelength components up to second order) that will eventually enter a complete model for the radial transport of toroidal angular momentum in a tokamak in the low flow ordering. Finally, we provide an explicit and detailed proof that the system consisting of second-order gyrokinetic Fokker-Planck and quasineutrality equations leaves the long-wavelength radial electric field undetermined; that is, the turbulent tokamak is intrinsically ambipolar.

physics.plasm-ph↗

arXiv2014

Optimizing stellarators for large flows

Plasma flow is damped in stellarators because they are not intrinsically ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric current vanishes for any value of the radial electric field. Only quasisymmetric stellarators are intrinsically ambipolar, but exact quasisymmetry is impossible to achieve in non-axisymmetric toroidal configurations. By calculating the violation of intrinsic ambipolarity due to deviations from quasisymmetry, one can derive criteria to assess when a stellarator can be considered quasisymmetric in practice, i.e. when the flow damping is weak enough. Let us denote by $α$ a small parameter that controls the size of a perturbation to an exactly quasisymmetric magnetic field. Recently, it has been shown that if the gradient of the perturbation is sufficiently small, the flux-surface averaged radial electric current scales as $α^2$ for any value of the collisionality. It was also argued that when the gradient of the perturbation is large, the quadratic scaling is replaced by a more unfavorable one. In this paper, perturbations with large gradients are rigorously treated. In particular, it is proven that for low collisionality a perturbation with large gradient yields, at best, an $O(|α|)$ deviation from quasisymmetry. Heuristic estimations in the literature incorrectly predicted an $O(|α|^{3/2})$ deviation.

physics.plasm-ph↗

arXiv2014

When omnigeneity fails

A generic non-symmetric magnetic field does not confine magnetized charged particles for long times due to secular magnetic drifts. Stellarator magnetic fields should be omnigeneous (that is, designed such that the secular drifts vanish), but perfect omnigeneity is technically impossible. There always are small deviations from omnigeneity that necessarily have large gradients. The amplification of the energy flux caused by a deviation of size $ε$ is calculated and it is shown that the scaling with $ε$ of the amplification factor can be as large as linear. In opposition to common wisdom, most of the transport is not due to particles trapped in ripple wells, but to the perturbed motion of particles trapped in the omnigeneous magnetic wells around their bounce points.

physics.plasm-ph↗

arXiv2014

Stellarators close to quasisymmetry

Rotation is favorable for confinement, but a stellarator can rotate at high speeds if and only if it is sufficiently close to quasisymmetry. This article investigates how close it needs to be. For a magnetic field $\mathbf{B} = \mathbf{B}_0 + α\mathbf{B}_1$, where $\mathbf{B}_0$ is quasisymmetric, $α\mathbf{B}_1$ is a deviation from quasisymmetry, and $α\ll 1$, the stellarator can rotate at high velocities if $α< ε^{1/2}$, with $ε$ the ion Larmor radius over the characteristic variation length of $\mathbf{B}_0$. The cases in which this result may break down are discussed. If the stellarator is sufficiently quasisymmetric in the above sense, the rotation profile, and equivalently, the long-wavelength radial electric field, are not set neoclassically; instead, they can be affected by turbulent transport. Their computation requires the $O(ε^2)$ pieces of both the turbulent and the long-wavelength components of the distribution function. This article contains the first step towards a formulation to calculate the rotation profile by providing the equations determining the long-wavelength components of the $O(ε^2)$ pieces.

physics.plasm-ph↗

arXiv2014

A current driven electromagnetic mode in sheared and toroidal configurations

The induced electric field in a tokamak drives a parallel electron current flow. In an inhomogeneous, finite beta plasma, when this electron flow is comparable to the ion thermal speed, the Alfven mode wave solutions of the electromagnetic gyrokinetic equation can become nearly purely growing kink modes. Using the new "low-flow" version of the gyrokinetic code GS2 developed for momentum transport studies [Barnes et al 2013 Phys. Rev. Lett. 111, 055005], we are able to model the effect of the induced parallel electric field on the electron distribution to study the destabilizing influence of current on stability. We identify high mode number kink modes in GS2 simulations and make comparisons to analytical theory in sheared magnetic geometry. We demonstrate reassuring agreement with analytical results both in terms of parametric dependences of mode frequencies and growth rates, and regarding the radial mode structure.

physics.plasm-ph↗

arXiv2013

Extension of gyrokinetics to transport time scales

Gyrokinetic simulations have greatly improved our theoretical understanding of turbulent transport in fusion devices. Most gyrokinetic models in use are delta-f simulations in which the slowly varying radial profiles of density and temperature are assumed to be constant for turbulence saturation times, and only the turbulent electromagnetic fluctuations are calculated. New massive simulations are being built to self-consistently determine the radial profiles of density and temperature. However, these new codes have failed to realize that modern gyrokinetic formulations, composed of a gyrokinetic Fokker-Planck equation and a gyrokinetic quasineutrality equation, are only valid for delta-f simulations that do not reach the longer transport time scales necessary to evolve radial profiles. In tokamaks, due to axisymmetry, the evolution of the axisymmetric radial electric field is a challenging problem requiring substantial modifications to gyrokinetic treatments. In this thesis, I study the effect of turbulence on the global electric field and plasma flows. By studying the current conservation equation, or vorticity equation, I prove that the long wavelength, axisymmetric flow must remain neoclassical and I show that the tokamak is intrinsically ambipolar, i.e., the radial current is zero to a very high order for any long wavelength radial electric field. Intrinsic ambipolarity is the origin of the problems with the modern gyrokinetic approach since the lower order gyrokinetic quasineutrality (if properly evaluated) is effectively independent of the radial electric field. I propose a new gyrokinetic formalism to solve for the global radial electric field.

physics.plasm-ph↗

arXiv2013

Conditions for up-down asymmetry in the core of tokamak equilibria

A local magnetic equilibrium solution is sought around the magnetic axis in order to identify the key parameters defining the magnetic-surface's up-down asymmetry in the core of tokamak plasmas. The asymmetry is found to be determined essentially by the ratio of the toroidal current density flowing on axis to the fraction of the external field's odd perturbation that manages to propagate from the plasma boundary into the core. The predictions are tested and illustrated first with an analytical Solovev equilibrium and then using experimentally relevant numerical equilibria. Hollow current-density distributions, and hence reverse magnetic shear, are seen to be crucial to bring into the core asymmetry values that are usually found only near the plasma edge.

physics.plasm-ph↗

arXiv2013

Turbulent momentum pinch of diamagnetic flows in a tokamak

The ion toroidal rotation in a tokamak consists of an $E\times B$ flow due to the radial electric field and a diamagnetic flow due to the radial pressure gradient. The turbulent pinch of toroidal angular momentum due to the Coriolis force studied in previous work is only applicable to the $E\times B$ flow. In this Letter, the momentum pinch for the rotation generated by the radial pressure gradient is calculated and is compared with the Coriolis pinch. This distinction is important for subsonic flows or the flow in the pedestal where the two types of flows are similar in size and opposite in direction. In the edge, the different pinches due to the opposite rotations can result in intrinsic momentum transport that gives significant rotation peaking.

physics.plasm-ph↗

arXiv2012

Perpendicular momentum injection by lower hybrid wave in a tokamak

The injection of lower hybrid waves for current drive into a tokamak affects the profile of intrinsic rotation. In this article, the momentum deposition by the lower hybrid wave on the electrons is studied. Due to the increase in the poloidal momentum of the wave as it propagates into the tokamak, the parallel momentum of the wave increases considerably. The change of the perpendicular momentum of the wave is such that the toroidal angular momentum of the wave is conserved. If the perpendicular momentum transfer via electron Landau damping is ignored, the transfer of the toroidal angular momentum to the plasma will be larger than the injected toroidal angular momentum. A proper quasilinear treatment proves that both perpendicular and parallel momentum are transferred to the electrons. The toroidal angular momentum of the electrons is then transferred to the ions via different mechanisms for the parallel and perpendicular momentum. The perpendicular momentum is transferred to ions through an outward radial electron pinch, while the parallel momentum is transferred through collisions.

physics.plasm-ph↗

arXiv2012

Analytic fluid theory of beam spiraling in high-intensity cyclotrons

Using a two-dimensional fluid description, we investigate the nonlinear radial-longitudinal dynamics of intense beams in storage rings and cyclotrons. With a multiscale analysis separating the time scale associated with the betatron motion and the slower time scale associated with space-charge effects, we show that the longitudinal-radial vortex motion can be understood in the frame moving with the charged beam as the nonlinear advection of the beam by the $\mathbf{E}\times\mathbf{B}$ velocity field, where $\mathbf{E}$ is the electric field due to the space charge and $\mathbf{B}$ is the external magnetic field. This interpretation provides simple explanations for the stability of round beams and for the development of spiral halos in elongated beams. By numerically solving the nonlinear advection equation for the beam density, we find that it is also in quantitative agreement with results obtained in PIC simulations.

physics.acc-ph↗

arXiv2012

Intrinsic rotation with gyrokinetic models

The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed.

physics.plasm-ph↗

arXiv2012

Sources of intrinsic rotation in the low flow ordering

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.

physics.plasm-ph↗

arXiv2011

Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks

Two symmetries of the local nonlinear delta-f gyrokinetic system of equations in tokamaks in the high flow regime are presented. The turbulent transport of toroidal angular momentum changes sign under an up-down reflection of the tokamak and a sign change of both the rotation and the rotation shear. Thus, the turbulent transport of toroidal angular momentum must vanish for up-down symmetric tokamaks in the absence of both rotation and rotation shear. This has important implications for the modeling of spontaneous rotation.

physics.plasm-ph↗