Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

Landreman, Matt; Smith, H. M.; Mollén, A.; Helander, P.

doi:10.1063/1.4870077

Cited by 90 publications

(150 citation statements)

References 49 publications

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“…We note that equation (19) is able to describe only the 1/ν or √ ν regimes of neoclassical transport of the bulk ions. However, at low collisionalities, and especially for small radial electric fields, the contribution from the so-called superbanana-plateau regime to the transport of bulk ions cannot be neglected.…”

Section: Equationsmentioning

confidence: 99%

Large tangential electric fields in plasmas close to temperature screening

Velasco¹,

Calvo²,

García-Regaña³

et al. 2018

Plasma Phys. Control. Fusion

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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 [1,2], 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).

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Section: Equationsmentioning

confidence: 99%

Large tangential electric fields in plasmas close to temperature screening

Velasco¹,

Calvo²,

García-Regaña³

et al. 2018

Plasma Phys. Control. Fusion

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“…While the DKES model does not conserve µ when the radial electric field E r = 0, the adjoint operator under the DKES model takes a particularly simple form as discussed in section 3.1. This model also does not introduce any unphysical constraints on the distribution function when E r = 0, as occurs for the full trajectory model (Landreman et al 2014). These constraints motivate the introduction of particle and heat sources, which are discussed in the following section.…”

Section: Drift Kinetic Equationmentioning

confidence: 99%

An adjoint method for neoclassical stellarator optimization

et al. 2019

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Received xx; revised xx; accepted xx)Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring O(N ) flux computations, where N is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop.With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large (O(10 2 )), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Furthermore, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.

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“…The employed collision operator is frequently used in modern neoclassical solvers, and the results can thus be directly compared with the output from such codes. In the final sections, we look at a few example magnetic configurations, where we compare the magnitude of the classical transport to that of the neoclassical transport calculated with the Sfincs † drift-kinetic solver (Landreman et al 2014), and investigate the collisionality dependence of the ratio of classical to neoclassical transport.…”

Section: Introductionmentioning

confidence: 99%

The importance of the classical channel in the impurity transport of optimized stellarators

et al. 2019

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In toroidal magnetic confinement devices, such as tokamaks and stellarators, neoclassical transport is usually an order of magnitude larger than its classical counterpart. However, when a high-collisionality species is present in a stellarator optimized for low Pfirsch-Schlüter current, its classical transport can be comparable to the neoclassical transport. In this letter, we compare neoclassical and classical fluxes and transport coefficients calculated for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we find that the classical transport of a collisional impurity is comparable to the neoclassical transport for all radii, while it is negligible in the LHD cases, except in the vicinity of radii where the neoclassical transport changes sign. In the LHD case, electrostatic potential variations on the flux-surface significantly enhance the neoclassical impurity transport, while the classical transport is largely insensitive to this effect in the cases studied.

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Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

Cited by 90 publications

References 49 publications

Large tangential electric fields in plasmas close to temperature screening

Large tangential electric fields in plasmas close to temperature screening

An adjoint method for neoclassical stellarator optimization

The importance of the classical channel in the impurity transport of optimized stellarators

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