Superbanana and superbanana plateau transport in finite aspect ratio tokamaks with broken symmetry

Abstract. In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, and they exhibit neoclassical transport levels comparable to those of axisymmetric tokamaks. However, the effect of deviations from omnigeneity cannot be neglected in practice, and it is more deleterious at small collisionalities. For sufficiently low collision frequencies (below the values that define the 1/ν regime), the components of the drifts tangential to the flux surface become relevant. This article focuses on the study of such collisionality regimes in stellarators close to omnigeneity when the gradient of the non-omnigeneous perturbation is small. First, it is proven that closeness to omnigeneity is required to actually preserve radial locality in the drift-kinetic equation for collisionalities below the 1/ν regime. Then, using the derived radially local equation, it is shown that neoclassical transport is determined by two layers located at different regions of phase space. One of the layers corresponds to the so-called √ ν regime and the other to the so-called superbanana-plateau regime. The importance of the superbanana-plateau layer for the calculation of the tangential electric field is emphasized, as well as the relevance of the latter for neoclassical transport in the collisionality regimes considered in this paper. In particular, the role of the tangential electric field is essential for the emergence of a new subregime of superbanana-plateau transport when the radial electric field is small. A formula for the ion energy flux that includes the √ ν regime and the superbanana-plateau regime is given. The energy flux scales with the square of the size of the deviation from omnigeneity. Finally, it is explained why below a certain collisionality value the formulation presented in this article ceases to be valid.

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“…In the quasineutrality equation defined by (21) and (22) the expansions (17) and (18) have not been employed yet. Using them, we obtain…”

Section: Low-collisionality Drift-kinetic Equation In Stellarators CLmentioning

confidence: 99%

“…The second layer (see subsection 4.2) gives the superbanana-plateau regime, derived in [21] for finite aspect ratio tokamaks with broken symmetry. Here, the √ ν and superbanana-plateau regimes are derived and analyzed in a much broader setting and in deeper detail than previously available in the literature.…”

Section: Introductionmentioning

confidence: 99%

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

Calvo¹,

Parra

Velasco³

et al. 2017

Plasma Phys. Control. Fusion

205

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“…As shown in the example below, the shear term may lead to a significant modification of the superbanana resonance condition. This term is retained if linearization is applied after bounce-averaging the kinetic equation 10 . It should be noted that the guiding center Lagrangian (20) used as a starting point here is valid for the general case of the magnetic field, which is not necessarily a force-free field.…”

Section: B Action-angle Variables In the Axisymmetric Tokamakmentioning

confidence: 99%

Evaluation of toroidal torque by non-resonant magnetic perturbations in tokamaks for resonant transport regimes using a Hamiltonian approach

et al. 2016

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Toroidal torque generated by neoclassical viscosity caused by external non-resonant, nonaxisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks.In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant NTV regimes including superbanana plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.

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“…Resonances between the different frequencies lead to the formation of resonant transport regimes, which are described by asymptotical formulas in the collisionless limit [10,5,16,6]. The resonance condition for the superbanana-plateau (sb-p) regime [26,11] is given by Ω tE + Ω tB b = 0, whereas for drift-orbit resonances [10,16,6,11] the condition m ϑ ω b +n(Ω tE + Ω tB b ) = 0 must be fulfilled for trapped particles. Here, the bounce frequency mode number m ϑ can take any positive or negative integer value.…”

Section: Ntv Torque In Asdex-upgradementioning

confidence: 99%

Effect of 3D magnetic perturbations on the plasma rotation in ASDEX Upgrade

Martitsch

Kasilov

Kernbichler

et al. 2016

Plasma Phys. Control. Fusion

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The toroidal torque due to the non-resonant interaction with external magnetic perturbations (TF ripple and perturbations from ELM mitigation coils) in ASDEX Upgrade is modelled with help of the NEO-2 and SFINCS codes and compared to semi-analytical models. It is shown that almost all non-axisymmetric transport regimes contributing to neoclassical toroidal viscosity (NTV) are realized within a single discharge at different radial positions. The NTV torque is obtained to be roughly a quarter of the NBI torque. This indicates the presence of other important momentum sources. The role of these momentum sources and possible integral torque balance measurements are briefly discussed.

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Superbanana and superbanana plateau transport in finite aspect ratio tokamaks with broken symmetry

Cited by 31 publications

References 21 publications

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

Evaluation of toroidal torque by non-resonant magnetic perturbations in tokamaks for resonant transport regimes using a Hamiltonian approach

Effect of 3D magnetic perturbations on the plasma rotation in ASDEX Upgrade

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