Alfvén continuum and Alfvén eigenmodes in the National Compact Stellarator Experiment

Abstract. Alfvén oscillations in three-dimensional toroidal magnetic configurations (stellarators) are considered. It is shown that the wave functions of the Alfvén continuum can be trapped in certain "waveguides" when there are sufficiently large harmonics with sufficiently close periods along the magnetic field lines in the Fourier spectrum of the magnetic configuration. Such trapping is typical in the frequency range of the helicity-induced continuum gaps, in which case the wave functions are typically trapped at the inner circumference of the magnetic flux surface. Trapping also takes place near the crossings of continuum gaps, the localization of the wave becoming stronger with approach to the crossing point. At the crossing point, the continuum wave functions are localized at single field lines, which is shown to result in "annihilation" of the gaps (the width of the joint gap is the difference of the widths that the two gaps would have is they were alone). It is shown with the use of the ballooning formalism that the Alfvén eigenmodes (AEs) associated with the trapped continua are also trapped in regions of the same shape. Experimental observations on the stellarator Wendelstein 7-AS are reported, which indicate that trapping of AEs at the inner circumference of the plasma indeed takes place.

“…Similar picture was obtained in [34] (figure 5), where no such assumptions were made. These assumptions were needed here only to reach better numerical resolution.…”

Section: Vicinity Of the Crossing: Numerical Studysupporting

confidence: 68%

“…This explains the computational difficulties observed in continuum calculations [34] near the flux surfaces where pairs of wide gaps cross.…”

Section: Vicinity Of the Crossing: Numerical Studymentioning

confidence: 80%

Poloidal trapping of the high-frequency Alfvén continuum and eigenmodes in stellarators

Yakovenko¹,

Weller²,

Werner³

et al. 2007

“…TAEs, EAEs and NAEs) are also affected by the three-dimensionality. Calculations with the continuum codes COBRA [38] and STELLGAP [75] show that the shapes of these gaps are sensitive to 3D effects. In addition, it turns out that even weak three-dimensionality is able to change significantly the structure of the eigenmodes existing in tokamaks (TAEs, EAEs and NAEs), making their dependence on ϕ strongly anharmonic [24].…”

Section: Effect Of Three-dimensionality On Taes and Eaesmentioning

confidence: 99%

“…The narrow AC bands seen in figure 3 are the 'quantum levels' appearing due to the trapping; the finite width of these bands is produced Notations are the same as in figure 2. The AC was calculated with the continuum code COBRA in [38]. The gap width at r/a = 0.3, where the gaps intersect, is considerably reduced.…”

Section: Alfvén Continuum In Cold Plasma In Ideal-mhd Approximationmentioning

confidence: 99%

Affinity and difference between energetic-ion-driven instabilities in 2D and 3D toroidal systems

Kolesnichenko

Könies

Lutsenko

et al. 2011

Most of the published theoretical works on plasma instabilities driven by energetic (superthermal) ions are relevant to tokamaks. However, these instabilities play an important role not only in tokamaks but also in stellarators. That is why it is of importance to analyse the limits of applicability of theoretical results obtained for tokamaks and understand in which cases using these results for the description of similar phenomena in stellarators is justified and, if so, to what extent. On the other hand, stellarator theory incorporating effects of 3D geometry in some cases can be useful for understanding instabilities in tokamaks. Therefore, comparative analysis of instabilities in various types of toroidal systems is of interest for both stellarator and tokamak communities. Such an analysis based on an overview of energetic-ion-driven instabilities in tokamaks and stellarators is carried out in this paper. Instabilities in wide frequency range, from the ion/electron diamagnetic frequency to high frequencies of specific stellarator modes, are considered. Effects of the instabilities on the confinement of both the energetic ions and the bulk plasma are described. Numerical tools available for simulation of instabilities driven by the energetic ions are reviewed.

“…Thus, in the covariant representation the background magnetic field is B ≈ B φ ∇φ. Analogously to [9] we assume that the magnetic field strength is…”

Section: Shear Alfvén Dynamics With Finite Parallel Electric Fieldmentioning

confidence: 99%

Unstable drift-kinetic Alfvén modes with helicity close to the rotational transform

Eremin¹

2008

An important feature of some modern facilities (such as optimized stellarators) with low shear is that the value of their rotational transform is close to a rational number. If a mode helicity is close to the rotational transform of the background magnetic field, the Alfvén continuum frequency can lie in the range of the diamagnetic frequencies of the background electrons. An analytical analysis shows that if the local electron diamagnetic frequency curve crosses the Alfvén continuum from above as one proceeds from the axis to the plasma edge at a radial location relatively distant from the axis, a family of unstable drift-kinetic Aflvén modes (DKAEs) arises due to the coupling between the drift and Alfvén waves having same poloidal numbers. The coupling is mediated by the parallel electric field and the mode is destabilized due to parallel resonances. The mode growth rate can be relatively large and comparable to the real part of the mode frequency. The growth rate peaks at a small radial number, so that the most unstable mode can appear global and be confused with the magnetohydrodynamic (MHD) modes which can occur in this part of the spectrum. It follows that it is important to consider the diamagnetic effects and finite parallel electric field, which are frequently neglected for such phenomena in tokamaks, when studying Alfvén phenomena in the lowest part of the electromagnetic spectrum in optimized stellarators.