Survey of magnetohydrodynamic instabilities in the advanced stellarator Wendelstein 7-AS

Weller, A.; Anton, M.; Geiger, J.; Hirsch, M.; Jaenicke, R.; Werner, A.; Nührenberg, C.; Sallander, E.; Spong, D. A.; Team, W As

doi:10.1063/1.1346633

Cited by 122 publications

(149 citation statements)

References 76 publications

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“…The temporal evolution of the ACM frequency is completely different from the NGAE frequency evolution observed in the stellarator Wendelstein 7-AS (W7-AS). 2 In addition, ACMs are localized near the radius where the tokamak safety factor is minimum (i.e., where the rotational transform has a maximum), whereas the maximum of the NGAE mode can be located far from this point in small-shear devices.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3] These instabilities can have very different forms and consequences. They are not necessarily harmful and can be used for diagnostics.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, there are more various kinds of eigenmodes in stellarators than in tokamaks [namely, there are Mirrorinduced Alfvén Eigenmodes (MAE) and various Helicity-induced Alfvén Eigenmodes (HAE) in the high frequency part of the Alfvén spectrum [6][7][8] ]; there exist also non-axisymmetric resonances of the wave-particle interaction and resonances associated with the finite orbit width of the energetic ions; 5,9 the high-frequency modes are strongly localized poloidally (typically having anti-ballooning structure); 10 thermal crashes may occur during Alfvén instabilities. 2 Many features of Alfvén instabilities are associated with the features of the Alfvén continuum. In the upper part of the Alfvén spectrum, continuum regions are compressed into extremely narrow threads, so that the gaps in the continuum strongly dominate.…”

Section: Introductionmentioning

confidence: 99%

“…2 A W7-AS discharge where various quasi-steady state low frequency Alfvén instabilities occurred simultaneously was selected for analysis, and a numerical simulation of the destabilized modes was carried out, using equations derived in this work.…”

Section: Introductionmentioning

confidence: 99%

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Conventional and nonconventional global Alfvén eigenmodes in stellarators

et al. 2007

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Conditions of the existence of the Global Alfvén Eigenmodes (GAE) and Nonconventional Global Alfvén Eigenmodes (NGAE) predicted for stellarators by Ya. I. Kolesnichenko et al. [Phys. Rev. Lett. 94, 165004 (2005)] have been obtained. It is found that they depend on the nature of the rotational transform and that conditions for NGAE can be most easily satisfied in currentless stellarators. It is shown that the plasma compressibility may play an important role for the modes with the frequency about or less than that of the Toroidicity-induced Alfvén Eigenmodes (TAE). It is found that features of the Alfvén continuum in the vicinity of the k = 0 radius (k is the longitudinal wave number) can be very different, depending on a parameter which we refer to as "the sound parameter". Specific calculations modeling low-

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Section: Introductionmentioning

confidence: 99%

“…[1][2][3] These instabilities can have very different forms and consequences. They are not necessarily harmful and can be used for diagnostics.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conventional and nonconventional global Alfvén eigenmodes in stellarators

et al. 2007

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“…The NSTAB code predicts good nonlinear stability of these configurations, and the results are consistent with the observations. Moreover, experimental data at smaller values of ␤ validate an algorithm implemented in the NSTAB code to estimate the bootstrap current (11,12).…”

Section: Comparison With Experimentsmentioning

confidence: 99%

Three-dimensional stellarator codes

Garabedian

2002

Proc. Natl. Acad. Sci. U.S.A.

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Three-dimensional computer codes have been used to develop quasisymmetric stellarators with modular coils that are promising candidates for a magnetic fusion reactor. The mathematics of plasma confinement raises serious questions about the numerical calculations. Convergence studies have been performed to assess the best configurations. Comparisons with recent data from large stellarator experiments serve to validate the theory.M odular stellarators can be viewed as an advanced tokamak hybrid appropriate for implementation as a fusion reactor (1). Quasisymmetry of the magnetic spectrum is predicted to give good confinement at high temperatures, and adequate rotational transform from the external magnetic field is expected to stabilize the plasma. New configurations have been designed by making imaginative use of three-dimensional computer codes. Because the mathematics of these stellarators is complicated, we have performed convergence studies applicable to proof of principle experiments that are being planned.We are primarily concerned with the NSTAB equilibrium and stability code and the TRAN Monte Carlo transport code developed at New York University by Octavio Betancourt and Mark Taylor (2-5). The codes are applied to a compact stellarator called the MHH2 that has two field periods and excellent quasiaxial symmetry. For the calculations we selected a configuration with realistic physical parameters that provide good convergence, enabling us to perform long runs and make estimates of numerical errors. Theoretical conclusions can be drawn that are relevant to a wider range of examples, such as the optimized stellarator specified in Table 1.The NSTAB code is a computer implementation of the variational principle of ideal magnetohydrodynamics (MHD). If B is the magnetic field and p is the pressure, solutions of the magnetostatics equations are found by minimizing the potential energyin a coordinate system compatible with toroidal geometry in three dimensions. An accurate finite difference scheme is used in the radial direction, and dependence on the poloidal and toroidal angles is handled by the spectral method. It is assumed that there are nested toroidal flux surfaces, and the differential equations are written in a conservation form that captures islands and current sheets. The resolution is so good that questions of stability can be settled by a mountain pass theorem asserting that when more than one solution of the problem can be found then an unstable equilibrium must exist corresponding to a saddle point in the energy landscape. Bifurcated equilibria are calculated whose magnetic surfaces have Poincaré sections displaying the structure of the most unstable modes.The TRAN code uses a split time algorithm to calculate the confinement time of test particles by alternately tracking guiding center orbits and applying a random walk that represents collisions. The magnetic field B and the flow field U of the plasma in a background obtained by using NSTAB are held fixed during iterations that impose quasineutrali...

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