Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

Slaby, C.; Könies, A.; Kleiber, R.

doi:10.1063/1.4961916

Cited by 5 publications

(9 citation statements)

References 32 publications

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“…The damping rate weakly depends on the particle density and temperature profiles because the mode width is rather small: it does not change appreciably if we take n e = const or T i = T i (r * ) = const. Artificially setting the mode frequency to values as high as 70 kHz gives the damping rates shown in Table (2). All these magnitudes are in qualitaive agreement with the local estimate above.…”

Section: Damping Of Tae Modes In Wendelstein 7-xsupporting

confidence: 81%

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Landau damping of Alfvénic modes in stellarators

Kolesnichenko¹,

Tykhyy²

2018

Plasma Phys. Control. Fusion

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It is found that the presence of the so-called non-axisymmetric resonances of wave-particle interaction in stellarators [which are associated with the lack of axial symmetry of the magnetic configuration, Kolesnichenko et al., Phys. Plasmas 9 (2002) 517 ] may have a strong stabilizing influence through Landau mechanism on the Toroidicity-induced Alfvén Eigenmodes (TAE) and isomon modes (Alfvénic modes with equal poloidal and toroidal mode numbers and frequencies in the continuum region) destabilized by the energetic ions. These resonances involve largest harmonics of the equilibrium magnetic field of stellarators and lead to absorption of the mode energy by thermal ions in medium pressure plasma, in which case the effect is large. On the other hand, at the high pressure attributed to, e.g., a Helias reactor, thermal ions can interact also with high frequency Alfvén gap modes [Helicity-induced Alfvén Eigenmodes (HAE) and mirror-induced Alfvén Eigenmodes (MAE)], leading to a considerable damping of these modes. Only resonances with passing particles are considered. The developed theory is applied to various modes in the Wendelstein 7-X stellarator and a Helias reactor, and to two TAE modes in the LHD helical device.

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Section: Damping Of Tae Modes In Wendelstein 7-xsupporting

confidence: 81%

“…These mechanisms are Landau damping, continuum damping, radiative damping, and collisional damping. A brief overview of them in stellarators can be found in, e.g., [1], see also a more recent work [2]. The physics of the damping is rather similar in both tokamaks and stellarators.…”

Section: Introductionmentioning

confidence: 97%

Landau damping of Alfvénic modes in stellarators

Kolesnichenko¹,

Tykhyy²

2018

Plasma Phys. Control. Fusion

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“…Refs. [28,34]). Furthermore, the linear mode structure can change in the non-linear phase since it may react to changes of the fast-particle drive [36].…”

Section: Introductionmentioning

confidence: 99%

Effects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators

et al. 2018

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The non-linear saturation dynamics of TAEs (toroidicity-induced Alfvén eigenmodes) is investigated numerically in tokamaks and stellarators. Special attention is given to the influence that pitch-angle collisions among the fast ions have in the non-linear regime. For this investigation a perturbative model is used. We employ the three-dimensional ideal reduced MHD eigenvalue code CKA to obtain the mode frequency and mode structure. This information is given to the non-linear gyro-kinetic particle-in-cell code EUTERPE, which calculates the growth rate of the mode and the temporal evolution of the mode amplitude. The mode structure remains fixed for the entire calculation. In the tokamak, analytical predictions regarding the transition from periodic non-linear behaviour to a steady-state solution and the scaling of the saturated amplitude are available. Both are influenced by collisions. The numerical results are in agreement with the theoretical predictions within the validity range of the theory [H. L. Berk et al., Phys. Rev. Lett. 68, 3563 (1992)]. Beyond the validity range of the theory different scaling laws are found numerically. We show that using a momentum-conserving collision operator does not change the scaling significantly for small ν, but is important for high collision frequencies. The stellarator case, a Wendelstein 7-X high-mirror configuration, shows some differences when compared with the tokamak. Most notably, the saturated perturbed magnetic field becomes a non-monotonic function of ν.

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“…For both co-and cntr-GAEs, increasing beam density results in a modest decrease in mode frequency. This likely reflects changes in the equilibrium, and is supported by work done by Slaby et al which found that the continuum frequencies are decreased in the presence of increased alpha particle pressure 37 . Also apparent in this comparison is that the mode has a different stability threshold in J depending on if J is decreased through n b /n e or v 0 /v A , as the mode can still exist for small J provided that v 0 /v A is sufficiently large.…”

Section: A Equilibrium Effectsmentioning

confidence: 59%

“…Previous work has demonstrated the substantial effects that the beam contribution can have on the equilibrium 29 . Moreover, there is recent work showing that the inclusion of alpha particles can significantly deform the Alfvén continuum 37 . It is important to investigate if these changes in frequency can be attributed to changes in the self-consistent equilibrium or changes in the fast particles driving the mode, independent of the equilibrium.…”

Section: Equilibrium Vs Fast Ion Effectsmentioning

confidence: 99%

Energetic-particle-modified global Alfvén eigenmodes

2018

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Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to subcyclotron global Alfvén eigenmodes (GAE) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function -the normalized injection velocity v 0 /v A and central pitch -are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v 0 /v A . This unexpected result is present for both counter-propagating GAEs, which are routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE (EP-GAE). Additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.

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Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

Cited by 5 publications

References 32 publications

Landau damping of Alfvénic modes in stellarators

Landau damping of Alfvénic modes in stellarators

Effects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators

Energetic-particle-modified global Alfvén eigenmodes

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