Active control of Alfvén Eigenmodes (AEs)

In magnetically confined fusion devices, super-thermal particles must be well confined until they slow down to the plasma bulk [1]. Fusion born alpha particles as well as energetic particles produced by external heating systems such as neutral beam injectors (NBI) or ion cyclotron resonance heating (ICRH) are, however, a source of free energy that can destabilize a rich spectrum of magnetohydrodynamic (MHD) fluctuations. Alfvén waves [2] are electromagnetic perturbations inherent to a magnetized plasma that are often driven unstable by spatial gradients in a resonant energetic particle population. In present day tokamaks and stellarators, a net wave–particle energy and momentum exchange is always accompanied by a transport of energetic particles.

Fig.1. AUG. TAE suppression via externally applied 3D fields.

A secular transport can end in a particle loss that, if it is not mitigated, can lead to a degradation of the reactor performance. An intense and localized energetic particle loss can even pose serious threats to the integrity of the plasma facing components and vacuum vessel. Indeed, in tokamaks, under unfavourable conditions, toroidal Alfvén eigenmodes (TAEs) [3] have been observed to cause a loss of over 50% of the injected beam power leading to a significant ablation of plasma facing components [4]. In realistic 3D configurations with magnetic field ripple such as that produced by the toroidal field coils, TAE induced energetic particle transport has been observed to cause, under certain conditions, severe damage of the vacuum vessel leading to machine venting [5].  Future burning plasmas with a large population of super-Alfvénic alpha particles are prone to develop Alfvén perturbations that, if not mitigated, can lead to unacceptable consequences. Alfvén eigenmode (AE) mitigation techniques based on external, and controlled, actuators are therefore mandatory. Based on the main AE drive and damping mechanisms, several control techniques have been successfully explored during the last years [6, 7] though their applicability to future devices is still under investigation. 

One of the main goals of the PSFT team is to demonstrate a robust control of AEs in present devices by means of reliable external actuators such as Resonant Magnetic Perturbations (RMPs), Electron Cyclotron Resonance Heating (ECRH) and Current Drive (ECCD) as well as variable fast-ion sources.

[1] Fasoli A et al., Chapter 5: Physics of energetic ions, Nucl. Fusion 47, S264 (2007).
[2] Alfvén H., Existence of Electromagnetic-Hydrodynamic Waves, Nature 150, 405 (1942).
[3] Cheng C. Z., Chen L. and Chance M. S., High-n ideal and resistive shear Alfvén waves in tokamaks, Ann. Phys. 161, 21 (1985).
[4] Duong H. H. et al., Loss of energetic beam ions during TAE instabilities, Nucl. Fusion 33, 749 (1993).
[5] White R. B. et al., Toroidal Alfvén eigenmode‐induced ripple trapping, Phys. Plasmas 2, 2871 (1995).
[6] Herrmann M. C. and Fisch N. J., Cooling Energetic α Particles in a Tokamak with Waves, Phys. Rev. Lett. 79, 1495 (1997).
[7] Graves J. P. et al., Control of magnetohydrodynamic stability by phase space engineering of energetic ions in tokamak plasmas, Nat. Commun. 3, 624 (2012).

MHD induced fast-ion losses

Besides Alfven Eigenmodes, a rich spectrum of MHD fluctuations have been observed to cause significant fast-ion losses in most of the large fusion devices. While a net wave-particle energy and momentum exchange typically leads to a fast-ion transport / loss, the properties of this transport depends on the nature of the MHD fluctuation and interacting energetic particle population in particle phase-space.

Scintillator-based fast-ion los detectors (FILDs) constitute a very powerful tool to investigate this phenomenon due to their high temporal and velocity-space resolution.

The PSFT team studies the mechanisms leading to fast-ion losses in the presence of a broad spectrum of MHD fluctuations using mainly scintillator based FILD systems in most of the large magnetically confined fusion devices in the world.

For more details about fast-ion losses induced by NTMs in the ASDEX Upgrade tokamak see:
[1] M.Garcia-Munoz et al., NTM induced fast ion losses in ASDEX Upgrade, Nucl. Fusion Letter 47, L10-L15 (2007).
[2] J.Galdon-Quiroga et al., Velocity space resolved absolute measurement of fast ion losses induced by a tearing mode in the ASDEX Upgrade tokamak, Nucl. Fusion 58, 036005 (2018).
[3] J.Gonzalez-Martin et al., First measurement of a magnetically driven fast-ion loss detector on ASDEX Upgrade, JINST 14, C11005 (2019).

Fast-ion losses induced by RMPs

Toroidal symmetry is the basis of magnetically confined fusion devices. Nested flux surfaces and particle constants of motion ensure plasma confinement in tokamaks and stellarators. However,the application of symmetry-breaking 3D fields, e.g. Resonant Magnetic Perturbations (RMPs), can lead to a deterioration of the confinement and consequent particle loss.

Energetic particles are especially sensitive to this complex 3D magnetic background due to their relatively long mean free path and slowing down times. An optimal confinement of fast-ions is essential to achieve a good performance of current and future fusion devices. Consequently, it is crucial to make a detailed assessment of the impact that RMP fields have on the fast-ion population. This is one of the goals of the PSFT team.

[1] M. Garcia-Munoz et al, Fast-ion redistribution and loss due to edge perturbations in the ASDEX Upgrade, DIII-D and KSTAR tokamaks, Nucl. Fusion 53, 123008 (2013).
[2] M.A. Van Zeeland et al, Fast ion transport during applied 3D magnetic perturbations on DIII-D, Nucl. Fusion 55, 073028 (2015).
[3] T. Kurki-Suonio et al., Protecting ITER walls: fast ion power loads in 3D magnetic field, Plasma Phys. Control. Fusion 59, 014013 (2016).
[4] K. Särkimäki, Efficient and rigorous evaluation of fast particle losses in non-axisymmetric tokamak plasmas, Nucl. Fusion 60, 036002 (2020).

Edge Resonant Transport Layer (ERTL)

The fast-ion transport in the presence of externally applied magnetic perturbations has been analyzed in terms of the variation of the toroidal canonical momentum (Pφ). The Pφ is a particle constant of motion in axi-symmetric configurations. In cases where the toroidal symmetry is broken, this quantity is no longer conserved and its variation is associated to a radial transport.

The analysis of the dPf revealed an Edge Resonant Transport Layer (ERTL) where the fast-ion transport is enhanced due to wave-particle resonant interactions with the magnetic perturbation. The ERTL is located at the plasma edge and involves a combination of linear and nonlinear resonances that are strongly affected by the poloidal mode spectra of the perturbation, magnetic equilibrium and particle orbit topology. The ability to create a resonant transport layer at the edge of a tokamak plasma opens new avenues for the control of the energetic particle population and associated magnetohydrodynamic fluctuations in future burning plasmas.

[1] L. Sanchis et al, Characterisation of the fast-ion edge resonant transport layer induced by 3D perturbative fields in the ASDEX Upgrade tokamak through full orbit simulations, Plasma Phys. Control. Fusion 61, 014038 (2019).
[2] P. Cano-Megias et al, Nucl. Fusion,  (submitted).

Fig. 2. Variation of dPphi for differrent RMP configurations in the particle (R,E) plane.

Fig. 3. Variation of dPphi for differrent RMP configurations in the particle (phi, R) plane.

ELM induced fast-ion losses

Edge Localized Modes (ELMs) are MHD instabilities that appear at the edge of tokamak plasmas and expel energy and particles in repetitive cycles, jeopardizing the integrity of the machine. Enhanced fast-ion losses have been measured during ELMs, typically showing a filamentary like behaviour, with multiple spikes of increased losses during single ELM crashes. The fast-ion losses present a high energy feature above the fast-ion injection energy, suggesting a resonant interaction between the fast-ions and the ELM perturbation. The acceleration and transport mechanisms are being studied and modelled with the Monte Carlo full-orbit code ASCOT and electromagnetic perturbations resolved with MHD codes like MEGA or JOREK. The results show a resonant interaction between the fast-ions and the parallel electric field arising during the ELM crash, when magnetic reconnection is believed to take place, leading to fast-ion acceleration and increase in the fast-ion transport.

For more details about ELM induced fast-ion losses see:
[1] M.Garcia-Munoz et al., Fast-ion redistribution and los due to edge perturbations in the ASDEX Upgrade, DIII-D and KSTAR tokamaks, Nucl. Fusion 53, 123008 (2013).
[2] M.Garcia-Munoz et al., Fast-ion losses induced by ELMs and externally applied magnetic perturbations in the ASDEX Upgrade tokamak, Plasma Phys. Control. Fusion 55, 124014 (2013).
[3] J.Galdon-Quiroga et al., Beam-ion acceleration during Edge Localized Modes in the ASDEX Upgrade tokamak, Phys. Rev. Lett. 121, 025002 (2018).
[4] J.Galdon-Quiroga et al., Observation of accelerated beam ion population during edge localized modes in the ASDEX Upgrade tokamak, Nucl. Fusion 59, 066016 (2019).

Fig. 4. AUG. Fast-ion trapped orbit overplotted on a poloidal projection of a JOREK calculated 3D perturbation induced by an ELM crash.

3D nonlinear hybrid kinetic MHD modelling of ELMs

Motivated by these experimental findings, the 3D nonlinear hybrid kinetic MHD code MEGA [1] is being applied to an ASDEX Upgrade discharge to model the interaction of fast-ions and ELMs. A spontaneous ELM has been successfully obtained in a realistic X-point geometry using the MHD model of MEGA. A ballooning structure develops in the pedestal region at the LFS. After the explosive growth of the instability, both the edge pressure gradient and the current density decrease, leading to a saturated phase in which the filamentary structure extends into the SOL. Preliminary hybrid kinetic-MHD simulations using a realistic off-axis distribution show that fast-ions have a stabilizing effect on ballooning modes [2].

Fig. 5.

[1] Y. Todo et al., Linear and nonlinear particle-magnetohydrodynamic simulations of the toroidal Alfvén eigenmode, Phys. Plasmas 5, 1321 (1998).
[2] J. Dominguez-Palacios et al, 16th Technical Meeting on Energetic Particles in Magnetic Confinement Systems -Theory of Plasma Instabilities (2019), oral contribution.
[2] J. Dominguez-Palacios et al, The 29th International Toki Conference on Plasma and Fusion Research (2020), oral contribution.