Session ZI02: Invited: Magnetic Fusion: Fast Ions

Live

We report results of studies in D-$^{\mathrm{3}}$He plasmas on JET ($n(^{\mathrm{3}}$He)/$n_{\mathrm{e}}\approx $20-25{\%}) using the 3-ion radio frequency (RF) scheme [1,~2] for the core acceleration of deuterons from neutral beam injection (NBI) to higher energies to generate alpha particles from D$+^{\mathrm{3}}$He fusion reactions. The fast-ion distribution of RF-accelerated D-NBI ions was controlled by varying the RF/NBI power ratio ($P_{\mathrm{RF}}\approx $4-6MW, $P_{\mathrm{NBI}}\approx $3-20MW). With as little as $P_{\mathrm{RF}}\approx $6~MW and $P_{\mathrm{NBI}}\approx $7-10~MW, rather high D-D neutron ($\approx $1x10$^{\mathrm{16}}$ 1/s) and D-$^{\mathrm{3}}$He alpha rates ($\approx $2\texttimes 10$^{\mathrm{16}}$ 1/s) were achieved. For the first time in JET-ILW, the upgraded gamma-ray diagnostic [3] provided spatial images of the alpha birth profile, validating this essential diagnostic for its use in future D-T experiments. Dominant fast-ion heating and a rich variety of fast-ion driven Alfv\'{e}n eigenmodes (AEs) were observed in these discharges, which allowed mimicking several aspects of future burning plasmas, where alphas will largely affect heating and global confinement. The sawtooth period in D-$^{\mathrm{3}}$He pulses on JET varied between $\approx $200-300~ms and 3.9~s, depending on the RF/NBI power ratio, $n_{\mathrm{e}}$, etc. During long period sawteeth (\textgreater $\approx $1s), reversed shear AEs were additionally detected by magnetic coils. This indicates that a non-monotonic $q$-profile was developed and sustained by large fast-ion populations. AE dynamics were different in pulses with short sawteeth periods. In these conditions, $n$~$=$~0 global AEs were regularly observed, hinting at the presence of fast ions with an inverted distribution. The possibility that some of the observed AEs were driven by fusion-born alphas is under investigation. Surprisingly, this complex AE activity is not detrimental for the thermal confinement, which is actually enhanced in the inner core, especially for the ions. [1] Kazakov, Y \textit{et al.} \textit{Nature Phys} \textbf{13, }973--978 (2017) [2] Ongena, J \textit{et al.} \textit{EPJ Web of Conferences} \textbf{157}, 02006 (2017) [3] Rigamonti, D \textit{et al.} \textit{Rev. Sci. Instrum.} \textbf{89}, 10I116 (2018)   

Live

An integrated, quasilinear analysis framework to quantify the losses of fast ions in tokamaks that is both fast and comprehensive has been realized through the development of the Resonance Broadened Quasilinear (RBQ) code. It formulates the 2D quasilinear diffusive beam ion relaxation in action variables (i.e., in both the canonical toroidal momentum and the unperturbed particle kinetic energy) via a generalized alternating direction implicit method. Since the success of next-generation fusion devices relies on their ability to confine fusion alpha particle products long enough to for them to transfer a substantial fraction of their energies to the reacting thermal particles via collisions, it is essential to develop efficient and robust capabilities to predict the level of energetic ion losses in tokamak experiments. The RBQ model is analytically constructed from first principles and is designed to efficiently evolve amplitudes of several interacting Alfv\'{e}n modes, in regimes of both overlapping and isolated resonances, while self-consistently relaxing the fast ion distribution function in the presence of collisions and turbulence. The developed framework employs realistic eigenstructures, mode damping rates and wave-particle interaction matrices.~Rigorous verification exercises have been undertaken in limiting cases in which there exist analytical solutions for single mode saturation levels. The quasilinear simulation output provide unprecedented mapping of fast ion flows and are useful in informing phase-space engineering solutions for neutral-beam-driven instabilities. The simulations are integrated with TRANSP with the calculated neutron loss rate, yielding reasonable quantitative agreement compared with measurements from DIII-D, which suggests that the integrated model is a promising predictor of fast ion confinement in scenario development studies.   

Live

Recently, JET has realized an ITER-relevant scenario with a sufficiently large population of MeV-range ions, exciting a variety of Alfvén Eigenmodes (AEs), by using the innovative 3-ion ICRF heating scheme [J. Ongena et al., EPJ Web. Conf. 157, 02006 (2017)]. Despite the presence of strong AE activity, a significant improved thermal ion confinement was observed. By means of the state-of-the-art gyrokinetic code GENE [F. Jenko et al., Phys. Plasmas 7(5), 1904 (2000)], it is shown that, unlike previous studies in JET with less energetic fast ions [J. Citrin et al., Phys. Rev. Lett. 111, 155001 (2013), J. Garcia et al., Nucl. Fusion 55, 053007 (2015)], the ITG-driven electrostatic transport is totally suppressed in the presence of a large MeV-range fast-ion population. Realistic nonlinear electromagnetic simulations with three ion species and kinetic electrons are presented to unveil a complex interplay between AEs and nonlinearly generated zonal flows. Evidences of such an interplay rely on the enhancement of ZF shearing concurrently with the onset of the fast ion electrostatic energy flux, and it is thereby envisaged to be the underlying mechanism for the reduction of the ion-scale microturbulence. In these conditions, the magnetic fluctuations dominate the thermal turbulent transport, leading to a pure magnetic system in which the fast-ion transport is dominant. Extended studies show that negative magnetic shear further reduces such fast ion transport by stabilizing TAEs. In turn, this has led, for the first time on JET, to an optimum plasma state where both thermal and fast ion transport are reduced.   

Live

A series of DT experiments, including the JET DT campaign, SPARC, and ITER, are expected to have large alpha particle populations. In some cases these populations dominate plasma heating and control tokamak behavior. Such experiments motivate new attention to the theory and modelling of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from magnetohydrodynamic modes like Alfv\'{e}n eigenmodes and neoclassical tearing modes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power, or damage to device walls. Alpha interaction with these perturbations is often studied with single particle theory. In contrast, we derive a drift kinetic formulation capable of calculating the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided the frequency and periodicity can be studied drift kinetically). Novel features of this technique include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits, and finite orbit effects. The calculated heat flux scales with the square of the perturbation amplitude and increases with toroidal mode number. The heat flux expression can be used to derive a constraint on mode amplitude for avoidance of significant alpha depletion. The talk concludes by discussing the implications of the work for future DT experiments. For example, a simple saturation condition suggests that toroidal Alfv\'{e}n eigenmodes in SPARC will not lead to significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, could cause significant transport.   

Live

Alfv\'{e}n eigenmodes with frequency close to the ion cyclotron frequency (f $=$ 0.58 f$_{\mathrm{ci}})$ are stabilized via a controlled energetic ion density ramp for the first time in a fusion research plasma. The particle injection rate of a neutral heating beam is slowly decreased while holding particle energy constant in a low field (B$_{\mathrm{T}}=$ 1.28T) DIII-D discharge. A mode is abruptly stabilized as the injection rate crosses below a critical threshold, providing a controlled demonstration of the competition between fast-ion drive and wave damping processes. The mode amplitude scaling with injection rate is consistent with the theoretical scaling for single mode collisional saturation near marginal stability, notably weaker than the previously established scaling from simulations of GAEs in the collisionless regime and far from marginal stability. Analysis of the fast-ion population shows that the mode is driven by anisotropy in the distribution for a Doppler-shifted cyclotron resonant (DCR) high-energy subset of the fast ions. The mode is identified as a shear-polarized global Alfv\'{e}n eigenmode (GAE) via the measured frequency in conjunction with AE dispersion relations and the resonance condition for fast-ion drive. This is the first identification of a DCR GAE in a conventional aspect ratio tokamak (R/a \textgreater 2). The measured frequency of the mode agrees with predictions of linear theory for DCR AE stability [Lestz, PoP 2020] and simulations using the hybrid MHD code HYM [Belova, PRL 2015]. Both models predict DCR GAEs to be the most unstable modes for these plasma conditions and fast-ion distribution in this frequency range. Measurements of the GAE density perturbation show the mode is core localized with a broad spatial structure, as seen in HYM simulation. These results are a significant advance in predictive capability for DCR instabilities in fusion plasmas.   

Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

The physical picture of interacting magnetic flux tubes provides a useful paradigm for certain plasma dynamics in a variety of astrophysical environments, such as the solar corona, the heliosheath, and Weibel-generated magnetic fields in supernova shocks. We investigate a system of parallel flux tubes as well as more generic magnetically dominated turbulent systems, of which the long-term evolution is dictated by the mergers of magnetic structures. We propose that the mergers are dynamically constrained by the conservation of ideal invariants (the magnetic potential and axial fluxes of each tube), and the flux tubes evolve in a critically-balanced fashion (along the direction perpendicular to the merging plane). An analytical model for the time evolution of quantities such as the magnetic energy and the energy-containing scale is constructed in the reduced-magnetohydrodynamic description, as borne out by our direct numerical simulations. An important conclusion is that such systems exhibit an inverse transfer of magnetic energy that terminates only at the system scale. Magnetic reconnection is identified as its underlying key mechanism and sets the time scale of the system evolution. This quantitative description of inverse energy transfer could improve our understanding of longstanding problems such as coronal heating, galactic magnetogenesis, and high-energy emission in gamma-ray bursts. As an example, we estimate the scale and strength of the initial seed field for the Galactic dynamo problem by considering the interaction between inverse magnetic transfer and ambient galactic turbulence.