Fast Ion Population Research Articles

Experimental and numerical investigation of the Doppler-shifted resonance condition for high frequency Alfvén eigenmodes on ASDEX Upgrade

Abstract The Doppler-shifted resonance condition for high frequency Alfvénic eigenmodes has been extensively studied on ASDEX Upgrade in the presence of one or a combination of two neutral beam injected (NBI) fast ion populations. In general, only centrally deposited NBI sources drive these modes, while off-axis sources globally stabilize the mode activity. For the case of a single central NBI source, the observed trend is: the highest frequency modes are driven by the lowest energy and lowest pitch angle NBI sources, in line with the expectation from the Doppler-shifted resonance condition. The expected mode frequencies are determined analytically from the two-fluid cold plasma dispersion relation and the most unstable frequency relation, while the mode growth rates are estimated using the fast ion slowing down distribution functions from the ASCOT code. The overall mode frequency trend in a source-to-source variation is tracked, although a systematic overestimate of ∼1 MHz is observed. Possible causes of this overestimate include the finite size of the resonant fast ion drift orbit and non-linear effects such as mode sideband formation. Alternatively, the expected mode frequencies are determined by tracking the growth rate maxima trajectories, this method improves the agreement with the experimentally measured values. A combination of two central mode-driving NBI sources results in the suppression of the mode driven by the lowest energy and the lowest pitch angle NBI source. Computing the analytically expected mode frequency following the method outlined above, again, generally tracks the experimentally observed trend. The mode’s Alfvénic nature allows for a practical application to track the core hydrogen fraction by following the mode frequency changes in response to a varying ion mass density. Such application is demonstrated in a discharge where the average ion mass is varied from ∼2m p to ∼1.5m p (where m p is the proton mass) via a hydrogen puff in a deuterium plasma, in the presence of a strong mode activity. The expected mode frequency changes are computed from the existence of the resonance condition, and the values track the measured results with an offset of ∼0.5 MHz. Overall, the results suggest an intriguing possibility to monitor and control the D-T ion fraction in the core of a fusion reactor in real time using a non-invasive diagnostic.

OPTEMIST: A neutral beam for measuring quasi-omnigenity in Wendelstein 7-X

A new neutral beamline (OPTEMIST) uniquely capable of exploring the predicted improvement of fast ion confinement in Wendelstein 7-X (W7-X), which comes with increasing plasma beta, is proposed. As the plasma beta increases in the W7-X device, the high mirror magnetic configuration has drift orbits that begin to close, enhancing the confinement of the deeply trapped particles. The existing neutral beam system is found to produce particle populations that do not adequately probe the deeply trapped orbits. Fast tritons generated by thermal deuterium–deuterium fusion reactions are found to probe the necessary conditions for demonstrating this effect. However, it is found that diagnostically measuring this effect will be difficult. A scoping study of a neutral beamline that directly populates the trapped orbits is performed. It is found that a monoenergetic population of 120 kV injected protons provides the largest confinement enhancement in the fast ion population as the plasma beta is increased. The necessity to raise plasma density to increase plasma beta results in blinding of spectroscopic beam measurements by bremsstrahlung. An array of novel fast ion loss detectors that would adequately assess the confinement of these particles is proposed.

Active control of Alfvén eigenmodes by external magnetic perturbations with different spatial spectra

Alfvén eigenmodes have been suppressed and excited in tokamak plasmas by (just) modifying the poloidal spectra of externally applied static magnetic perturbations. This effect is observed experimentally when toroidal spectra of n = 2, n = 4 as well as a mixed spectrum of n = 2 and n = 4 is applied. Under the n = 2 magnetic perturbations, the modes are excited or suppressed by modifying the coil phasing between the upper and the lower set of coils. Regardless of the absolute rotation, an even parity for the n = 4 perturbation is observed to reduce the amplitude of the Alfvénic instabilities, while an odd parity amplifies it. To combine the stabilizing (and destabilizing) effect of n = 2 and n = 4, a mixed spectrum is applied, finding similar reduction (and amplification) trends. However, the impact on the mode amplitude is more subtle, due to the reduced coil current required for a mixed spectrum. The signal level on the fast-ion loss detector is sensitive to the applied poloidal spectrum, which is consistent with Hamiltonian full-orbit modelling of an edge resonant transport layer activated by the 3D perturbative fields. An internal redistribution of the fast-ion population is induced, modifying the phase-space gradients driving the Alfvénic instabilities, and ultimately determining their existence. The calculated edge resonant layers for both n = 2 and n = 4 toroidal spectra are consistent with the observed suppressed and excited phases. Moreover, hybrid kinetic-magnetohydrodynamic (MHD) simulations reveal that this edge resonant transport layer overlaps in phase-space with the population responsible for the fast-ion drive. The results presented here may help to control fast-ion driven Alfvénic instabilities in future burning plasmas with a significant fusion born alpha particle population.

Recent results on high-β plasma confinement studies in the Gas Dynamic Trap

This paper is devoted to experimental studies of plasma confinement with high relative pressure ( $\beta$ ) in the Gas Dynamic Trap (BINP, Novosibirsk). In previous high- $\beta$ confinement studies a maximum local $\beta = 0.6$ was achieved in the fast-ion turning point, contributed to by a beam-driven population of fast ions with an anisotropic distribution function. In this study the axial magnetic field profile was modified to bring the turning points closer to one another, which effectively increased the energy density of plasma and pushed the $\beta$ value higher. Experiments were performed for two non-standard magnetic configurations, where the axial fast-ion confinement region length was reduced by 1.5 and 2 times compared with the standard configuration. The average values of $\langle \beta _{\perp } \rangle$ over the plasma central cross-section were found to be 0.1 and 0.18, respectively, for the two configurations, with the latter value significantly exceeding the $\langle \beta _{\perp } \rangle =0.08$ of the standard configuration, in which the previous record was set. Moreover, halving the fast ion confinement region almost doubled the D–D fusion proton flux from the trap centre compared with the standard configuration. The electron temperature in both new magnetic configurations was only slightly smaller than in the standard configuration. In addition, an effect of Alfvén ion–cyclotron instability (AICI) development on the pressure in the turning points is discussed. Presumably, with some decrease in magnetic field an evolving AICI does not result in considerable pressure axial redistribution, so the pressure maximum is in the turning points’ vicinity despite the instability.

Studying fast-ion populations using oscillations in solid-state neutral-particle analyzer signal and neutral-beam injection power.

A method for determining the fast-ion population density in magnetically confined plasmas as a function of pitch-radius, (λ, R), using a solid-state neutral-particle analyzer (ssNPA) signal and neutral-beam injection (NBI) power-output data has been developed. Oscillations in the NBI power output are replicated only in the active part of the ssNPA signal, allowing this to be separated from the passive and background signals, which usually complicate data from this diagnostic. Results obtained using this method are compared with those from standard techniques using data from the Mega-Amp Spherical Tokamak Upgrade spherical tokamak.

Experimental characterization of the active and passive fast-ion H-alpha emission in W7-X using FIDASIM

This paper presents the first results from the analysis of Balmer-alpha spectra at Wendelstein 7-X which contain the broad charge exchange emission from fast-ions. The measured spectra are compared to synthetic spectra predicted by the FIDASIM code, which has been supplied with the 3D magnetic fields from VMEC, 5D fast-ion distribution functions from ASCOT, and a realistic Neutral Beam Injection geometry including beam particle blocking elements. Detailed modeling of the beam emission shows excellent agreement between measured beam emission spectra and predictions. In contrast, modeling of beam halo radiation and Fast-Ion H-Alpha signals (FIDA) is more challenging due to strong passive contributions. While about 50% of the halo radiation can be attributed to passive signals from edge neutrals, the FIDA emission—in particular for an edge-localized line of sights—is dominated by passive emission. This is in part explained by high neutral densities in the plasma edge and in part by edge-born fast-ion populations as demonstrated by detailed modeling of the edge fast-ion distribution.

On how fast ions enhance the regulation of drift wave turbulence by zonal flows

This paper presents a mechanism for enhanced regulation of drift wave turbulence by zonal flows in the presence of a fast ion population. It demonstrates that dilution effects due to the energetic particles (EPs) have a far-reaching impact on all aspects of the nonlinear dynamics. The modulational growth of zonal flow shear and the corresponding evolution of drift wave energy are calculated with dilution effects. The coupled zonal flow growth and drift wave energy equations are reduced to a predator–prey model. This is solved for the fixed points, which represents the various states of the system. Results display a strong dependence on dilution, which leads to greatly reduced levels of saturated turbulence and transport. Implications for the FIRE mode plasma of KSTAR are discussed in detail. This model is perhaps the simplest dynamical one which captures the beneficial effects of EPs on confinement.

Turbulence stabilization in tokamak plasmas with high population of fast ions

This letter provides a new physical insight into the fast ion effects on turbulence in plasmas having a high fast ion fraction and peaked fast ion density profile. We elucidate turbulence stabilization mechanisms by fast ions that result in internal transport barrier formation in the fast ion regulated enhancement mode plasma. Both linear and nonlinear gyrokinetic simulations show that the dominant turbulence suppression mechanisms are the dilution effects. In particular, we find that turbulence can be sufficiently suppressed solely by an inverted main ion density gradient due to fast ions, for the first time. New physical findings reported here improve our understanding of fast ion effects on turbulence, essential for fusion energy production where . Moreover, they will open up a new methodology to control plasma turbulence applicable to a wide range of plasma confinement regimes.

Stabilization of the Alfvén-ion cyclotron instability through short plasmas: Fully kinetic simulations in a high-beta regime

The Alfvén-ion cyclotron (AIC) mode is an instability that can be driven in magnetized plasmas with anisotropic pressure. Its chief deleterious effect is the driving of enhanced pitch-angle scattering of ions. Although the AIC mode has been observed in several mirror devices, it has not yet been observed in FRC devices developed by TAE Technologies [H. Gota et al., Nucl. Fusion 61, 106039 (2021)]. Previous theoretical work [T. Tajima et al., Phys. Rev. Lett. 39, 201 (1977)] has suggested that sufficient axial inhomogeneity, quantified by a critical axial plasma length, can stabilize this mode. This stabilization mechanism is examined in fully kinetic particle-in-cell simulations with one spatial dimension modeling a simplified magnetic mirror geometry for a plasma with β∼1. A fast-ion population provides the driving anisotropy for the AIC mode, and the resulting effect on the fast-ion pitch angle distribution is examined. The severity of mode activity is recorded for a scan of plasma lengths for multiple fast-ion injection angles. This scan yields critical lengths that show good qualitative agreement with those from the past theoretical work.

ORBIT simulations of fast ion power loads on the wall of the Divertor Tokamak Test

Neutral beam injection in tokamaks produces a population of fast ions, which interact with 3D magnetic fields in a variety of ways, often resulting in energetic particle losses in very short times to the wall. Careful design of neutral beams and active control of error fields helps to keep these losses to a minimum. Nevertheless, past experience in tokamaks in the 1980s and detailed simulations for future machines, such as International Thermonuclear Experimental Reactor, suggest that very localized fast ion losses (‘hot spots’) can be present, even if the overall losses are low. In this paper, we discuss this issue in the Divertor Tokamak Test (DTT) project, and we show that in the standard single-null full-power scenario of the DTT, fast ions produce two hot spots, corresponding approximately to the beam injection and exit toroidal angles: the former being mainly due to prompt losses/passing particles, while the latter is due to trapped ions. However, the maximum power load in these spots is of the order kW m−2, below the tolerance of plasma-facing components of the machine.

Analysis of high frequency Alfvén eigenmodes observed in ASDEX Upgrade plasmas in the presence of RF-accelerated NBI ions

High frequency Alfvén eigenmodes in the ion cyclotron frequency range are actively researched on the ASDEX Upgrade tokamak (AUG). The general properties of this particular mode type are: (a) the mode is beam-driven and, if excited, can persist for the entire duration of the beam-on time window; (b) the mode is sub-cyclotron with the frequency ω ∼0.5ω ci, where ωci corresponds to the on-axis cyclotron frequency of the beam ions; (c) the mode propagates in the counter-current/counter-injection direction; and (d) the field-aligned (∼toroidal) mode number is large: |n //| ∼50. It has been observed on AUG that radio frequency- (RF)-acceleration of beam-injected ions at the 3rd cyclotron harmonic significantly expands the number of excited modes. In this work we demonstrate how this observation is consistent with the global Alfvén eigenmode (GAE) behavior. The RF-driven fast ion population is modeled using a combination of an orbit-following Monte Carlo code (ASCOT-RFOF) and an electro-magnetic wave code (TORIC). The application of this code combination is a first to model beam-ion RF-acceleration at the 3rd cyclotron harmonic. The RF-accelerated fast ion distributions are then used to analytically calculate anisotropy-driven mode growth rates. We see that the region of positive (unstable) growth rates is expanded by RF-accelerated fast ions in both the frequency and the mode number directions for the GAEs, consistent with the measurements. Although the compressional Alfvén eigenmode growth rates are also positive for our particular fast ion distributions, the growth rate values are ∼3 orders of magnitude lower. The plasma conditions on AUG are more destabilizing to the GAEs. Overall, our results are consistent with the observation of similar modes on other conventional tokamaks, namely JT-60U and DIII-D.

Parametric Decay Instabilities during Electron Cyclotron Resonance Heating of Fusion Plasmas, Problems and Possibilities

We review parametric decay instabilities (PDIs) expected in connection with electron cyclotron resonance heating (ECRH) of magnetically confined fusion plasmas, with a specific focus on conditions relevant for the ITER tokamak. PDIs involving upper hybrid (UH) waves are likely to occur in O-mode ECRH scenarios at ITER if electron density profiles allowing trapping of UH waves near the ECRH frequency are present. Such PDIs may occur near the plasma center in ITER full-field scenarios heated by 170 GHz O-mode ECRH and on the high-field side of half-field ITER plasmas heated by 110 GHz or 104 GHz O-mode ECRH. Additionally, 110 GHz O-mode ECRH of half-field ITER scenarios may have low ECRH absorption, due to the electron cyclotron resonance being located on the high-field side of the main plasma. This potentially allows PDIs driven by a significant amount of ECRH radiation reaching the UH resonance in X-mode to occur, as X-mode radiation can be generated by reflection of unabsorbed O-mode radiation from the high-field side wall. The occurrence of PDIs during ECRH may damage microwave diagnostics, such as the electron cyclotron emission and low-field side reflectometer systems at ITER, as well as complicate the calculation of heating and current drive characteristics. However, if PDIs are induced in a controlled manner, they may provide novel diagnostic tools and allow the generation of a moderate fast ion population in plasmas heated only by ECRH.

Upgrade of the neutral beam heating system on the TCV tokamak – second high energy neutral beam

The TCV tokamak continues to leverage its unique shaping capabilities, flexible heating systems and modern control system to provide a stepladder approach for extrapolations of experimental results from different machines to ITER and DEMO. TCV's configurational flexibility has recently been enhanced by the installation of two heating neutral beams, new dual frequency gyrotrons, removable divertor gas baffles together with upgrades of its diagnostic infrastructure.Plasma regimes with high plasma pressure, a wider range of temperature ratios and significant fast-ion population are now attainable on TCV. A 1.3 MW/28 keV heating beam (NBI-1) has been operated on TCV from 2015 introducing the direct ion auxiliary heating. A second 1MW/50–60 keV high-energy neutral beam (NBI-2) has since been procured, manufactured and installed on TCV in July 2021. NBI-2 injected near anti-co-linearly to NBI-1 is designed to probe plasma physics issues of higher plasma density, fast ion plasma interactions with static and dynamic fields and plasma rotation. The higher NBI-2 energy greatly enhances the operational space for fast ion studies. NBI-2 commissioning is presently ongoing in parallel with TCV experiments using both NBIs.This paper summarises the experience with intensive use and improvements of the NBI-1, together with the status of NBI-2 commissioning.

Imaging Neutral Particle Analyzer Engineering Design and Installation for the ASDEX Upgrade Tokamak

An imaging neutral particle analyzer (INPA) has been installed in the ASDEX Upgrade (AUG) tokamak to provide simultaneous measurements of the radial profile and the energy of the confined fast-ion (FI) population. The INPA diagnostic leverages the advantages of neutral particle analyzers (NPAs) and FI loss detectors (FILDs) by measuring charge exchange (CX) neutrals ionized by an ultrathin carbon foil is deflected into a scintillator by the local magnetic field. The design of this diagnostic has been developed under a series of constraints, such as the lack of space and hazardous environment (high level of neutron and gamma radiation), the need of high precision in the alignment of the nonsequential optical system (with six optical axes), and the optimization of the scintillator plate (signal emitter). To this end, a modular and adjustable design has been pursued with several degrees of freedom to ensure precise positioning during the installation and optical calibration. The induced electromagnetic and thermal stresses have been assessed and compared against the material limits of the detector, showing that no significant stress is expected for the system. The thermal analysis shows that the diagnostic scintillator can work efficiently during normal operation conditions. The CAD design, a comparison between the synthetic and real optical signals and the mechanical assessment [based on finite element analysis (FEA)], is presented in this contribution.

ITER collective Thomson scattering-Preparing to diagnose fusion-born alpha particles (invited).

The ITER Collective Thomson scattering (CTS) diagnostic will measure the dynamics of fusion-born alpha particles in the burning ITER plasma by scattering a 1MW 60GHz gyrotron beam off fast-ion induced fluctuations in the plasma. The diagnostic will have seven measurement volumes across the ITER cross section and will resolve the alpha particle energies in the range from 300keV to 3.5MeV; importantly, the CTS diagnostic is the only diagnostic capable of measuring confined alpha particles for energies below ∼1.7MeV and will also be sensitive to the other fast-ion populations. The temporal resolution is 100ms, allowing the capture of dynamics on that timescale, and the typical spatial resolution is 10-50cm. The development and design of the in-vessel and primary parts of the CTS diagnostic has been completed. This marks the beginning of a new phase of preparation to maximize the scientific benefit of the diagnostic, e.g., by investigating the capability to contribute to the determination of the fuel-ion ratio and the bulk ion temperature as well as integrating data analysis with other fast-ion and bulk-ion diagnostics.

Modelling the Alfvén eigenmode induced fast-ion flow measured by an imaging neutral particle analyzer

An imaging neutral particle analyzer (INPA) provides energy and radially resolved measurements of the confined fast-ion population ranging from the high-field side to the edge on the midplane of the DIII-D tokamak. In recent experiments, it was used to diagnose fast-ion flow in the INPA-interrogated phase-space driven by multiple, marginally unstable Alfvén eigenmodes (AEs). The key features of this measured fast-ion flow are: (I) a fast-ion flow from q min and the injection energy (81 keV) towards lower energies and plasma periphery.(II) A flow from the same location towards higher energies and the plasma core, (III) a phase-space ‘hole’ at the injected energy and plasma core and (IV) a pile-up at the plasma core at lower energies (∼60 keV). Ad hoc energetic particle diffusivity modelling of TRANSP significantly deviates from the observation. Comparably, a reduced modelling, i.e. a combination of NOVA-K and ASCOT5 code with the measured mode structure and amplitude, generally reproduce some key features of the observed phase-space flow, but largely failed to interpret fast ion depletion near the plasma axis. At last, self-consistent, first-principle multi-phase hybrid simulations that include realistic neutral beam injection and collisions are able to reproduce most features of the time-resolved phase-space flow. During consecutive hybrid phases, an RSAE consistent with the experiment grows and saturates, redistributing the injected fast ions. The resulting synthetic INPA images are in good agreement with the measurement near the injection energy. The simulations track the fast-ion redistribution within the INPA range, confirming that the measured fast-ion flow follows streamlines defined by the intersection of phase-space surfaces of constant magnetic moment μ and constant E′ = nE + ωP ϕ , where n and ω are the instability toroidal mode number and frequency, and E and P ϕ the ion energy and toroidal canonical momentum. Nonperturbative effects are required to reproduce the depletion of fast ions near the magnetic axis at the injection energy.

Gyrokinetic simulation of low-n Alfvénic modes in tokamak HL-2A plasmas

The turbulence characteristics of plasmas with internal transport barriers in the HL-2A tokamak are analyzed by means of linear gyrokinetic simulations. It is found that turbulence is dominated by the ion temperature gradient (ITG) mode together with large-scale modes characterized by high-frequency electromagnetic fluctuation, which are destabilized by the steep ion temperature gradient in the weak magnetic shear regime. Comparison with solutions of analytical dispersion relations shows that their linear features match well with the beta-induced Alfvén eigenmode branch of the shear Alfvénic spectrum. It is further clarified that the large population of fast ions in these plasmas plays a stabilization role through the dilution mechanism in high-n ITG mode regimes.

Modelling of sawtooth-induced fast ion transport in positive and negative triangularity in TCV

Internal kinks are a common magneto hydro-dynamic (MHD) instability observed in tokamak operation when the q profile in the plasma core is close to unity. This MHD instability impacts both the transport of the bulk plasma (current, particle and energy transport) and minority species, such as fast ions. In tokamak à configuration variable (TCV) (R 0/a = 0.88 m/0.25 m) the fast ion population is generated in the plasma by neutral beam tangential injection of energies up to 28 keV. TCV features 16 active shaping coils permitting a great flexibility in plasma shape, including negative triangularity (δ) configurations that show surprisingly high confinement. This study focuses on the transport of fast ions induced by sawteeth, by comparing two triangularity cases and simulation results with experimental data. Comparison of two equilibria with opposite δ shows that the fast ion drifts are larger for δ < 0. Furthermore, the sawtooth-induced transport in this case is larger than δ > 0 in similar conditions. Comparison with experimental data confirms the dominance of the modification of thermal kinetic profiles following the sawtooth crash in explaining drops in the neutron rates and fast ion D-α signals. Additional fast ion diffusion, however, improves the interpretation of the experimental data. For δ < 0, the amplitude of the perturbation better representing the experimental data is larger. Finally, an exploratory study for 50 keV particles (soon available in TCV) shows that the situation does not worsen for such particles.

Experimental validation of an integrated modelling approach to neutron emission studies at JET

An integrated modelling methodology for the calculation of realistic plasma neutron sources for the JET tokamak has been developed. The computational chain comprises TRANSP plasma transport and DRESS neutron spectrum calculations, and their coupling to the MCNP neutron transport code, bridging plasma physics and neutronics. In the paper we apply the developed methodology to the analysis of neutron emission properties of deuterium and helium plasmas at JET, and validate individual modelling steps against neutron diagnostic measurements. Two types of JET discharges are modelled—baseline-like and three-ion radio-frequency scenarios—due to their diversity in plasma heating, characteristics of the induced fast ion population, and the imprint of these on neutron emission properties. The neutron emission modelling results are quantitatively compared to the total neutron yield from fission chambers, neutron emissivity profiles from the neutron camera, neutron spectra from the time-of-flight spectrometer, and neutron activation measurements. The agreement between measured and calculated quantities is found to be satisfactory for all four diagnostic systems within the estimated experimental and computational uncertainties. Additionally, the effect of neutrons not originating from the dominating D(D, n)3He reactions is studied through modelling of triton burnup DT neutrons, and, in mixed D-3He plasmas, neutrons produced in the 9Be(D, nγ)10B reaction on impurities. It is found that these reactions can contribute up to several percent to the total neutron yield and dominate the neutron activation of samples. The effect of MeV-range fast ions on the neutron activation of 115In and 27Al samples is measured and computationally validated.

Fast ion transport by sawtooth instability in the presence of ICRF–NBI synergy in JET plasmas

JET experiments have shown that the three-ion scenarios using waves in the ion cyclotron range of frequencies (ICRF) is an efficient way to build fast ion population through beam ion acceleration by radio frequency (RF) waves. Such a heating scheme is applied to plasmas with at least two thermal ion species. Analysis of mixed discharges with complex heating schemes requires a workflow that allows to model thermal and fast ion transport consistently. This paper is dedicated to modelling of a mixed plasma discharge with significant fraction of fast ions and contributes to development of fast ion transport models. For interpretive analysis with the TRANSP code a JET hydrogen–deuterium plasma discharge with neutral beam injection (NBI) and ICRF heating has been chosen. The task is complicated by NBI–ICRF synergy and plasma magnetohydrodynamic activity, like sawtooth crashes. D beam ions accelerated by RF waves form a high energy tail in fast ion distribution. Significant difference between the neutron rate computed by TRANSP and measured one is observed if the same diffusivity for electrons and ions is assumed. Sensitivity studies show that uncertainties in input plasma parameters and thermal ion transport models are crucial for modelling mixed plasma discharges and increased D transport is required to reach the plasma composition consistent with diagnostic measurements at the plasma edge. Fast ion redistribution by a sawtooth instability is characterised by non-resonant transport due to reconnection of magnetic field lines and resonant transport caused by resonance interaction between the instability and fast ions. With ORBIT simulations it has been shown that resonant interaction strongly affects fast ions of high energies, like beam ions accelerated by RF waves and fusion products. For the considered case, fast ion profiles simulated by ORBIT remain peaked after the sawtooth crashes.