Propagation of ion cyclotron emission in the DIII-D tokamak

Diagnosis of the fast ion population will be essential in future fusion reactors but will be challenged by harsh radiation environments, motivating development of novel diagnostic methods. One such technique entails measuring coherent ion cyclotron emission (ICE), a collective phenomenon wherein narrow peaks are excited at ion cyclotron frequency (⁠ $fci$⁠) harmonics of an energetic population (e.g., beam ions or fusion products). Magnetic pickup loops are often used to measure ICE and are integrated with the first wall, making them durable and potentially compatible with ITER and other reactor relevant devices.^2,3 However, the connection between observed ICE spectra and the fast ion population has not been sufficiently established, meriting diagnostic upgrades and dedicated experiments.

Anticipated in magnetic confinement devices as early as 1959,⁴ ICE has been seen on TFR,⁵ PLT,⁶ PDX,⁷ TFTR,⁸ JET,⁹ AUG,¹⁰ JT-60U,¹¹ KSTAR,¹² TUMAN-3M,¹³ NSTX(-U),¹⁴ DIII-D,¹⁵ EAST,¹⁶ LHD,¹⁷ W7-AS,¹⁸ and HL-2A.¹⁹ ICE resonances are typically found either in the core of the plasma or near the last closed flux surface (LCFS) and roughly determined by comparing the spacing between observed spectral peaks to $fci=qB/2πm$ values throughout the plasma, where q and m are the particle charge and mass, and the magnetic field (B) is discerned via equilibria reconstructions. Possible shifts in the ICE emission location due to a resonant Doppler shift (finite $k∥v∥$⁠, where $k∥$ is the parallel wavenumber and $v∥$ is the parallel fast ion velocity) are ignored. We can approximate $k∥≈nϕ/R$⁠, and for this study, the toroidal mode number $nϕ=5$ and radius $R=1.67$ m with a maximum parallel beam velocity of 81 keV would result in a $k∥v∥∼$ 1.3 MHz shift, which is much lower than the $f∼30$ MHz that is the focus of this work. While ignoring the Doppler shift is largely typical of ICE literature, some studies include its effects on ICE.^20–22 Historically, studies have largely focused on edge ICE as it is mainly observed in more reactor-relevant H-mode plasmas, both with^12,23–25 and without edge localized modes (ELMs). Peaks corresponding to roughly 1–9  $fci$ (and sometimes higher) as evaluated at the LCFS have been observed on DIII-D,^26–28 appearing near the time of the L-H transition and sometimes in conjunction with core ICE modes.²⁷ Edge ICE is not heavily dependent on neutral beam injection (NBI) geometry,²⁷ but instead likely driven by barely trapped ions with large excursion orbits.^8–10 Several driving mechanisms have been proposed to explain edge ICE, including the magnetoacoustic cyclotron instability (MCI),^20,29–33 compressional Alfvén eigenmodes,^34,35 ion Bernstein waves,^36–38 and spin-flip MASER emission.³⁷ Aside from ELMs, other fast ion-loss inducing instabilities can either stabilize or destabilize edge ICE, including off-axis fishbones²⁸ and toroidal Alfvén eigenmodes.¹⁵ 

ICE with resonances near the core of the plasma (deemed “core ICE”) is a burgeoning area of study and has been documented on fewer machines, namely, JFT-2M,³⁹ JT-60U,¹¹ DIII-D,^26,27 TUMAN-3M,⁴⁰ AUG,⁴¹ EAST,⁴² LHD,⁴³ and HL-2A.¹⁹ Contrary to its edge counterpart, core ICE on DIII-D depends heavily on NBI geometry with co- $IP$⁠, on-axis beams primarily exciting harmonics 1–4  $fci$ as evaluated at the magnetic axis, and the ctr- $IP$ beams exciting 1–7  $fci$⁠.^27,44 Off-axis beams have not been observed to destabilize ICE.^27,44 Possible mechanisms for core ICE include the MCI^{25,41,42,45,46} or possibly electrostatic modes.²⁵ 

Following upgrades to the ICE diagnostic system⁴⁷ on DIII-D, recent experiments have explored mode structure of both core and edge ICE in deuterium L- and H-mode plasmas.⁴⁴ The modes exhibited compressional polarization at the plasma edge, and core ICE toroidal mode numbers were calculated as roughly $n∈[−10,5]$⁠.⁴⁴ The modes were also found to be poloidally extended as loops on both the low- and high-field side (LFS and HFS) of the machine observed the same modes. In these studies, the focus was characterizing core and edge ICE in conditions that were held as constant as possible and with the plasma at a fixed distance from the loops. However, previous studies concerning low-frequency whistler modes (⁠ $f≳10fci$⁠) observed decreasing mode crosspower as the distance between the plasma and the detecting loops was increased.¹ This dependence was attributed to the evanescent region growing larger and attenuating the modes as they propagated to the detecting loops. At sufficiently low densities, fast waves—one of the interpretations of ICE—are evanescent like whistlers.^48–50 

Discerning the extent to which ICE frequency, amplitude, and mode structure depend on shifts in the plasma location vs characteristics of the fast ion population is necessary for ICE to serve as a measure of fast ion properties. Simultaneously, investigating how the size of the vacuum region between the plasma and the pickup loops affects the aforementioned ICE mode properties may inform evaluations of diagnostic sensitivity in future devices. Disentangling these effects may help reconcile experimental observations with synthetic diagnostic measurements in future modeling efforts. This work aims to investigate at least some of these effects and motivate further investigations in both DIII-D and future devices.

Section II details the experimental setup and the ICE diagnostic. Section III concerns core ICE in L-mode plasmas, and Sec. IV explores edge ICE in H-mode plasmas. Conclusions are presented in Sec. V.

The L-mode studies presented here build on ICE^27,51 and sub-cyclotron⁵² work previously conducted on DIII-D. The L-mode plasmas in this experiment were of a diverted upper single null shape [Fig. 1(a) in blue] with the ion $∇B$ and curvature drifts directed away from the divertor to prevent accessing H-mode.⁵³ These shots had toroidal magnetic field strengths of $|BT|$ = 1.25 and 2.17 T, plasma current of $IP$ = 0.6 MA, core electron densities of $ne∈[1.5,3]×1013$ cm⁻³ as measured by the CO2 interferometer diagnostic,⁵⁴ and core electron temperatures of roughly $Te∈[1,3]$ keV determined by the electron cyclotron emission diagnostic⁵⁵ [Fig. 2(c)]. The shot with $|BT|$ = 2.17 T is primarily considered in this work, as it was the only L-mode shot featuring a scan in plasma proximity to the outer wall (discussed further in Sec. III). These plasmas were originally designed to probe mode dependence on the fast ion distribution by cycling through a variety of neutral beam configurations [Fig. 2(b)] with beam energies ranging from roughly 50 to 81 keV and beam powers from 1 to 2.5 MW. Though some of the beams can be tilted vertically with respect to the magnetic axis, these beams have not been observed to drive ICE,^27,44 and so only pulses from on-axis beams are considered. The density and temperature in the scrape off layer (SOL) and edge of the plasma were measured via the midplane reciprocating probe,⁵⁶ which was plunged twice during the shot. Figure 3 depicts the resultant density and temperature vs radius (⁠ $∼$ 2.28–2.38 m) from a plunge centered about 3900 ms. The density reached a maximum of roughly 6.5  $×1012$ cm⁻³ just inside the LCFS, and the temperature ranged from $∼$ 2 to 13 eV. Full profiles of temperature are gathered from Thomson scattering⁵⁷ and electron cyclotron emission⁵⁵ measurements, and the density profiles from Thomson scattering and reflectometry⁵⁸ as a function of $ρ$⁠.

The H-mode plasmas in this experiment were of a diverted lower single null shape [Fig. 1(a) in red], with $|BT|$ of either 1.65 or 1.95 T, $IP$ = 0.95 MA, $q95∈[5,5.8]$⁠, $βN∈[1.75,3]$⁠, $ne∈[1.5,6]×1013$ cm⁻³, and $Te∈[1,2.5]$ keV. These shots start in L-mode and transition to H-mode around 1550–1650 ms (determined by a sharp decrease in $Dα$ signal), and consequently the apparent ICE resonance shifts from near the magnetic axis to around the LCFS. Through the H-mode phase, the beam power is increased in steps from 2.6 to 5.2, 7.2, and then 9.2 MW. Three of these H-mode shots feature a scan in plasma-outer wall proximity similar to that conducted in the 2.17 T L-mode shot, as detailed further in Sec. IV.

The toroidal LFS and HFS loops used to collect outer- and inner-wall autopower spectrum measurements of toroidal magnetic field fluctuations (⁠ $δBtor$⁠) are located at $ϕ=248.0$° [Fig. 1(a), orange] and $ϕ=260.7$° [Fig. 1(b)], respectively. These two loops are somewhat displaced (toroidally by $∼12.7$°, vertically by roughly 12.3 cm), and the effects of eddy currents are assumed to be negligible. The long LFS toroidal loops used to calculate toroidal mode numbers (Sec. III B) are at a lower vertical position near the midplane of the machine, and the possible loop pairs are separated toroidally by $Δϕ=$ 13.1, 17.6, and 30.7°. As the digitizer employed by this diagnostic has a sampling rate of 200 MSamples/s, 100 MHz lowpass filters (Mini-Circuits BLP-100+) were used for both the small poloidal and toroidal loop channels in an attempt to suppress $f>100$ MHz aliased signals. These filters nominally have a DC-98 MHz passband and 3 dB $fcutoff$ of 108 MHz.⁵⁹ 

Though none of the loops are absolutely calibrated, the HFS and small LFS loops' signals are expected to be comparable, considering cable losses and loop area size (15 and 19 cm², respectively). Furthermore, all ICE channels are dispersionless in the frequency range considered here and have extremely similar frequency responses (including all components from the in-vessel loops to the cables in the data acquisition room as illustrated in Ref. 47).

During the main phase of the 2.17 T L-mode shot, up to seven different NBI geometries were cycled, as depicted in Figs. 2(a) and 2(b). The 2.5 MW (81 keV) near-tangential, on-axis beam pulses [e.g., from 1940 to 2060 ms as shown in Fig. 2(b)] in particular consistently excited the deuterium ion cyclotron frequency here is $fci≃16$ MHz. As illustrated in Fig. 2(a), modes appear at $f/fci∼$ 2, 3, and 4, with the second harmonic having the highest amplitude by a factor of roughly 10. However, these modes do not necessarily occur at a fixed frequency but instead can downsweep by up to $∼$ 500 kHz throughout the course of a beam pulse [Figs. 4(a) and 4(c)]. In the case of the aforementioned 2.5 MW beam pulse, the line-averaged density and core temperature both increase [Fig. 4(b)], as do the magnetic axis position and the proximity of the LCFS at the midplane to the outer wall (termed the “gapout” parameter in DIII-D and automatically computed as part of the equilibrium reconstruction). However, a frequency downshift is still present for ICE during a pulse from a beam with the same geometry but lower power [Fig. 4(c)], when the line-averaged density and core temperature do not change appreciably [Fig. 4(d)]. In both cases, there is sub-harmonic splitting which has been observed before on DIII-D^27,44 and is explored further in Sec. III B.

Equilibria reconstructions constrained by the motional Stark effect (MSE) diagnostic⁶⁰ indicate that gapout and the magnetic axis shift at least slightly with each beam pulse. These equilibria are averaged over 4 ms (at 4 ms intervals) on a 129  $×$ 129 grid. The output magnetic field strengths $B(R)$ are then used for comparison against the highest peaks detected in the autopower measured by an ICE loop on the outer wall, as shown in Fig. 5(a). The detected peaks (centered about the aforementioned equilibria intervals) are shown in yellow, and then the nearest match to these peaks in the equilibria data (⁠ $fci(R)=qeB(R)/2πmD$⁠) are represented by magenta dots, $fci$ corresponding to the magnetic axis determined by the equilibrium reconstruction in red, and the LCFS in lime (which has been offset by 9 MHz for plot readability). ICE frequency tracks best with the magnetic axis position, as the downsweeping over the duration of the beam pulse aligns well with the axis shifting outwards, whereas $fci$ calculated at the LCFS appears somewhat stable throughout this pulse. This dependence on the magnetic axis position is replicated to a lesser extent during pulses from other beams, which are either near-perpendicular with respect to the centerpost and/or operating at a much lower power. In the latter case, the beams impart less pressure and thus likely introduce a lower Grad-Shafranov shift such that the movement of the magnetic axis is comparatively subtle. Similar observations of ICE shifting with the plasma have been made of chirping ICE on NSTX(-U)^14,61 and core ICE on AUG.⁶² As depicted in Figs. 5(b) and 5(c), the density and temperature profiles do not possess discernible features that track with the suspected ICE emission locations. These findings agree with previous observations in DIII-D,²⁷ as well as NSTX(-U),¹⁴ LHD,¹⁷ and TUMAN-3M,⁴⁰ that the observed ICE frequency does not follow changes in density. Further investigations could try employing longer beam pulses to allow the magnetic axis to settle into a final [R, Z] position and, if the frequency remains fixed, even more definitively rule out density as a factor in frequency sweeping.

In addition to the plasma's slight movements due to beam injection, a dedicated shaping scan was conducted toward the end of the aforementioned $|BT|=2.17$ T L-mode shot to explore how the distance between the plasma and the loops affects measured ICE signals. Figure 6 illustrates this end phase, where the gapout parameter was changed to alter the vacuum region near the outer wall (Fig. 6) while four different beams were pulsed in succession for a duration of 110–170 ms [Fig. 6(b)]. The distance between the centerpost and the plasma was held constant; consequently, the magnetic axis position also shifted slightly, approximately half as much as gapout. Time windows during pulses from the same 2.5 MW on-axis beam considered in Sec. III A are highlighted by colored rectangles. The line-averaged electron density and core temperature are depicted in Fig. 6(c), where density measurements ranged from $2.6 to 4.8×1013$ cm⁻³ and temperature ranged from roughly 0.7 to 2.2 keV.

Autopower spectra as measured by the LFS and HFS loops described in Sec. II are compared with the harmonics' relative amplitudes easiest to discern using the time-averaged spectrum data (Fig. 7). In keeping with Sec. III A, the second harmonic remains dominant. Its likely resonance location seems to shift closer to that of the magnetic axis as gapout increases; however, recall that the magnetic axis itself moves slightly when gapout is increased. Before the gapout scan [Fig. 7(b)], the amplitudes measured by both loops are quite similar—however, for subsequent pulses with different average gapout values (markedly, the smallest at 3.38 cm), the LFS loop detects a slightly stronger $∼2fci$ peak than the HFS loop. Aside from the period before the scan in Fig. 7(b), the second harmonic amplitude generally decreases as gapout is increased, though obviously is still detectable by the loops. The third harmonic is absent for the pulses that have the most extreme average gapout values [Figs. 7(a) and 7(d)].

Each of these peaks exhibit fine-scale frequency splitting, as is particularly evident for the second harmonic (Fig. 8). The ICE with the highest overall amplitude is observed in the period just before the gapout scan starts, at roughly 3140–3260 ms during a period with an average gapout value of roughly 7 cm [Fig. 8(c)]. This mode [Fig. 8(c)] exhibits a set of multiple strong spectral lines spaced roughly 150–200 kHz apart that persist through the beam pulse, as has been observed previously.²⁷ ICE onsets shortly after the beam is turned on (⁠ $≲10$ ms), and the modes briefly diminish or disappear entirely as sawteeth expel fast ions from the core [Figs. 4(a), 4(c), and 8(c)], returning soon after when the driving fast ion population is replenished and remaining until the beam injection ceases. For these core ICE cases, the NUBEAM Monte Carlo module⁶³ within the TRANSP transport code⁶⁴ is used to calculate the fast ion distributions at the beginning (not pictured here) and end of each beam pulse. The velocity profiles for each beam pulse are averaged over $R∈[165,195]$ cm (or roughly $ρ∼0−0.5$⁠) and over $|Z|<$ 15 cm to encompass the inferred emission location during the initial 20 ms (not pictured) and the last 50 ms of each pulse. All figures are normalized to appear on the same color scale. Though all distributions are peaked at a pitch of $v∥/v∼0.7$ with full, half, and third energies of roughly 81, 40.5, and 27 keV, there are significant differences in the fast ion density. The ICE case featuring the most fine-scale frequency splitting [Fig. 8(c)] occurs in conjunction with the velocity profile with the largest fast ion density of $∼2.5×1012$ cm⁻³ [Fig. 8(d)].

In the lowest fast ion density pulse [Fig. 8(a)], the delay between beam turn on and mode destabilization is $≳3$ times (or roughly $∼$ 20 ms) longer than observed for other pulses. When the mode does appear, it manifests as a solid spectral line. This mode is continuous over the duration of the beam pulse, as this time period is devoid of sawteeth. Toward the end of this beam pulse, six small blips appear nearly 900 kHz above the main mode [circled in green in Fig. 8(a)]. Unsurprisingly, the case with the longest delay between beam turn-on and mode destabilization [Figs. 8(a) and 8(b)] corresponded to the lowest fast ion density of $nfast∼1.5×1012$ cm⁻³. The spatial profiles of the fast ion distributions computed for each beam pulse examined here, generated by summing the fast ion distributions in velocity space, are very similar and as such are less likely to be driving changes in the ICE spectra than the velocity profiles.

This core ICE dependence on fast ion density is reminiscent of past observations from the JFT-2M device, where core ICE excitation mandated a beam-to-bulk plasma density ratio of $nb/ne>0.1%$⁠.³⁹ (Note, this ratio is unusually high, as ICE is excited in many machines with very small fast ion fractions.) Varying the bulk plasma density and temperature can effect significant changes in fast ion density, despite unchanging beam energy and geometry [Fig. 6(c)]. Said fast ion density is roughly proportional to the product of the beam power and slowing down time $τs$⁠,^65,66 the latter of which increases with low core $ne$ and high $Te$⁠. In the highest fast ion density case, the line-integrated core $ne$ is relatively low in the context of this particular L-mode plasma at $∼3.0×1019$ m⁻³ and core $Te$ is roughly 1.8 keV (both averaged over the course of the beam pulse) [Fig. 6(c)]. In comparison, over the course of the beam pulse with the lowest fast ion density, the line-averaged $ne$ decreases from roughly 4.2 to $∼3.2×1019$ m⁻³ and the core $Te$ nearly doubles from roughly 0.8 to 1.6 keV. In the case with the most ICE fine splitting, the slowing down time was 56 ms, whereas the ICE with one main spectral line corresponded to the shortest slowing down time of 35 ms. Comparisons of observed frequency splitting to predictions via various theoretical explanations are largely left for future investigations, though initial attempts have been made.⁶⁷ 

Further evidence suggesting that core ICE is insensitive to the gap between the plasma and the outer wall comes from simulations performed using the PETRA-M code.

To study the propagation of ICE in core and SOL plasmas, we use the full-wave simulation code Petra-M.^68,69 This code was developed to analyze plasma waves under various background conditions and has been widely used in fusion devices and space plasmas.^70–74 Its accuracy has been verified through code benchmarking activities.⁷⁵ The Petra-M code offers solutions in both 1D and 3D; for simplicity, this paper focuses on a 2D simulation assuming a cold plasma.

While previous numerical simulations of ICE concentrated on wave propagation in the plasma core,⁷⁶ we examine ICE propagation in both the SOL and core plasmas to compare with the experiments. We adopt the magnitude of the magnetic field from the L-mode, $|BT|=2.17$ T DIII-D shot#184342. To compare the gapout effect, we consider the smallest and largest gapouts of 3.38 and 13.04 cm, respectively, marked in pink and orange in Figures 9(a)–9(c).

Figures 9(d)–9(i) depict the fluctuating magnetic field in the $r,ϕ,z$ directions in the cylindrical coordinates (⁠ $|δBr|$⁠, $|δBϕ|$⁠, and $|δBz|$⁠) for 3.38 and 13.04 cm gapout, respectively. The fluctuating magnetic field is calculated by assuming the generated wave power is 2.5 MW. For the 3.38 cm gapout case in Figs. 9(d)–9(f), the simulation demonstrates a wave across the entire domain, with the wave power being more substantial in the core plasma than in the SOL due to lower collisionality. These waves exhibit a power enhancement in $δBϕ$⁠, which is highly parallel to the magnetic field line, confirming that these are compressional fast waves. Additionally, the wave power in $δBϕ$ differs slightly between the higher and lower magnetic field sides, with the power being slightly stronger on the lower side. Despite the wave absorption being much stronger on the lower magnetic field side, this is close to the wave source location, and the LCFS is near the boundary, making the power relatively easy to reach in this area. When waves are excited near the center of the plasmas, they propagate toward the SOL and are partially reflected near the LCFS due to the density gradient (see supplementary material Movie 1). They are then reflected back to the core of the plasma and eventually exhibit a quasi-standing wave mode. The waves are dampened near the LCFS due to higher collisionality. However, because the gapout is relatively short, the waves can reach the outer boundary on the lower magnetic field side. Although these waves would be reflected at the cutoff condition for the higher field side, the wavelength is long enough for the waves to reach the boundary on the higher magnetic field side.

The wave structure seen in Figs. 9(g)–9(i) for the larger gapout value of 13.04 cm is similar to that of the narrow gapout case in Figs. 9(d)–9(f). The compressional fast mode is predominantly present in the $Bϕ$ component and the waves oscillate globally, reaching the SOL. Due to the lower density in the SOL, the wavelength is long enough for the waves to reach the inner and outer measurement locations easily. In this case, the absorption profile in $ρ$ is similar to the case with the smallest gapout. However, the wave amplitude at the outer boundary becomes weaker compared to the case with a gapout width of 3.6 cm due to the wider gapout width. On the higher magnetic field side, there are no significant differences visible because the inner gap between the LCFS and the inner boundary is almost the same in both cases.

The results suggest that the ICE generated in the core of the plasma can propagate to both the lower and higher field sides, consistent with the experiments. Additionally, we found that the width of the gap does not have a significant effect on the wave propagation. However, the amplitude on the higher and lower magnetic field sides at the detected location depends on the wave eigenmode structure, which is strongly influenced by the source location and size. Therefore, the amplitude cannot be directly compared with the experiment. Moreover, because the wave damping rate in the SOL can significantly affect the wave power that reaches both magnetic field sides, it is crucial to investigate the wave-damping mechanisms in the SOL, which we plan to address in future work.

The second phase of the experiment explored edge ICE in H-mode plasmas whose basic parameters were described in Sec. II. Gapout scans, similar to those performed in the L-mode plasma in Sec. III and illustrated in Fig. 10, start at roughly 3500 ms. The average gapout value is decreased significantly from its original value of $∼$ 6 to 4 cm, and then back up to roughly 8 and then 12 cm. The line-averaged density is kept fairly constant throughout at $∼$ 5.75–6.25  $×1013$ cm⁻³; however, the core temperature decreases throughout the scan from $Te∼2.5$ to 1.8 keV [Fig. 10(c) in green and blue, respectively]. As these are standard H-mode plasmas, ELMs are present throughout most of the H-mode phase [Fig. 10(b) in purple].

In many cases here, ELMs do not suppress edge ICE but instead introduce a broadband RF signal in addition to the existing edge ICE peaks, as illustrated in Fig. 11 in red. To avoid this feature and study only the effects of gapout changes, ICE data can be considered during periods between ELMs, which here constitute time intervals of roughly 10–30 ms as illustrated in purple and green in Fig. 11(a). Higher harmonics may be obfuscated by aliased harmonics (⁠ $f>100$ MHz) and there exists a lower frequency (⁠ $∼$ 5 MHz) RF pickup signal often very close to $fci$ at the edge—thus, only harmonics 2–7  $fci$ are considered here. The effects of altering gapout on ICE amplitude are, as with core ICE in Sec. III B, most visible in the time-averaged data taken by LFS and HFS ICE loops (Fig. 12). Beginning with the response of the lower harmonics (⁠ $f/fci<5$⁠), the second harmonic generally features the largest difference between the inboard and outboard loops which increases with gapout, from roughly 470 kHz to nearly 900 kHz at the largest average gapout value of 12.39 cm. Note, differences in LFS and HFS-measured frequency are observed here for edge ICE, but were not seen for any gapout value in the core ICE studies. The gapout scan appears to disturb ICE such that different features are observed throughout the gapout scan than those in the “original” plasma.

Once the plasma is perturbed from this initial state [Fig. 12(b)], signal from the HFS is no longer upshifted, but instead the LFS loop routinely sees the second harmonic peak at slightly higher frequencies than its HFS counterpart. This is illustrated in Fig. 13(a), where this trend is observed in two other H-mode shots with gapout scans. Both of these shots are well matched in bulk plasma density and temperature, though one of the shots had a higher magnetic field strength of $|BT|=1.96$ T. The fourth harmonic does not exhibit a large frequency difference between inboard and outboard peaks; however, there is an amplitude difference that increases with gapout. This is replicated in two other H-mode shots [Fig. 13(b)] at different magnetic fields, where the log of the ratio of the fourth harmonic peak amplitudes as measured by the LFS and HFS loops generally increases with gapout, aside from points before the gapout scan (marked by an orange oval). The third harmonic appears very similar in amplitude and frequency in the inboard and outboard data for most gapout values, save for the time window with the lowest average gapout value, where the LFS loop observes the peak at a slightly higher amplitude. The fundamental harmonic also may see some differences in frequency between LFS and HFS measurements, and generally the amplitude is lower during the gapout scan than beforehand—however, this peak is near a $∼$ 5 MHz signal suspected to be stray RF pickup from a power supply that is sometimes detected, and thus is a little difficult to characterize. In all, there appears to be a slight trend in LFS vs HFS second harmonic frequency and fourth harmonic amplitude as gapout is changed, but nothing so significant to suggest the kind of mode attenuation previously seen with whistler modes.¹ All edge ICE harmonic frequencies follow shifts in the LCFS frequency very closely; all peaks are very nearly centered about $fci|LCFS$⁠, as shown in Fig. 12.

The higher harmonics also do not show any uniform trends as gapout is altered. As with the lower harmonics, higher harmonics of ICE are seemingly disturbed by the gapout scan such that the spectrum behaves differently in time periods beyond that depicted in Fig. 12(b). Peaks at $f≃$ 5, 6, and 7  $fci$ that were observed at nearly equal, relatively high amplitudes by both the inboard and outboard loops before the gapout scan are of much lower amplitudes in subsequent time windows, regardless of whether the average gapout value is larger [Figs. 12(c) and 12(d)] or smaller [Fig. 12(a)] than the initial average value of 6.83 cm. Furthermore, where there was little difference in amplitude between the two loops initially, the HFS loop is more sensitive to these harmonics in these later times. These higher harmonic trends hold for the other two shots with gapout scans. As with the lower harmonics, the higher harmonics' frequencies also very closely track changes in $fci|LCFS$⁠.

The velocity distribution of the fast ions for each time of interest in DIII-D#184354 is illustrated in Fig. 14, where all averages were taken during 23 ms intervals centered in the middle of the ELM-free time periods denoted in Figs. 10(b) and 10(c). In all cases, the spatial average is over the two [R, z] points that are closest to the LCFS at the outer midplane. The velocity profiles here are peaked at a pitch of $v∥/v=0.5$ with presumably some of the higher pitch particles ionizing in the edge. Some particles ionized on the inside of the plasma, due to the low density and concomitant low beam attenuation that allowed more neutrals to make it to the inner edge [e.g., Fig. 14(d), with the lowest density and thus highest amplitude at $P=1$]. The fast ion distributions for all gapout cases are exceedingly similar, save for a bump in the velocity distribution near half the injection energy (⁠ $∼$ 40 keV), which is more prominent for small gapout values. This may contribute to the small differences in spectra in Fig. 12 as ICE is driven by velocity space gradients; however, it is not clear whether this bump is significant enough to appreciably affect ICE. These bumps also do not correlate with the uniform decrease in high harmonic (⁠ $f≳5fci$⁠) amplitude illustrated in Figs. 12(a), 12(c), and 12(d).

Figures 14(e) and 14(f) depict bulk plasma profiles of $ne$ and $Te$⁠. Time-averaging windows of 20 ms were selected, centered roughly in the ELM-free time windows highlighted in Figs. 10(b)–10(d). Again, the equilibria used to determine $ρ$ were constrained by the motional Stark effect (MSE) diagnostic.⁶⁰ There appear to be slight changes in the density [Fig. 14(e)] at the edge of the plasma (⁠ $ρ≳0.95$⁠) between the different time periods, but no trends that correspond to the drastic changes in ICE signal from before and after the gapout scan is initiated. $Te$ at the edge is extremely similar for all time periods.

Other modes present could also instigate fast ion losses, which in turn may affect edge ICE activity. During the second power step (⁠ $Pinj∼$ 5 MW), m/n = 3/2 tearing modes arise and are present throughout the rest of all H-mode discharges [Fig. 10(d)]. However, the ratio of the measured neutron rate to that predicted by NUBEAM hovers around one throughout the H-mode phase, indicating that the tearing modes do not induce appreciable fast ion losses. Furthermore, the amplitude of these n = 2 modes decreases over the course of the discharge in a way that does not clearly align with ICE amplitude.

The only other modes present in these plasmas are ELMs. The associated fast ion losses have been observed to alter existing ICE¹² or, in some cases, to suppress it.^9,23,25 The ELMs in these plasmas appear to be type-I ELMs due to the relatively large change in stored energy they incur (⁠ $ΔWMHD/WMHD∼−5%$⁠); however, their amplitude and frequency change slightly throughout the discharge. A Gaussian ELM-detection method from the OMFIT⁷⁷ profile fitting package was used to identify ELMs in data from filterscope data with the resultant detected ELMs depicted in Fig. 15(b) and the time between them in pane (c). During the initial phase in the discharge, when the plasma is in H-mode but no shape changes have occurred, there are strong continual ICE harmonics at $f∼5,6,$ and $7fci$⁠. This continues until the gapout scan is initiated around 3700 ms (Fig. 15), which coincides with increased ELM frequency and decreased amplitude. This is also when the ICE appears to be disrupted, with primarily broadband RF signals visible in the spectrogram [Fig. 15(a)] rather than the strong continual harmonics seen prior. Around 4200 ms, when the next gapout scan value is reached, the frequency between ELMs decreases again and there is a slight concomitant increase in fifth, sixth, and seventh ICE harmonic amplitudes. During the last phase of the gapout scan, there does not appear to be a large change in ELM activity or ICE. Further work should investigate ICE dependence on tearing and ELM activity, potentially involving a survey of ICE behavior in different plasma scenarios with varied pedestal and ELM characteristics.

As edge ICE toroidal mode numbers have not yet been determined on DIII-D due to generally low coherence between probe signals compared to core ICE measurements, PETRA-M simulations akin to those in Sec. III C were not attempted without an estimate for $nϕ$ to use for the launched fast waves. However, whenever these toroidal mode numbers are determined, PETRA-M simulations might launch fast compressional waves from either right at or just outside the LCFS, to align with the frequencies observed in Fig. 12.

A recent experiment in DIII-D explored core and edge ICE in L- and H-mode plasmas, leveraging ICE diagnostic upgrades to explore mode propagation to the low- and high-field sides of the tokamak. Core ICE is minimally affected by the distance between the wall and the plasma, with no discernible trend observed when the gapout parameter was altered. Instead, inadvertent scans of the fast ion density are likely driving the changes observed in mode amplitude and fine splitting, with more spectral bands (⁠ $Δf∼$ 150 kHz) observed in the cases with higher fast ion densities. Second harmonic ICE was observed to track movements in the magnetic axis very closely, as even small shifts due to single beam injection appear in the ICE spectra as downshifts of up to roughly 500 kHz.

Simulations using the PETRA-M code saw no core ICE dependence on gapout, in agreement with experimental observations. Fast compressional waves were launched from a location roughly matching the experimental core ICE emission location, with the frequency (⁠ $f=30$ MHz) and toroidal mode number (⁠ $nϕ=5$⁠) of second harmonic ICE modes observed in Sec. III B. Bulk plasma profiles and equilibrium reconstructions from experiment were implemented. In both the largest and smallest gapout cases, the launched waves were able propagate through the SOL to reach the ICE probe locations on the centerpost and the LFS of the machine.

Similar scans of gapout were conducted during the end phase of H-mode plasmas to assess edge ICE dependence on the vacuum region. In these cases, differences in both frequency and amplitude were observed in the time-averaged spectra as measured by the LFS and HFS loops for specific harmonics. Contrary to the core ICE cases, there is little difference in the fast ion distribution for the various time windows of interest in the edge region and the dependence on gapout is not obvious. During the time periods with different average gapout values, there are changes in ELM frequency and amplitude which seem to correlate with variations in edge ICE amplitude (particularly that of the higher harmonics). It is still unclear as to whether it is local fast ion losses in the edge that affect ICE that change as gapout is altered, or perhaps changing pedestal conditions that then manifest in changes to the ELMs.

Though we observe small differences in ICE spectra in both L- and H-mode plasmas, these changes are somewhat small and potentially less relevant to the fast ion properties one might want to infer from a future ICE diagnostic. As ICE is still observed in all cases, even those with relatively large gapout values, it may be that future ICE diagnostics in reactors could be placed further from areas of high radiation without significantly degrading measurement capabilities.

See the supplementary material for Movie 1, which shows the time-dependent wave solutions in the ϕ direction ( δBϕ) for (a) 3.38 cm gap-out and (b) 13.04 cm gapout.

The authors would like thank to David Piglowski, Ben Penaflor, and the rest of the diagnostic and operations teams at General Atomics for their assistance. They also thank William S. Boyes for very helpful discussions. This work was supported by U.S. Department of Energy under DE-FC02-04ER54698, DE-SC0020337, DE-AC02-09CH11466, DE-FG02-07ER54917, DE-SC0020649, and DE-SC0018270. DISCLAIMER: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

The authors have no conflicts to disclose.

G. H. DeGrandchamp: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Project administration (equal); Visualization (lead); Writing – original draft (lead). W. W. Heidbrink: Conceptualization (supporting); Funding acquisition (lead); Project administration (equal); Resources (equal); Supervision (lead); Writing – review & editing (equal). X. D. Du: Data curation (equal); Investigation (supporting); Supervision (supporting). J. B. Lestz: Investigation (supporting); Supervision (supporting); Writing – review & editing (supporting). E.-H. Kim: Formal analysis (equal); Resources (supporting); Writing – original draft (supporting). S. Shiraiwa: Formal analysis (supporting); Software (supporting). M. A. Van Zeeland: Conceptualization (supporting); Supervision (supporting). J. A. Boedo: Formal analysis (supporting). K. E. Thome: Conceptualization (supporting); Methodology (supporting); Supervision (supporting); Writing – review & editing (supporting). N. A. Crocker: Supervision (supporting). R. I. Pinsker: Conceptualization (supporting); Supervision (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.