Radio frequency measurements of energetic-particle-driven emission using the ion cyclotron emission diagnostic on the DIII-D tokamak

Diagnosis of the fast-ion population in burning plasmas is critical to optimizing reactor performance. Superthermal ions, including fusion alphas, injected beam ions, and rf-accelerated ions, are responsible for heating the thermal ions to thermonuclear fusion temperatures. Thus an understanding of the confinement and dynamics of these energetic ions is critical to mitigating radial fast-ion transport and fast-ion losses, particularly the first wall damage from fast ions.¹ In modern-day tokamaks, energetic ions are often diagnosed using cameras and probes, which will not survive sufficiently long in a reactor neutron radiation environment.² 

An alternative diagnostic tool of fast ions in a burning plasma is a simple magnetic pick-up loop. Many modern fusion experiments have observed emission in the Ion Cyclotron Range of Frequencies (ICRFs) excited by energetic ions with such a diagnostic.³ This high-frequency emission is predicted to occur in ITER plasmas, driven by the various fast ions present.⁴ A magnetic pickup loop on ITER would be compatible with its D-T radiation environment and would serve as a passive non-invasive diagnostic that could also provide information about the reactor fast-ion population.

Recently on DIII-D,⁵ the Ion Cyclotron Emission (ICE) diagnostic has been re-established and significantly upgraded to measure this ICRF emission.⁶ Energetic ions, primarily ions generated by the neutral beams, have been observed to drive two categories of signals on DIII-D. The first energetic-ion-driven signal is referred to simply as Ion Cyclotron Emission (ICE), which this version of this diagnostic was established to measure. This emission with f ≥ f_ci where f_ci is the ion cyclotron frequency has been studied since the late 1980s on DIII-D,^7–9 and initial observations of this emission measured with the upgraded diagnostic were presented in 2016.⁶ ICE is sharply peaked at integer harmonics of f_ci. It has been detected on many past and present-day tokamaks: first on TFR,¹⁰ then in the D-T machines TFTR¹¹ and JET,¹² and more recently on ASDEX-U,¹³ JT-60U,¹⁴ and KSTAR^15,16 and also on the stellarator LHD.¹⁷ The other kind of energetic-ion-driven emission, characterized by f < f_ci, is the Compressional Alfvén Eigenmode (CAE), first documented on DIII-D in 2006.¹⁸ CAEs are observed regularly on the spherical tokamaks NSTX¹⁹ and MAST,²⁰ and the CAEs have been found to enhance energy transport on these devices.²¹ Another type of ICRF energetic-particle-driven emission, whistler waves with f ≫ f_ci, has recently been observed by this diagnostic on DIII-D. This is the first observation of whistler waves in a tokamak,²² which are excited by multi-MeV runaway electrons present in low-density n_e ∼ 10¹⁹ m⁻³ plasmas.

In this paper, we describe the DIII-D ICE diagnostic (Sec. II) and its data analysis and initial results (Sec. III).

At DIII-D, diagnostic locations are identified by their toroidal angle; this applies to all subsequent angle measurements. The ICE diagnostic consists of two outboard midplane systems as shown in Fig. 1. The two outer straps of the 180° ICRF antenna [System 1 in Fig. 1(a)] were instrumented for this diagnostic in 2015. These two straps are 10° toroidally apart. The second system of dedicated magnetic probes incorporated into the carbon tiles [System 2 in Fig. 1(b)] was restored in 2017. This system was previously used for density interferometer and ion species reflectometer measurements.^23,24 System 2 contains two antenna probes located behind the plasma facing portion of the carbon tiles with a spacing of 15° toroidally, separated by approximately 50° from System 1. Another tile antenna probe, separated poloidally from the other probes, is also used for low and high bandpass measurements and was previously described in the work of Heidbrink et al.⁹ These tile antenna probes (System 2 and bandpass) each consist of only a single loop to maintain their low inductance and thus high frequency response. Great care is taken to avoid contact between the tile antenna loops and neighboring tiles.

A block diagram of the electronic components of these two systems is shown in Fig. 2. The outputs of the antenna straps (System 1) connect to a plastic enclosure via a RG58 cable. Within the vacuum vessel, the antenna probes (System 2) connect to a SubMiniature version A (SMA) feedthrough via a semi-rigid bakeable vacuum-compatible coaxial cable with a characteristic impedance of about 30 Ω. On the air side of the feedthrough, the SMA connectors are connected in parallel to a 75 Ω impedance-matching resistor and 50 Ω semi-rigid cables. Another semi-rigid coaxial cable transmits the signal to a BNC breakout panel within the plastic box. Inside this box, both ICE systems then connect to safety breaks, designed to provide 5 kV DC isolation for both inner and outer conductors. All three systems use slightly different DC break designs, but all originate from the RF program. The signal is transmitted to the electronic annex via RG213 (System 1) or RG214 (System 2) cables that have an electrical length of at least 75 m. In the annex, the cables terminate on a BNC breakout panel. Within the DIII-D annex, RG58 cables are used. First, the signals are amplified by 5× (14 dB) with a 350 MHz SR445A preamplifier, and then, they are digitized using a 200 MHz GaGe CSE1642 digitizer. Typically, the signals are anti-aliased using a Mini-Circuits BLP-100+ low-pass filter before the amplifier, providing data below the 100 MHz Nyquist frequency. However, in the case of whistler waves, either the data are intentionally aliased using a Mini-Circuits BHP-100+ high-pass filter to acquire signals in the 100–200 MHz band or the data are mixed down to the 0–100 MHz band.

The frequency response of these systems is limited by the DC breaks. These breaks have an approximately flat electrical response from 1 MHz to ∼120 MHz, with a 3 dB point at ∼150 MHz. Data up to 200 MHz have been recorded. The frequency response of these breaks includes a few-MHz-wide resonance between 40 and 60 MHz, an artifact of the old design. Future designs of the DC breaks will improve the frequency response by removing this resonance and increasing the frequency bandwidth to higher frequencies, thus facilitating further study of whistler waves.

The magnetic fluctuation data are stored in MDSplus in 80 ms segments for up to 5.04 s of data. This amounts to 8 GB per channel per shot of data storage, typically 32 GB per shot. The data are recorded in volts with the range typically set to +/−1 V. A typical segment of raw data is shown in Fig. 3(a). Several high-frequency bursts of magnetic fluctuations are seen in this figure. As this magnetic diagnostic is unshielded in the machine hall, it is also susceptible to electrical noise and pickup. An example of such an electrical pickup is demonstrated by the broadband data spike at 0.912 s in Figs. 3(a)–3(c). The level of the amplified magnetic fluctuations varies from 0.1 V_pp to 2 V_pp. These low voltage magnetic fluctuations are on the order of μW, whereas the highest fluctuations correspond to mW. However, it should be noted that the plasma volume that the diagnostic samples is unknown, so the total signal generated by the plasma could be larger. The amplitude and spatial response of this diagnostic is currently uncalibrated.

The data analysis for the ICE diagnostic is conducted within the One Modeling Framework for Integrated Tasks (OMFIT) integrated modeling framework.²⁵ A dedicated OMFIT ICE module was developed and used to perform detailed analysis of over 50 DIII-D discharges. The OMFIT ICE module provides a front end for data fetching, signal processing, and data visualization for the ICE diagnostic. The high sampling rate of the ICE signals results in large data sets, which required developing routines that were carefully crafted to avoid running out of memory, while handling the data.

Specifically, the Windowed Fast Fourier transform (WFFT) analysis was carried out in such a way to always operate on only a single 80 ms data segment at a time (∼2²⁴ data points). Only the data segments that fall within a range of times selected by the user are analyzed. A typical WFFT analysis uses 2¹⁴ data points (corresponding to a ∼80 μs slice), weighted by a Hann window function in order to reduce the high-frequency side lobe contributions. The transformed slices from each of the 80 ms segments are usually downsampled by 10×, to preserve computer memory, and then joined together to form the final spectrogram. The resulting spectrograms are then stored within the OMFIT ICE module for further post-processing. The raw data are not typically stored within OMFIT after transforming the data to reduce computer memory usage.

The extremely large number of data points is such that even plotting the raw data is a non-trivial task, which is occasionally performed for only a few segments of data. A simple down-sampling approach was first attempted but later discarded because important features in the signal might be missed. Hence, a dedicated plotting routine that bins the data and then plots the maximum and minimum value in each of the bins was developed. As the time range or voltage range is changed in this plot, the bins are automatically recalculated and replotted. This plotting method was found to be over 100× faster than plotting all the data points and capable of conveying the salient raw data information to the user.

An example of this data analysis approach is shown in Fig. 3 for a DIII-D discharge during its L-mode phase. The raw data in Fig. 3(a) are Fourier transformed in Fig. 3(b). The frequency range has been decreased for clarity. High-frequency emission is observed at several frequencies in this figure, correlating with the raw magnetic fluctuations observed in Fig. 3(a). Typically, the ICE power at specific frequencies or times of data is analyzed as demonstrated in Figs. 3(c) and 3(d). The time variation of the averaged power of the signal from 27.2 to 32.2 MHz is shown in Fig. 3(c) as well as the pulses of injected neutral beams. As shown here, these high-frequency magnetic fluctuations occur with the application of neutral beam injection. Three time slices with 2 ms averaging times during this discharge are analyzed further in Fig. 3(d). The ICE power frequency spectrum differs for these times due primarily to the different injected beams. The 150L beam is a co-current “near-tangential” beam with tangency radius (R_tan = 1.15). The 210R beam is a counter-current “near-tangential” beam with tangency radius (R_tan = 1.15). The frequency spectra at 0.862 s and 0.925 s are very similar due to the use of the same beam (150L), whereas at 0.9185 s with the injection of the 210R neutral beam, the frequency spectrum is shifted to slightly higher frequencies when compared to the other two time points. The ICE signal-to-noise ratio at a given time for any discharge can be improved by increasing this averaging time; typically 0.001–1 s averaging times are employed depending upon the signal strength and the noise level.

Using this diagnostic, three different types of energetic-particle-driven emission have been observed and are being characterized on DIII-D. The signal shown in Fig. 3 corresponds to ICE, which is the ICRF emission most often observed with this diagnostic. ICE is observed at harmonics of f_ci, with resulting frequencies ranging from 5 to 100 MHz. CAEs are occasionally observed on DIII-D with f < f_ci, corresponding to 2–10 MHz. Whistler waves are observed only in low density or disrupting plasmas at f ≫ f_ci, corresponding to 100–200 MHz. These three types of energetic-particle-driven emission will be described in greater detail in forthcoming publications, including the work of Spong et al.²² 

Since ICE has been theoretically predicted^26–29 and experimentally observed^{3,4,6,10,12–14,17} to occur at harmonics of f_ci, the radial location of the emission, assuming no or only a small Doppler shift, can be determined. The radial location of CAEs and whistler waves is not as easily determined, so this diagnostic primarily serves as a global indicator of excitation for them.

The location of ICE is determined by matching the magnetic field to a particular ICE frequency by using the EFIT equilibrium reconstruction code.³⁰ In Fig. 3(d) at 0.862 s, three frequency peaks are clearly observed. These peaks are at 29.56, 44.22, and 58.88 MHz, with a spacing of 14.66 MHz. The plasmas shown in this paper are deuterium plasmas with deuterium neutral beam heating. Thus, these peaks correspond to the second, third, and fourth harmonics of the deuterium cyclotron frequency f_cD = 14.66 MHz, mapping to the radial plasma center R ≈ 1.8 m, as described in the following analysis. Since a weak peak is also observed at ∼15 MHz, some of this emission is certainly excited by the deuterium beam ions. However, ICE excited by fusion products could also be contributing to the total signal level. The dominance of the second harmonic and weakness of the fundamental frequency are not atypical for DIII-D plasmas and have been observed elsewhere.³¹ 

EFIT, constrained via only the magnetic diagnostics without accounting for the fast-ion pressure, was used to calculate the magnetic field at this discharge time in Fig. 4. The various magnetic field components from EFIT are shown at the midplane in Fig. 4(a). The total magnetic field B_TOT is the square root of the sum of the squares of the toroidal B_T, radial B_R, and vertical B_Z magnetic fields. As demonstrated in this figure, the toroidal field dominates the other fields and for the most part determines the total magnetic field on DIII-D. In Fig. 4(b), B_TOT is shown for three vertical locations, highlighting the near-invariance of B_TOT with vertical position. These figures illustrate that it is possible to determine the radial position of ICE but not the vertical position from its measured fundamental frequency. f_cD varies in this plasma from ∼25 MHz on the high-field-side of the plasma to ∼11 MHz on the low-field-side of the plasma. The toroidal field applied to DIII-D plasmas typically is in the range of 1–2 T on axis; in this plasma, the field was ∼2 T. Hence f_cD is in the range of 5–26 MHz in DIII-D plasmas. Typically, only one harmonic (generally the fundamental) is present within the plasma, aiding in the identification of the radial location of the ICE excitation. Finally, in Fig. 4(c), the EFIT equilibrium reconstruction is shown for this discharge time, as well as a contour representing the radial location of f_cD = 14.66 MHz. Thus, in this plasma at this time, ICE is likely emitted from R ≈ 1.8 m, the radial plasma center. Emission of ICE from this region of the plasma is routinely observed in many DIII-D plasmas.

In summary, this version of the ICE diagnostic was established in 2015 and expanded in 2017 to document ICRF emission driven by energetic particles. Several possible upgrades that could be done in the future to improve and expand this high-frequency diagnostic include improving the DC break frequency response and bandwidth, reduction of noise and electrical pickup, amplitude and spatial calibration, digitization at higher frequency, and expansion of the diagnostic by replacing the high-field-side center stack loops described in the work of Ikezi et al.³² that are no longer operable.

The authors thank A. Nagy for his support of this diagnostic. The authors also thank C. Chrobak for the image of this diagnostic system. This work was supported by the U.S. Department of Energy under No. DE-FC02-04ER54698 and by the Science Undergraduate Laboratory Internship (SULI) program. The data shown in this paper can be obtained in digital format by following the links at https://fusion.gat.com/global/D3D_DMP.

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.