Intense intermittent radiation at the plasma frequency on EAST

Intense intermittent radiation has been observed regularly in EAST plasmas. The duration of radiation bursts is with a characterization time of a few microseconds. The radiation is very intense, with an equivalent radiation temperature higher than the electron cyclotron emission by a few orders of magnitude. An electron density threshold exists to terminate the bursts, and it is strongly dependent on the toroidal magnetic field. The radiation frequency f  is at the plasma frequency, and the frequency bandwidth is very narrow (∼1.5 MHz FWHM, ). The fine structure of the spectrum in the frequency domain has been observed, and the frequency spacing is around 3 MHz. The cavity modes model is capable of explaining the radiation frequency and the frequency spacing. However, a quantitative and complete description of this phenomenon is still lacking.


Introduction
Electron cyclotron emission (ECE) measurement has been widely employed as a powerful diagnostic in tokamak plasmas since the 1970s. Along with the development of this diagnostic, some of the characteristics of the measured spectra were not as the ECE theory predicts. Under certain plasma conditions, additional peaks besides the ECE harmonics occur at the electron plasma frequency ω pe0 , corresponding to the measured value of electron density n e0 [1,2]. This quiescent emission has been interpreted as a consequence of a Cherenkov resonance with the runaway electrons [3][4][5]. Fluctuating ω pe emission with narrow bandwidth was also observed and studied on Alcator [6,7]: the emission typically lasts 5-10 µs and is very intense, with radiation temperatures exceeding 10 5 eV. The spectral width of the emission is in the range of 400-800 kHz. Similar fluctuating emission was observed as well on DIII-D [8]. Two individual theories (cavity mode [9,10] and triplewave resonance model [11]) have been proposed to interpret the fluctuating ω pe emission. Both theories involve two stages. The first stage is the generation of a tail with a bump of the electron velocity distribution parallel to the magn etic field. Under certain plasma conditions, the Maxwellian electron distribution begins to grow a runaway electron tail in the presence of a longitudinal electric field. This distribution function with a tail becomes unstable in a strong magnetic field owing to the anomalous Doppler effect. Consequently, a bump is generated on the tail as a result of the instability due to the anomalous Doppler effect. The physics of the first stage is well accepted [12], and adopted by both of the theories as the origin of the free energy. However, the two theories have differences in explaining the origin of the ω pe emission. The first theory assumes that the cavity mode is excited, while the other theory proposes that the ω pe emission is caused by a triple-wave resonance instability. A recent study [13] on the nonlinear kinetic simulations of the anomalous Doppler instability of suprathermal electrons in plasmas reveals that it exhibits a spectral feature which may correspond to the fluctuating ω pe emission.
Besides the observations in laboratory plasmas, different types of emission bursts at the plasma frequency have been detected in astrophysical plasmas ever since [14][15][16]. This has been explained as a multi-stage mech anism, with the first stage being generation of Langmuir waves through a streaming instability driven by a positive gradient df (ν )/dν > 0, and subsequent stages involving partial conversion of the Langmuir turbulence into escaping radiation at the plasma frequency [17][18][19]. Despite many successes of this theory, the question is still open because this theory still has difficulty in explaining the type I bursts [20].
All of the existing theories/models for explaining the bursts of emission at plasma frequency in either the tokamak or astrophysical plasmas rely on the assumption of the non-Maxwellian electron velocity distribution. Provided that the mechanism is well understood, this phenomenon can be used to infer the information on the energetic electrons which are of serious concern with regard to the safe operation of tokamaks. On the other hand, the bursts are in the millimeterwave frequency range, and are so intense that this could be one of the reasons for the malfunction of the millimeter-wave comp onents of reflectometry diagnostics on some tokamak machines [21]. This study is also of particular interest for designing the ITER collective Thomson scattering (CTS) diagnostic. CTS has been proposed to measure the fast ion phase space distribution in ITER [22]. It also holds the potential to measure the fuel ion ratio in ITER [23], and at present there is no established method to accomplish the mission. In order to meet the requirements of the measurements in ITER, a CTS system using a probe frequency of 60 GHz is proposed after investigating different systems with probe frequencies in the range of 60 GHz, 170 GHz, 3 THz, and 28 THz. On one hand, the ω pe emission may pollute the scattering emission. On the other hand, the ω pe emission is so intense that it may destroy the heterodyne receiver. Therefore, it is essential to fully understand the phenomenology and the underlying physics of the ω pe emission.
On the Experimental Advanced Superconducting Tokamak (EAST), millimeter wave bursts at the plasma frequency (hereinafter ω pe bursts) were observed and studied. In this work, section 2 describes the essential diagnostics relevant to the study, section 3 presents the phenomenology of the ω pe bursts on EAST, section 4 summarizes the observations and discusses the underlying physics with a focus on the unsolved questions, and the cavity mode numerical results are briefly summarized in the appendix.

Q-band radiometer system
Bursts have been observed regularly, using a Michelson interferometer, ever since it was commissioned on EAST in [24]. However, the bursts are not observed by the radiometer systems [25] in the ECE frequency range. The ECE radiometer systems are able to detect either the second or third harmonic ECE as the toroidal magnetic field varies. In order to demonstrate the frequency range of the bursts, a 90 GHz dichroic plate, which acts as a high pass filter, was placed in front of the input aperture of the Michelson interferometer. The comparison of the results for discharges with similar plasma parameters rules out the possibility of higher ECE harmonics. Based on the observations on other tokamak machines, it is very likely that the bursts observed on EAST are ω pe bursts. Thereafter, a Q-band radiometer system was built in 2016 to distinguish the radiation frequency of the bursts and consequently characterize the bursts.
This Q-band radiometer system shares the same transmission line with the Michelson interferometer and the ECE radiometer systems, and the system schematic is shown in figure 1. A synthesizer (Anritsu MG3692C) and multiplier (input frequency: 8.25-12.50 GHz) are used as a local oscillator (LO) to down-convert the plasma emission. The frequency of the synthesizer is set to be 8.4 GHz in the 2016 EAST campaign (EAST#70273-71742), and is 8.5 GHz in the 2017 EAST campaign (EAST#73727-74031). After amplification, the intermediate frequency (IF) signal is divided into eight channels. One channel (#1) is detected directly, while the remaining channels are filtered by bandpass filters. Two of the bandpass filters (#2, 3) are yttriumiron-garnet (YIG) filters with adjustable central frequency in the range of 6-18 GHz, and the other five (#4-8) are with fixed central frequency (8/10/12/14/16 GHz). The IF bandwidth of the YIG filters are roughly 100-250 MHz, and it is 500 MHz for the fixed frequency filters. The IF frequency coverage of channel #1 is roughly 2-18 GHz, which is determined mainly by the amplifier before the power divider.
Even though the radiation frequency of the bursts can be determined approximately by the radiometer system, the spectral resolution is limited by the bandwidth of the bandpass filters. In order to obtain the frequency spectra of the bursts, the diode detector in channel #1 is replaced with a real-time spectrum analyzer (realized by the combination of a 26.5 GHz PXI vector signal analyzer PXIe-5668 and a PXI high-speed data storage module HDD-8261 loaned from National Instruments) for a few dedicated discharges. In principle, the vector signal analyzer is a heterodyne system. It comprises a radio frequency (RF) analog signal generator (PXIe-5653), RF signal downconverter (PXIe-5606), and IF digitizer (PXIe-5624). For the measurements discussed in this work, the LO frequency is set to be 7.5 GHz, and the I&Q data are recorded with a sampling rate of 200 MHz.
For the remainder of this paper, the experimental results on the bursts are detected with this Q-band radiometer system when not otherwise specified.

Runaway electron diagnostic
Gamma ray measurement [26] has been used to indicate the existence of runaway electrons on EAST. The system measures both count rate and energy spectrum of the gamma ray in the energy range from 0.3 to 6 MeV.

Existence of an electron density threshold
The ω pe bursts have been observed regularly in ohmic plasmas. There exists an electron density window for the occurrence of the ω pe bursts, and the upper threshold is strongly dependent on the toroidal magnetic field. In order to obtain the threshold, a number of discharges for both with and without ω pe bursts are analyzed statistically. The threshold is determined to be the average value for two discharges, with the closest electron density on the map of the ω pe burst occurrence. Figure 2(a) shows the trend of the upper electron density threshold (the line-averaged electron density along a chord close to the plasma center) versus the toroidal magn etic field at the major radius of 1.85 m. Figure 2(b) depicts the comparison between the plasma frequency f pe0 corre sponding to the electron density threshold at the plasma core n e0 and the first-harmonic ECE frequency f ECE at the low-field-side plasma edge. The coefficient relating the central electron density n e0 and the line-averaged electron density ranges from 1.3 to 1.8 [27], and this is represented by the error bar in figure 2(b). As the results show, f pe0 is slightly larger than f ECE , and the ratio does not change much as the toroidal magnetic field changes. Figure 3 is a typical example showing the correlation between the ω pe bursts (indicated by the spikes on the interferograms of a Michelson interferometer as shown in figure 3(a)) and the runaway electrons (indicated by the γ ray counts in figures 3(d) and (e)). The generation of runaway electrons is attributed to a combination of low electron density and high loop voltage. The count rate of γ rays increases as the electron density ramps up before LHW is switched on. The loop voltage drops remarkably when LHW is switched on, and the count rate of γ rays decreases consequently. The ω pe bursts begin to occur as the number of runway electrons increases to a certain value (indicated by the dashed line in figure 3(d)), and the phenomenon disappears when the number of runway electrons drops to a similar value. The critical energy E crit above which the electrons are able to become runaway electrons is also shown in figure 3(d), and lower E crit results in a higher population of runaway electrons. As figure 3(e) shows, the counts of γ ray with energy of 3.9 MeV reaches its maximum (around 60) at 2 s. This indicates that the energy of the runway electrons is up to roughly 4 MeV.

Time scale
A typical example illustrating the pattern of the occurrence of the ω pe bursts is shown in figure 4. Figures 4(a)  each individual ω pe burst has a timescale of a few µs, and the burst frequency can reach upto tens of kHz within a timescale of a few milliseconds (see figure 4(c)), followed by a quiescent period on the order of ten milliseconds (see figure 4(b)). Figure 5 illustrates a typical measurement (EAST #70444) of the Q-band radiometer system during electron density ramp up phase. It is clear that the radiation frequency (indicated as the label on the vertical axis) changes as the electron density ramps up. The plasma frequencies calculated from the electron density profiles measured by a microwave reflectometer and the radiation frequency at a few time slices are shown in figure 6, and the radiation frequency of the ω pe bursts is smaller than the central plasma frequency. Also shown in figure 6 is the first-harmonic ECE frequency, and it is clear that the radiation frequency of the ω pe bursts is smaller than the ECE frequency.

Radiation frequency and fine structure
Limited by the bandwidth of the bandpass filters used in the Q-band radiometer system, the uncertainty of the radiation frequency shown in figures 5 and 6 is roughly 0.5 GHz.
More accurate values of the radiation frequency are determined by using a real-time spectrum analyzer (using a carrier wave of 7.5 GHz and sampling the data with a rate of 200 MHz s −1 ), and figure 7 shows (a) the raw data and (b)  spectrogram for a time interval of 150 µs. Both the raw data and spectrogram indicate that the frequency spectra of the bursts have multiple peaks. Frequency chirping with a rate of a magnitude of 1 MHz µs −1 has been observed for these bursts. Figure 8 shows the raw data and the spectrum within a time scale of 3 µs, and also shows a clear structure with multiple peaks. Table 1 summarizes the results of Gaussian fitting of the peaks in figure 8(b). The frequency spacing is roughly 3 MHz, and the FWHM of the peaks is about 1-1.7 MHz. The radiation frequency is the summation of the number in the column 'Frequency', the carrier wave frequency of the realtime spectrum analyzer (7.5 GHz), and the LO frequency of the radiometer (34 GHz).

Estimation of the equivalent radiation temperature
At the moment, the Q-band radiometer is not absolutely calibrated. The power of the emission is measured with the equivalent radiation temperature by comparison with other radiometer systems in the ECE frequency range. The gain of the Q-band radiometer is roughly two orders of magnitude smaller. However, the output of Q-band radiometer is even a few times larger. Besides, the bandwidth of the ω pe bursts is about 1.5 MHz, and the bandwidth of an individual channel of the ECE radiometer is about 500 MHz. In addition, a factor of roughly five is added due to the difference in the transmission loss at different frequencies [28]. Hence, the bursts have an equivalent radiation temperature higher than the ECE intensity by a few magnitudes.

Discussion and conclusions
The ω pe bursts have been observed regularly in EAST plasmas. An individual burst has a time scale of a few microseconds, and the equivalent radiation temperature is higher than the ECE intensity by a few orders of magnitude. An electron density window exists for the occurrence of the related instability, and the upper electron density threshold is strongly dependent on the toroidal magnetic field. The radiation frequency f is at the plasma frequency (for a discharge with dedicated measurement of the electron density profiles and radiation frequency, the corresponding normalized radius is 0.2-0.3), and the frequency bandwidth ∆f is very narrow (∼1.5 MHz FWHM, ∆f /f ∼ 3 × 10 −5 ). Fine structure of the spectrum in frequency domain has been observed, and the frequency spacing is around 3 MHz.
As described in the introduction, a few attempts have been carried out to explain this phenomenon. In this work, numerical simulation of cavity modes using EAST param eters is performed and the results are briefly summarized in the appendix. The characterization of the cavity modes includes findings that (i) the cavity modes are approximate to be quasi-static electric modes, (ii) the corresponding eigenmode frequencies are higher than the central plasma frequency for modes with lowest mode numbers, (iii) the eigenmode frequency decreases as the mode numbers (m, n) increase, and high mode numbers (m, n) are needed in order to match the experimental frequencies (see figure A2), (iv) the longitudinal mode spacing for the (0, 0) mode has a similar value with the measured frequency spacing of the fine structure when N 2 -3.5, while N 1.8 for modes with high n (see figure A3).
Even though the model of cavity modes is capable of explaining the observed radiation frequency and frequency spacing, there are still many unsolved questions regarding the phenomenology of the ω pe bursts. First of all, the excitation mechanism of the waves is still not clear. Only if the underlying physics is understood is one able to quantitatively explain the duration of an individual burst and the burst repetition frequency. Second, it is unknown what determines the radiation intensity. In [10], it was proposed that the radiation is due to coherent maser action, but this lacks a quantitative description. Last but not least, it is critical to explain how the radiation escapes from the plasma. One of the characteristics of the cavity modes is that the modes are localized in the plasma core, and the field at the plasma edge is negligible. In [10], it is speculated that this is due to scattering. In brief summary, the explanation of the ω pe bursts is still not satisfying, and a quantitative description of this phenomenon is required. Predicting the ω pe bursts in ITER is critical for the diagnostic design. However, one is unable to predict this phenom enon with confidence unless the underlying physics is well accepted.

Appendix. Characterization of cavity modes
In the present work, we are following the cavity mode theory developed by Hutchinson and Gandy et al [9,10]. Coupled mode equations have been derived to describe the cavity mode structure and dispersion relations, and the solutions are Table 1. Results of Gaussian fitting for the fine structure of the ω pe bursts shown in figure 8(b). Radiation frequency is the summation of the number in the column 'Frequency', the carrier wave frequency of the real-time spectrum analyzer (7.5 GHz), and the LO frequency of the radiometer (34 GHz). proportional to e i(kz+mθ) . Because the condition for analytical analysis is not satisfied for the cases of our interest, the equations are solved numerically in this work. It was found that the cavity mode structure and dispersion relations are not sensitive to the specific profile for a monotonically decreasing plasma density profile. Therefore, we chose a similar density profile to that in [9,10] as follows: where n edge and n e0 are respectively the electron density at the last closed magnetic surface and the magnetic axis, and r is the normalized radius. Then the coupled normalized eigenmode E z and B z equations can be solved for a given longitudinal refractive index N, and the corresponding eigenfrequency ω is obtained. Followed the definitions in [9], the mode number n is defined to be the number of the zero E z with respect to the r direction.
In figure A1, the eigenmode structure of the E z modes (m, n) = (0, 60) are shown for N = 1.8, toroidal magnetic field B 0 = 2.25 T, n e0 = 2.0 × 10 19 m −3 , major radius R 0 = 1.85 m, and minor radius a = 0.46 m. The results indicate that E and B are both localized near the axis, and the field at the plasma edge is negligible for the present plasma   parameters. It is also found that B/E 1, and this means that the present electromagnetic modes are approximate to be quasi-static electric modes. Figure A2 shows the dispersion relations with respect to the longitudinal refractive index N for the E z modes (m, n) = (0, 0), (0, 30), (0, 60), (1, 0), (1,30), (1,60). For the eigenmode with lowest (m, n), the wave frequency is larger than ω pe0 . As the mode number increases, the wave frequency decreases and becomes smaller than ω pe0 . This may explain the phenomena whereby the observed radiation frequency of the bursts diverges from the central plasma frequency (see figure 6) in EAST plasma. The frequency difference of two neighboring modes (with a difference of 1 for either m or n) is around 0.1%×ω pe0 , and is much larger than the observed frequency difference of the fine structure shown in figure 8 and table 1.
As pointed out in [9], the observed fine structure can be explained with the longitudinal mode spacing, which is defined as ∆ω = dω dk 1 R . Figure A3 shows the longitudinal mode spacing ∆f = ∆ω 2π with respect to N for the same eigenmodes shown in figure A2. For the eigenmodes with low (m, n), ∆f increases with N monotonically for N 1.7. For eigenmodes with higher (m, n), there is a peak around N = 1.95.