Fast frequency sweeping events in the electron cyclotron emission of nonequilibrium plasma confined in a tabletop mirror trap

Complex dynamics has been observed in the spectra of electron cyclotron emission of nonequilibrium plasma confined in a tabletop mirror trap. Microwave emission is a set of highly chirped radiation bursts with both increasing and decreasing frequencies which are repeated periodically. Such chirped bursts are not described well in the framework of a standard quasilinear approach. On the other hand, the simultaneous observation of several chirped bursts in the same frequency range is typical of the formation of nonlinear phase-space structures in the vicinity of the wave-particle resonances in the kinetically unstable plasma, also known as the “holes and clumps” mechanism.


Introduction
Chirped electromagnetic emission in a frequency range of 30−300 kHz is generally observed in toroidal magnetic traps during the development of the Alfven wave turbulence driven by high-energy beams of ions or alpha particles [1,2]. The frequency sweeping events associated with the development of the high-energy particle-driven Alfven instabilities were detected at the DIII-D, JT-60U, ASDEX-Upgrade, MAST, NSTX, START, and LHD machines in regimes with neutral beam injection heating. To study and interpret such chirped emission bursts, the "holes and clumps" mechanism (or Berk-Breizman model [3]) has been suggested, where the simultaneous observation of several chirped bursts in the same frequency range is described as the formation of nonlinear phasespace structures in the vicinities of the wave-particle resonances in the kinetically unstable plasma.
In the laboratory experiments we have observed potentially the same mechanism acting in a much higher frequency range. The obtained data provided the first experimental evidence in favor of the spontaneous formation of the self-consistent structures similar to the Bernstein-Green-Kruskal waves near the wave-particle resonances in the frequency range corresponding to millimeter wavelengths in the laboratory plasma confined in a mirror trap. The goal of this work is to study the fine timefrequency characteristics of the electromagnetic radiation. It became possible to perform such studies only recently due to the development of methods for measuring the electromagnetic field with high temporal resolution. First experimental results were discussed in [4]. Here we will analyze the general features of the frequency sweeping events in decaying ECR discharge plasma.

Experimental setup
The experiments were performed in by gyrotron radiation (frequency open axially symmetric mirror magnetic trap [5]. The schematic view of the setup is shown in Figure 1. Microwave radiation is region of the discharge chamber. The radiation int average power density is 100 W/cm The discharge chamber is placed inside the mirror magnetic trap, consisting of maximum magnetic field strength magnetic trap is 22.5 cm, mirror ratio is about 5. Plasma is initiated radiation under ECR conditions which corresponded to a magnetic field strength of 1.34 magnetic mirror and the center of the discharge chamber. and it increases up to 10 -4 -10 -3 periodic regime with at least 10 seconds delay between shots.

Experimental results
In the experiments, we obtained data on electromagnetic plasma radiation antenna which has the uniform oscilloscope (Keysight DSA-Z 594A 160 GSample/s). The antenna bandwidth the electron gyrofrequency f ce in the trap center. The dynamic spectr recorded data by the short-time Fourier transform with reduction algorithm. Simultaneously high-energy electrons (>10 keV) of approximately 1 ns.
The ECR discharge plasma consists of at least two components: (N c ~ 10 12 -10 13 cm -3 , T c ~ 100component with anisotropic distribution function and energies are in the range from 10 to hundreds of keV) [5].
Experiments were performed in t plasma decay, which start after the ECR heating is switched off, are characterized by scales. The decay of nitrogen plasma proceeds faster due to the dissociative recombination of molecular ions, which is the main recombination mechanisms in the late decay stage [6]. In argon plasma, the plasma density decay is mainly cau 54 experimental shots were performed in nitrogen plasma, while only 23 of them contained the frequency sweeping events which will be the fraction of unstable events in argon plasma was much less: 146 experimental shots were performed, while only 11 observations of the instability have been found. performed in plasma of electron cyclotron resonance (ECR) discharge sustained by gyrotron radiation (frequency is 37.5 GHz, power is up to 80 kW, and pulse duration open axially symmetric mirror magnetic trap [5]. The schematic view of the setup is shown in 1. Microwave radiation is launched through the input window and is focused region of the discharge chamber. The radiation intensity in the focal plane is about 10 kW/cm average power density is 100 W/cm 3 . The discharge chamber is placed inside the mirror magnetic trap, consisting of strength of 4.3 T; the pulse duration is about 7 ms. magnetic trap is 22.5 cm, mirror ratio is about 5. Plasma is initiated and sustained by gyrotron under ECR conditions at the fundamental cyclotron harmonic at a frequency of 37.5 to a magnetic field strength of 1.34 T. The resonance surface is between the magnetic mirror and the center of the discharge chamber. Pressure of neutral gas is about Torr during the ECR discharge. The facility is working in a pulse periodic regime with at least 10 seconds delay between shots. obtained data on the intensity and dynamic spectrum radiation. In the microwave measurements, we used uniform bandwidth in the range of 2−20 GHz and the high Z 594A, the analog bandwidth is 59 GHz, and the The antenna bandwidth covered the frequency range up to the in the trap center. The dynamic spectra were time Fourier transform with the Hamming window and Simultaneously with the electromagnetic radiation, we measured precipitation keV) from the trap ends using a p-i-n diode detector with plasma consists of at least two components: the cold dense component -300 eV) with an isotropic velocity distribution and the less dense with anisotropic distribution function which consists of hot electrons ( from 10 to hundreds of keV) [5]. Experiments were performed in two gases: nitrogen and argon. In these gases, the processes of plasma decay, which start after the ECR heating is switched off, are characterized by scales. The decay of nitrogen plasma proceeds faster due to the dissociative recombination of molecular ions, which is the main recombination mechanisms in the late decay stage [6]. In argon plasma, the plasma density decay is mainly caused by the three-body electron recombination. In total, 54 experimental shots were performed in nitrogen plasma, while only 23 of them contained the which will be discussed below. At the same parameters of the experiment, tion of unstable events in argon plasma was much less: 146 experimental shots were performed, while only 11 observations of the instability have been found. plasma of electron cyclotron resonance (ECR) discharge sustained pulse duration is 1 ms) in an open axially symmetric mirror magnetic trap [5]. The schematic view of the setup is shown in window and is focused in the heating ensity in the focal plane is about 10 kW/cm 2 and the The schematic view of the experimental setup. The discharge chamber is a cylindrical tube with an inner diameter of 38 mm which is widened in the central part by the tube with an inner diameter of 72 mm and a length of 50 mm.
The discharge chamber is placed inside the mirror magnetic trap, consisting of pulsed coils with the ms. The length of the and sustained by gyrotron the fundamental cyclotron harmonic at a frequency of 37.5 GHz . The resonance surface is between the Pressure of neutral gas is about 10 -6 Torr; is working in a pulseand dynamic spectrum of the stimulated the broadband horn 20 GHz and the high-performance and the sampling rate is the second harmonic of calculated from the and the original noise , we measured precipitation of n diode detector with a time resolution cold dense component 300 eV) with an isotropic velocity distribution and the less dense of hot electrons (N h ~ 10 10 −10 11 cm −3 In these gases, the processes of plasma decay, which start after the ECR heating is switched off, are characterized by the different time scales. The decay of nitrogen plasma proceeds faster due to the dissociative recombination of molecular ions, which is the main recombination mechanisms in the late decay stage [6]. In argon body electron recombination. In total, 54 experimental shots were performed in nitrogen plasma, while only 23 of them contained the discussed below. At the same parameters of the experiment, tion of unstable events in argon plasma was much less: 146 experimental shots were Microwave emission with the frequency sweeping events was observed in the stage of plasma decay with a time delay of 0.1−2 ms after the ECR heating was switched off. The time delay between the end of ECR heating pulse and the start of the instability development could be explained by the polarization depression effect in the background plasma [4], when instability is suppressed in dense plasma. Another important feature which accompanies the instability development is a decreasing ambient magnetic field.  initial phase, which is out of the scope of the present study, the emission is observed only in a few frequency bands which are independent of the experimental conditions. The emission frequency is always less than the electron gyrofrequency in the trap center. Within each frequency band, the emission spectrum is a set of fast narrowband chirped bursts, which consist from periodical batches with several bursts in each or quasi-continuous series of bursts with duration of up to 1 ms. The instability development is illustrated in Figure 2, where the dynamic spectrum is shown. We note that the second harmonic of the microwave emission was observed and its spectrum repeated the fine spectral structure of the emission of the fundamental harmonic.
The statistical analysis of the experimental data shows that the separate frequency bands in the emission spectra are similar for all experimental shots performed in a certain gas. Figure 3 shows histograms of the emission frequencies of the separate chirps for the discharges in nitrogen and argon. It can be seen that there are several narrow frequency peaks from which the chirps with raising and falling frequencies start. The widths of the peaks are determined by the maximum frequency deviations from the initial frequency in the chirped structures. For the discharges in nitrogen, the peaks are observed at frequencies of 4.35, 4.9, 6.2, 7.3, 7.6 and 9 GHz. For the discharges in argon, the peaks are observed at frequencies of 7.6, 8.8, 9 and 9.85 GHz. The central frequencies of the peaks do not depend on the ambient magnetic field. Therefore, they can be associated with the excitation of certain electromagnetic modes in a metal discharge chamber filled with rarefied magnetized plasma.

Discussion and conclusions
The frequency sweeping events in the microwave emission spectrum may be well explained in the framework of the Berk-Breizman model [3]. As an electromagnetic mode develops, most of the particles respond adiabatically to the wave and only a small group of resonant particles becomes mixed and causes the local flattening of the distribution function in phase space within or near the separatrixes formed by the waves. However, when there is the linear dissipation in the background plasma, the plateau distribution becomes unstable and the mode tends to grow explosively. That results in the formation and subsequent development of the long-living structures (as compared to the linear growth) in the particle distribution, the so-called holes (a depletion of particles) and clumps (an excess of particles). Their subsequent convective motion in phase space is synchronized to the change in the wave frequency, thus leading to the formation of complex chirped patterns in the dynamic spectra of unstable waves. The distinctive feature of the instability under investigation is the considerable effect of electron collisions on its development which provides a dissipation channel for electromagnetic energy, which results in the formation of characteristic chirped elements in the emission spectra.