Harmonic Plasma Emission Research Articles

Fundamental, harmonic, and third-harmonic plasma emission from beam–plasma instabilities: a first-principles precursor for astrophysical radio bursts

ABSTRACT Electromagnetic fundamental and harmonic emission is ubiquitously observed throughout the heliosphere, and in particular it is commonly associated with the occurrence of type II and III solar radio bursts. Classical analytic calculations for the plasma-emission process, though useful, are limited to idealized situations; a conclusive numerical verification of this theory is still lacking, with earlier studies often providing contradicting results on e.g. the precise parameter space in which fundamental and harmonic emission can be produced. To accurately capture the chain of mechanisms underlying plasma emission – from precursor plasma processes to the generation of electromagnetic waves over long times – we perform large scale, first-principles simulations of beam–plasma instabilities. By employing a very large number of computational particles we achieve very low numerical noise, and explore (with an array of simulations) a wide parameter space determined by the beam–plasma density ratio and the ion-to-electron temperature ratio. In particular, we observe direct evidence of both fundamental and harmonic plasma emission when the beam-to-background density ratio ≤0.005 (with beam-to-background energy ratio ∼0.5), tightly constraining this threshold. We observe that, asymptotically, in this regime $\sim 0.1~{{\ \rm per\ cent}}$ of the initial beam energy is converted into harmonic emission, and $\sim 0.001~{{\ \rm per\ cent}}$ into fundamental emission. In contrast with previous studies, we also find that this emission is independent of the ion-to-electron temperature ratio. In addition, we report the direct detection of third-harmonic emission in all of our simulations, at power levels compatible with observations. Our findings have important consequences for understanding the viable conditions leading to plasma emission in space systems, and for the interpretation of observed electromagnetic signals throughout the heliosphere.

Solar Coronal Density Turbulence and Magnetic Field Strength at the Source Regions of Two Successive Metric Type II Radio Bursts

We report spectral and polarimeter observations of two weak, low-frequency (≈85–60 MHz) solar coronal type II radio bursts that occurred on 2020 May 29 within a time interval ≈2 minutes. The bursts had fine structures, and were due to harmonic plasma emission. Our analysis indicates that the magnetohydrodynamic shocks responsible for the first and second type II bursts were generated by the leading edge (LE) of an extreme-ultraviolet flux rope/coronal mass ejection (CME) and interaction of its flank with a neighboring coronal structure, respectively. The CME deflected from the radial direction by ≈25° during propagation in the near-Sun corona. The estimated power spectral density and magnetic field strength (B) near the location of the first burst at heliocentric distance r ≈ 1.35 R ⊙ are ≈2 × 10−3 W2m and ≈1.8 G, respectively. The corresponding values for the second burst at the same r are ≈10−3 W2m and ≈0.9 G. The significant spatial scales of the coronal turbulence at the location of the two type II bursts are ≈62–1 Mm. Our conclusions from the present work are that the turbulence and magnetic field strength in the coronal region near the CME LE are higher compared to the corresponding values close to its flank. The derived estimates of the two parameters correspond to the same r for both the CME LE and its flank, with a delay of ≈2 minutes for the latter.

Polarization Observations of a Split-band Type II Radio Burst from the Solar Corona

Using temporal observations of circular polarized harmonic plasma emission from a split-band type II solar radio burst at 80 MHz, we separately estimated the coronal magnetic field strengths (B) associated with the lower (L) and upper (U) frequency bands of the burst. The corresponding Stokes I and V data were obtained with the polarimeter operating at the above frequency in the Gauribidanur observatory. The burst was associated with a flare/coronal mass ejection on the solar disk. Simultaneous spectral observations with the spectrograph there in the frequency range 80–35 MHz helped to establish that the observed polarized emission was from the harmonic component of the burst. The B values corresponding to the polarized emission from the L and U bands at 80 MHz are B L ≈ 1.2 G and B U ≈ 2.4 G, respectively. The different values of B for the observed harmonic emission at the same frequency (80 MHz) from the two bands imply unambiguously that the corresponding fundamental emission at 40 MHz must have originated at different spatial locations. Two-dimensional radio imaging observations of the burst with the radioheliograph in the same observatory at 80 MHz indicate the same. As comparatively higher B is expected behind a propagating shock due to compression as well as the corresponding coronal regions being closer to the Sun, our results indicate that the sources of L- and U-band emission should be located ahead of and behind the associated coronal shock, respectively. These are useful to understand the pre- and postshock corona as well as locations of electron acceleration in a propagating shock.

Plasma Emission Induced by Electron Cyclotron Maser Instability in Solar Plasmas with a Large Ratio of Plasma Frequency to Gyrofrequency

Abstract In plasmas with a large ratio of plasma frequency to gyrofrequency (ω pe/Ωce), energetic electrons characterized by can excite electron cyclotron maser instability (ECMI), generating waves of upper hybrid (UH), Z, and W modes. It has been presumed that these ECMI waves can somehow convert to escaping X–O modes as fundamental (F) or harmonic (H) plasma emission. Here we perform a fully kinetic, electromagnetic particle-in-cell simulation to investigate the proposed radiation process. ECMI is driven by energetic electrons with a Dory–Guest–Harris distribution representative of a double-sided loss cone, and ω pe/Ωce is set to be 10. We find that the electrostatic UH mode is the fastest-growing mode. Around the time when its energy starts to decline, the W mode grows to be dominant. During this stage, we observe significant F and H plasma emission. The F emission is in the O mode with a bandwidth around 0.1–0.2 Ωce, and the H emission is contributed by both X and O modes with a narrower bandwidth. We suggest that the O–F emission is caused by coalescence of almost counterpropagating Z and W modes, while the H emission arises from coalescence of an almost counterpropagating UH mode at relatively large wave number. Thus the plasma emission investigated here is induced by a combination of wave growth due to ECMI and further nonlinear wave-coupling processes. The result is relevant to understanding solar radio bursts as well as other astronomical radio sources that are excited by energetic electrons trapped within certain magnetic structures.

The laser plasma of TAC targets with Cu inclusions

The experimental results of laser-plasma interaction are discussed. Plasma was formed at the exposure of laser radiation on the low density targets with Cu inclusions. The scattering radiation emitted by the laser-produced plasma has investigated. In experiments diagnostics data on temporal characteristics of second harmonic plasma emission; integrated in time spectral characteristics plasma radiation; x-ray plasma emission were obtained.

Densities Probed by Coronal Type III Radio Burst Imaging

We present coronal density profiles derived from low-frequency (80-240 MHz) imaging of three type III solar radio bursts observed at the limb by the Murchison Widefield Array (MWA). Each event is associated with a white light streamer at larger heights and is plausibly associated with thin extreme ultraviolet rays at lower heights. Assuming harmonic plasma emission, we find average electron densities of 1.8 x10^8 cm^-3 down to 0.20 x10^8 cm^-3 at heights of 1.3 to 1.9 solar radii. These values represent roughly 2.4-5.4x enhancements over canonical background levels and are comparable to the highest streamer densities obtained from data at other wavelengths. Assuming fundamental emission instead would increase the densities by a factor of 4. High densities inferred from type III source heights can be explained by assuming that the exciting electron beams travel along overdense fibers or by radio propagation effects that may cause a source to appear at a larger height than the true emission site. We review the arguments for both scenarios in light of recent results. We compare the extent of the quiescent corona to model predictions to estimate the impact of propagation effects, which we conclude can only partially explain the apparent density enhancements. Finally, we use the time- and frequency-varying source positions to estimate electron beam speeds of between 0.24 and 0.60 c.

Simultaneous Near-Sun Observations of a Moving Type IV Radio Burst and the Associated White-Light Coronal Mass Ejection

We present rare contemporaneous low-frequency ( $< 100~\mbox{MHz}$ ) imaging, spectral, and polarimetric observations of a moving type IV radio burst that had close spatio-temporal association with a white-light coronal mass ejection (CME) near the Sun. We estimate the electron density near the burst region from white-light coronagraph polarized brightness (pB) images of the CME as well as the two-dimensional radio imaging observations of the thermal free-free emission at a typical radio frequency such as 80 MHz. We analyze the burst properties such as the degree of circular polarization, the spectral index, and fine structures using the radio polarimeter and the radio spectral observations. The obtained results suggest that second harmonic plasma emission from the enhanced electron density in the leading edge of the CME is the cause of the radio burst. We determine the strength of the coronal magnetic field ( $B$ ) for the first time based on this interpretation. The estimated value ( $B \approx 1$ gauss) in the CME leading edge at a heliocentric distance of $\approx 2.2~R_{\odot }$ agrees well with the similar $B$ values reported earlier based on other types of observations.

Self-consistent particle-in-cell simulations of fundamental and harmonic plasma radio emission mechanisms

Aims. The simulation of three-wave interaction based plasma emission, thought to be the underlying mechanism for Type III solar radio bursts, is a challenging task requiring fully-kinetic, multi-dimensional models. This paper aims to resolve a contradiction in past attempts, whereby some studies indicate that no such processes occur. Methods. We self-consistently simulate three-waved based plasma emission through all stages by using 2D, fully kinetic, electromagnetic particle-in-cell simulations of relaxing electron beams using the EPOCH2D code. Results. Here we present the results of two simulations; Run 1 (nb/n0 = 0.0057, vb/{\Delta}vb = vb/Ve = 16) and Run 2 (nb/n0 = 0.05, vb/{\Delta}vb = vb/Ve = 8), which we find to permit and prohibit plasma emission respectively. We show that the possibility of plasma emission is contingent upon the frequency of the initial electrostatic waves generated by the bump-in-tail instability, and that these waves may be prohibited from participating in the necessary three-wave interactions due to frequency conservation requirements. In resolving this apparent contradiction through a comprehensive analysis, in this paper we present the first self-consistent demonstration of fundamental and harmonic plasma emission from a single-beam system via fully kinetic numerical simulation. We caution against simulating astrophysical radio bursts using unrealistically dense beams (a common approach which reduces run time), as the resulting non-Langmiur characteristics of the initial wave modes significantly suppresses emission. Comparison of our results also indicates that, contrary to the suggestions of previous authors, an alternative plasma emission mechanism based on two counter-propagating beams is unnecessary in an astrophysical context.

AN ESTIMATE OF THE CORONAL MAGNETIC FIELD NEAR A SOLAR CORONAL MASS EJECTION FROM LOW-FREQUENCY RADIO OBSERVATIONS

We report ground-based, low-frequency (<100 MHz) radio imaging, spectral, and polarimeter observations of the type II radio burst associated with the solar coronal mass ejection (CME) that occurred on 2013 May 2. The spectral observations indicate that the burst has fundamental (F) and harmonic (H) emission components with split-band and herringbone structures. The imaging observations at 80 MHz indicate that the H component of the burst was located close to leading edge of the CME at a radial distance of r ≈ 2 R {sub ☉} in the solar atmosphere. The polarimeter observations of the type II burst, also at 80 MHz, indicate that the peak degree of circular polarization (dcp) corresponding to the emission generated in the corona ahead of and behind the associated MHD shock front are ≈0.05 ± 0.02 and ≈0.1 ± 0.01, respectively. We calculated the magnetic field B in the above two coronal regions by adopting the empirical relationship between the dcp and B for the harmonic plasma emission and the values are ≈(0.7-1.4) ± 0.2 G and ≈(1.4-2.8) ± 0.1 G, respectively.

Fundamental and harmonic plasma emission in different plasma environments

Aims: Emission of radio waves from plasmas through plasma emission with fundamental and harmonic frequencies is a familiar process known from solar type II radio bursts. Current models assume the existence of counterstreaming electron beam populations excited at shocks as sources for these emission features, which limits the plasma parameters to reasonable heliospheric shock conditions. However, situations in which counterstreaming electron beams are present can also occur with different plasma parameters, such as higher magnetisation, including but not limited to our Sun. Similar radio emissions might also occur from these situations. Methods: We used particle-in-cell simulations, to compare plasma microphysics of radio emission processes from counterstreaming beams in different plasma environments that differed in density and magnetization. Results: Although large differences in wave populations are evident, the emission process of type II bursts appears to be qualitatively unaffected and shows the same behaviour in all environments.

LOW-FREQUENCY OBSERVATIONS OF DRIFTING, NON-THERMAL CONTINUUM RADIO EMISSION ASSOCIATED WITH THE SOLAR CORONAL MASS EJECTIONS

Low-frequency (80 MHz) imaging and spectral (≈85-20 MHz) observations of moving type IV radio bursts associated with coronal mass ejections (CMEs) from the Sun on three different days are reported. The estimated drift speed of the bursts is in the range ≈150-500 km s–1. We find that all three bursts are most likely due to second harmonic plasma emission from the enhanced electron density in the associated white-light CMEs. The derived maximum magnetic field strength of the latter is B ≈ 4 G at a radial distance of r ≈ 1.6 R ☉.

First-order thermal correction to the quadratic response tensor and rate for second harmonic plasma emission

Three-wave interactions in plasmas are described, in the framework of kinetic theory, by the quadratic response tensor (QRT). The cold-plasma QRT is a common approximation for interactions between three fast waves. Here, the first-order thermal correction (FOTC) to the cold-plasma QRT is derived for interactions between three fast waves in a warm unmagnetized collisionless plasma, whose particles have an arbitrary isotropic distribution function. The FOTC to the cold-plasma QRT is shown to depend on the second moment of the distribution function, the phase speeds of the waves, and the interaction geometry. Previous calculations of the rate for second harmonic plasma emission (via Langmuir-wave coalescence) assume the cold-plasma QRT. The FOTC to the cold-plasma QRT is used here to calculate the FOTC to the second harmonic emission rate, and its importance is assessed in various physical situations. The FOTC significantly increases the rate when the ratio of the Langmuir phase speed to the electron thermal speed is less than about 3.

Multiple harmonic plasma emission

A generalized weak turbulence theory for electromagnetic emission at multiple harmonics of the plasma frequency is developed. In the literature, the electromagnetic emission at the plasma frequency and/or its second harmonic has been intensively studied. However, the emission at harmonics higher than the second harmonic is scarcely discussed. In the present paper, the higher harmonic plasma emission is explained by taking the interactions between the transverse mode and electrostatic nonlinear eigenmodes into consideration. The present analysis incorporates electrostatic nonlinear harmonic Langmuir waves into the fully electromagnetic weak turbulence formalism recently reformulated on the basis of the statistical mechanical Klimontovich approach. The wave kinetic equations for the transverse electromagnetic and Langmuir waves interacting with the harmonic Langmuir waves are derived, on the basis of which the emission of electromagnetic waves near multiple harmonics of the plasma frequency is qualitatively discussed.

A solar radio moving type IV burst of expanding arches type involving multi-sources

A complex solar radio moving type IV burst was observed on 23 September 1998 with the broadband (1.0-2.0 GHz and 2.6-3.8 GHz) spectrometers with high temporal and spectral resolutions at National Astronomical Observatories of China (NAOC). Comparing to the high spatial resolution data of Siberian Solar Radio Telescope (SSRT), we find that this burst is a rare type of moving type IV burst which is caused by the expanding arches, and the spatial structure oscillations of the radio sources are related with the time structure pulsations of the radio emission. Furthermore, the burst is associated with the multiple quasi-periodic long-term pulsations, and this suggests the existence of multi-scale magnetic structures in a large expanding coronal arch. We think the moving type IV burst is due to the synchrotron emission of the energetic electrons trapped in the expanding arch, and the multiple quasi-periodic pulsations are due to the second harmonic plasma emission.

THE POLARISATION OF SECOND HARMONIC CORONAL TYPE III BURSTS

The process of second harmonic plasma emission is considered, where two simplifying approximations made in previous treatments are relaxed. The revised theory can account for strong polarisation observed in some harmonic coronal type III bursts, and predicts that a correlation between these bursts and the fastest electron beam speeds associated with type III emission should be apparent. These high observed degrees of polarisation could not be explained in the earlier theory. In most cases, polarisation in the sense of the magnetoionic o-mode is predicted. The predicted degree of polarisation is shown to be strongly dependent on the form of the Langmuir wave number spectrum, and in particular on the magnitude of the wave number offset between beam-driven and backscattered Langmuir waves.

Solar Second Harmonic Plasma Emission and the Head-on Approximation

AbstractThe coalescence of two Langmuir waves, L and L′, produces emission at twice the plasma frequency in type II and type III solar radio bursts. The analysis of the coalescence process is usually simplified by assuming the head-on approximation, where the wavevectors of the coalescing waves satisfy kL′ ≈ −kL, corresponding to the two Langmuir waves meeting head on. However, this is not always a valid approximation, particularly when the peak of the Langmuir spectrum lies at small wavenumbers, for narrow band spectra, and for spectra with broad angular ranges. Realistic Langmuir wave spectra are used to investigate the effects of relaxing the head-on approximation.

A new investigation of microbursts at meter-decameter wavelengths

We report on a new investigation of microbursts at meter-decameter wavelengths observed using the Broad Band Array at Gauribidanur Radio Observatory. This is an independent set of observations of microbursts: previous observations had been obtained only by the Clark Lake multifrequency radioheliograph. We confirm several properties of microbursts reported earlier. In addition, we have studied some new properties of microbursts such as time profile characteristics, flux density and energy spectra for comparison with the corresponding properties of normal type III bursts. The present study supports the idea that the microbursts and the normal type III bursts are generated by electron beams of similar characteristics. We interpret the low brightness temperature of microbursts as follows: plasma waves generated by the electron beams through beam-plasma instability are quickly isotropized as they scatter on the density fluctuations in the corona. The resulting low levels of plasma waves are converted into transverse radiation of low brightness temperature. One important consequence of the isotropization is that the second harmonic plasma emission dominates the fundamental and hence the microbursts are expected to be predominantly a harmonic plasma emission.

Plasma emission from isotropic Langmuir turbulence - Are radio microbursts structureless?

The brightness temperature of radio emission through the fundamental and second harmonic plasma processes is determined for isotropic Langmuir waves of low-energy density in order to account for the microbursts at meter-dekameter wavelengths. The probable cause for low levels of Langmuir turbulence is the presence of isotropic density fluctuations in the corona which isotropize the beam-generated Langmuir waves. We determined the energy density of Langmuir waves attainable from the beam-plasma instability in the presence of isotropic density fluctuations. Since the electron density fluctuations isotropize the beam-generated plasma waves, the head-on collision of plasma waves becomes efficient to produce the second harmonic plasma emission. For reasonable beam parameters, the brightness temmperature of the fundamental never exceeds 10 exp 6 K, while the second harmonic covers the observed range of microburst brightness temperatures. Thus, the microbursts are predominantly at second harmonic. This leads to an important conclusion that the microbursts are structureless, similar to a population of normal type III bursts of low polarization with no fundamental-harmonic structure.

Radioheliograph and white-light coronagraph studies of a coronal mass ejection event

We analyze the radioheliograph and SMM-C/P observations of 1986 November 3 mass ejection event. The metric radio emissions are the only detected activity associated with the mass ejection, but are adequate to study the evolution of the event. The start time of the ejection seems to precede a possible flare behind the limb indicated by the early type III bursts. We discuss the physical relation between various types of bursts and the CME. We interpret moving type IV bursts as a plasma emission process. It is also shown using white-light coronagraph data that the density in the source region of the moving type IV is sufficient to support second harmonic plasma emission at the observed frequency of 50 MHz.

Second harmonic plasma emission involving ion sound waves

The theory for second harmonic plasma emission by the weak turbulence (or random phase) processes L + L ± S→T, proceeding in two three-wave steps, L ± S→L′ and L + L′→T, where L, S and T denote Langmuir. ion sound and electromagnetic waves, respectively, is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes, and constraints on the characteristics of the source plasma, are derived. Limits on the brightness temperature of the radiation and the levels of the L′ and S waves are determined. Expressions for the growth rates and path-integrated wave temperatures are derived for simple models of the wave spectra and source plasma.