Anomalous Doppler Resonance Research Articles

Nonlinear saturation of whistler modes driven by runaway electrons

Runaway electrons exhibit kinetic instabilities with potentially beneficial consequences. The anomalous Doppler resonance between the electrons and whistler modes is a primary underlying mechanism. These instabilities require a first-principle nonlinear theoretical analysis, which would ultimately enable assessment of their impact on disruption mitigation and diagnostics, especially in ITER-relevant conditions. This paper presents recent progress in developing the required theoretical framework for isolated nonlinear resonances. By employing the generic bump-on-tail model, we predict the wave saturation levels in both near-threshold and strongly driven regimes. Remarkably, for the waves of interest, the parallel component of the wave vector dictates the parallel momentum of the resonant particles. This feature, together with the expected wave saturation level, provides a complete description of the resonance impact on the runaway electron distribution function. We show that the parametric dependence of the nonlinearly saturated mode provides a way to recover certain features of the runaway momentum distribution function.

Marginal stability constraint on runaway electron distribution

High-frequency kinetic instabilities of the strongly anisotropic runaway electrons (RE) can enhance the pitch-angle scattering of the runaways significantly. This wave-induced scattering can easily prevail over runaway scattering on high-Z impurities. In a steady state, collisional damping balances the kinetic drive of the unstable waves, keeping the RE distribution function at marginal stability. The marginal stability constraint limits the achievable RE densities and the shape of the RE distribution function. In this study, we consider whistler and compressional Alfvén waves as the primary source of enhanced elastic scattering of the runaways. By balancing the anomalous Doppler resonance drive with the collisional wave damping, we find the RE distribution function in the ultra-relativistic range of the phase space. We also derive an expression for the spectral energy density of the waves. We show that the power needed to compensate for the wave dissipation is negligible compared to the work of the electric field. The latter is in balance with the synchrotron losses of the runaway electrons.

Overview of physics results from MAST towards ITER/DEMO and the MAST Upgrade

New diagnostic, modelling and plant capability on the Mega Ampère Spherical Tokamak (MAST) have delivered important results in key areas for ITER/DEMO and the upcoming MAST Upgrade, a step towards future ST devices on the path to fusion currently under procurement. Micro-stability analysis of the pedestal highlights the potential roles of micro-tearing modes and kinetic ballooning modes for the pedestal formation. Mitigation of edge localized modes (ELM) using resonant magnetic perturbation has been demonstrated for toroidal mode numbers n = 3, 4, 6 with an ELM frequency increase by up to a factor of 9, compatible with pellet fuelling. The peak heat flux of mitigated and natural ELMs follows the same linear trend with ELM energy loss and the first ELM-resolved Ti measurements in the divertor region are shown. Measurements of flow shear and turbulence dynamics during L–H transitions show filaments erupting from the plasma edge whilst the full flow shear is still present. Off-axis neutral beam injection helps to strongly reduce the redistribution of fast-ions due to fishbone modes when compared to on-axis injection. Low-k ion-scale turbulence has been measured in L-mode and compared to global gyro-kinetic simulations. A statistical analysis of principal turbulence time scales shows them to be of comparable magnitude and reasonably correlated with turbulence decorrelation time. Te inside the island of a neoclassical tearing mode allow the analysis of the island evolution without assuming specific models for the heat flux. Other results include the discrepancy of the current profile evolution during the current ramp-up with solutions of the poloidal field diffusion equation, studies of the anomalous Doppler resonance compressional Alfvén eigenmodes, disruption mitigation studies and modelling of the new divertor design for MAST Upgrade. The novel 3D electron Bernstein synthetic imaging shows promising first data sensitive to the edge current profile and flows.

Interaction of electromagnetic waves and suprathermal electrons in the near-critical electric field limit

The velocity-space anisotropy of suprathermal electron distributions is a source of free energy that may destabilize plasma waves through a resonant interaction between the waves and the energetic electrons. In this work we use a suprathermal electron distribution appropriate for the case when the accelerating electric field is near-critical and we investigate the frequencies, wave numbers and propagation angles of the most unstable waves using a general dispersion relation. It is shown that if the electric field is sub-critical, the anisotropy is not enough to drive electromagnetic waves unstable, as the Landau damping of the waves overwhelms the drive through the anomalous Doppler resonance. In the case when the electric field is supercritical, two types of electromagnetic waves will be destabilized, the electron-whistler and the extraordinary electron wave. The number of electrons for destabilization of the latter is several orders of magnitude lower than for the electron-whistler wave. Consequently, the threshold for destabilization of the extraordinary electron wave is much lower.

Characteristic of slide away discharges in the KSTAR tokamak

Low density slide away discharges with anomalous Doppler resonance (ADR) effects have been observed in the KSTAR tokamak. When the line averaged electron density was lower than 0.6×1019 m−3, the discharges went into the slide-away regime with relaxations in the electron cyclotron emission due to the ADR effects which transferred the runaway electron energy from parallel to perpendicular motion. The suppression of the ADR effects has been achieved by electron cyclotron resonance heating which enhanced the perpendicular energy of electrons and led to an isotropization of the electron distribution function.

A stochastic mechanism of electron heating

Due to Landau resonant interaction with lower hybrid waves in the lower hybrid current drive scheme part of electrons are accelerated and, as a result of this, a tail of energetic electrons is formed on the electron distribution function. The same situation takes place in the problem of type III radio bursts when the suprathermal burst electrons acquire a plateau distribution due to excitation of plasma waves in the solar wind plasma. These distributions are unstable with respect to the cyclotron excitation of waves at anomalous Doppler resonance (“fan” instability). In this case, the tail electrons interact simultaneously with both (i) waves that accelerate or decelerate them (Čerenkov resonance) and (ii) waves excited in the process of the fan instability that led to their pitch angle diffusion. Because velocity diffusion lines of electrons formed due to heir interaction with each type of waves intersect, this interaction can lead not only to pitch angle diffusion but also to heating of electrons mainly in perpendicular direction. We investigated this mechanism of electron heating and studied the temporal evolution of the electron temperature and the energy of excited waves. Our results show significant enhancement of the electron perpendicular temperature T⊥ due to this stochastic heating mechanism.

Experimental observation of interaction of runaway electrons with lower hybrid waves in slide-away regime in the HT-7 tokamak

The characters of slide-away regime in the HT-7 tokamak have been investigated, and evidences that lower hybrid waves (LHW) are excited in slide-away regime are presented based on local fast electron bremsstrahlung (FEB) emission profile and FEB emission spectrum. The interaction of high energy runaway electrons with those excited LHW via anomalous Doppler resonance is analyzed and the resonance energy is derived with which the behavior of those relevant signals in the experiment can be explained very well. It is shown that this interaction can provide an effective way to reduce the damage to the machine caused by runaway electrons.

Comparison of anomalous Doppler resonance effects with molybdenum and graphite limiters on HT-7

The material of limiter in HT-7 tokamak was changed from graphite to molybdenum in the last experimental campaign. The pitch angle scattering of runaway electrons due to anomalous Doppler resonance effects was observed. The experimental results agree very well with the stable boundary condition expected from the linear resistive theory but only agree with that from the nonlinear evolutionary of runaway-electron distribution theory in low electric field region. The current carried by runaway electrons is the same under different limiter conditions.

Present Status of the Electron Cyclotron Emission Measurements on HT-7 and EAST

Present status of the diagnostics for electron cyclotron emission measurements on both HT-7 and EAST is reported. A 16-channel heterodyne radiometer system and a 20-channel grating polychromator, have been installed on HT-7 and EAST. A 32-channel heterodyne radiometer system, with a wider frequency coverage and better spatial resolution, is being built. In order to provide a reliable electron temperature profile, an in-situ absolute calibration system is currently being built. With the ECE measurements, study on the electron heat transport and the anomalous Doppler resonance is conducted.

Stability of the strahl electron distribution function and its dynamics

Abstract. It is shown that core-strahl electron system in the solar wind plasma is unstable with respect to excitation of the lower hybrid waves at anomalous Doppler resonance due to anisotropy of the strahl electron velocity distribution. Dynamics of the strahl electron distribution due to interaction with excited waves is studied.

Anomalous Doppler resonant interaction of runaway electrons with lower hybrid waves in the HT-7 tokamak

Due to the decrease of the relativistic cyclotron frequency and increase of the Larmor radius with an increase in runaway electron energy, cyclotron harmonic interaction between runaway electrons and lower hybrid waves (LHWs) may occur. In this paper, the anomalous Doppler resonance interaction between runaway electrons and launched LHWs has been investigated in the HT-7 tokamak.

Identification of anomalous Doppler resonance effect during current ramp down in HT-7 tokamak

The abrupt steep jump of electron cyclotron emission (ECE) signals during current ramp-down has been observed and explained by an anomalous Doppler resonance effect (ADR). The identifying process of ADR was presented based on the fast Fourier transform (FFT) technique. The threshold value for triggering a steep jump on ECE signals has been identified under different discharge conditions.

Lower-hybrid waves generated by anomalous Doppler resonance in auroral plasmas

AbstractThis paper describes some aspects of lower-hybrid wave activity in space plasmas. Lower-hybrid waves are particularly important since they can transfer energy efficiently between electrons and ions in a collisionless magnetized plasma. We consider the ‘fan’ or anomalous Doppler resonance instability driven by energetic electron tails and show that it is responsible for the generation of lower-hybrid waves. We also demonstrate that observations of their intensity are sufficient to drive the modulational instability.

Characteristics of the runaway electron beam instability in the HT-7 tokamak

AbstractRunaway electron ream instabilities have been observed in Ohmic plasmas in the HT-7 tokamak. The instability regime is characterized by relaxations in the electron cyclotron emission due to the relativistic anomalous Doppler resonance effect which transfers energy from parallel to perpendicular motion. Two types of instabilities in the slide-away regime have been observed in the HT-7 tokamak. The scaling of the threshold value for the instabilities to occur has been derived. It is found that the threshold value is linearly dependent on the plasma current and independent of the toroidal magnetic field strength.

Effect of gas puffing on current ramp-down ohmic discharges in HT-7 tokamak

A new behaviour of current ramp-down ohmic deuterium discharges has been observed by additional deuterium fueling/gas puffing in HT-7 tokamak. It has been investigated, that the additional gas puffing converts the fast pitch angle scattering (FPAS) event to normal pitch angle scattering (NPAS) event characterized by higher electron energies and shifting the trigger time of the event, which is dependent on the pulse injection time. The attempt has also been made to investigate the scaling of critical values for runaway electrons generation and determination of their related energies along with trigger parameters of the instability and conversion relation between NPAS and FPAS events by ramping-down plasma current and changing the toroidal magnetic field in low-density ohmic discharges. The direct and inverse relationship has been observed for critical trigger value ω p e / ω c e of runaways generation with the plasma current and the toroidal magnetic field strength respectively. The runaway instability regime is characterized by relaxations in the electron cyclotron emission due to relativistic anomalous Doppler resonance (ADR) effect, which transfers energy from parallel to perpendicular motion.

On the origin of the circular polarization in radio pulsars

The properties of circularly polarized waves are studied in the pulsar magnetosphere plasma. It is shown that some observational characteristics of the circular polarization observed in the pulsar radio emission can be qualitatively explained in the framework of the model based on anomalous Doppler resonance. Performed analysis provides that if the difference between Lorentz factors of electrons and positrons is relatively high, one of the circularly polarized waves becomes superluminal and therefore cannot be generated by cyclotron instability. We suggest that this case corresponds to pulsars with the domination of one hand of circular polar-ization through the whole averaged pulse profile at all observed frequencies. For intermediate values of the difference between Lorentz factors, both circularly polarized waves are generated, but the waves of one handedness are much more effectively generated for high frequencies, whereas generation of another handedness dominates for low frequencies. This should correspond to pulsars with strong frequency dependence of the degree of circular polarization. The case of relatively small difference between Lorentz factors corresponds to pulsars with sign reversal of the circular polarization in the centre of averaged pulse profiles.

Interaction of suprathermal solar wind electron fluxes with sheared whistler waves: fan instability

Abstract. Several in situ measurements performed in the solar wind evidenced that solar type III radio bursts were some-times associated with locally excited Langmuir waves, high-energy electron fluxes and low-frequency electrostatic and electromagnetic waves; moreover, in some cases, the simultaneous identification of energetic electron fluxes, Langmuir and whistler waves was performed. This paper shows how whistlers can be excited in the disturbed solar wind through the so-called "fan instability" by interacting with energetic electrons at the anomalous Doppler resonance. This instability process, which is driven by the anisotropy in the energetic electron velocity distribution along the ambient magnetic field, does not require any positive slope in the suprathermal electron tail and thus can account for physical situations where plateaued reduced electron velocity distributions were observed in solar wind plasmas in association with Langmuir and whistler waves. Owing to linear calculations of growth rates, we show that for disturbed solar wind conditions (that is, when suprathermal particle fluxes propagate along the ambient magnetic field), the fan instability can excite VLF waves (whistlers and lower hybrid waves) with characteristics close to those observed in space experiments.Key words. Space plasma physics (waves and instabilities) – Radio Science (waves in plasma) – Solar physics, astrophysics and astronomy (radio emissions)

Electromagnetic wave excitation in a dense plasma (?Pe>?Be) by ?tail? electrons

We consider the possibility of electromagnetic wave generation in a plasma with ωPe>ωBe by “tail” electrons which scatter on anomalous Doppler resonance of potential waves with ω2≦ωBe. These oscillations, organized into periodic waves, resonantly excite potential waves of harmonic frequencies ω1=s·ω2≧ωPe, s=2, 3, .., easily transformable to electromagnetic radiation. A coherent mechanism for solar radio flares is developed.

On the anomalous Doppler/inner Lindblad resonance

There are strong formal similarities between the condition for anomalous Doppler resonance in plasmas ( omega -k/sub ///v/sub ///=- Omega , where omega is the frequency of the perturbing wave field, k/sub ///v/sub /// measures the Doppler shift due to guiding-centre motion, and Omega is the cyclotron frequency) and the condition for inner Lindblad resonance in stellar discs ( Omega b- Omega 0=- kappa /m, where Omega b is the frequency of the perturbing wave field, whose azimuthal harmonic number is m, Omega 0 is the natural frequency of equilibrium guiding-centre circulation, and kappa is the epicyclic frequency). It is shown that this similarity reflects a close underlying correspondence between the two forms of resonance.

Runaway electron distributions and their stability with respect to the anomalous Doppler resonance

The stability of nonrelativistic runaway electron distributions with respect to the anomalous Doppler resonance is examined in a range of parameters of interest to tokamaks, i.e., for Y≡ωpe/Ωce≤2 and for Ohmic electric fields ε≡E/Ec≤0.1. Distribution functions are calculated numerically within a region up to 35ve (thermal velocities) using a finite-element 2-D Fokker–Planck code. Alternatively, an analytic approximation for the runaway distribution function is used, valid beyond the critical velocity vc≂ve(Ec/E)1/2. Stability thresholds in (ω,k∥) space are then determined. For example, for Y=1 and ε=0.1, and providing that the runaway tail extends at least to 30ve, unstable waves exist having ω≤0.6Ωce and k∥≤0.03Ωce/ve.