Dissipative Trapped Electron Instability Research Articles

Nature of the isotope effect on transport in tokamaks.

The reduction of energy and particle losses with the increasing mass of the hydrogen isotope is more pronounced under conditions of improved confinement when the dominant ion temperature gradient instability is suppressed and other channels of anomalous transport are of importance. In this Letter, we reconsider the dissipative trapped electron (DTE) instability by taking into account finite Larmor radius effects in the analysis of the ion response to perturbations. By applying the improved mixing length approximation in order to estimate the transport coefficients, it is demonstrated that DTE contribution is intrinsically dependent on the isotope mass and provides a plausible explanation for the isotope effect. Contrary to the common belief, it is shown that the DTE turbulence may be of importance for reactor plasmas of low collisionality.

Interplay of Confinement Improvement, Density Peaking and Particle Recycling in the Radiatively Improved Mode

Possible channels for suppression of ion temperature gradient (ITG) instability in radiatively improved (RI) mode through peaking of the plasma density are discussed. An interpretive transport analysis is done which shows that increasing ratio between pinch velocity and diffusivity is of the most importance for the peaking. This validates theoretical models which predict a principle difference in this ratio for cases when transport is dominated by ITG or dissipative trapped electron instability. In transport computations these models allow to reproduce changes in the density profile and pattern of recycling by the L-RI transition.

Interplay of Confinement Improvement, Density Peaking and Particle Recycling in the Radiatively Improved Mode

Possible channels for suppression of ion temperature gradient (ITG) instability in radiatively improved (RI) mode through peaking of the plasma density are discussed. An interpretive transport analysis is done which shows that increasing ratio between pinch velocity and diffusivity is of the most importance for the peaking. This validates theoretical models which predict a principle difference in this ratio for cases when transport is dominated by ITG or dissipative trapped electron instability. In transport computations these models allow to reproduce changes in the density profile and pattern of recycling by the L-RI transition.

Confinement mechanisms in the radiatively improved mode

The characteristics of the toroidal ion temperature gradient (ITG) instability, considered as the main source of anomalous transport in the low (L) confinement mode of tokamaks, are analysed for the conditions of the radiatively improved (RI) mode triggered by seeding of impurities. Based on experimental profiles from TEXTOR-94 we deduce that the ITG-induced turbulence is quenched in the RI-mode in a large part of the plasma radius. Under those conditions the dissipative trapped electron (DTE) instability dominates the transport. The peaking of the electron density, one of the most remarkable features of the L-RI transition, is explained by the difference in contributions of ITG and DTE unstable modes to the diffusive and convective components of the electron flow. The shearing of the plasma toroidal velocity observed in the RI-modes with unbalanced neutral injection is successfully modelled by taking into account both the anomalous plasma viscosity due to ITG-turbulence and predictions of the revisited neoclassical theory.

Effects of magnetic geometry, fluctuations, and electric fields on confinement in the Advanced Toroidal Facility

Recent experiments in the Advanced Toroidal Facility (ATF) [Fusion Technol. 10, 179 (1986)] have been directed toward investigations of the basic physics mechanisms that control confinement in this device. Measurements of the density fluctuations throughout the plasma volume have provided indications for the existence of theoretically predicted dissipative trapped electron and resistive interchange instabilities. These identifications are supported by results of dynamic configuration scans of the magnetic fields during which the magnetic well volume, shear, and fraction of confined trapped particles are changed continuously. The influence of magnetic islands on the global confinement has been studied by deliberately applying error fields which strongly perturb the nested flux-surface geometry, and the effects of electric fields have been investigated by means of biased limiter experiments.

Transport through dissipative trapped electron mode and toroidal ion temperature gradient mode in TEXTOR

A self-consistent transport code is used to evaluate how plasma confinement in tokamaks is influenced by the microturbulent fields excited by the dissipative trapped electron (DTE) instability. As shown previously, the saturation theory on which the code is based has been developed from first principles. The numerical results reproduce well the Neo-Alcator scaling law observed experimentally (for example in TEXTOR) in non-detached Ohmic discharges, the confinement degradation resulting when auxiliary heating is applied and a large number of other experimental observations. The potential impact of the toroidal ion temperature gradient (ηi) mode on energy confinement is assessed by estimating the ion thermal flux with the help of the mixing length approximation. The temperature and density profiles measured in TEXTOR (qa ≃ 2.45) are compared at either variable mean density or variable additional power, and their stability against DTE and ηi modes is checked; in the latter case, a new criterion is used, which is valid for arbitrary curvature. All profiles examined are marginally unstable for the two modes, essentially between the q = 1 and q = 2 magnetic surfaces. The code results and the stability analysis lead to the following conclusions and suggestions: (1) The DTE instability is sufficient to explain the anomalous heat transport in low density discharges (attached plasmas) with or without additional heating; the marginal instability for the DTE mode thus follows from heat flux constraints. (2) The observed marginal instability against the ηi mode must then follow from particle flux constraints. (3) The condition that both γηi and γDTE (γ = growth rate) must be small is the restriction which determines the profiles that correspond to the experimental conditions and which determines, to a large extent, profile consistency. (4) Finally, it is suggested that the deviation from Neo-Alcator scaling, the density limit and the phenomenon of plasma detachment are interrelated effects which arise at high densities, when the constraint on the electron heat flux becomes harder to satisfy.

Enhanced small-scale turbulence oscillations correlated with sawtooth relaxations in the TEXTOR tokamak

A periodic enhancement of the microturbulence level by sawtooth relaxations has been detected by CO2 laser forward scattering in the TEXTOR tokamak. This feature is reproduced quantitatively by a heat transport code in which the anomalous electron transport coefficient is calculated self-consistently, following a theoretical model of the saturation of the dissipative trapped electron instability. The code also predicts a strong modulation of the heat flux throughout the plasma and a strong ‘profile consistency’ as demonstrated elsewhere by continuous temperature measurements. A simple interpretation of these results is given. The calculated global plasma parameters, such as the energy confinement time and the loop voltage, are in good agreement with the measured values.

Observations of the dissipative trapped electron instability in a mirror plasma produced by electron-cyclotron resonance

The dissipative trapped electron instability driven by the finite Larmor radius effects is observed in a mirror plasma produced by electron-cyclotron resonance using the Lisitano coil. The effect of the radial electron temperature gradient on the excitation of this mode is studied theoretically and experimentally. It is found that the electron temperature gradient opposite to the density gradient tends to stabilize this mode.

Dissipative trapped-electron instability in a magnetic quadrupole

Drift wave instability in a magnetic quadrupole is analysed. Formulas are derived for the growth rate due to a dissipative trapped-electron mechanism and the damping rate due to ion viscosity. A numerical study is made of the drift waves which occur spontaneously in the shared flux region of the UMIST quadrupole. The calculated growth rate is of the same order as the experimental estimates but the viscous damping is not sufficiently large to account for the upper limit on the axial wave number of the observed spectrum.

Optimal Control of Trapped Electron Instability by a Modulated Neutral Beam

Equivalent lumped parameter system representation for dissipative trapped electron instability involving many modes is obtained. Optimal control theory in the presence of noise is used to design a stabilizing feedback network, with a modulated neutral beam as a remote suppressor. The optimality criterion is the minimization of the total energy of control and instability fluctuations. It is shown that the control power does not depend on the level of instability fluctuations in the absence of feedback, but on the noise level in plasma.

Curvature and gradient drift effects on trapped-electron modes

Computer simulations of local trapped-electron modes in toroidal plasmas, including curvature and gradient drift effects, are presented. These simulations are based on the linearized electron drift-kinetic equation, Fourier transformed with respect to the poloidal and toroidal angles. No à priori distinction is made between trapped and circulating particles, and collisions are represented by a Lorentz model giving pitch-angle diffusion. A series of computations shows the dependence of the growth rates on ρe/r and on νef/ω* (ρe is the thermal electron gyroradius, r is the flux surface minor radius, νef is the effective collision frequency, and ω* is the drift wave frequency). For νef≲0.5 ω*, strong drift resonance effects are observed, but these are destabilizing only for ρe/r below a critical value. These growth rates decrease rapidly for collision frequencies νef≳ω*. For νef≳≳ω*, the dissipative trapped-electron instability occurs. In this regime, curvature and gradient drifts are stabilizing; Landau damping due to resonant circulating electrons reduces the growth rates and significantly modifies the mode structure of the dissipative trapped-electron instability.

Trapped electron instability in a linear multi-mirror experiment

The dissipative trapped electron instability is observed in the linear multi-mirror experiment. This instability is observed in two forms, one driven by the electron temperature gradient, and one driven by finite Larmor radius effects. The experimental results are in reasonable agreement with the theoretical predictions of the linear dispersion relation.

Nonlinear saturation of the dissipative trapped electron instability

The nonlinear saturation amplitude of the dissipative trapped electron instability is calculated. Comparison is made with an experiment carried out in linear mirror geometry and near threshold, with only a single mode predominating. A model in which the untrapped electrons respond in a Boltzmann fashion yields good agreement. A model in which Landau damping is included predicts saturation amplitudes much smaller than observed. The first model seems appropriate for linear geometries while the second may apply to closed devices.

Spectral formulation of the dissipative trapped-electron instability

An analysis and computer simulations of dissipative trapped electron modes in toroidal plasmas based on the electron drift-kinetic equation Fourier transformed with respect to the poloidal and toroidal angles are presented.

Turbulence theory for the dissipative trapped electron instability

Drift orbit diffusion induced by turbulence acting on trapped electrons is shown to reduce and broaden the magnetic drift resonance and produce the dominant nonlinear saturation mechanism for the dissipative trapped electron instability. The fluctuation level obtained from such a theory is found to be consistent with present experimental observations.

Effects of finite Larmor radius and ion Landau damping on the dissipative trapped electron instability

The authors have experimentally observed a dissipative universal instability caused by the presence of magnetically trapped electrons and excited by finite Larmor radius effects. The experiment is performed in a linear device having two magnetic mirrors. An ion cyclotron resonance scheme is used to heat the ions (protons) from one to ten eV in order to enhance the effect of finite ion Larmor radius. Ion Landau damping is observed to become important in the case of hot ions and short magnetic mirror cell length. The measured real frequency ( omega R approximately 25 kHz) and fluctuation amplitude (n/n0 approximately 25%) are found to vary in the same manner as the frequency and growth rate predicted by a linear theory, taking into account the finite axial structure of the mode.

An experimental study of the trapped electron instability using a feedback diagnostic

The dissipative trapped electron instability has been studied experimentally and theoretically in a linear device. Special emphasis is given to the effects of changing the length of the magnetic trapping cell (30 cm<2L<75 cm) and to the development of feedback as a diagnostic technique. It is shown that the dominant axial wavenumber k2, is determined by the length of the trapping cell, and this in turn has an effect on the real frequency omega R approximately=50 kHz. The minimum mirror ratio for instability onset is found to be Rc approximately=1.2. The dissipative nature of the instability is also demonstrated using feedback. The mode is definitely identified as the dissipative trapped electron instability through the dependence of the growth rate on electron collision frequency mirror ratio and through the radial and axial localization of the mode. The saturation amplitude of the density fluctuations is compared with the measured growth rate to show that the growth rate is proportional to the square of the saturation level.

Observation of the dissipative trapped electron instability in toroidal geometry

Low frequency plasma density fluctuations have been observed in the common flux volume of the dc octopole. For collision frequencies comparable to the fluctuation frequency (which is close to the diamagnetic drift frequency), the fluctuations are identified as dissipative trapped electron modes. In the high collision frequency range the collisional drift wave is observed. A strong quenching of the trapped electron modes is observed when the local safety factor is a low-order rational number. Very little transport is associated with the observed fluctuations.

Numerical study of the dissipative trapped-electron instability in tokamaks

The dispersion relation for the dissipative trapped-electron mode including the effects of magnetic shear, finite ion Larmor radius, banana-plateau velocity space separation, magnetic curvature drift resonance, ion-ion collisions, etc. is used to examine the plasma stability of recent tokamak experiments. Regimes of importance of various effects in these experiments are also discussed. Instabilities mostly occur at kθ ρi ∼ 1, where kθ is the azimuthal wave number and ρi is the ion Larmor radius. The often used anomalous heat conduction coefficient, , predicts losses comparable to those observed in TFR, ST, and ATC.

Collisional effects on trapped electron instabilities

The effects of collisions on dissipative trapped electron instabilities are evaluated by distinguishing between the perpendicular and parallel electron velocity components when calculating trapped and untrapped electron contributions. The growth rate is obtained for all regimes of collisionality and reduces to previous results in appropriate limits. It is shown that the dominant effect of finite collisionality is to determine the number of trapped and untrapped electrons and that collisional broadening removes the resonant electron response only for collision frequencies greater than or equal to ten times the wave frequency, νe≳10ω. For such large νe/ω, ion-ion collisions are found to exert a far stronger stabilizing influence than broadening.