Precession Drift Frequencies Research Articles

The synergetic effects of three-dimensional magnetic perturbations and finite beta on collisionless trapped electron mode in tokamak plasmas

The effects of three-dimensional (3D) magnetic perturbations (MPs) and finite beta (β, i.e., the ratio of plasma kinetic pressure to magnetic pressure) on the instability of collisionless trapped electron mode (CTEM) have been studied. Based on the local 3D equilibrium model, we have derived general expressions for longitudinal invariant and the corresponding precession drift frequency of trapped electrons, which include the synergetic effects of MPs and finite β. It is found that 3D effects can either stabilize or destabilize CTEM instability by analytically solving the linear dispersion relation of CTEM. These effects depend on the poloidal and toroidal mode numbers as well as the phase of 3D MPs. Specially, for the destabilizing phase of MPs, the stabilizing effect of finite β on CTEM can be even reversed when the displacement of magnetic flux surface exceeds a critical value. Moreover, the synergetic effects of 3D MPs with stabilizing phase and finite β can further reduce the required absolute value of negative magnetic shear to completely stabilize CTEM instability. This indicates that 3D MPs might be used as an actuator for lowing the level of anomalous electron heat transport, and thus facilitate the formation of electron internal transport barrier (eITB).

The synergetic effects of three-dimensional magnetic perturbations and finite beta on collisionless trapped electron mode in tokamak plasmas

Abstract The effects of three-dimensional (3D) magnetic perturbations (MPs) and finite beta (β, i.e., the ratio of plasma kinetic pressure to magnetic pressure) on the instability of collisionless trapped electron mode (CTEM) have been studied. Based on the local 3D equilibrium model, we have derived general expressions for longitudinal invariant and the corresponding precession drift frequency of trapped electrons, which include the synergetic effects of MPs and finite β. It is found that 3D effects can either stabilize or destabilize CTEM instability by analytically solving the linear dispersion relation of CTEM. These effects depend on the poloidal and toroidal mode numbers as well as the phase of 3D MPs. Specially, for the destabilizing phase of MPs, the stabilizing effect of finite β on CTEM can be even reversed when the displacement of magnetic flux surface exceeds a critical value. Moreover, the synergetic effects of 3D MPs with stabilizing phase and finite β can further reduce the required absolute value of negative magnetic shear to completely stabilize CTEM instability. This indicates that 3D MPs might be used as an actuator for lowing the level of anomalous electron heat transport, and thus facilitate the formation of electron internal transport barrier (eITB).

Simulation study of energetic-particle driven off-axis fishbone instabilities in tokamak plasmas

Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave–particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.

Effect of precession drift motion of trapped thermal ions on ballooning modes in helical plasmas

The linear stability analysis of resistive ballooning modes in Large Helical Device plasmas has been carried out by numerical simulation based on the kinetic magnetohydrodynamic (MHD) model where thermal ions are simulated with the drift-kinetic model. Due to the curvature drift and the gradient B drift, the orbit of trapped ions not only deviates from the magnetic surface but also has the precession motion in the poloidal and toroidal directions. Even when the trapped ions remain well inside the radial profile of the MHD mode, the response of the trapped ions is weakened when the precession drift frequency of the trapped ions with respect to the mode phase is close to or larger than the linear growth rate of the instability. This results in the suppression of the ion perpendicular pressure perturbation to the magnetic field leading to the reduction of the linear growth rate.

Landau resonant modification of multiple kink mode contributions to 3D tokamak equilibria

Detailed measurements of the plasma’s response to applied magnetic perturbations provide experimental evidence that the form of three-dimensional (3D) tokamak equilibria, with toroidal mode number n = 1, is determined by multiple stable kink modes at high-pressure. For pressures greater than the ideal magnetohydrodynamic (MHD) stability limit, as calculated without a stabilizing wall, the 3D structure transitions in a way that is qualitatively predicted by an extended MHD model that includes kinetic wave-particle interactions. These changes in poloidal mode structure are correlated with the proximity of rotation profiles to thermal ion bounce and the precession drift frequencies suggesting that these kinetic resonances are modifying the relative amplitudes of the stable modes. These results imply that each kink may eventually be independently controlled.

Trapped energetic ion dynamics affected by localized electric field perturbations

Trapped energetic ion orbits in helical systems are numerically simulated using the Lorentz model. Simulation results of precession drift frequencies of trapped energetic ions are benchmarked by those of analytic solutions. The effects of the electric field perturbation localized at the rational surface on trapped energetic ions are examined, where the perturbation has an arbitrary rotation frequency and an amplitude fixed in time. It is found that the trapped energetic ions resonantly interact with the perturbation, when the rotation frequency of the perturbation is comparable to the precession drift frequencies of trapped energetic ions. The simulation results are suggestive to a mechanism of the energetic-ion-induced interchange mode, which might be associated with the fishbone mode observed in helical systems.

Novel Theory of Energetic-Ion-Induced Interchange Mode

On the basis of a kinetic energy principle, it is shown that the interchange mode in helical systems is excited by trapped energetic ions, where the ideal interchange mode is stable. The mode has a rotation frequency comparable to precession drift frequencies of trapped energetic ions. The theory explains how to apply the fishbone mode theory originally developed in tokamaks to helical systems.

Electron fishbones in FTU and Tore Supra tokamaks

This work presents a comparative study of the experimental observation of MHD instabilities identified as electron fishbone-like modes that appear in plasmas with lower hybrid current drive in FTU and Tore Supra tokamaks. Initially, the mode-induced electronic temperature oscillations measured by electron cyclotron emission were used to study the evolutions of the frequency and position of these modes. In FTU, where fishbones with and without bursting behaviour are observed, it was found that the evolutions of the mode position and frequency follow opposite trend in the two regimes. In Tore Supra, where abrupt changes between modes with different mode structures are often observed, it was found that the mode position evolves continuously and the wavenumbers follow an inverse cascade starting from an m/n = 4/4 mode and finishing in an 1/1 mode. In a second step, the energy of resonant electrons was estimated from the resonant condition of the precession drift frequency. It was found that in Tore Supra the resonant condition does not change during the frequency jumps. The relevance of the correction due to the pitch angle of the resonant electrons and the possible role of the energetic passing particles in the drive of these modes are discussed from the results obtained in both machines.

Effect of Collisionality on Kinetic Stability of the Resistive Wall Mode

The impact of collisionless, energy-independent, and energy-dependent collisionality models on the kinetic stability of the resistive wall mode is examined for high pressure plasmas in the National Spherical Torus Experiment. Future devices will have decreased collisionality, which previous stability models predict to be universally destabilizing. In contrast, in kinetic theory reduced ion-ion collisions are shown to lead to a significant stability increase when the plasma rotation frequency is in a stabilizing resonance with the ion precession drift frequency. When the plasma is in a reduced stability state with rotation in between resonances, collisionality will have little effect on stability.

Magnetic drift kinetic damping of the resistive wall mode in large aspect ratio tokamaks

An analytical, large aspect ratio, calculation of the drift-kinetic energy perturbation is carried out for the resistive wall mode, due to the mode resonance with the magnetic precession drifts of trapped thermal ions and electrons. Four asymptotic cases are identified and analyzed in detail. Generally, a partial stabilization of the mode is possible thanks to the kinetic correction to the perturbed plasma energy. A complete stabilization can occur only in a narrow space of the plasma equilibrium parameters. Kinetic destabilization of the mode is also possible due to a finite pressure correction to the precession drift frequency.

Resistive wall mode stabilization in slowly rotating high beta plasmas

DIII-D experiments show that the resistive wall mode (RWM) can remain stable in high β scenarios despite a low net torque from nearly balanced neutral beam injection heating. The minimization of magnetic field asymmetries is essential for operation at the resulting low plasma rotation of less than 20 krad s−1 (measured with charge exchange recombination spectroscopy using C VI emission) corresponding to less than 1% of the Alfvén velocity or less than 10% of the ion thermal velocity. In the presence of n = 1 field asymmetries the rotation required for stability is significantly higher and depends on the torque input and momentum confinement, which suggests that a loss of torque-balance can lead to an effective rotation threshold above the linear RWM stability threshold. Without an externally applied field the measured rotation can be too low to neglect the diamagnetic rotation. A comparison of the instability onset in plasmas rotating with and against the direction of the plasma current indicates the importance of the toroidal flow driven by the radial electric field in the stabilization process. Observed rotation thresholds are compared with predictions for the semi-kinetic damping model, which generally underestimates the rotation required for stability. A more detailed modeling of kinetic damping including diamagnetic and precession drift frequencies can lead to stability without plasma rotation. However, even with corrected error fields and fast plasma rotation, plasma generated perturbations, such as edge localized modes, can nonlinearly destabilize the RWM. In these cases feedback control can increase the damping of the magnetic perturbation and is effective in extending the duration of high β discharges.

Rotational Stabilization of Resistive Wall Modes by the Shear Alfvén Resonance

It is found that resistive wall modes with a toroidal number n = 1 in tokamaks can be stabilized by plasma rotation at a low Mach number, with the rotation frequency being lower than the ion bounce frequency but larger than the ion and electron precession drift frequencies. The stabilization is the result of the shear-Alfvén resonance, since the thermal resonance effect is negligible in this rotation frequency range. This indicates that tokamaks can operate at normalized pressure values beyond the no-wall stability limit even for low values of plasma rotation, such as those expected in fusion reactor scale devices.

Resistive wall mode in collisionless quasistationary plasmas.

The stability analysis of the n=1 resistive wall mode is carried out for a simplified model of collisionless tokamak plasma. It is found that the trapped particle compressibility and the resonance between the mode and the precession drift frequency lead to a significant improvement of the beta stability limits. It is shown that, within the frame of the simplified model, the resistive wall mode can be fully suppressed and the plasma can be stable up to the wall beta limits for a slow plasma rotation.

Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks

The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady-state solution of the wave-kinetic equation. Distant nonlinear interactions between low-kθ and high-kθ modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low-kθ [kθρs ≪(Ln/R)1/2] modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from kθρs ≂(Ln/R)1/2 to kθρs≂1 according to an approximate power law k−3θ. Various fluctuation amplitudes at saturation and the fluctuation-induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher Ti/ Te, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.