Magnetic Drift Resonance Research Articles

The phase-space structure of a nonlinear ion diffusion tensor in ion-temperature-gradient-driven turbulence

The phase-space structure of an ion diffusion tensor in ion temperature gradient (ITG)-driven turbulence is studied using the newly developed numerical code Numerical Diagnosis of Transport Matrix. The numerical results show that at both the linear and nonlinear stage, the diffusion tensor of ITG turbulence presents a typical ballooning structure in the poloidal direction and a magnetic drift resonance structure in velocity space. The D rr and D rK components of the diffusion tensor satisfy the Stokes–Einstein relation. It is found that the phase-space structure of the ion diffusion tensor at the linear stage is induced by the resonance between ions and ITG eigenmodes, while that at the nonlinear stage is induced by the resonance between ions and the daughter ballooning modes under the poloidal acceleration of nonlinear zonal radial electric fields.

Kinetic ballooning mode unstable in the 2nd stability regime as a possible source of the low-k broadband fluctuation observed in the wide-pedestal QH-mode

The kinetic ballooning mode destabilized by the ion magnetic curvature drift resonance in the 2nd ballooning stability regime is shown to be a plausible candidate for the low-k broadband fluctuation recently observed in the wide-pedestal quiescent-H (QH) mode of DIII-D. With its intrinsic real frequency approaching very closely to the ion pressure diamagnetic frequency in the pedestal-like condition with a steep gradient, this mode can be nearly free from the first-order ExB flow shear effect driven by the ion pressure gradient. As a result, it can be sensitive to the next-order one by toroidal rotation, with the possible strong excitation in the low toroidal rotation limit. The frequency in the lab frame and the peak wavenumber spectrum of the mode appear to be in the range similar to those of the observed low-k fluctuation.

Application of the gyrokinetic velocity moment theory in finite beta plasma

The calculation of the velocity moment in the gyrokinetic theory is investigated in the finite beta plasma. According to the scalar invariance property in the Lie-transform method, the particle velocity in terms of the gyrocenter coordinates is derived, where the drift velocity driven by the second-order Hamiltonian is illustrated. The parallel component of particle velocity is found to be the same as that from the pull-back transformation of the parallel velocity variable v¯∥. The parallel and perpendicular velocity moments are systematically calculated according to the parallel and perpendicular components of particle velocity. The poloidal Reynolds stress (PRS) driven by the electromagnetic fluctuation is illustrated. By considering the magnetic drift resonance in the quasilinear analysis, the PRS contains two parts: one is related to the electrostatic fluctuation and the other is related to the parallel magnetic vector fluctuation; compared to the case with the electrostatic fluctuation, the PRS in the case with the electromagnetic fluctuation is enhanced by the electromagnetic effects, which may be beneficial for the enhancement of zonal flows and the reduction of turbulent transport.

Toroidal drift modes driven by the magnetic drift resonances

Here, we find that the kinetic and fluid linear drift resonances have several similarities. The reason for our interest in this is that our fluid model has recently been shown to be exact for drift waves and other modes in that frequency range. Thus, transport is driven by the fluid linear growth rate and our drift wave system behaves like a cold beam-plasma system although it has a finite temperature. A main similarity is that neither fluid nor kinetic responses should be expanded in the curvature in the bulk interior of tokamaks. That we can use the fluid response close to the magnetic drift resonance is a consequence of the fact that the closure is exact. A systematic orbit integration technique is introduced for deriving the fluid model and evaluating the effects of nonlinearities.

Quasilinear transport due to the magnetic drift resonance with the ion temperature gradient instability in a rotating plasma

The quasilinear transport fluxes due to the ion temperature gradient instability are calculated in a toroidal plasma, in which the magnetic drift resonance is treated rigorously. The effects of the equilibrium parallel flow and flow shear on the radial particle and heat fluxes are studied numerically in detail. In the radial component of parallel viscosity, there exist the pinches driven by the density gradient, the temperature gradient, and the curvature of the background magnetic field. The direction of these pinches is discussed. It is found that each pinch can be inward or outward, which depends crucially on the resonance condition.

Ion heat pinch due to the magnetic drift resonance with the ion temperature gradient instability in a rotating plasma

The ion heat pinch due to the magnetic drift resonance with the ion temperature gradient instability is investigated by using the Lie-transform method. In a tokamak plasma with an equilibrium parallel flow, the total heat flux is found to direct inward with a strong flow shear. The proposed heat pinch can provide possible explanations for some experimental observations.

Toroidal momentum channeling of geodesic acoustic modes driven by fast ions

Toroidal momentum channeling by fast ion-driven geodesic acoustic mode (EGAM) is proposed based on a quasi-linear analysis. We focus on a branch due to the magnetic drift resonance. Without the magnetic drift resonance, the eigenfunction of the EGAM has up–down anti-symmetric property in the poloidal direction, and the toroidal momentum flux by the EGAM is zero. If the magnetic drift resonance is considered, the up–down anti-symmetry in the poloidal eigenfunction is violated, and, as a result, the toroidal momentum flux becomes finite. Comparing its magnitude to the other processes such as external momentum input, and the turbulent residual stress, the momentum flux induced by the EGAM is found to be significant in the total momentum balance. This suggests that EGAMs can be used as a control knob for the toroidal rotation.

A branch of energetic-particle driven geodesic acoustic modes due to magnetic drift resonance

Eigenmode analysis of geodesic acoustic modes (GAMs) driven by fast ions is performed, based on a set of gyrokinetic equations. Resonance to the magnetic drift of the fast ions can destabilize GAMs. A new branch is found in the family of GAMs, whose frequency is close to the magnetic drift frequency of the fast ions. The poloidal eigenfunction of this branch has bump structures in the poloidal direction where the resonance of the magnetic drift with the mode is strong. The ion heating rate by the GAMs is evaluated in the framework of quasi-linear theory. The heating is localized poloidally around the resonance locations. Owing to the bumps in the eigenfunction, the magnitude of the heating is much larger than that estimated without the magnetic drift resonance.

Effects of parallel sound wave damping and drift kinetic damping on the resistive wall mode stability with various plasma rotation profiles

The effect of a parallel viscous force induced damping and the magnetic precessional drift resonance induced damping on the stability of the resistive wall mode (RWM) is numerically investigated for one of the advanced steady-state scenarios in international thermonuclear experimental reactor (ITER). The key element of the investigation is to study how different plasma rotation profiles affect the stability prediction. The single-fluid, toroidal magnetohydrodynamic (MHD) code MARS-F (Liu et al., Phys. Plasmas, vol. 7, 2000, p. 3681) and the MHD–kinetic hybrid code MARS-K (Liu et al., Phys. Plasmas, vol. 15, 2008, 112503) are used for this purpose. Three extreme rotation profiles are considered: (a) a uniform profile with no shear, (b) a profile with negative flow shear at the $q=2$ rational surface ($q$ is the equilibrium safety factor), and (c) a profile with positive shear at $q=2$. The parallel viscous force is found to be effective for the mode stabilization at high plasma flow speed (about a few percent of the Alfven speed) for the no shear flow profile and the negative shear flow profile, but the stable domain does not appear with the positive shear flow profile. The predicted eigenmode structure is different with different rotation profiles. With a self-consistent inclusion of the magnetic precession drift resonance of thermal particles in MARS-K computations, a lower critical flow speed, i.e. the minimum speed needed for full suppression of the mode, is obtained. Likewise the eigenmode structure is also modified by different rotation profiles in the kinetic results.

Collisionless microtearing modes in hot tokamaks: Effect of trapped electrons

Collisionless microtearing modes have recently been found linearly unstable in sharp temperature gradient regions of large aspect ratio tokamaks. The magnetic drift resonance of passing electrons has been found to be sufficient to destabilise these modes above a threshold plasma β. A global gyrokinetic study, including both passing electrons as well as trapped electrons, shows that the non-adiabatic contribution of the trapped electrons provides a resonant destabilization, especially at large toroidal mode numbers, for a given aspect ratio. The global 2D mode structures show important changes to the destabilising electrostatic potential. The β threshold for the onset of the instability is found to be generally downshifted by the inclusion of trapped electrons. A scan in the aspect ratio of the tokamak configuration, from medium to large but finite values, clearly indicates a significant destabilizing contribution from trapped electrons at small aspect ratio, with a diminishing role at larger aspect ratios.

Role of Trapped Electrons on Global Gyrokinetic Linear Stability of Collisionless Microtearing Modes

Unstable collisional MicroTearing Mode (MTMs) have been found in experiments of high-β Spherical Tokamaks and are believed to be driven by drift resonance of trapped electrons. It has been recently shown that at large aspect ratio, the magnetic drift resonance of highly passing electrons is a minimal mechanism to drive the collisionless MTM unstable. In this work, a preliminary study of inclusion of trapped electrons in large aspect ratio tokamaks indicate that for the reference parameters investigated, the collisionless MTM retain their essential mode structures, while growth rates are only moderately affected.

Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient ηe. Scans at different β values show an inverse relationship between the ηe threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.

Toroidal universal drift instability: A global gyrokinetic study

An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau resonance and transit resonance, which are considered to be important for the toroidal universal mode, are kept for both species. A systematic parametric study is carried out for the mode. The toroidal universal drift mode is observed to sustain finite temperature gradient and can thus coexist with the temperature gradient driven modes and may contribute to the observed particle transport along with other drift modes. Especially at intermediate scales between the ion temperature gradient driven mode and electron temperature gradient driven mode, this branch of the drift instability can also be a plausible candidate for the observed particle loss. The effect of magnetic fluctuations on the mode is also investigated. In contrast to the slab mode, the toroidal branch of the universal drift mode is found to be strongly stabilized by electromagnetic effects at finite plasma β. Finally, the effect of trapped electrons on the universal mode is studied and compared with the other possible modes in the same parameter regime, namely, ion temperature gradient mode in the presence of trapped electrons and pure trapped electron modes.

Plasma shaping effects on the geodesic acoustic mode in the large orbit drift width limit

Plasma shaping effects on the geodesic acoustic mode (GAM) are revisited analytically in the large orbit drift width limit. Comparing with results from the small orbit drift width expansion method [Z. Gao et al., Phys. Plasmas 15, 074502 (2008)] the behavior of the real frequency is almost the same but the effect on the damping rate is different due to the change of dominant resonant mechanism, from low order harmonic transit resonance to high order harmonic resonance, or equivalently, to the magnetic drift resonance. As a result, although the GAM frequency decreases with an increasing elongation κ by dependence of [2/(κ2+1)]1/2, the damping is weakened mildly in the large orbit drift width limit, which is quite different from the result in the low small orbit drift limit, where the damping is enhanced exponentially with the decrease in frequency. Also, in the large orbit drift width limit, the dependence of the GAM damping rate on inverse aspect ratio ε is analytically obtained for the first time. As ε increases, the frequency behaves as a weakly decreasing parabola function of ε, and the damping rate increases parabolically, but more rapidly than the frequency decreases. The GAM with longer radial wavelength is more easily damped by the finite aspect ratio effect. It is also found that the Shafranov shift gradient has the similar effect as the inverse aspect ratio.

Temperature ratio dependence of ion temperature gradient and trapped electron mode instability thresholds

The impact of ion to electron temperature ratio Ti∕Te on the instability thresholds of ion temperature gradient (ITG) and trapped electron modes (TEMs) is both analytically and numerically addressed. An analytical kinetic approach is developed accounting for the ion (electron, respectively) magnetic drift resonance and for the electron (ion, respectively) nonresonant response. This leads to a significant temperature ratio dependence of both ITG and TEM instability thresholds. Moreover nonresonant effects are able to reverse the scaling of ITG and TEM thresholds with Ti∕Te beyond the flat density limit. Analytical predictions are successfully tested against linear gyrokinetic thresholds and growth rates using the code KINEZERO [C. Bourdelle et al., Nucl. Fusion 42, 892 (2002)].

Kinetic ballooning instability for substorm onset and current disruption observed by AMPTE/CCE

A new interpretation of AMPTE/CCE observation of substorm onset and current disruption and the corresponding physical processes are presented. Toward the end of late growth phase the plasma β increases to ≥50 and a low frequency instability with a wave period of 50–75 sec is excited and grows to a large amplitude at the current disruption onset. At the onset, higher frequency instabilities are excited so that the plasma and electromagnetic field form a turbulent state. Plasma transport takes place to modify the ambient pressure profile so that the ambient magnetic field recovers from a tail‐like geometry to a more dipole‐like geometry. A new theory of kinetic ballooning instability (KBI) is proposed to explain the low frequency instability and the high β threshold (βc≥50) observed by AMPTE/CCE. The stabilizing effect is mainly due to kinetic effects of trapped electrons and finite ion Larmor radii which give rise to a large parallel electric field and hence a parallel current that greatly enhances the stabilizing effect of field line tension. As a result βc is greatly increased over the ideal MHD ballooning instability threshold by ≥ O(10² ‐ 10³). The wave‐ion magnetic drift resonance effect produces a perturbed resonant ion velocity distribution centered at a duskward velocity roughly equal to the average ion magnetic drift velocity. This perturbed ion distribution explains the enhanced duskward ion flux during the explosive growth phase and can excite higher frequency instabilities (such as the cross‐field current instability).

On electromagnetic ballooning modes in fluid and kinetic descriptions

A comparison between two-fluid, gyrofluid, and gyrokinetic descriptions of the collisionless ballooning mode in the toroidal limit is performed. The two-fluid model [A. Jarmén et al., Nucl. Fusion 27, 941 (1987)] is reactive and expanded in the finite-Larmor radius (FLR), in contrast to the gyrofluid model [R. E. Waltz et al., Phys. Fluids B 4, 3138 (1992)], which is dissipative and includes finite-Larmor-radius effects to all orders. The eigenmode differential equation is derived and solved numerically. It is shown that the fluid models are able to reproduce the gyrokinetic result, at least qualitatively. The role of the ion magnetic drift resonance and the ion FLR terms, in the fluid and kinetic descriptions, is discussed.

Ballooning modes in the magnetohydrodynamic second stability region

The ion temperature gradient driven ballooning mode is investigated using two-fluid, gyrofluid, and gyrokinetic descriptions. The linear eigenmode equation is solved numerically in a model equilibrium with shifted circular magnetic surfaces. The localization of the eigenmodes, which persist in the magnetohydrodynamic (MHD) second stability region, and the mode structure, are displayed. The role of finite-Larmor radius (FLR) and magnetic drift resonance effects on the growth rate are elucidated. Negative magnetic shear is found to have a stabilizing effect on the mode.

Ion temperature gradient-driven ballooning mode in tokamaks

It is shown that an ion temperature gradient (ηi) induces a collisionless ballooning mode in the MHD (magnetohydrodynamic) second stability regime. Both two-fluid and fully kinetic analyses predict the instability, in qualitative agreement, indicating that the ion magnetic drift resonance plays a key role in destabilization. The instability is characterized by broad eigenfunctions in the ballooning space and at a small magnetic shear has a growth rate comparable with that of the MHD mode. Trapped electrons, the ion transit effect, and magnetosonic perturbation have stabilizing influences, but are unable to suppress the mode.

Effects of anisotropic ηi and collisions on the mixed slab and toroidal ITG mode

The effects of collisions and anisotropy in the ion temperature gradient on the ion-temperature-gradient-driven (ITG) mode are investigated with dissipative trapped electrons and fully kinetic ions, in the presence of both transit and magnetic drift resonances. For the slab and toroidal modes, electron collisions stabilize the ion branch but destabilize the electron branch. For the mixed slab and toroidal mode, a coupling effect is found that causes a split of the stability region in the ηi∥-ηi⊥ plane. A second stability region at large ηi⊥ with electron collisions may provide a possible stabilization scheme for ITG instabilities.