Mode-particle Resonances Research Articles

Asymmetric and endogenous magnetic reconnection processes in quasi-collisionless plasmas

We define an endogenous magnetic reconnection process as the one having a driving factor that lies within the region where a drastic change in magnetic field topology occurs. A process of this kind is shown to take place when an electron temperature gradient is present in a plasma column and when, referring to quasi-collisionless regimes, the evolving electron temperature fluctuations are anisotropic. A two-fluid theory, for weakly collisional plasma regimes and confinement configurations which have sheared magnetic fields, is formulated, and two classes of reconnecting modes are identified. The localized class of modes is characterized by a transverse reconnecting magnetic field B̃x of odd parity, as a function of the radial variable (across the reconnection layer). The width of this remains significant even when large macroscopic distances, such as those of interest to space and astrophysics, are considered. The relevant reconnection can be referred to as antisymmetric. In fact, the (additional and realistic) presence of a finite current density gradient leads to finding modes with mixed B̃x parity which are no longer localized within the reconnection layer. Then, the resulting magnetic islands are not symmetric. In view of the fact that there are plasmas in the Universe with considerable electron thermal energy contents, the features of the novel reconnecting modes can be relied upon in order to produce generation of magnetic fields or conversion of magnetic energy into particle energy (through a sequence of mode-particle resonances).

Beam-Ion Acceleration during Edge Localized Modes in the ASDEX Upgrade Tokamak.

The acceleration of beam ions during edge localized modes (ELMs) in a tokamak is observed for the first time through direct measurements of fast-ion losses in low collisionality plasmas. The accelerated beam-ion population exhibits well-localized velocity-space structures which are revealed by means of tomographic inversion of the measurement, showing energy gains of the order of tens of keV. This suggests that the ion acceleration results from a resonant interaction between the beam ions and parallel electric fields arising during the ELM. Orbit simulations are carried out to identify the mode-particle resonances responsible for the energy gain in the particle phase space. The observation motivates the incorporation of a kinetic description of fast particles in ELM models and may contribute to a better understanding of the mechanisms responsible for particle acceleration, ubiquitous in astrophysical and space plasmas.

Magneto-thermal reconnection processes, related mode momentum and formation of high energy particle populations

In the context of a two-fluid theory of magnetic reconnection, when the longitudinal electron thermal conductivity is relatively large, the perturbed electron temperature tends to become singular in the presence of a reconnected field component and an electron temperature gradient. A finite transverse thermal diffusivity removes this singularity while a finite ‘inductivity’ can remove the singularity of the relevant plasma displacement. Then (i) a new ‘magneto-thermal’ reconnection producing mode, is found with characteristic widths of the reconnection layer remaining significant even when the macroscopic distances involved are very large; (ii) the mode phase velocities can be both in the direction of the electron diamagnetic velocity as well in the opposite (ion) direction. A numerical solution of the complete set of equations has been carried out with a simplified analytical reformulation of the problem. A sequence of processes is analyzed to point out that high-energy particle populations can be produced as a result of reconnection events. These involve mode-particle resonances transferring energy of the reconnecting mode to a superthermal ion population and the excitation of lower hybrid waves that can lead to a significant superthermal electron population. The same modes excited in axisymmetric (e.g. toroidal) confinement configurations can extract angular momentum from the main body of the plasma column and thereby sustain a local ‘spontaneous rotation’ of it.

Determination of broken KAM surfaces for particle orbits in toroidal confinement systems

The destruction of Kolmogorov–Arnold–Moser surfaces in a Hamiltonian system is an important topic in nonlinear dynamics, and in particular in the theory of particle orbits in toroidal magnetic confinement systems. Analytic models for transport due to mode-particle resonances are not sufficiently correct to give the effect of these resonances on transport. In this paper we compare three different methods for the detection of the loss of stability of orbits in the dynamics of charged particles in a toroidal magnetic confinement device in the presence of time dependent magnetic perturbations.

Guiding center equations of high accuracy

Guiding center simulations are an important means of predicting the effect of resistive and ideal magnetohydrodynamic instabilities on particle distributions in toroidal magnetically confined thermonuclear fusion research devices. Because saturated instabilities typically have amplitudes of δB/B of a few times 10−4 numerical accuracy is of concern in discovering the effect of mode particle resonances. We develop a means of following guiding center orbits which is greatly superior to the methods currently in use. For full implementation, the method requires some breaking of axisymmetry, either through toroidal field ripple or magnetohydrodynamic instabilities. In the presence of ripple or time dependent magnetic perturbations both energy and canonical momentum are conserved in a time step to better than one part in 1014, an improvement of nine orders of magnitude over standard Runge–Kutta integration, and the relation between changes in canonical momentum and energy is also conserved to very high order.

Guiding center equations for ideal magnetohydrodynamic modes

Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through δB→=∇×(ξ→×B→), however, perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories, the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement ξ→ are derived which preserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.

Perturbative study of energetic particle redistribution by Alfvén eigenmodes in ITER

The modification of particle distributions by magnetohydrodynamic modes is an important topic for magnetically confined plasmas. Low amplitude modes are known to be capable of producing significant modification of injected neutral beam profiles. Flattening of a distribution due to phase mixing in an island or due to portions of phase space becoming stochastic is a process extremely rapid on the time scale of equilibrium parameter changes in an experiment. In this paper, we examine the effect of toroidal Alfvén eigenmodes (TAE) and reversed shear Alfvén eigenmodes (RSAE) in ITER on alpha particle and injected beam distributions using theoretically predicted mode amplitudes using perturbative linear theory. It is found that for the equilibrium of a hybrid scenario even at ten times the predicted saturation level the modes have negligible effect on these distributions. A strongly reversed shear (or advanced) scenario, having a spectrum of modes that are much more global, is somewhat more susceptible to induced loss due to mode resonance, with alpha particle losses of over 1% with predicted amplitudes and somewhat larger with the assistance of toroidal field ripple. The elevated q profile contributes to stronger TAE (RSAE) drive and more unstable modes. An analysis of the existing mode-particle resonances is carried out to determine which modes are responsible for the profile modification and induced loss. We find that losses are entirely due to resonance with the counter-moving and trapped particle populations, with co-moving passing particles participating in resonances only deep within the plasma core and not leading to loss.

Measurements of fast-ion transport by mode-particle resonances on DIII-D

Magnetohydrodynamic (MHD) instabilities in tokamak plasmas manifest in a variety of ways, characterized by different scale lengths and mode frequencies. MHD activity can cause significant degradation of plasma performance due to transport of particles, energy and current. Among the many different types of MHD, arguably fishbones, sawteeth and Alfvén eigenmodes (AEs) are observed to cause the largest fluxes of superthermal ions. DIII-D's expansive suite of diagnostics makes it possible to rigorously characterize these instabilities and study their interaction with fast ions. This review paper first presents an overview of the recent additions to DIII-D's collection of fast-ion diagnostics. The extended diagnostic capabilities are employed in a series of experiments to investigate fast-ion dynamics in the presence of fishbones, sawteeth and AEs. Results from these seemingly unrelated studies are highlighted, and they reveal that mode-particle resonances play the central role in the observed deterioration of fast-ion confinement.

Effect of Trapped Energetic Particles on the Resistive Wall Mode

A stability analysis for the resistive wall mode is studied in the presence of trapped energetic particles (EPs). When the EPs' beta exceeds a critical value, a fishbonelike bursting mode (FLM) with an external kink eigenstructure can exist. This offers the first analytic interpretation of the experimental observations [Phys. Rev. Lett. 103, 045001 (2009)]. The mode-particle resonances for the FLM and the q=1 fishbone occur in different regimes of the precession frequency of EPs. In certain ranges of the plasma rotation speed and the EPs' beta, a mode conversion can occur between the resistive wall mode and FLM.

Process dynamics and thermodynamics of charged particle beams which remain equipartitioned

This paper examines the process dynamics and thermodynamics of charged particle beams which remain equipartitioned. Considering a high-intensity ion beam in a space-charge dominated regime and with an initially large mismatched RMS beam size, we observe a fast increasing spatial anisotropy of the beam. Since space-charge interactions in a high-intensity linear accelerator can lead to energy equipartition between the degrees of freedom, this anisotropization phenomena suggest a kind of route to equipartition. In this paper we show that the particle-particle resonances and mode-particle resonances lead to the anisotropization of the beam, that is, both the envelope ratio and the emittance ratio are different from one. We propose that this anisotropy is responsible for the beam’s equipartitioning. The results suggest that the beam remains equipartitioned when it exhibits a macroscopic anisotropy, which is characterized by the following properties: the development of an elliptical shape with increasing size along a direction, the presence of a coupling between transversal emittances, halo formation along a preferential direction, stationarity of the temperature and a growth of the entropy in the cascade form. We call the state characterized by these properties as an anisotropic equipartition state.

Mode–particle resonances during near-tangential neutral beam injection in the Tokamak Fusion Test Reactor

Coherent magnetohydrodynamic modes have been observed previously during neutral beam injection in the PDX tokamak [Phys. Rev. Lett. 50, 891 (1983)] and they have now been seen in the TFTR tokamak [Phys. Fluids 26, 2958 (1983)]. Periodic bursts of oscillations were detected with several plasma diagnostics, and Fokker–Planck calculations show that the populations of trapped particles in both tokamaks are sufficient to account for fishbone destabilization if a resonant interaction, between the mode and the beam ions, is assumed. Estimates of mode parameters are in reasonable agreement with the experiments, and they indicate that the fishbone mode may continue to affect the performance of intensely heated tokamaks.

Plasma decontamination and energy transport by impurity driven modes

A radial flow of impurities toward the outer edge of a magnetically confined plasma is produced, following an accumulation of impurities at the center of the plasma column, by impurity density gradient driven modes for realistic values of the temperature gradient of the main ion population relative to its density gradient. At the same time an outward transport of the main ion thermal energy is also induced. For mean free paths of the main ion population shorter than the relevant longitudinal wavelengths, these modes can be described by moment equations and are associated with the finite thermal conductivity of the main ions. In the opposite (collisionless) limit, mode-particle resonances replace the effects of finite ion thermal conductivity and in addition, modes that are standing along the magnetic field lines are affected by the magnetic trapping of a fraction of the main ion population. The expression for their growth rate is strongly influenced by the ratio of the effective trapped ion collision frequency to the mode frequency and under realistic conditions, can be independent of mode− particle resonance processes that involve only a relatively small portion of velocity space.

Fluid-like instability of trapped electrons in confined plasmas

An instability, which does not depend on mode-particle resonances, can be driven by the drift of trapped electrons in the unfavorable curvature region of the confining magnetic field for selected values of the relevant mode transverse wavelengths.

Transport and particle scattering due to toroidal plasma modes

Electrostatic modes are shown to be excited, in two-dimensional plasma equilibrium configurations, with frequency and parity characteristics such as to significantly affect the orbits of trapped ions by proper mode-particle resonances in regimes where the single-particle collision mean free paths are considerably longer than the periodic particle excursions. In particular, new modes driven by the ion temperature gradient are shown to become unstable in the presence of trapped particles under less restrictive conditions and with considerably larger transverse wavelengths than the ion temperature gradient driven modes arising in a one-dimensional equilibrium configuration. The resulting enhancement in the transport of ion thermal energy across the magnetic field is discussed.

Resonant scattering of trapped particles by Toroidal plasma modes

In two dimensional configurations electrostatic modes are shown to be excited with frequency and parity characteristics such as to affect significantly the orbital (`quasi-bananas' of trapped ions by proper mode-particle resonances. Processes of this kind may in fact provide an effective scattering mechanism in regimes where the single-particle collision mean free paths are considerably longer than the periodic particle excursions