Particles In Fusion Plasmas Research Articles

A new paradigm for fast and repetitive chirping of Alfvén eigenmodes

A novel 2D nonlinear dynamical paradigm is constructed to interpret the fast and repetitive frequency chirping and amplitude oscillation of Alfvén eigenmodes excited by energetic particles in fusion plasmas as observed in global gyrokinetic simulations. In this non-perturbative paradigm of the collisionless phase-space dynamics, wave-particle resonant interactions cause the phase-space structure to continuously twist and fold, leading to the repetitive excitation and decay of the Alfvén eigenmode. The radial (perpendicular to the dominant wave-particle interaction) dependence of the mode amplitude and toroidal precessional drifts of the energetic particles leads to the 2D dynamics of wave-particle interactions, which is found to be responsible for the repetitive process of formation and destruction of the mode structure.

Physics of drift Alfvén instabilities and energetic particles in fusion plasmas

Shear Alfvén wave (SAW)/drift Alfvén wave (DAW) fluctuations can be destabilized by energetic particles (EPs) as well as thermal plasma components, which play a key role in the EP energy and momentum transport processes in burning fusion plasmas. The drift Alfvén energetic particle stability (DAEPS) code, which is an eigenvalue code using the finite element method, was developed to analyze Alfvén instabilities excited by EPs. The model equations, consisting of the quasineutrality condition and the Schrödinger-like form of the vorticity equation, are derived within the general fishbone-like dispersion relation theoretical framework, which is widely used to analyze SAW/DAW physics. The mode structure decomposition approach and asymptotic matching between the inertial/singular layer and ideal regions are adopted. Therefore, the DAEPS code can provide not only frequency and growth/damping rate but also the parallel mode structure as well as the asymptotic behavior corresponding to the singular-layer contribution. Thus, it fully describes fluid and kinetic continuous spectra as well as unstable and damped modes. The model equations have been extended to include general axisymmetric geometry and to solve for the response of circulating and trapped particles by means of the action-angle approach. In this work, we discuss linear dispersion relation and parallel mode structure of drift Alfvén instabilities excited by EPs, computed with the DAEPS code with realistic experimental plasma profile and magnetic configuration. We compare DAEPS results with FALCON/LIGKA to provide a verification of the code. We then adopt the Dyson–Schrödinger model (DSM) to further analyze the EP energy and momentum flux. We will briefly discuss how the parallel mode structure of the drift Alfvén instabilities can be used in the DSM to calculate the nonlinear radial envelope evolution and the EP transport.

Dynamic evolution of microturbulence with an improved confinement mode in the ramp-down phase of plasma current on EAST

Micro-instabilities are often invoked to account for the anomalous transport of energy and particles in fusion plasmas, whose origin and contributions to anomalous transport remain uncertain. The dynamic features of the microturbulence in the plasma core and the gradient region are investigated simultaneously by a poloidal CO2 laser coherent scattering diagnostic system on the experimental advanced superconducting tokamak (EAST). In 2018, an improved confinement mode characterized by a peaked density profile is observed in the current ramp-down phase with no auxiliary heating, which has rarely been studied. The experimental result suggests that the gradual shut off of the LHW heating might trigger the mode transition. The transition is accompanied with a great suppression of microturbulence and significant change in the cross-correlation spectrum. A possible mechanism for the suppression could be ascribed to the increasing shear flow. These results could shed light on the understanding of the nonlinear mechanism of confinement mode transition on EAST.

Verification and validation of integrated simulation of energetic particles in fusion plasmas

This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes.

Benchmark of gyrokinetic, kinetic MHD and gyrofluid codes for the linear calculation of fast particle driven TAE dynamics

Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model.

Dynamic Control of Defective Gap Mode Through Defect Location**supported by National Natural Science Foundation of China (No. 11405271)

A one dimensional model is developed for defective gap mode (DGM) with two types of boundary conditions: conducting mesh and conducting sleeve. For a periodically modulated system without defect, the normalized width of spectral gaps equals to the modulation factor, which is consistent with previous studies. For a periodic system with local defects introduced by the boundary conditions, it shows that the conducting-mesh-induced DGM is always well confined by spectral gaps while the conducting-sleeve-induced DGM is not. The defect location can be a useful tool to dynamically control the frequency and spatial periodicity of DGM inside spectral gaps. This controllability can be potentially applied to the interaction between gap eigenmodes and energetic particles in fusion plasmas, and optical microcavities and waveguides in photonic crystals.

Bayesian derivation of plasma equilibrium distribution function for tokamak scenarios and the associated Landau collision operator

A class of parametric distribution functions was proposed in (Di Troia 2012 Plasma Phys. Control. Fusion 54 105017) as equilibrium distribution functions (EDFs) for charged particles in fusion plasmas, representing supra-thermal particles in anisotropic equilibria for Neutral Beam Injection and Ion Cyclotron Heating scenarios. Moreover, those EDFs can be used to represent also nearly isotropic equilibria for Slowing-Down alpha particles and core thermal plasma populations. Such EDFs depend on constants of motion (COMs). In axisymmetric system with no equilibrium electric field, they depend on toroidal canonical momentum , kinetic energy w and magnetic moment μ.In the present work, the same EDFs are obtained from first principles and general hypothesis. The derivation is probabilistic and makes use of the Bayes’ Theorem. The bayesian argument is used to describe how the plasma is far from the prior probability distribution function (pdf), e.g. Maxwellian, based on the information obtained from magnetic moment and guiding center velocity pdf.Once the general functional form of the EDF has been settled, it is shown how to associate a modified Landau collision operator in the Fokker–Planck equation, to describe the system relaxation towards the proposed EDF.

The impact of magnetic geometry on wave modes in cylindrical plasmas

Both space and laboratory plasmas can be associated with static magnetic field, and the field geometry varies from uniform to non-uniform. This thesis investigates the impact of magnetic geometry on wave modes in cylindrical plasmas. The cylindrical configuration is chosen so as to explore this impact in a tractable but experimentally realisable configuration. Three magnetic geometries are considered: uniform, focused and rippled. These studies suggest suppressing drift waves in a uniformly magnetised plasma by increasing the field strength, enhancing the efficiency of helicon wave production of plasma by using a focused magnetic field, and forming a gap eigenmode on a linear plasma device by introducing a local defect to the system's periodicity, which is useful for understanding the gap-mode formation and interaction with energetic particles in fusion plasmas.

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, “Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation,” Phys. Plasmas 21, 072121 (2014)].

On visibility of carbon dust particles in fusion plasmas with fast framing cameras

The visibility of carbon dust particles in fusion plasmas with fast framing cameras is evaluated using computer and theoretical modelling. Dust heating and ablation in the plasmas, ionization dynamics of the ablation cloud around the dust particle, thermal radiation of the dust and line radiation of the cloud are considered. The minimal size of carbon dust particles visible with the cameras is calculated as a function of the plasma parameters and the distance from the dust to the camera objective. The relative contributions of thermal radiation from the grain and line radiation from the cloud to the total dust radiation are analysed.

The role of energetic particles in fusion plasmas

In the burning fusion plasmas of next step devices such as ITER (2001 ITER-FEAT Outline Design Report IAEA/ITER EDA/DS/18 (Vienna: IAEA) p 21), the majority of the heating of the fusing fuel will come from the plasma self-heating by fusion born α -particles. Recent advances in theoretical understanding, together with the development of new diagnostic techniques, make this a timely opportunity to survey the role of energetic particles in fusion plasmas and how it projects to future burning plasma devices.

GTNEUT: A code for the calculation of neutral particle transport in plasmas based on the Transmission and Escape Probability method

GTNEUT is a two-dimensional code for the calculation of the transport of neutral particles in fusion plasmas. It is based on the T ransmission and E scape P robabilities (TEP) method and can be considered a computationally efficient alternative to traditional Monte Carlo methods. The code has been benchmarked extensively against Monte Carlo and has been used to model the distribution of neutrals in fusion experiments. Program summary Title of program: GTNEUT Catalogue identifier: ADTX Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTX Computer for which the program is designed and others on which it has been tested: The program was developed on a SUN Ultra 10 workstation and has been tested on other Unix workstations and PCs. Operating systems or monitors under which the program has been tested: Solaris 8, 9, HP-UX 11i, Linux Red Hat v8.0, Windows NT/2000/XP. Programming language used: Fortran 77 Memory required to execute with typical data: 6 219 388 bytes No. of bits in a word: 32 No. of processors used: 1 Has the code been vectorized or parallelized?: No No. of bytes in distributed program, including test data, etc.: 300 709 No. of lines in distributed program, including test data, etc.: 17 365 Distribution format: compressed tar gzip file Keywords: Neutral transport in plasmas, Escape probability methods Nature of physical problem: This code calculates the transport of neutral particles in thermonuclear plasmas in two-dimensional geometric configurations. Method of solution: The code is based on the Transmission and Escape Probability (TEP) methodology [1], which is part of the family of integral transport methods for neutral particles and neutrons. The resulting linear system of equations is solved by standard direct linear system solvers (sparse and non-sparse versions are included). Restrictions on the complexity of the problem: The current version of the code can handle only one species of atomic neutrals. Typical running time: It depends on the size of the problem and the computing platform. For example, it takes 15.6 seconds of user time to run the second test problem on a SUN Ultra 10 workstation, using the sparse linear matrix solver. Unusual features of the program: The program requires linking with the publicly available LAPACK linear algebra library which is usually included with the Fortran compilers of many UNIX vendors or can be obtained from NETLIB ( www.netlib.org). To use the optional sparse matrix solver, the UMFPACK library is required which can be obtained from http://www.cise.ufl.edu/research/sparse/umfpack.

Phenomenological description of nonlinear waves produced by the drift-dissipative instability of a magnetized inhomogeneous plasma

A one-dimensional phenomological equation to describe nonlinear evolution of drift waves generated by dissipative instability of a magnetized plasma with density inhomogeneous across the magnetic field is proposed. A set of solutions describing monochromatic traveling waves is obtained together with conditions providing their full stability against small perturbations. Some approximate results concerning the stability against finite perturbations are also obtained. Then a collision between two asymptotically (at x → ± ∞) monochromatic waves is considered. It is demonstrated that the collision always results in suppressing a wave with a smaller wavenumber and a larger amplitude by a wave with a larger wavenumber and a smaller amplitude, what suggests a way to reduce the instability-induced transfer of heat and particles in fusion plasmas.

Fueling of Fusion Reactors By Means of Pellet Injection

The fueling requirements of fusion reactors are analyzed on the basis of a recent assessment performed for NET (Next European Torus). Results of penetration depth calculations applied to single pellets under thermonuclear plasma conditions are described. Data corresponding to the commonly used neutral gas shielding ablation model and a magnetic shielding approximation are compared. The pellet size and pellet velocity requirements for central fueling are established. Scenario calculations are performed with the help of a 1D tokamak transport code. The pellet size, pellet velocity, and injection frequency requirements for continuous fueling or, for example, ignition with the help of pellets are obtained. The effect of runaway electrons, NB ions and alpha particles is estimated by calculating the ablation rates caused by these particles in fusion plasmas and comparing them with the ablation rate induced by thermal electrons.