FOXTAIL: Modeling the nonlinear interaction between Alfv\'en eigenmodes and energetic particles in tokamaks

FOXTAIL is a new hybrid magnetohydrodynamic-kinetic code used to describe interactions between energetic particles and Alfv\'en eigenmodes in tokamaks with realistic geometries. The code simulates the nonlinear dynamics of the amplitudes of individual eigenmodes and of a set of discrete markers in five-dimensional phase space representing the energetic particle distribution. Action-angle coordinates of the equilibrium system are used for efficient tracing of energetic particles, and the particle acceleration by the wave fields of the eigenmodes is Fourier decomposed in the same angles. The eigenmodes are described using temporally constant eigenfunctions with dynamic complex amplitudes. Possible applications of the code are presented, e.g., making a quantitative validity evaluation of the one-dimensional bump-on-tail approximation of the system. Expected effects of the fulfillment of the Chirikov criterion in two-mode scenarios have also been verified.Comment: Preprint submitted to Computer Physics Communications on June 3, 201

Стресс снижает функциональную активность кальцийактивируемых калиевых каналов гладкомышечных клеток изолированного кольца аорты и коронарных сосудов крыс

СТРЕССКАЛИЕВЫЕ КАНАЛЫ КАЛЬЦИЕМ-АКТИВИРУЕМЫЕАОРТАКОРОНАРНЫЕ СОСУДЫЭКСПЕРИМЕНТЫ НА ЖИВОТНЫ

The dynamics of Alfvén eigenmodes excited by energetic ions in toroidal plasmas

Experiments for the development of fusion power that are based on magnetic confinement deal with plasmas that inevitably contain energetic (non-thermal) particles. These particles come e.g. from fusion reactions or from external heating of the plasma. Ensembles of energetic ions can excite plasma waves in the Alfvén frequency range to such an extent that the resulting wave fields redistribute the energetic ions, and potentially eject them from the plasma. The redistribution of ions may cause a substantial reduction heating efficiency, and it may damage the inner walls and other components of the vessel. Understanding the dynamics of such instabilities is necessary to optimise the operation of fusion experiments and of future fusion power plants. A Monte Carlo model that describes the nonlinear wave-particle dynamics in a toroidal plasma has been developed to study the excitation of the abovementioned instabilities. A decorrelation of the wave-particle phase is added in order to model stochasticity of the system (e.g. due to collisions between particles). Based on the nonlinear description with added phase decorrelation, a quasilinear version of the model has been developed, where the phase decorrelation has been replaced by a quasilinear diffusion coefficient in particle energy. When the characteristic time scale for macroscopic phase decorrelation becomes similar to or shorter than the time scales of nonlinear wave-particle dynamics, the two descriptions quantitatively agree on a macroscopic level. The quasilinear model is typically less computationally demanding than the nonlinear model, since it has a lower dimensionality of phase space. In the presented studies, several effects on the macroscopic wave-particle dynamics by the presence of phase decorrelation have been theoretically and numerically analysed, e.g. effects on the growth and saturation of the wave amplitude, and on the so called frequency chirping events with associated hole-clump pair formation in particle phase space. Several effects coming from structures of the energy distribution of particles around the wave-particle resonance has also been studied.QC 20150330</p

Modeling the dynamics of toroidal Alfvén eigenmodes

A model describing nonlinear dynamics of a single Alfvén eigenmode excited by an inverted energy distribution of energetic ions is presented, suitable for drift orbit averaged Monte Carlo codes. The nonlinear dynamics of the wave mode is modeled with a complex wave amplitude, and is characterized by the formation of coherent structures in phase space, caused by wave-particle interaction. The transition to a quasilinear regime is modeled with a phenomenological decorrelation of the wave-particle phase. As the decorrelation is increased the coherent phase-space structures diminishes, and frequency chirping events in the marginal stability region is limited. The strength of the decorrelation modifies the saturation level and saturation time of the eigenmode amplitude.QC 20150319</p

A bump-on-tail model for Alfvén eigenmodes in toroidal plasmas

Presented is a numerical model for solving the nonlinear dynamics of Alfvén eigenmodes and energetic ions self-consistently. The model is an extension of a previous bump-on-tail model [1,2], taking into account particle orbits and wave fields in realistic toroidal geometries. The model can be used in conjunction with an orbit averaged Monte Carlo code that handles heating and current drive (similar to e.g. the SELFO code), which enables modeling of the effects of MHD activity on plasma heating. For rapid particle tracing, the unperturbed guiding center orbits are described with canonical action-angle coordinates [3], and the perturbed Hamiltonian for wave-particle interaction is included as Fourier components in the same angles [4]. This allows the numerical integrator to take time steps over several transit periods, which efficiently resolves the relevant time scales for nonlinear wave-particle dynamics. The wave field is modeled by a static eigenfunction and a dynamic complex amplitude driven by the interactions with resonant and non-resonant particles. [1] E. Tholerus, T. Hellsten and T. Johnson, Phys. Plasmas 22, 082106 (2015) [2] S. Tholerus, T. Hellsten and T. Johnson, J. Phys.: Conf. Ser. 561, 012019 (2014) [3] A. N. Kaufman, Phys. Fluids 15, 1063 (1972) [4] H. L. Berk, B. N. Breizman and M. S. Pekker, Nucl. Fusion 35, 1713 (1995)QC 20160927</p

Modelling the Dynamics of Energetic Ions and MHD Modes Influenced by ICRH

FOXTAIL is a code used to describe the nonlinear interactions between toroidal Alfvén eigenmodes and an ensemble of resonant energetic particles in tokamaks with realistic geometries. This report introduces an extension of the code, including effects from ion cyclotron resonance heating (ICRH) of energetic ions using a quasilinear diffusion operator in adiabatic invariant space. First results of the effects of ICRH diffusion on the system consisting of a single Alfvén eigenmode linearly excited by resonant ions are presented. It is shown that the presence of ICRH diffusion allows for the mode amplitude to grow larger than in the case of nonlinear saturation in the absence of sources and sinks. Gradually increasing the strength of ICRH diffusion also decreases the linear growth rate of the mode. Both these phenomena are previously observed also for the case of a finite phase decorrelation operator in bump-on-tail systems with a single eigenmode.QC 20160927</p

A bump-on-tail model for Alfvén eigenmodes in toroidal plasmas

Presented is a numerical model for solving the nonlinear dynamics of Alfvén eigenmodes and energetic ions self-consistently. The model is an extension of a previous bump-on-tail model [1,2], taking into account particle orbits and wave fields in realistic toroidal geometries. The model can be used in conjunction with an orbit averaged Monte Carlo code that handles heating and current drive (similar to e.g. the SELFO code), which enables modeling of the effects of MHD activity on plasma heating. For rapid particle tracing, the unperturbed guiding center orbits are described with canonical action-angle coordinates [3], and the perturbed Hamiltonian for wave-particle interaction is included as Fourier components in the same angles [4]. This allows the numerical integrator to take time steps over several transit periods, which efficiently resolves the relevant time scales for nonlinear wave-particle dynamics. The wave field is modeled by a static eigenfunction and a dynamic complex amplitude driven by the interactions with resonant and non-resonant particles. [1] E. Tholerus, T. Hellsten and T. Johnson, Phys. Plasmas 22, 082106 (2015) [2] S. Tholerus, T. Hellsten and T. Johnson, J. Phys.: Conf. Ser. 561, 012019 (2014) [3] A. N. Kaufman, Phys. Fluids 15, 1063 (1972) [4] H. L. Berk, B. N. Breizman and M. S. Pekker, Nucl. Fusion 35, 1713 (1995)QC 20160927</p