Andreas Bierwage

Multi-phase simulation of fast ion profile flattening due to Alfvén eigenmodes in a DIII-D experiment

A multi-phase simulation that is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid is developed to simulate the nonlinear dynamics on the slowing down time scale of the energetic particles. The hybrid simulation code is extended with realistic beam deposition profile, collisions and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111, the stored beam ion energy is saturated due to Alfven eigenmodes (AE modes) at a level lower than in the classical simulation. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. It is demonstrated that the fast ion spatial profile is significantly flattened due to the interaction with the multiple AE modes with amplitude v/vA ~ δB/B ~ O(10−4). The dominant AE modes are toroidal Alfven eigenmodes (TAE modes), which is consistent with the experimental observation at the simulated moment. The amplitude of the temperature fluctuations brought about by the TAE modes is of the order of 1% of the equilibrium temperature. This is also comparable with electron cyclotron emission measurements in the experiment.

Validation of comprehensive magnetohydrodynamic hybrid simulations for Alfvén eigenmode induced energetic particle transport in DIII-D plasmas

A multi-phase simulation, which is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid including neutral beam injection, slowing-down, and pitch angle scattering, is applied to DIII-D discharge #142111 where the fast ion spatial profile is significantly flattened due to multiple Alfven eigenmodes (AEs). The large fast ion pressure profile flattening observed experimentally is successfully reproduced by these first of a kind comprehensive simulations. Temperature fluctuations due to three of the dominant toroidal Alfven eigenmodes in the simulation results are compared in detail with electron cyclotron emission measurements in the experiment. It is demonstrated that the temperature fluctuation profile and the phase profile are in very good agreement with the measurement, and the amplitude is also in agreement within a factor of two. This level of agreement validates the multi-phase hybrid simulation for the prediction of AE activity and alpha particle transport in burning plasmas.

Dynamics of low- n shear Alfvén modes driven by energetic N-NB ions in JT-60U

Dynamics of fast ions and shear Alfven waves are simulated using MEGA, a global nonlinear hybrid code. The scenario considered is based on JT-60U shot E039672, driven by strong negative-ion-based neutral beams (N-NB), just before the onset of a so-called abrupt large event (ALE). It is found that modes with toroidal mode numbers n = 2, 3, 4 can be destabilized, besides the n = 1 mode studied previously. The properties of the modes with n > 1 are sensitive to the value of the plasma beta and the form of the fast ion distribution, so simulation conditions are set up as realistically as presently possible. When the fast ion drive exceeds a certain threshold, the n = 3 mode is enhanced through a convective amplification process while following fast ions were displaced either by the n = 3 mode itself or by the n = 1 mode. The fast ion transport in several cases, simulated with single- or multiple-n modes, is analysed and implications of the results for the explanation of ALEs are discussed.

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

The nonlinear interactions between shear Alfven modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectra of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfven modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-di...

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. I. Effective mode number profile and resonant frequency tracking

The nonlinear interactions between shear Alfven modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in a JT-60U tokamak scenario with realistic geometry, large magnetic drifts, and strong beam drive. For this purpose, the recently developed orbit-based resonance analysis (ORA) method for circulating particles is extended, so that it can be applied to the nonlinear regime, where the spectrum of orbit-based poloidal mode numbers morb varies in time as the fast ions undergo wave-particle trapping and radial transport. In particular, the extended ORA method captures the effect of nonlinear overlaps between resonances associated with neighboring harmonics (morb,n) and (morb+1,n) that cause long-distance ballistic transport. Two cases with low toroidal mode numbers n≳1 are studied: an n = 1 mode without resonance overlap and a strongly driven n = 3 mode with resonance overlap. For both cases, an effective radial profile of the resonant poloidal mode number mres=Meff(r) is ...

Sensitivity study for N-NB-driven modes in JT-60U: boundary, diffusion, gyroaverage, compressibility

The sensitivity of the growth and nonlinear evolution of fast-ion-driven modes is examined with respect to the choice of particle boundary conditions, diffusion coefficients, fast ion gyroradii and bulk compressibility. The primary purpose of this work is to justify the choice of parameters to be used in the self-consistent long-time simulations of fast ion dynamics using global MHD-kinetic hybrid codes that include fast ion sources and collisions. The present study is conducted for a scenario based on the N-NB-driven JT-60U shot E039672, which is subject to abrupt large events (ALE). We use realistic geometry, a realistic fast ion distribution, and focus on experimentally observed harmonics with low toroidal mode numbers n = 1, 2, 3. The use of realistic boundary conditions and finite Larmor radii for the fast ions is shown to be essential. The usual values used for resistivity, viscosity and thermal diffusivity, and used for the specific heat ratio (controlling the effect of compressibility) are shown to be reasonable choices. Our method for performing the parameter scans around the threshold for the onset of convective amplification is proposed as a strategy for nonlinear benchmark studies.

Orbit-based representation of equilibrium distribution functions for low-noise initialization of kinetic simulations of toroidal plasmas

Abstract This work deals with the initial loading of phase space markers for global gyrokinetic particle-in-cell (PIC) simulations of plasmas that are magnetically confined in a toroidally axisymmetric configuration. A method is presented, which allows to prepare a marker distribution that is independent of time. This is achieved by discretizing the phase space along lines of constants of motion, which allows to load markers on the toroidal surfaces of unperturbed guiding center orbits. On each orbit surface, markers are distributed uniformly in time, so their distribution represents the compressible motion of physical particles. This method allows to initialize global PIC codes with an accurate equilibrium distribution function for charged particles, taking into account prompt losses to the wall. It facilitates simulations with lower noise levels and minimal noise–signal correlation; especially, in the linear regime. The problem considered is the representation of energetic ions in tokamaks, which are characterized by large drifts across magnetic surfaces.

Dynamics of multiple flux tubes in sawtoothing KSTAR plasmas heated by electron cyclotron waves: I. Experimental analysis of the tube structure

Multiple (two or more) flux tubes are commonly observed inside and/or near the q = 1 flux surface in KSTAR tokamak plasmas with localized electron cyclotron resonance heating and current drive (ECH/CD). Detailed 2D and quasi-3D images of the flux tubes obtained by an advanced imaging diagnostic system showed that the flux tubes are m/n = 1/1 field-aligned structures co-rotating around the magnetic axis. The flux tubes typically merge together and become like the internal kink mode of the usual sawtooth, which then collapses like a usual sawtooth crash. A systematic scan of ECH/CD beam position showed a strong correlation with the number of flux tubes. In the presence of multiple flux tubes close to the q = 1 surface, the radially outward heat transport was enhanced, which explains naturally temporal changes of electron temperature. We emphasize that the multiple flux tubes are a universal feature distinct from the internal kink instability and play a critical role in the control of sawteeth using ECH/CD.

Orbit-based analysis of resonant excitations of Alfvén waves in tokamaks

The exponential growth phase of fast-ion-driven Alfvenic instabilities is simulated and the resonant wave-particle interactions are analyzed numerically. The simulations are carried out in realistic magnetic geometry and with a realistic particle distribution for a JT-60U plasma driven by negative-ion-based neutral beams. In order to deal with the large magnetic drifts of the fast ions, two new mapping methods are developed and applied. The first mapping yields the radii and pitch angles at the points, where the unperturbed orbit of a particle intersects the mid-plane. These canonical coordinates allow to express analysis results (e.g., drive profiles and resonance widths) in a form that is easy to understand and directly comparable to the radial mode structure. The second mapping yields the structure of the wave field along the particle trajectory. This allows us to unify resonance conditions for trapped and passing particles, determine which harmonics are driven, and which orders of the resonance are in...

Investigation of fast ion behavior using orbit following Monte–Carlo code in magnetic perturbed field in KSTAR

The fast ion dynamics and the associated heat load on the plasma facing components in the KSTAR tokamak were investigated with the orbit following Monte-Carlo (OFMC) code in several magnetic field configurations and realistic wall geometry. In particular, attention was paid to the effect of resonant magnetic perturbation (RMP) fields. Both the vacuum field approximation as well as the self-consistent field that includes the response of a stationary plasma were considered. In both cases, the magnetic perturbation (MP) is dominated by the toroidal mode number n = 1, but otherwise its structure is strongly affected by the plasma response. The loss of fast ions increased significantly when the MP field was applied. Most loss particles hit the poloidal limiter structure around the outer mid-plane on the low field side, but the distribution of heat loads across the three limiters varied with the form of the MP. Short-timescale loss of supposedly well-confined co-passing fast ions was also observed. These losses started within a few poloidal transits after the fast ion was born deep inside the plasma on the high-field side of the magnetic axis. In the configuration studied, these losses are facilitated by the combination of two factors: (i) the large magnetic drift of fast ions across a wide range of magnetic surfaces due to a low plasma current, and (ii) resonant interactions between the fast ions and magnetic islands that were induced inside the plasma by the external RMP field. These effects are expected to play an important role in present-day tokamaks.