arXiv subjects

Andreas Bierwage

Publications and source records attributed to Andreas Bierwage.

At least 19 recordsLinked to original sources

arXiv2026

Study of Low-Frequency Core-Edge Coupling in a Tokamak: II. Spatial Channeling & Focusing In Antenna-Driven MHD

Motivated by evidence for core-edge coupling in the form of double-peaked fishbone-like low-frequency modes ($\lesssim 20\,{\rm kHz}$) in KSTAR, which exhibit synchronized Alfv\'{e}nic activity both in the central core and near the plasma edge [1], we study the nonlocal response of a tokamak plasma in a visco-resistive full MHD simulation model using the code MEGA. The waves are driven by an internal "antenna" that is localized both radially and azimuthally in the poloidal $(R,z)$ plane and has a sinusoidal form $\exp(in\zeta - i\omega t)$ with Fourier mode number $n=\pm 1$ in the toroidal angle $\zeta$ and fixed angular frequency $\omega$ in time $t$. By flattening the safety factor profile $q(r)$ at suitable locations in the minor radius $r$, we created plateaus in the low-frequency Alfv\'{e}n continua that act as wave "receivers". First, we confirm that such continuum plateaus respond with a coherent quasi-mode even when the driving antenna is located at a distant radius. Second, by varying the antenna location, we confirm the expectation of inward drive being more efficient than outward drive, which we attribute to volumetric focusing. Third, we find that the central core also responds well at frequencies below the central Alfv\'{e}nic continuum plateau, which could facilitate chirping. Our results show that a core-localized low-frequency response does not necessarily require core-localized drive nor an exactly matching continuum, but may be driven from the edge and sub-resonantly. It remains to be seen to what extent the examined effects play a role in double-peaked fishbone-like activity. Other possible contributing mechanisms are discussed to motivate further study. Our analyses also elucidate the mode structure formation process, from transients to quasi- or eigenmodes, here in the realm of MHD, and to be followed by a verification study against kinetic models.

physics.plasm-ph↗

arXiv2026

Study of Low-Frequency Core-Edge Coupling in a Tokamak: I. Experimental Observation in KSTAR

Double-peaked fishbone events across multiple KSTAR discharges are investigated. The normalized beta $\beta_{\mathrm{N}}$ and the edge safety factor $q_{\mathrm{95}}$ under which the fishbones appear vary depending on the presence and form of external magnetic perturbations. The fishbone strength is closely related to $\beta_{\mathrm{N}}$ and $q_{\mathrm{95}}$: as $\beta_{\mathrm{N}}$ increases and $q_{\mathrm{95}}$ decreases, the fishbone strength increases. Measured fishbone-relevant signals are decomposed into amplitude envelope and phase components in the temporal domain, which are analyzed separately. In terms of the amplitude envelope component, the edge electron temperature fluctuation $\tilde T_\mathrm{e}^{\mathrm{Edge}}$ becomes more correlated with the poloidal magnetic fluctuation $\dot{B}_\mathrm{\theta}$ compared to the core electron temperature fluctuation $\tilde T_\mathrm{e}^{\mathrm{Core}}$ as fishbone strength increases. In terms of the phase component, the phase of $\tilde T_\mathrm{e}^{\mathrm{Edge}}$ precedes the phase of $\tilde T_\mathrm{e}^{\mathrm{Core}}$ except in the case of very weak fishbones where the phase relations are inconclusive due to weak fishbone activity at the edge plasma, which is comparable to background fluctuations. The investigation suggests the possibility that the edge activity is not a mere side effect of the core activity, but could play an active role.

physics.plasm-ph↗

arXiv2026

Burst Intensification by Singularity Emitting Radiation in Laser Plasma

Burst Intensification by Singularity Emitting Radiation (BISER) appears as a bright temporally and spatially coherent Extreme Ultraviolet (XUV) and x-ray source driven by compact multi-terawatt femtosecond lasers in gas targets. There BISER originates from relativistic plasma singularities, so that the emission source size has a nanometer scale. The BISER x-ray yield quadratically depends on the driving laser power. BISER spectra have hundreds of electronvolt (eV) bandwidth embracing the 'water window' region (284 - 543 eV). Simulations predict that BISER pulses have durations close to the transform limit, which promises pulses shorter than the atomic unit of time (24 attoseconds). Based on the BISER brightness at ~20 terawatt laser power and the quadratic scaling, the brightness of BISER driven by petawatt-class lasers is predicted to exceed XUV free electron lasers. The BISER concept creates a new framework for a wide range of media emitting travelling waves capable of constructive interference, including gravitational waves. Here we review the BISER experimental discovery, its explanation based on the relativistic laser plasma simulations and catastrophe theory, experimental validation of the theoretical BISER model, proposal for imaging fast moving singularities, driving laser requirements, and future prospects emphasizing the driving laser wavelength scalability and possibility of terawatt attosecond coherent x-ray pulse generation.

physics.plasm-ph↗

arXiv2024

Construction and analysis of guiding center distributions for tokamak plasmas with ambient radial electric field

The contribution of a time-independent toroidally-symmetric radial electric field $E_r$ is implemented in VisualStart [Comp. Phys. Comm. 275 (2022) 108305; arXiv:2111.08224], a code whose purposes include the construction of guiding center (GC) drift orbit databases for the study of plasma instabilities in tokamaks. $E_r$ is important for the thermal part of the velocity distribution and for fast particle resonances in the kHz frequency range. KSTAR, JT-60U and ITER tokamak cases are used as working examples to test our methods and discuss practical issues connected with $E_r$. Two points are worth noting: First, the GC orbit space is sampled in the magnetic midplane as before, and we find that in the presence of $E_r$, midplane-based coordinates are not only equivalent but superior to conventional constants of motion, allowing to attain high numerical accuracy and efficiency with a relatively simple mesh. Second, the periodic parallel acceleration and deceleration of GCs via the mirror force is modulated by $E_r$. Although this parallel electric acceleration averages to zero during a poloidal transit (or bounce) period, it has important consequences, one being the known shift of the trapped-passing boundary. Another consequence is that electric frequency shifts depend on the chosen reference point, so that some care is required when evaluating the $E_r$-dependence of transit frequencies for resonance analyses.

physics.plasm-ph↗

arXiv2022

Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of ${\bf E}$ and ${\bf B}$

For an axisymmetric tokamak plasma, Hamiltonian theory predicts that the orbits of charged particles must stay on invariant tori of conserved energy in the moving frame of reference of a wave that propagates along the torus with a fixed angular phase velocity. In principle, this is true for arbitrary mode structures in the poloidal plane, but only if the fluctuations are expressed in terms of potentials $Φ$ and ${\bf A}$, which satisfy Faraday's law by definition. Here, we use the physical fields ${\bf E}$ and ${\bf B}$, where Faraday's law may be violated by errors introduced during the process of computing or designing the wave field through numerical inaccuracies, approximations, or gross negligence. Numerical heating caused by noise-like artifacts on the grid scale can to some extent be reduced via shorter time steps. In contrast, coherent inconsistencies between ${\bf E}$ and ${\bf B}$ cause spurious acceleration that is independent of time steps or numerical methods, but can be sensitive to geometry. In particular, we show that secular acceleration is enhanced when one imposes nonnormal modes that possess strong up-down asymmetry instead of the usual in-out asymmetry of normal toroidal (eigen)modes. Our tests are performed for full gyroorbit and guiding center (GC) models, which give similar results. In addition, we show that $N$-point gyroaveraging is not a recommendable method to enhance the realism of GC simulations. Besides breaking conservation laws, $N$-point gyroaveraging in our example makes the GC results deviate further from the full orbit results, showing that this method can even give the wrong trend.

physics.plasm-ph↗

arXiv2022

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating a term containing the covariant component $B_{Ψ_{\rm P}}$ of the magnetic field vector with respect to the poloidal flux function $Ψ_{\rm P}$. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency and a single toroidal mode number $n$, we show that simulations using the code ORBIT with and without $B_{Ψ_{\rm P}}$ yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the Appendix), which show that the unabridged GC Lagrangian with $B_{Ψ_{\rm P}}$ retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation, and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) & (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen)modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

physics.plasm-ph↗

arXiv2022

Representation and modeling of charged particle distributions in tokamaks

Experimental diagnostics, analysis tools and simulations represent particle distributions in various forms and coordinates. Algorithms to manage these data are needed on platforms like the ITER Integrated Modelling & Analysis Suite (IMAS), performing tasks such as archiving, modeling, conversion and visualization. A method that accomplishes some of the required tasks for distributions of charged particles with arbitrarily large magnetic drifts in axisymmetric tokamak geometry is described here. Given a magnetic configuration, we first construct a database of guiding center orbits, which serves as a basis for representing particle distributions. The orbit database contains the geometric information needed to perform conversions between arbitrary coordinates, modeling tasks, and resonance analyses. Using that database, an imported or newly modeled distribution is mapped to an exact equilibrium, where the dimensionality is reduced to three constants of motion (CoM). The orbit weight is uniquely given when the input is a true distribution: one that measures the number of physical particles per unit of phase space volume. Less ideal inputs, such as distributions estimated without drifts, or models of particle sources, can also be processed. As an application example, we reconstruct the drift-induced features of a distribution of fusion-born alpha particles in a large tokamak, given only a birth profile, which is not a function of the alpha's CoM. Repeated back-and-forth transformations between CoM space and energy-pitch-cylinder coordinates are performed for verification and as a proof of principle for IMAS.

physics.plasm-ph↗

arXiv2022

Energy-selective confinement of fusion-born alpha particles during internal relaxations in a tokamak plasma

Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as `sawtooth crashes'. The physical picture -- consisting of a synergy between magnetic geometry, optimal crash duration and rapid particle motion -- is completed by clarifying the role played by magnetic drifts. Besides causing asymmetry between co- and counter-going particle populations, magnetic drifts determine the size of the confinement window by dictating where and how much `reconnection' occurs in particle orbit topology.

physics.plasm-ph↗

arXiv2021

On the effect of beating during nonlinear frequency chirping

Spectral analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit multiple simultaneous chirps. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the electromagnetic field vanishes globally between beats and reappears with opposite phase. This implies that there can be a single field mode that oscillates at multiple frequencies simultaneously when resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories. In this treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Through amplitude pulsations and phase jumps, beating is found to drive the evolution of EP phase space structures. Observations: (1) Beating causes density wave fronts to advance radially in pulses. The resulting chirps become staircase-like. (2) The beats facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may delay detachment of solitary vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping occurs when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. The detached vortices can remain robust and, on average, maintain their concentric nested layers while being perturbed by the field's continued beating.

physics.plasm-ph↗

arXiv2019

Similarity of magnetized plasma wake channels behind relativistic laser pulses with different wavelengths

Using particle-in-cell simulations of relativistic laser plasma wakes in the presence of an external magnetic field, we demonstrate that there exists a parameter window where the dynamics of the magnetized wake channel are largely independent of the laser wavelength $λ_{\rm las}$. One condition for this manifestation of "limited similarity" is that the electron density $n_{\rm e}$ is highly subcritical, so that the plasma does not affect the laser. The freedom to choose a convenient laser wavelength can be useful in experiments and simulations. In simulations, an up-scaled wavelength (and, thus, a coarser mesh and larger time steps) reduces the computational effort, while limited similarity ensures that the overall structure and evolutionary phases of the wake channel are preserved. In our demonstrative example, we begin with a terrawatt$\cdot$picosecond pulse from a ${\rm CO}_2$ laser with $λ_{\rm las} = 10\,μ{\rm m}$, whose field reaches a relativistic amplitude at the center of a sub-millimeter-sized focal spot. The laser is shot into a sparse deuterium gas ($n_{\rm e} \sim 10^{13}\,{\rm cm}^{-3}$) in the presence of a tesla-scale magnetic field. Limited similarity is demonstrated in 2D for $4\,μ{\rm m} \leq λ_{\rm las} \leq 40\,μ{\rm m}$ and is expected to extend to shorter wavelengths. Assuming that this limited similarity also holds in 3D, increasing the wavelength to $40\,μ{\rm m}$ enables us to simulate the after-glow dynamics of the wake channel all the way into the nanosecond regime.

physics.plasm-ph↗

arXiv2009

Pressure-gradient-induced Alfven eigenmodes: I. Ideal MHD and finite ion Larmor radius effects

In the second magnetohydrodynamic (MHD) ballooning stable domain of a high-beta tokamak plasma, the Schroedinger equation for ideal MHD shear Alfven waves has discrete solutions corresponding to standing waves trapped between pressure-gradient-induced potential wells. Our goal is to understand how these so-called alpha-induced toroidal Alfven eigenmodes alpha-TAE are modified by the effects of finite Larmor radii (FLR) and kinetic compression of thermal ions in the limit of massless electrons. In the present paper, we neglect kinetic compression in order to isolate and examine in detail the effect of FLR terms. After a review of the physics of ideal MHD alpha-TAE, the effect of FLR on the Schroedinger potential, eigenfunctions and eigenvalues are described with the use of parameter scans. The results are used in a companion paper to identify instabilities driven by wave-particle resonances in the second stable domain.

physics.plasm-ph↗

arXiv2009

Pressure-gradient-induced Alfven eigenmodes: II. Kinetic excitation with ion temperature gradient

The kinetic excitation of ideal magnetohydrodynamic (MHD) discrete Alfven eigenmodes in the second MHD ballooning stable domain is studied in the presence of a thermal ion temperature gradient (ITG), using linear gyrokinetic particle-in-cell simulations of a local flux tube in shifted-circle tokamak geometry. The instabilities are identified as alpha-induced toroidal Alfven eigenmodes (alpha-TAE); that is, bound states trapped between pressure-gradient-induced potential barriers of the Schroedinger equation for shear Alfven waves. Using numerical tools, we examine in detail the effect of kinetic thermal ion compression on alpha-TAEs; both non-resonant coupling to ion sound waves and wave-particle resonances. It is shown that the Alfvenic ITG instability thresholds (e.g., the critical temperature gradient) are determined by two resonant absorption mechanisms: Landau damping and continuum damping. The numerical results are interpreted on the basis of a theoretical framework previously derived from a variational formulation. The present analysis of properties and structures of Alfvenic fluctuations in the presence of steep pressure gradients applies for both positive or negative magnetic shear and can serve as an interpretative framework for experimental observations in (future) high-performance fusion plasmas of reactor relevance.

physics.plasm-ph↗

arXiv2008

AWECS: A Linear Gyrokinetic Delta-f Particle-in-Cell Simulation Code for the Study of Alfvenic Instabilities in High-Beta Tokamak Plasmas

A 1-D linear gyrokinetic code called AWECS is developed to study the kinetic excitation of Alfvenic instabilities in a high-beta tokamak plasma, with beta being the ratio of thermal to magnetic pressure. It is designed to describe physics associated with a broad range of frequencies and wavelengths. For example, AWECS is capable of simulating kinetic ballooning modes, Alfvenic ion-temperature-gradient-driven modes, as well as Alfven instabilities due to energetic particles. In addition, AWECS may be used to study drift-Alfven instabilities in the low-beta regime. Here, the layout of the code and the numerical methods used are described. AWECS is benchmarked against other codes and a convergence study is carried out.

physics.plasm-ph↗

arXiv2007

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.

physics.plasm-ph↗

arXiv2007

Dynamics of resistive double tearing modes with broad linear spectra

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied in a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable. In this paper, it is first demonstrated that linear DTM theory predicts the dominance of high-m DTMs. A semi-empirical formula for estimating the poloidal mode number of the fastest growing mode, m_peak, is obtained from the existing linear theory. Second, using nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, whereby small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant for the understanding of the magnetohydrodynamic (MHD) activity near the minimum of q and may thus be of interest to studies concerned with stability and confinement in advanced tokamaks.

physics.plasm-ph↗

arXiv2007

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear

The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (DTM) which dominate at lower shearing rates. The possible application of these results in tokamaks with internal transport barrier is discussed.

physics.plasm-ph↗

arXiv2006

Nonlinear evolution of the m=1 internal kink mode in the presence of magnetohydrodynamic turbulence

The nonlinear evolution of the m=1 internal kink mode is studied numerically in a setting where the tokamak core plasma is surrounded by a turbulent region with low magnetic shear. As a starting point we choose configurations with three nearby q=1 surfaces where triple tearing modes (TTMs) with high poloidal mode numbers m are unstable. While the amplitudes are still small, the fast growing high-m TTMs enhance the growth of the m=1 instability. This is interpreted as a fast sawtooth trigger mechanism. The TTMs lead to a partial collapse, leaving behind a turbulent belt with q ~= 1 around the unreconnected core plasma. Although, full reconnection can occur if the core displacement grows large enough, it is shown that the turbulence may actively prevent further reconnection. This is qualitatively similar to experimentally observed partial sawtooth crashes with post-cursor oscillations due to a saturated internal kink.

physics.plasm-ph↗

arXiv2005

Fast growing double tearing modes in a tokamak plasma

Configurations with nearby multiple resonant surfaces have broad spectra of linearly unstable coupled tearing modes with dominant high poloidal mode numbers m. This was recently shown for the case of multiple q = 1 resonances [Bierwage et al., Phys. Rev. Lett. 94 (6), 65001 (2005)]. In the present work, similar behavior is found for double tearing modes (DTM) on resonant surfaces with q >= 1. A detailed analysis of linear instability characteristics of DTMs with various mode numbers m is performed using numerical simulations. The mode structures and dispersion relations for linearly unstable modes are calculated. Comparisons between low- and higher-m modes are carried out, and the roles of the inter-resonance distance and of the magnetic Reynolds number S_Hp are investigated. High-m modes are found to be destabilized when the distance between the resonant surfaces is small. They dominate over low-m modes in a wide range of S_Hp, including regimes relevant for tokamak operation. These results may be readily applied to configurations with more than two resonant surfaces.

physics.plasm-ph↗