Stochastic Magnetic Field Research Articles

Fundamental properties of ideal and resistive infernal modes in tokamaks

Infernal modes are unstable in regions of weak magnetic shear and significant pressure gradients. These modes comprise a broad class of instabilities, encompassing interchange modes and kink modes, with both short and long length scales. Toroidal effects and fully electromagnetic fields are of crucial importance for their description. The role of resistive diffusion and compressibility are also critical. In order to investigate this awkward problem while still enabling fundamental physics interpretation, a new resistive MHD eigensolver has been developed. An outcome of this study is the identification of an unstable spectrum of resistive infernal modes in regions of the plasma with weak average curvature, and in regions where the average curvature is destabilising. These fast growing modes may be collectively important for our understanding of global reconnection events, stochastic magnetic fields states, and neighbouring supercritical bifurcations.

Lagrangian Perspectives on the Small-scale Structure of Alfvénic Turbulence and Stochastic Models for the Dispersion of Fluid Particles and Magnetic Field Lines in the Solar Wind

Lagrangian perspectives on the small-scale structure of anisotropic Alfvénic turbulence are adopted. We are interested in relating the statistical properties of the Eulerian field increments evaluated along the fluid particle trajectories, in the direction perpendicular to the guiding magnetic field and along the magnetic field lines. We establish the basis for a unified multifractal phenomenology of Eulerian and Lagrangian Alfvénic turbulence. The critical balance condition is generalized to structure functions of an order different than 2. A Lagrangian perspective is not only useful for investigating the small-scale structure of Alfvénic turbulence, it is also tailored to the modeling of large-scale turbulent transport. Therefore, we develop Lagrangian stochastic models for the dispersion of fluid particles and magnetic field lines in the solar wind. The transport models are based on the integrated Ornstein–Uhlenbeck process that is not Markov, yielding smooth stochastic fluid particle trajectories and magnetic field lines. Brownian diffusion is recovered by tending the integral scale parameter to zero while keeping the diffusivity finite.

Roles of non-axisymmetric perturbations in free drift vertical displacement events on EAST

The safe operation of most tokamaks, especially the large ones, relies on the feedback control of vertical displacement events (VDEs). However, most of these feedback control systems are based on axisymmetric VDE models. In this study, we use NIMROD simulations to study the role of non-axisymmetric perturbations in free drift vertical displacement events on EAST. The high-n modes in the non-axisymmetric VDE grow first, which drives the formation of high-n magnetic island chains. Subsequently, the magnetic island chains grow and overlap with each other, leading to the destruction of the magnetic flux surface, which induces a minor disruption and accelerates the start of the following major disruption. The magnetic island and the stochastic magnetic field allow the toroidally non-axisymmetric poloidal plasma current to jet towards the hoop force direction, forming finger-like and filamentary structures. Such a plasma current non-axisymmetry strongly depends on the anisotropy in the thermal transport coefficients.

Nonlinear MHD modeling of soft β limits in W7-AS

An important question for the outlook of stellarator reactors is their robustness against pressure driven modes, and the underlying mechanism behind experimentally observed soft β limits. Towards building a robust answer to these questions, simulation studies are presented using a recently derived reduced nonlinear MHD model. First, the initial model implementation is extended to capture fluid compression by including the influence of parallel flows. Linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and interchange modes in a finite β, net-zero current carrying stellarator with low magnetic shear are then used to demonstrate the modeling capabilities. Finally, a validation study is conducted on experimental reconstructions of finite β W7-AS discharges. In agreement with past experimental analysis, it is shown that (i) the MHD activity is resistive, (ii) a soft β limit is observed, when the plasma resistivity approaches the estimated experimental value, and (iii) low n MHD activity is observed at intermediate β values, particularly a nonlinearly dominant (2, 1) mode. The MHD activity is mild, explaining the soft β limit, because the plasma volume remains separated into distinct sub-volumes in which field lines are ergodically confined. For the assumed transport parameters, the enhanced perpendicular transport along stochastic magnetic field lines can be overcome with the experimental heating power. The limitations in the current modeling are described, alongside an outlook for characterizing the quasi-steady state operational limit in W7-AS and other devices in more detail in future work.

Effects of Stochastic Magnetic Noise on the SERF Co‐Magnetometer

AbstractStochastic magnetic field noise has a non‐negligible negative impact on the performance of quantum precision measurement instruments such as spin‐exchange relaxation‐free (SERF) co‐magnetometer in terms of sensitivity and stability. Conventional magnetic field error analysis and suppression methods are not applicable to stochastic magnetic field noise. In this paper, a stochastic model of the SERF co‐magnetometer is proposed to analyze the mechanism of stochastic magnetic field noise. The mean and covariance propagation model of the SERF co‐magnetometer is given based on the stochasticity model and statistical principles. The analysis of simulation experiments reveals that reducing the longitudinal electron spin polarization can somewhat reduce the standard deviation of the system output caused by stochastic magnetic field noise. And the atomic ensembles are most resistant to stochastic magnetic field noise when the electron spin polarization strongly couples with the nuclear spin polarization. Finally, the experiments verified the above conclusions. In conclusion, this paper provides theoretical and experimental support for analyzing and suppressing the effect of stochastic magnetic field noise on the SERF co‐magnetometer, which is of great significance for improving the sensitivity and stability of the measurement.

Timescale of fast thermal quench based on general thermal diffusion induced by stochastic magnetic fields

Timescale of fast thermal quench based on general thermal diffusion induced by stochastic magnetic fields

Resonant graviton-photon transitions with cosmological stochastic magnetic field

We explore the possibility of detecting resonant conversions of high frequency gravitational waves to radio-signals. We show how the graviton-photon transitions, from Gertsenshtein effect, can be resonantly amplified in a cosmological stochastic magnetic background. In particular, we found parametric resonances for both the monochromatic and scale invariant power spectrum models of magnetic field fluctuations. Our results substantially departs from those predicted in resonance-less magnetic domain-like models in a large region of magnetic and oscillation wavelength scales. Resonances can be tested by radio telescopes such as ARCADE 2 and EDGES as a probe of high frequency gravitational wave sources and new physics models for magnetogenesis. Analysis are performed with a robust perturbative approach in discrete scheme for including cosmological decoherence in graviton-photon oscillations.

Two-stage crash process in resistive drift ballooning mode driven ELM crash

We report a two-stage crash process in edge localized mode (ELM) driven by resistive drift-ballooning modes (RDBMs) numerically simulated in a full annular torus domain with a scale-separated four-field reduced MHD (RMHD) model using the BOUT++ framework. In the early nonlinear phase, the small first crash is triggered by linearly unstable RDBMs, and m/n=2/1 magnetic islands are nonlinearly excited by nonlinear coupling of RDBMs as well as their higher harmonics. Here, m is the poloidal mode number, n is the toroidal mode number, the q = 2 rational surface exists near the pressure gradient peak, and q is the safety factor. Simultaneously, middle-n RDBM turbulence develops but is poloidally localized around X-points of the magnetic islands, leading to the small energy loss. The second large crash occurs in the late nonlinear phase. Higher harmonics of m/n=2/1 magnetic islands well develop around the q = 2 surface via nonlinear coupling and make the magnetic field stochastic by magnetic island overlapping. Turbulence heat transport develops at X-points of higher harmonics of m/n=2/1 magnetic islands, resulting in the turbulence spreading in the poloidal direction. The large second crash is triggered when the turbulence covers the whole poloidal region so that the magnetic island generation and magnetic field stochastization before the large crash can be interpreted as ELM precursors. It is concluded that the ELM trigger is attributed to the turbulent spreading in the poloidal direction in synchronization with the magnetic field stochastization and the crash is driven by E × B convection rather than the conventional Rechester–Rosenbluth anomalous electron heat transport.

Universe inflation and nonlinear electrodynamics

We analyse the inflation of the universe when the source of gravity is electromagnetic fields obeying nonlinear electrodynamics, with two parameters and without singularities. The cosmology of the universe with stochastic magnetic fields is considered, and the condition for universe inflation is obtained. It is demonstrated that singularities of energy density and pressure are absent as the scale factor approaches zero. When the scale factor goes to infinity, we have the equation of state for the ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of the universe shows that at large time scales, the scale factor corresponds to the radiation era. The duration of universe inflation is also analysed. We study the classical stability and causality by computing the speed of sound. Cosmological parameters including the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the running of the spectral index αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _s$$\\end{document} are evaluated.

Quasi-mode evolution in a stochastic magnetic field

We present a multi-scale model of quasi-mode evolution in a stochastic magnetic field. The similarity between a quasi-mode and a ballooning mode enables us to address the challenges arising from the disparate geometries in the theories of ballooning modes in the presence of resonant magnetic perturbations. We obtain useful insights into our understanding of ballooning mode dynamics in a stochastic background. To maintain quasi-neutrality at all scales, the beat between the quasi-mode and the stochastic magnetic field drives microturbulence, which drives the turbulent background that promotes mixing and damps the quasi-mode. As a result of the broad mode structure of the quasi-mode, the turbulent viscosity and the turbulent diffusivity produced by the microturbulence are larger than those in our related study on resistive interchange modes. The stochastic magnetic field can also enhance the effective plasma inertia and reduce the effective drive, thereby slowing the mode growth. A nontrivial correlation between the microturbulence and the magnetic perturbations is shown to develop. This could account for the reduction in the Jensen–Shannon complexity of pedestal turbulence in the Resonant Magnetic Perturbation Edge-Localized Mode suppression phase observed in recent experiments. Directions for future experimental and theoretical studies are suggested.

Anisotropic heat diffusion in stochastic magnetic fields

AbstractThe magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long.

Tailoring resonant magnetic perturbation to optimize fast-ion confinement during ELM control in KSTAR

3D resonant magnetic perturbation (RMP) is one promising way to control edge localized modes that can cause excessive material erosion of tokamak first walls. However, RMP can lead to undesired degradation of plasma confinement, including fast-particle losses, which can impact the performance and safety of the reactor. This work investigates the optimization of the poloidal spectrum of the 3D field to optimize fast ion confinement during edge localized mode (ELM) suppression. In the initial step, the validity of the modeling framework is tested against experimental data. Simulations successfully replicate an increase in poloidal limiter temperature with different poloidal spectra. Then, the simulation shows improvement of fast ion confinement with a reduction of core resonant response, while edge resonant magnetic fields are maintained above the threshold to sustain the ELM suppression. Reduction of the core resonant fields keeps the Kolmogorov–Arnold–Moser surface and reduces the fast particle losses due to the stochastic magnetic field lines. The results highlight the potential of edge localization of the resonant fields to enhance the performance of fusion reactors, but further investigation is needed to improve the validation of this approach.

Simulation study of interaction between energetic particles and magnetohydrodynamic modes in the JT-60SA inductive scenario with a flat q≈1 profile

Interactions between energetic particles (EPs), an internal kink mode, and other magnetohydrodynamic (MHD) instabilities in the inductive scenario of JT-60SA (scenario # 2) are simulated with MEGA, a global EP–MHD hybrid code. For this scenario, it was predicted by TOPICS, an integrated transport code that the internal kink mode can be unstable and the sawtooth relaxation results in a flat safety factor (q) profile with q ≈ 1 for r/a⩽0.6 . In this equilibrium, it is found in the simulation results that the stability of the internal kink mode depends strongly on the bulk plasma pressure gradient ( ∇Pb ). In the n = 1 simulations where the toroidal mode number is restricted to n = 0 and 1, the pressure-driven internal kink mode is dominant. In the presence of co-passing EPs generated by the negative-ion-based neutral beam (NB), these EPs transfer energy to the internal kink mode; however, the EP driving rate ( γh ) is much lower than the driving rate from the bulk plasma pressure gradient ( γP ). The mode’s frequency is less than 1 kHz because the toroidal orbit frequency (ω φ ) and poloidal orbit frequency (ω θ ) of the co-passing EPs are approximately equal within the q = 1 surfaces. This mode affects the EP and bulk plasma pressure redistributions. The feasibility of stabilizing the internal kink mode using trapped EPs is also investigated. It is found that the trapped EPs with energy 85 keV generated by the positive-ion-based NBs cannot stabilize the internal kink mode. Stabilization is observed when the injection energy is greater than 500 keV. In the multi-n simulations, where n⩽8 modes are retained, the most unstable modes are high n interchange modes with poloidal number m = n whose linear growth rates exceed that of the pressure-driven internal kink mode observed in the n = 1 simulations. The overlapping of these modes creates a stochastic magnetic field, leading to stronger EP and bulk plasma pressure redistributions than those observed in the n = 1 simulations. During the nonlinear phase, the transition from the high m = n modes to the low m = n modes is observed where the dominant mode is the m/n=1/1 mode with an internal kink-like structure. These low m = n modes are generated by the nonlinear coupling of the high m = n modes. The EP kinetic effect has a minor contribution to the dynamics of these nonlinearly generated m = n modes.

A quasi-linear model of particle, momentum and heat transport in a stochastic magnetic field

We present a quasi-linear treatment of the drift-kinetic equation in the presence of a stochastic magnetic field, which provides a self-contained description of particle, parallel momentum and heat transport. Explicit analytical expressions, which satisfy the Onsager reciprocal relations, are obtained by approximating the distribution function by a local shifted Maxwellian. This theory completes previous formulations (Harvey et al., Phys. Rev. Lett., vol. 47, 1981, p. 102) by including the momentum transport and by generalizing the derivation from the cylindrical tokamak configuration to an arbitrary cylindrical pinch. Application to the reversed field pinch provides satisfactory results.

Formation of the hydrogen line 21-cm in Dark Ages and Cosmic Dawn: dependences on cosmology and first light

ABSTRACT We analyse the formation of the redshifted hyperfine structure line 21-cm of hydrogen atom in the Dark Ages, Cosmic Dawn, and Reionization epochs. The evolution of the global differential brightness temperature in this line was computed to study its dependence on the values of cosmological parameters and physical conditions in the intergalactic medium. Variations of the depth of the Dark Ages absorption line at z ∼ 80 with variations of the cosmological parameters Ωb, Ωcdm, ΩΛ, ΩK, and H0 are studied. The standard model with post-Planck parameters predicts a value of the differential brightness temperature in the centre of the absorption line ∼30–50 mK. The profile of this line can be quite another in the non-standard cosmological models, which include the annihilating or decaying dark matter, a primordial stochastic magnetic field, etc. It can be shallower or be an emission bump instead of an absorption trough. It is also shown that the position and depth of the Cosmic Dawn absorption line formed at 10 < z < 30, due to the Wouthuysen–Field effect, is mainly defined by the spectral energy distribution of the first sources of light. If reionization occurs at zri = 7 ± 1, then the differential brightness temperature in the centre of this line is ∼80 mK. During the reionization, the emission with an amplitude of ∼20 mK is possible. It is also shown that the temperature, density, and degree of ionization of the baryonic component are decisive in calculating the intensity of the 21-cm absorption/emission line from these epochs.

Excitation of radially propagating electrostatic shear Alfvén wave during the formation of ambipolar radial electric field in a stochastic magnetic field

A radially propagating electrostatic shear Alfvén wave (ωH mode) is found during the formation of ambipolar radial electric field in a magnetic stochastic layer through gyrokinetic simulation. It is found that the times scale of the ambipolar radial electric field formation is the damping time of the ωH mode. The frequency and damping rate of the ωH mode are theoretical derived, which are in good agreement with the simulation results.

EUV/VUV Spectroscopy for the Study of Carbon Impurity Transport in Hydrogen and Deuterium Plasmas in the Edge Stochastic Magnetic Field Layer of Large Helical Device

The ergodic layer in the Large Helical Device (LHD) consists of stochastic magnetic fields exhibiting a three-dimensional structure that is intrinsically formed by helical coils. Spectroscopic diagnostics was employed in the extreme ultraviolet (EUV) and vacuum ultraviolet (VUV) wavelength ranges to investigate emission lines of carbon impurities in both hydrogen (H) and deuterium (D) plasmas, aiming to elucidate the impact of distinct bulk ions on impurity generation and transport in the edge plasmas of the LHD. The emission intensity of carbon CIII, CIV, CV, and CVI lines is significantly higher in the D plasma compared to the H plasma, indicating a greater sputtering rate of carbon materials in the D plasma, resulting in a higher quantity of carbon impurities originating from the divertor plates. A Doppler profile measurement of the second order of CIV line emission (1548.20 × 2 Å) was attempted using a 3 m normal-incidence VUV spectrometer in the edge plasma at a horizontally elongated plasma position. The flow velocity reaches its maximum value close to the outermost region of the ergodic layer, and the observed flow direction aligns with the friction force in the parallel momentum balance. The flow velocity increases with the electron density in H plasmas, suggesting that the friction force becomes more dominant in the force balance at higher density regimes. This leads to an increase in the impurity flow, which can contribute to the impurity screening. In contrast, the flow velocity in the D plasma is smaller than that in the H plasma. The difference in flow values between D and H plasmas, when the friction force term dominates in the momentum balance, could be attributed to the mass dependence of the thermal velocity of the bulk ions.

Role of magnetohydrodynamic activity in sawtooth induced heat pulse propagation in ADITYA tokamak

Fast propagation of sawtooth induced heat pulse is observed in the magnetohydrodynamic (MHD) active plasmas of ADITYA tokamak. The sawtooth crash deposits heat beyond the inversion radius, which gets transported to the edge region of the plasma, and is reflected as inverted sawtooth modulation in the edge channels of electron cyclotron emission (ECE) and spectral line emission. The time-lag analysis on ECE signal reveals the propagation time from plasma core to edge of ∼150 µs. From this analysis, the estimated transient electron heat diffusivity is found to be ∼50–60 m2 s−1, which is ten times higher than that of power balance heat diffusivity , in the MHD active discharges of ADITYA. It has been observed that the presence of MHD (m/n = 2/1, 3/1) activity in the intermediate region between the q = 1 and the edge radii, significantly influences the heat transport from the plasma core to the edge region. Stochastic magnetic field region formation with overlapping m/n = 2/1 and 3/1 MHD islands facilitates the fast heat-pulse propagation during a sawtooth crash in ADITYA tokamak. The disparity between the measured and the power-balance estimated diffusivity is significantly reduced by considering the electron heat diffusivity due to stochastization of magnetic field in the intermediate region.

Influence of toroidal rotation on nonlinear evolution of tearing mode in tokamak plasmas

The nonlinear evolution of the tearing mode instability with toroidal rotation is investigated using a three-dimensional toroidal geometry magnetohydrodynamic code (M3D). It is found that toroidal rotation plays a significantly stable role in reducing the width of magnetic island, which is independent of the direction of toroidal rotation. Compared with the stabilizing effect in the linear phase, the stabilizing effect of toroidal rotation is much stronger in the nonlinear phase. The magnetic island is almost suppressed by large enough rotation, even though the linear growth rate is weakly reduced in the linear phase. It is observed that the flow shear has a stabilizing effect, which is significant when the rotation frequency is large. However, it is shown that the magnitude of rotation plays a dominant role in stabilizing the magnetic island when the rotation frequency is small. The Coriolis force, rather than the centrifugal force, is found to play a dominant role in stabilizing the tearing mode in the nonlinear phase. When and tearing modes exist simultaneously, the sheared toroidal rotation is shown to effectively suppress the overlap of magnetic islands and field stochasticity caused by the coupling of neighboring islands.

Primordial black holes induced stochastic axion-photon oscillations in primordial magnetic field

Primordial black holes (PBHs) can be produced in the very early Universe due to the large density fluctuations. The cosmic background of axion-like particles (ALPs) could be non-thermally generated by PBHs. In this paper, we investigate the ALPs emitted by ultra-light PBHs with the mass range 10g ≲ M PBH ≲ 109 g, in which PBHs would have completely evaporated before the start of Big Bang Nucleosynthesis (BBN) and can therefore not be directly constrained. In this case, the minimal scenario that ALPs could interact only with photons is supposed. We study the stochastic oscillations between the ALPs and photons in the cosmic magnetic field in detail. The primordial magnetic field (PMF) can be modelled as the stochastic background field model with the completely non-homogeneous component of the cosmic plasma. Using the latest stringent limits on PMF, we show the numerical results of ALP-photon oscillation probability distributions with the homogeneous and stochastic magnetic field scenarios. The PBH-induced stochastic ALP-photon oscillations in the PMF may have the effects on some further phenomena, such as the cosmic microwave background (CMB), the cosmic X-ray background (CXB), and the extragalactic gamma-ray background (EGB).