We ask how a stationary cylindrical magnetic flux rope can sustain a field-aligned electric field while satisfying Maxwell’s equations, and what this implies for its helical structure and magnetic helicity. Since bold italic upper E bold dot bold italic upper B not equals 0 E ⋅ B ≠ 0 $\boldsymbol E\boldsymbol{\cdot }\boldsymbol B\neq 0$ , the electromagnetic field is algebraically non-degenerate and separates locally into two mutually orthogonal rank-two contributions. For stationary, axisymmetric profiles on a finite annulus, the homogeneous Maxwell equations lock these contributions: the observable magnetic pitch, the azimuthal electromotive period and the axial electric drive determine the complementary-sector amplitude and radial–temporal mixing pointwise. On every regular Lorentzian branch, the principal variables can be reconstructed locally from the two observable magnetic components and the two drive constants. The resulting field carries a helical electric current, and requires material force support, a parallel non-ideal response and external power. A constant-conductivity example demonstrates a smooth regular branch supported by a non-negative isotropic pressure. Only after an additional periodic axial identification do the fixed-radius surfaces become tori and the principal magnetic directions acquire winding classes. On this periodic annulus, the generalised magnetic helicity is the oriented area traced by the accumulated axial and azimuthal fluxes. Its principal-sector contributions are flux-weighted integrals of radial pitch shear, while their mutual contribution reduces, in a formal localised-shell limit, to the torus intersection pairing. Because the magnetic field is stationary, the generalised helicity is time independent; the variation of the raw Chern–Simons integral is compensated by the evolving harmonic periods. This is a balance specific to the periodic annulus, not a general helicity-conservation theorem for fields with bold italic upper E bold dot bold italic upper B not equals 0 E ⋅ B ≠ 0 $\boldsymbol E\boldsymbol{\cdot }\boldsymbol B\neq 0$ .
We investigate the appearance of a low-frequency 1 divided by f 1 / f $1/f$ magnetic spectrum in three-dimensional incompressible magnetohydrodynamic turbulence using direct numerical simulations and virtual spacecraft sampling. Our goal is to determine how the measured temporal spectra depend on the mean magnetic guide field, the probe velocity relative to the Alfvén speed and the sampling angle with respect to the guide field. We find that the clearest 1 divided by f 1 / f $1/f$ ranges are obtained for stronger guide fields and are favoured by faster sampler trajectories oriented more nearly perpendicular to the mean magnetic field. To characterise this behaviour, we introduce a quantitative score that measures the quality and spectral coverage of the detected 1 divided by f 1 / f $1/f$ interval. We further show that, as the probe speed increases, the measured temporal spectra become progressively more consistent with the corresponding Eulerian spectra at intermediate and high wavenumbers for both parallel and perpendicular sampling directions, particularly in the strong guide field case. These results indicate that the presence and clarity of a temporal 1 divided by f 1 / f $1/f$ range depend not only on the underlying turbulent dynamics, but also on the geometry and speed of the sampling process, with implications for the interpretation of low-frequency in situ measurements in the solar wind.
Abstract In this work, ARC and SPARC equilibria with randomly generated coil misalignments are analysed using the metric of quasisymmetry error, frequently used in stellarator theory as a proxy for fast ion confinement, and a strong correlation between this metric and ripple-induced alpha power loss is found. In discussions of magnetic confinement devices, it is often taken for granted that tokamaks, unlike stellarators, are devices with axisymmetric magnetic fields. However, any tokamak built from discrete toroidal field (TF) coils will have non-axisymmetric components of the magnetic field due to the effect of TF ripple, and these components only grow when inevitable assembly errors are taken into account. Physically constructed tokamaks therefore have magnetic fields which can best be classified as near axisymmetric, and which share many characteristics with quasi-axisymmetric stellarators, allowing both classes of devices to be analysed using similar methods.
Energy transfer across scales is essential for understanding the dissipation and heating of plasma turbulence. In the energy cascade scenario, the energy transfer rate can be assessed through the third-order law in the inertial range, and it is directly related to the rate of dissipation occurring at the small scale. To investigate the local properties of the energy transfer process, here, we employ three main diagnostics: the locally averaged dissipation rate epsilon Subscript r ε r $\varepsilon _r$ at different scales r r $r$ , the local energy transfer (LET) rate and the scale-filtered energy flux. The analyses are performed on direct numerical simulations of three-dimensional (3-D) incompressible magnetohydrodynamic (MHD) turbulence to evaluate these diagnostics. The outcomes of our study include: (i) an assessment of the spatial distribution of energy transfer rates across scales to determine which diagnostic best captures the features of energy transfer in different ranges; and (ii) a comparison of the outputs of the different diagnostics at significant scales, including a quantitative evaluation of their correlation using appropriate correlation coefficients. The latter shows that the energy dissipation rate, the LET and the scale-filtered energy flux have regional correlation, that is, although not exactly co-located, the intense regions of these three diagnostics occur in spatial proximity. Our results provide insights into understanding the energy transfer process in MHD and plasma turbulence, which shall be extended to more realistic systems.
