Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.29921

Exact nonsymmetric vacuum magnetic field with nested toroidal flux surfaces and nonzero rotational transform

Omar E. López
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that an exact vacuum magnetic field without continuous Euclidean symmetry can fill a bounded solid torus with nested toroidal flux surfaces and nonzero rotational transform. We construct such a field in closed form and show that it is nowhere vanishing. Every off-axis field line closes after one toroidal transit and one poloidal turn, with rotational transform $ι=-1$ on every flux surface. The solution provides an exact benchmark for three-dimensional equilibrium codes.

Explore related subjects

physics.plasm-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Omar E. López. 2026-10-21. Exact nonsymmetric vacuum magnetic field with nested toroidal flux surfaces and nonzero rotational transform. https://arxiv.org/abs/2610.29921

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Kinetic Fluctuation-Dissipation Relation in collisionless plasmas: a correlated noise source

We here focus on small-scale dynamics of collisionless plasmas by employing a generalized kinetic Langevin framework driven by a stochastic time-correlated forcing. Our investigation captures the steady-state Fluctuation-Dissipation Relation (FDR) where the energy injection at low frequencies is due to the time-correlated forcing and the small-scale energy conversion occurs via Landau damping, the latter --though formally reversible-- acting as an effective dissipation mechanism. We analytically extract the resulting asymptotic spectral scalings across multiple physical regimes and characterize the velocity-space cascade by decomposing the plasma distribution function with Hermite polynomials. The framework is then generalized to a multi-scale forcing scenario in which correlation rates are distributed according to a power-law distribution. This extension provides closed-form analytical expressions that may serve to interpret spacecraft in-situ observations. All analytical predictions are successfully validated through direct numerical integrations of the underlying kinetic equations.

physics.plasm-ph↗
arXiv2026

Semi-local Floquet theory for active azimuthal magnetic modulation of Hall-thruster high-frequency instabilities

We develop a semi-local Floquet model to screen active azimuthal magnetic modulation as a control approach for high-frequency drift instabilities in Hall thrusters. The uniform-field kinetic response supplies a local kernel for a finite sideband matrix, and stability is measured by the upper growth envelope over the Bloch zone. Root searches include both frequency branches, continuation, singular-value validation, and contour root counts. At the reference normalized parallel wave number k_z = 0.045, for sinusoidal profiles with periods of 10, 20, and 40 mm, every nonzero sampled modulation amplitude increases both the peak and integrated positive Bloch-zone growth. The uniform-field reference is already unstable, so these increases describe faster linear amplification rather than the onset of instability from a stable state. At a period of 20 mm and relative amplitude 0.5, the peak and integral increase by 26.74 and 26.44 percent, respectively; this large amplitude requires caution within the semi-local ordering. Selected projected wave-number windows still show reductions, but these coexist with enhanced global growth and do not establish stabilization. A supplementary parallel-wave-number scan finds weak global growth reduction at k_z = 0.09: at 20 mm and amplitude 0.3, the peak and integral decrease by 0.300 and 0.299 percent, respectively, while the spectrum remains unstable. The sign and magnitude of the modulation effect therefore depend on the tested plasma parameters; neither these small reductions nor the local projected changes establish improved nonlinear transport.

physics.plasm-ph↗
arXiv2026

Exact 1D Nonlinear Solutions for Proton-Driven Plasma Wakefields

We extend the classical 1D nonlinear relativistic plasma wakefield paradigm to evaluate the pristine fluid profiles driven by intense relativistic proton trains under the comoving coordinate approximation. Using an intense two-bunch scheme, our adaptive integration model is validated down to machine precision against exact closed-form cold-fluid invariants, confirming that interface boundary corners represent physical step discontinuities in the second potential derivative. Scaling to an $N=100$ micro-bunch train, we resolve macroscopic phase-accumulation and subsequent nonlinear detuning by deriving a closed-form, parameter-free piecewise analytical envelope expression. This solution successfully maps the initial unattenuated quadratic coherent growth alongside the flat asymptotic horizontal saturation horizon governed by nonlinear energy conservation. Furthermore, the framework analytically evaluates the transient envelope overshoot, tracking its decay onto the saturation boundary via an exact phase-slip integration length scale. Providing immediate, ready macro-envelope bounds, this computationally inexpensive tool eliminates empirical adjustments and yields a robust mathematical baseline designed to guide and accelerate complex, multi-dimensional particle-in-cell (PIC) simulations through rapid parameter space exploration before deploying heavy computational assets. It establishes an efficient foundation to optimize asymmetric, custom-shaped driver profiles required to break the fundamental symmetric transformer ratio limit of 2 to make current particle accelerators more efficient.

physics.plasm-ph↗