Some mathematics for quasi-symmetry

Burby, J. W.; Kallinikos, Nikos; MacKay, Robert S.

doi:10.1063/1.5142487

Cited by 39 publications

(77 citation statements)

References 25 publications

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“…(1967) and recently in Burby et al. (2019). The problem persists even if the magnetic shear is low if the rotation transform is close to a rational surface, such that a circulating particle takes a very long time to sample the torus.…”

Section: Omnigeneity and Quasisymmetry For Magnetic Field Systems Witmentioning

confidence: 78%

“…Differences between rational and irrational rotational transform also show up in the adiabatic invariants for circulating and trapped particles (Grad 1967; Burby et al. 2019). For ergodic field lines with flux surfaces, the drift orbits of circulating particles are always radially localized, unlike closed field-line systems.…”

Section: Discussionmentioning

confidence: 99%

“…Quasisymmetry (Landreman & Catto 2012; Burby et al. 2019; Imbert-Gerard, Paul & Wright 2019) is a local condition that is stricter than omnigeneity but guarantees that is satisfied identically. There are various equivalent definitions of QS (Helander 2014; Burby et al.…”

Section: Omnigeneity and Quasisymmetry For Magnetic Field Systems Witmentioning

confidence: 99%

“…There are various equivalent definitions of QS (Helander 2014; Burby et al. 2019; Landreman 2019). We restrict ourselves strictly to fields that are either vacuum or satisfy MHD equations.…”

Section: Omnigeneity and Quasisymmetry For Magnetic Field Systems Witmentioning

confidence: 99%

“…2019). While the search for finding exact QS in a volume is still ongoing (Burby, Kallinikos & MacKay 2019), it has been shown that QS can be satisfied on one surface (Garren & Boozer 1991; Plunk & Helander 2018; Henneberg, Drevlak & Helander 2019).…”

Section: Introductionmentioning

confidence: 99%

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Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

2020

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Understanding particle drifts in a non-symmetric magnetic field is of primary interest in designing optimized stellarators to minimize the neoclassical radial loss of particles. Quasisymmetry and omnigeneity, two distinct properties proposed to ensure radial localization of collisionless trapped particles in stellarators, have been explored almost exclusively for magnetic fields that generate nested flux surfaces. In this work, we extend these concepts to the case where all the field lines are closed. We then study charged particle dynamics in the exact non-symmetric vacuum magnetic field with closed field lines, obtained recently by Weitzner and Sengupta (arXiv:1909.01890), which possesses X-points. The magnetic field can be used to construct magnetohydrodynamic equilibrium in the limit of vanishing plasma pressure. Expanding in the amplitude of the nonsymmetric fields, we explicitly evaluate the omnigeneity and quasisymmetry constraints. We show that the magnetic field is omnigeneous in the sense that the drift surfaces coincide with the pressure surfaces. However, it is not quasisymmetric according to the standard definitions.

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Section: Omnigeneity and Quasisymmetry For Magnetic Field Systems Witmentioning

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Section: Omnigeneity and Quasisymmetry For Magnetic Field Systems Witmentioning

confidence: 99%

Section: Omnigeneity and Quasisymmetry For Magnetic Field Systems Witmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

2020

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Beijing Union Medical College Hospital and China’s Modern Medical Development

Zhang

2021

Western Influences in the History of Science and Technology in Modern China

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We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations. Firstly, we investigate the linear stability of the nonlinear modes in the focusing and defocusing cases, and get the stable and unstable domains of nonlinear localized modes. Then we validate the results by evolving them with 5% perturbations as an initial condition. Finally, we get stable solitons by considering excitations of the soliton via adiabatical change of system parameters. These findings of nonlinear modes can be potentially applied to physical experiments of matter waves in Bose-Einstein condensates.

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