Omnigenity is a desirable property of toroidal magnetic fields that ensures confinement of trapped particles. Confining charged particles is a basic requirement for any fusion power plant design, but it can be difficult to satisfy with the non-axisymmetric magnetic fields used by the stellarator approach. Every ideal magnetohydrodynamic equilibrium previously found to approximate omnigenity has been either axisymmetric, quasi-symmetric or has poloidally closed contours of magnetic field strength $B$. However, general omnigenous equilibria are a much larger design space than these subsets. A new model is presented and employed in the DESC stellarator optimization suite to represent and discover the full parameter space of omnigenous equilibria. Although exact omnigenity aside from quasi-symmetry is impossible, these results reveal that excellent particle confinement can be achieved in practice. Examples far from quasi-symmetry with poloidally, helically and toroidally closed $B$ contours are attained with DESC and shown to have low neoclassical collisional transport and fast particle losses.
The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren and Boozer (1991a). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman and Sengupta (2018); Landreman et al. (2019), enables their efficient numerica…
Any viable stellarator reactor will need to be nearly omnigenous, meaning the radial guiding-center drift velocity averages to zero over time for all particles. While omnigenity is easier to achieve than quasisymmetry, we show here that several properties of quasisymmetric plasmas also apply directly or with only minor modification to the larger class of omnigenous plasmas. For example, concise expressions exist for the flow and current, closely resembling those for a tokamak, and these expressions are explicit in that no magnetic differential equations remain. A helicity (M,N) can be defined …
Princeton University（普林斯顿大学）；Max Planck Institute for Plasma Physics（马普等离子体物理研究所）；Institute for Research in Electronics and Applied Physics, University of Maryland（马里兰大学电子与应用物理研究所）；Thea Energy（Thea能源公司）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）
Combination of quasi-isodynamic and piecewise omnigenous magnetic fields
Laboratorio Nacional de Fusión, CIEMAT（CIEMAT国家聚变实验室）；University of Science and Technology of China（中国科学技术大学）；Center for Computational Mathematics, Flatiron Institute（平顶山研究所计算数学中心）
A target using a paisley pattern generates 100-kT-level magnetic fields. Laser irradiation induces local charge separation on the target, which creates surface currents along the concave surface, generating a magnetic field. For a laser intensity of $10^{21}$ W/cm$^2$, the target generates a 150-kT magnetic field. We developed a simple model to describe the magnetic field as a function of laser intensity and target radius. A double paisley configuration extends the lifetime of the magnetic field to the picosecond scale. The paisley design generates comparable results even if it is simplified. …
A Multi-dipole line cusp configured Plasma Device (MPD) having six electromagnets with embedded Vacoflux-50 as a core material has been operated with a capability to experimentally control the field-free region, the radial profile of magnetic field, and pole magnetic field by changing magnet current. For the validation of multi-dipole line cusp magnetic field (MMF) configuration in a 3-D geometry, a finite element simulation has been performed using COMSOL software. This paper presents 3-D magnetic field simulation results of multi-pole line cusp magnetic field configuration performed over the…
Lorentz invariant scalar functions of the magnetic field are defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the {\it potential magnetic field} introduced by R. Hide in Ann. Geophys. 1, 59 (1983) on the line of Ertel's theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the Eulerian-Lagrangian variable mapping. In addition the adopted procedure allows us to formulate Alfvèn theorem for the conservation of the magnetic flux through a surface comoving with the plasma in a Loren…
Numerical studies of the effect of a dc magnetic field on dynamo action (development of magnetic fields with large spatial scales), due to helically-driven magnetohydrodynamic turbulence, are reported. The apparent effect of the dc magnetic field is to suppress the dynamo action, above a relatively low threshold. However, the possibility that the suppression results from an improper combination of rectangular triply spatially-periodic boundary conditions and a uniform dc magnetic field is addressed: heretofore a common and convenient computational convention in turbulence investigations. Physi…
The formation of breakdown pattern on an insulating surface under the influence of a transverse magnetic field is theoretically investigated. We have generalized the Dielectric Breakdown Model (DBM) for the case of external magnetic field. Concept of the Magnetic Fractal Dimensionality (MFD) is introduced and its universality is demonstrated. It is shown that MFD saturates with magnetic fields. The magnetic field dependence of the streamer curvature is obtained. It is conjectured that nonlinear current interaction is responsible for the experimentally observed 'spider-legs' like streamer patte…
Turbulence dynamo deals with amplification of a seed magnetic field in a turbulent medium and has been studied mostly for uniform or spatially homogeneous seed magnetic fields. However, some astrophysical processes (e.g. jets from active galaxies, galactic winds, or ram-pressure stripping in galaxy clusters) can provide localized seed magnetic fields. In this paper, we numerically study amplification of localized seed magnetic fields in a turbulent medium. Throughout the paper, we assume that driving scale of turbulence is comparable to the size of the system. Our findings are as follows. Firs…
The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089] that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that of the magnetic fields discussed by Janse & Low, only those containing magnetic null po…
A numerical study of dynamos in rotating convecting plane layers is presented which focuses on magnetic energies and dissipation rates, and the generation of mean fields (where the mean is taken over horizontal planes). The scaling of the magnetic energy with the flux Rayleigh number is different from the scaling proposed in spherical shells, whereas the same dependence of the magnetic dissipation length on the magnetic Reynolds number is found for the two geometries. Dynamos both with and without mean field exist in rapidly rotating convecting plane layers.
In this paper, we study the long-time behavior of the solution for the linearized ideal MHD around sheared velocity and magnetic field under Stern stability condition. We prove that the velocity and magnetic field will converge to sheared velocity and magnetic field as time approaches infinity. Moreover a new depletion phenomenon is proved: the horizontal velocity and magnetic field at the critical points will decay to 0 as time approaches infinity.
We generalize the mean field magnetic dynamo to include local evolution of the mean vorticity in addition to the mean magnetic field. The coupled equations exhibit a general mean field dynamo instability that enables the transfer of turbulent energy to the magnetic field and vorticity on larger scales. The growth of the vorticity and magnetic field both require helical turbulence which can be supplied by an underlying global rotation. The dynamo coefficients are derived including the backreaction from the mean magnetic field to lowest order. We find that a mean vorticity field can actually see…
