Steady plasma flows in a periodic non-symmetric domain

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In a toroidal domain, the requirement of double periodicity for physical quantities adds to the complications. In particular, the magnetohydrodynamics (MHD) model of plasma steady state with the flow in a non-symmetric toroidal domain allows the development of singularities when the rotational transform of the magnetic field is rational, much like the equilibrium MHD model. In this work, we show that steady flows can still be maintained provided the rotational transform is close to rational and the magnetic shear is weak. We extend the techniques developed in carrying out perturbation methods to all orders for static MHD equilibrium by Weitzner (Phys. Plasmas, vol. 21, 2014, p. 022515) to MHD equilibrium with flows. We construct perturbative MHD equilibrium in a doubly periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order. We then utilize an additional symmetry of the flow problem, first discussed by Hameiri (J. Math. Phys., vol. 22, 1981, pp. 2080–2088, § III), to obtain a generalized Grad–Shafranov equation for a class of non-symmetric three-dimensional MHD equilibrium with flows both parallel and perpendicular to the magnetic field. For this class of flows, we can obtain non-symmetric generalizations of integrals of motion, such as Bernoulli's function and angular momentum. Finally, we obtain the generalized Hamada conditions, which are necessary to suppress singular currents in such a system when the magnetic field lines are closed. We do not attempt to address the question of neoclassical damping of flows.

Magnetohydrodynamic Modeling of the Solar Corona with an Effective Implicit Strategy

In this paper, we design an effective and robust model to solve the 3D single-fluid solar wind plasma magnetohydrodynamics (MHD) problem of low plasma β. This MHD model is formulated on a six-component composite grid system free of polar singularities. The computational domain ranges from the solar surface to the super-Alfvénic region. As common to all MHD codes, this code must handle the physical positivity-preserving property, time-step enlargement, and magnetic field divergence-free maintenance. To maintain physical positivity, we employ a positivity-preserving Harten–Lax–van Leer Riemann solver and take a self-adjusting and positivity-preserving method for variable reconstruction. To loosen the time-step limitation, we resort to the implicit lower–upper symmetric Gauss–Seidel method and keep the sparse Jacobian matrix diagonally dominant to improve the convergence rate. To deal with the constant theme of a magnetic field that is divergence-free, we adopt a globally solenoidality-preserving approach. After establishing the solar wind model, we use its explicit and implicit versions to numerically investigate the steady-state solar wind in Carrington rotations (CRs) 2172 and 2210. Both simulations achieve almost the same results for the two CRs and are basically consistent with solar coronal observations and mapped in situ interplanetary measurements. Furthermore, we use the implicit method to conduct an ad hoc simulation by multiplying the initial magnetic field of CR 2172 with a factor of 6. The simulation shows that the model can robustly and efficiently deal with the problem of a plasma β as low as about 5 × 10−7. Therefore, the established implicit solar wind MHD model is very promising for simulating complex and strong magnetic environments.

Numerical simulation of low-current vacuum arc jet considering anode evaporation in different axial magnetic fields

As the main source of the vacuum arc plasma, cathode spots (CSs) play an important role on the behaviors of the vacuum arc. Their characteristics are affected by many factors, especially by the magnetic field. In this paper, the characteristics of the plasma jet from a single CS in vacuum arc under external axial magnetic field (AMF) are studied. A multi-species magneto-hydro-dynamic (MHD) model is established to describe the vacuum arc. The anode temperature is calculated by the anode activity model based on the energy flux obtained from the MHD model. The simulation results indicate that the external AMF has a significant effect on the characteristic of the plasma jet. When the external AMF is high enough, a bright spot appears on the anode surface. This is because with a higher AMF, the contraction of the diffused arc becomes more obvious, leading to a higher energy flux to the anode and thus a higher anode temperature. Then more secondary plasma can be generated near the anode, and the brightness of the ‘anode spot’ increases. During this process, the arc appearance gradually changes from a cone to a dumbbell shape. The appearance of the plasma jet calculated in the model is consistent with the experimental results.

Jet and counter-jet in transonic pulsar wind nebulae

X-ray observations show that a jet and a counter-jet in pulsar wind nebulae often differ one from another. Sometimes one of the jets is not observed at all. We show that the most likely reason for this difference is the relative motion of a pulsar and an ambient matter. Even the slow (subsonic or transonic) ambient matter stream in the pulsar rest frame strongly affects the jets, making the windward jet bright and dynamic, and the leeward jet dim and diffuse. The effect is illustrated using a relativistic MHD model of a double-torus pulsar wind nebula. The model is shown to explain reasonably well the observational appearance of the jets in the Vela nebula - a double-torus object which evolves in a transonic stream initiated by the passage of the reverse shock of the parent supernova.

Numerical Study of Divergence Cleaning and Coronal Heating/Acceleration Methods in the 3D COIN-TVD MHD Model

In the solar coronal numerical simulation, the coronal heating/acceleration and the magnetic divergence cleaning techniques are very important. The coronal–interplanetary total variation diminishing (COIN-TVD) magnetohydrodynamic (MHD) model is developed in recent years that can effectively realize the coronal–interplanetary three-dimensional (3D) solar wind simulation. In this study, we focus on the 3D coronal solar wind simulation by using the COIN-TVD MHD model. In order to simulate the heating and acceleration of solar wind in the coronal region, the volume heating term in the model is improved efficiently. Then, the influence of the different methods to reduce the ∇⋅B constraint error on the coronal solar wind structure is discussed. Here, we choose Carrington Rotation (CR) 2199 as a study case and try to make a comparison of the simulation results among the different magnetic divergence cleaning methods, including the diffusive method, the Powell method, and the composite diffusive/Powell method, by using the 3D COIN-TVD MHD model. Our simulation results show that with the different magnetic divergence cleaning methods, the ∇⋅B error can be reduced in different levels during the solar wind simulation. Among the three divergence cleaning methods we used, the composite diffusive/Powell method can maintain the divergence cleaning constraint better to a certain extent, and the relative magnetic field divergence error can be controlled in the order of 10−9. Although these numerical simulations are performed for the background solar corona, these methods are also suitable for the simulation of CME initiation and propagation.

Testing of the new JOREK stellarator-capable model in the tokamak limit

In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.