Full Set Of Magnetohydrodynamic Equations Research Articles

Locking effects of error fields on a tearing mode in tokamak

Locking effects of error fields on a tearing mode in Tokamak are studied numerically using the three-dimensional toroidal code based on a full set of magnetohydrodynamic equations. It is found that a threshold of the error field for mode locking exists and depends on the plasma rotation and the ramp-up time of the error field. The mode locking threshold increases with increasing the rotation frequency and the ramp-up time of the error field. Moreover, the results from the multiple helical error field suggest that the m/n = 3/1 and 4/2 error field along with the m/n = 2/1 error field can increase both the m/n = 2/1 perturbation and its higher-harmonics through the mode coupling due to both the toroidal and nonlinear effects, but it becomes more effective if the 4/2 error field is imposed directly. The 3/1 error field in-phase (anti-phase) with the 2/1 error field leads to a positive (negative) contribution to intensification of the 2/1 tearing mode and mode locking.

Self-heating in kinematically complex magnetohydrodynamic flows

The non-modal self-heating mechanism driven by the velocity shear in kinematically complex magnetohydrodynamic (MHD) plasma flows is considered. The study is based on the full set of MHD equations including dissipative terms. The equations are linearized and unstable modes in the flow are looked for. Two different cases are specified and studied: (a) the instability related to an exponential evolution of the wave vector and (b) the parametric instability, which takes place when the components of the wave vector evolve in time periodically. By examining the dissipative terms, it is shown that the self-heating rate provided by viscous damping is of the same order of magnitude as that due to the magnetic resistivity. It is found that the heating efficiency of the exponential instability is higher than that of the parametric instability.

Low-order stellar dynamo models

Stellar magnetic activity — which has been observed in a diverse set of stars including the Sun — originates via a magnetohydrodynamic dynamo mechanism working in stellar interiors. The full set of magnetohydrodynamic equations governing stellar dynamos is highly complex, and so direct numerical simulation is currently out of reach computationally. An understanding of the bifurcation structure, likely to be found in the partial differential equations governing such dynamos, is vital if we are to understand the activity of solar-like stars and its evolution with varying stellar parameters such as rotation rate. Low-order models are an important aid to this understanding, and can be derived either as approximations of the governing equations themselves or by using bifurcation theory to obtain systems with the desired structure. We use normal-form theory to derive a third-order model with robust behaviour. The model is able to reproduce many of the basic types of behaviour found in observations of solar-type stars. In the appropriate parameter regime, a chaotic modulation of the basic cycle is present, together with varying periods of low activity such as that observed during the solar Maunder minima.

Radiatively Inefficient Magnetohydrodynamic Accretion‐Ejection Structures

We present magnetohydrodynamic simulations of a resistive accretion disk continuously launching transmagnetosonic, collimated jets. We time-evolve the full set of magnetohydrodynamic equations but neglect radiative losses in the energetics (radiatively inefficient). Our calculations demonstrate that a jet is self-consistently produced by the interaction of an accretion disk with an open, initially bent large-scale magnetic field. A constant fraction of heated disk material is launched in the inner equipartition disk regions, leading to the formation of a hot corona and a bright collimated, superfast magnetosonic jet. We illustrate the complete dynamics of the "hot" near-steady state outflow (where thermal pressure ≃ magnetic pressure) by showing force balance, energy budget, and current circuits. The evolution to this near-stationary state is analyzed in terms of the temporal variation of energy fluxes controlling the energetics of the accretion disk. We find that unlike advection-dominated accretion flow, the energy released by accretion is mainly sent into the jet rather than transformed into disk enthalpy. These magnetized, radiatively inefficient accretion-ejection structures can account for underluminous thin disks supporting bright fast collimated jets as seen in many systems displaying jets (for instance, M87).

Numerical studies of reflection process on a field-reversed configuration plasma

A two-dimensional magnetohydrodynamic (MHD) simulation of a reflection on a field-reversed configuration (FRC) plasma is performed in the parameter range of the FRC injection experiment (FIX). The full set of MHD equations are solved on a rezoned Lagrangian mesh which employs an adaptive algorithm to concentrate the grid in regions of sharp plasma pressure gradients. It is shown from the simulation results that the FRC plasma is reflected by downstream magnetic mirror field at the end of the confinement region in the FIX machine without destroying the closed magnetic flux surfaces. The effects of this field on FRC plasma are discussed.

Marfes: a magnetohydrodynamic stability study of two-dimensional tokamak equilibria

The marfe is studied as a radiative thermal instability in a two-dimensional axisymmetric tokamak model. To obtain a detailed idea of the marfe onset, a linear analysis is performed, using a full set of magnetohydrodynamic equations. Some typical marfe shots from JET are simulated. It is demonstrated how the marfe is a result of a poloidally symmetric temperature decrease and an asymmetric density increase. It is found that the onset of the marfe is accompanied by significant perturbations of pressure and magnetic field. The evolution of the marfe is discussed, based on the linear results. The model proves to give not only qualitative, but also quantitative agreement. The plasma parameters for marfe onset can be predicted accurately. Thermal instabilities belong to a continuum in the MHD spectrum of eigenfrequencies. The thermal stability of an equilibrium can be tested very easily by calculating this continuum.

Shock-Capturing Approach and Nonevolutionary Solutions in Magnetohydrodynamics

Shock-capturing methods have become an effective tool for the solution of hyperbolic partial differential equations. Both upwind and symmetric TVD schemes in the framework of the shock-capturing approach are thoroughly investigated and applied with great success to a number of complicated multidimensional gasdynamic problems. The extension of these schemes to magnetohydrodynamic (MHD) equations is not a simple task. First, the exact solution of the MHD Riemann problem is too multivariant to be used in regular calculations. On the other hand, the extensions of Roe's approximate Riemann problem solvers for MHD equations in general case are nonunique and need further investigation. That is why, some simplified approaches should be constructed. In this work, the second order of accuracy in time and space high-resolution Lax–Friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characteristic splitting of Jacobian matrices. The necessity is shown to solve the full set of MHD equations for modeling of multishocked flows, even when the problem is axisymmetric, to obtain evolutionary solutions. For the numerical example, the MHD Riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain. If the problem is solved as purely coplanar, a slow compound wave appears in the self-similar solution obtained by any shock-capturing scheme. If the full set of MHD equations is used and a small uniform tangential disturbance is added to the magnetic field vector, a rotational jump splits from the compound wave, and it degrades into a slow shock. The reconstruction process of the nonevolutionary compound wave into evolutionary shocks is investigated. Presented results should be taken into account in the development of shock-capturing methods for MHD flows.

Self-similar magnetohydrodynamics

For the solution of the full set of magnetohydrodynamic equations in the presence of gravity due to a central point-mass, a self-similar theory for a general polytrope has already suggested a set of exact time-dependent solutions by analytical methods for a gamma =4/3 polytrope, since gamma =4/3 is the simplest to treat. In the present paper while going for a complete set of self-similar solutions, the authors find that gamma =4/3 is the only physically-possible polytrope and that then, pressure is independent of the scalar function A and depends on angle and time only. They also obtain a specific form of time-dependence for the self-similar variable.