Extreme ultraviolet emission lines of Ni xii in laboratory and solar spectra

A linear force-free field solution is presented in cylindrical coordinates, formulated in terms of trigonometric and Bessel functions. A numerical exploration has revealed that this solution describes magnetic field lines that meander in Cartesian space, as well as field lines that lie on toroidal flux surfaces. These tori are in (or close to) the plane perpendicular to the cylindrical axis. Nested tori, as well as tori with shells that have finite thickness, were found. The parameter space of the solution shows that the tori exist within a bounded range of values

A new family of solutions of the force-free field equation

A new family of solutions has been found for force-free magnetic fields and Beltrami flows, which admits a complete classification in terms of the eigenvalues of the problem. In the absence of boundary values to determine them uniquely, the eigenvalues correspond to the entire set of real numbers, except for zero. The eigenvalues are degenerate in that each eigenvalue has many eigensolutions associated with it. For each eigensolution we have been able to identify sets of equilibrium or null points and lines. The linear mappings of these null points and lines are all unstable. Finally, we derive the first integral of energy associated with this family of solutions

The structure of force-free magnetic fields

Incontrovertible evidence is presented that the force-free magnetic fields exhibit strong stochastic behavior. Arnold’s solution is given with the associated first integral of energy. A subset of the solution is shown to be non-ergodic whereas the full solution is shown to be ergodic. The first integral of energy is applied to the study of these fields to prove that the equilibrium points of such magnetic configurations are saddle points. Finally, the potential function of the first integral of energy is shown to be a member of the Helmholtz family of solutions. Numerical results corroborate the theoretical conclusions and demonstrate the robustness of the energy integral, which remains constant for arbitrarily long computing time

Differential rotation and angular momentum

Differential rotation not only occurs in astrophysical plasmas like accretion disks, it is also measured in laboratory plasmas as manifested in the toroidal rotation of tokamak plasmas. A re-examination of the Lagrangian of the system shows that the inclusion of the angular momentum’s radial variation in the derivation of the equations of motion produces a force term that couples the angular velocity gradient with the angular momentum. This force term is a property of the angular velocity field, so that the results are valid wherever differential rotation is present

Numerical simulations of sunspots

The origin, structure and evolution of sunspots are investigated using a numerical model. The compressible MHD equations are solved with physical parameter values that approximate the top layer of the solar convection zone. A three dimensional (3D) numerical code is used to solve the set of equations in cylindrical geometry, with the numerical domain in the form of a wedge. The linear evolution of the 3D solution is studied by perturbing an axisymmetric solution in the azimuthal direction. Steady and oscillating linear modes are obtained