# The relationship between flux coordinates and equilibrium-based frames of reference in fusion theory

@article{Kruger2019TheRB, title={The relationship between flux coordinates and equilibrium-based frames of reference in fusion theory}, author={S. E. Kruger and John Morton Greene}, journal={Physics of Plasmas}, year={2019} }

The properties of two local reference frames based on the magnetic field and the current density are investigated for magnetized plasmas in toroidal geometry with symmetric angle. The magnetic field-based local frame of reference has been well-studied for example by Dewar and colleagues [Phys. Fluids 27, 1723 (1984)] An analogous frame based on the current density vector is possible because it is also divergence free and perpendicular to the gradient of the poloidal flux. The concept of…

## 3 Citations

### Snell Law for an Electromagnetic Pulse Travelling over a Torus Surface and Scattered by a Flat

- Physics2022 International Conference on Electromagnetics in Advanced Applications (ICEAA)
- 2022

We apply a new tool that is the Maxwell-Fredholm equations, to study the collision of an electromagnetic pulse with a flat surface of separation between the two parts of a torus-shaped artefact with…

### Some mathematics for quasi-symmetry

- Mathematics, PhysicsJournal of Mathematical Physics
- 2020

Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-centre motion. Here we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an…

### An electromagnetic pulse over a torus, a particularization of Snell´s law

- PhysicsJournal of Physics: Conference Series
- 2022

We apply a new tool that is the Maxwell-Fredholm equations, to study the collision of an electromagnetic pulse with a flat surface of separation between the two parts of a torus-shaped artefact with…

## References

SHOWING 1-10 OF 32 REFERENCES

### Hydromagnetic equilibria and their proper coordinates

- Physics
- 1962

Proper coordinate systems are constructed in hydromagnetic equilibria and their properties are studied. First, the contra-gradient components of magnetic field and of current density are surface…

### The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma

- Physics
- 2016

A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for…

### Generalized reduced magnetohydrodynamic equations

- Physics
- 1998

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the…

### Steepest‐descent moment method for three‐dimensional magnetohydrodynamic equilibria

- Physics
- 1983

An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate…

### The second region of stability against ballooning modes

- Physics
- 1981

A new type of axisymmetric magnetohydrodynamic equilibrium is presented. It is characterized by a region of pressure and safety factor variation with a short scale length imposed as a perturbation.…

### Magnetic coordinates for equilibria with a continuous symmetry

- Mathematics
- 1984

Magnetic coordinates for hydromagnetic equilibria are defined which treat toroidal and ‘‘straight’’ helical plasmas equivalently and yet exploit the existence of a continuous symmetry to derive…

### A new form of the magnetohydrodynamic potential energy

- Physics
- 1996

In this Letter a useful and instructive form of the magnetohydrodynamic potential energy is presented. In this form all but one term is positive definite, each term is self‐adjoint, and it can be…

### Resistive instabilities in a diffuse linear pinch

- Geology, Physics
- 1966

The effects of small electrical resistivity, viscosity, and thermal conductivity on hydromagnetic instabilities for diffuse linear pinch configurations are considered. For finite-pressure systems,…