Hamada coordinates: Difference between revisions
Jump to navigation
Jump to search
→Magnetic field and current density expressions in Hamada vector basis
| Line 18: | Line 18: | ||
where the last identity follows from the [[Flux coordinates#Useful properties of the FSA|properties of the flux surface average]]. The Hamada angles are sometimes defined in 'turns' (i.e. <math>(\theta, \xi) \in [0,1)</math>) instead of radians (<math>(\theta, \xi) \in [0,2\pi)</math>)). This choice together with the choice of the volume <math>V</math> as radial coordinate makes the Jacobian equal to unity. Alternatively one can select <math>\psi = \frac{V}{4\pi^2}</math> as radial coordinate with the same effect. | where the last identity follows from the [[Flux coordinates#Useful properties of the FSA|properties of the flux surface average]]. The Hamada angles are sometimes defined in 'turns' (i.e. <math>(\theta, \xi) \in [0,1)</math>) instead of radians (<math>(\theta, \xi) \in [0,2\pi)</math>)). This choice together with the choice of the volume <math>V</math> as radial coordinate makes the Jacobian equal to unity. Alternatively one can select <math>\psi = \frac{V}{4\pi^2}</math> as radial coordinate with the same effect. | ||
== Magnetic field and current density expressions in Hamada vector basis == | == Magnetic field and current density expressions in a Hamada vector basis == | ||
With the form of the Hamada coordinates' Jacobian we can now write the explicit [[Flux coordinates#Contravariant Form|contravariant form]] of the magnetic field in terms of the '''Hamada''' basis vectors | With the form of the Hamada coordinates' Jacobian we can now write the explicit [[Flux coordinates#Contravariant Form|contravariant form]] of the magnetic field in terms of the '''Hamada''' basis vectors | ||
:<math> | :<math> | ||