Six ansatzes are investigated for their potential to allow
three-dimensional (3D)
ideal magnetohydrodynamic (MHD) equilibria. The ansatzes are based on a
Clebsch representation for the magnetic field,
B=∇H × ∇k,
and a ‘generalized Clebsch representation’,
B=∇×(∇K × ∇k), with
∇k being one of the coordinate directions
of a cylindrical coordinate system. Three classes of equilibria, all with
a straight
magnetic axis, are obtained. Equilibria of the first class have a purely
poloidal
magnetic field of the Clebsch type with k=z and include
the 3D equilibria already
known. Equilibria of the other two classes have a purely toroidal (i.e.
here
longitudinal) magnetic field and pressure surfaces that can be chosen
such that poloidal
sections are closed. The second class is based on a Clebsch representation
with
k=θ. Solutions contain a free function of θ that
determines the poloidal sections
of the pressure surfaces at, say, z=0. The behaviour in the
toroidal direction is
then fixed but not periodic. For the third class, the generalized Clebsch
representation with k=z is used. The equilibria are
similar to those of the second class,
with two important differences. They contain no free function and field
lines are
not planar. Finally, 3D vacuum fields, which exhibit 3D magnetic surfaces,
are
presented. They have the same geometry as the equilibria of the third class,
and in
fact can be obtained as a certain limit from these equilibria. Possible
applications
of the equilibria found are mentioned.