First post here in PF, so forgive me if this question is in the wrong place. I'm a student in computational plasma physics. The code I work with utilizes magnetic field aligned coordinates, and as a necessity, it is sometimes useful to convert between spatially regular coordinates (cartesian, cylindrical, toroidal, etc) to our field aligned coordinates. Although I have a system of equations which defines our magnetic coordinates, and a general idea that "magnetic field lines are straight in these coordinates" I find the coordinate system largely unintuitive. Does anyone know of a good resource for developing intuition on complicated coordinate systems? I have always felt a little fuzzy even on the relatively simple description of covariant and contravariant coordinates provided in Jackson's E&M. In one sentence, what is the salient benefit of using these coordinates. I also see descriptions of a scalar Jacobian, which I gather/guess is the determinant of the Jacobian matrix. Is this correct? I believe the matrix can be thought of as a way to convert between coordinate systems. Is there an intuitive, spatial way to think of what this scalar Jacobian value represents?