Magnetic field profiles for four flux ropes and along three different directions are shown in the middle part. Comparison of the MT solution (in black) to the zero- (in green) and first- (in red) order solutions and the uniform-twist solution (in blue). All flux ropes have circular cross sections with radius r₀, R₀/r₀ = 5, and br₀ = 1.5. Trajectories along which the profiles are displayed are shown by the thick arrows in the top sketches of the flux ropes. Panel a displays the profiles along the x-axis, panel b along the line parallel to the y-axis and crossing the x-axis at the point [R₀−r₀/ 2,0,0], and panel c along the line parallel to the z-axis and crossing the x-axis at the point [R₀,0,0]. The bottom part shows hodograms of the magnetic field vectors along the displayed trajectories. The color coding of the lines is the same as in the middle part. The arrows show directions of the hodograms and also indicate the entry into the toroid (blue) and the exit (green).