What Coil Length do you Want?

              This is a rather complicated question.  Most authors and manufacturers of birdcages refer to either the rung length (i.e., inside length), the overall length (i.e., to the outside of the rings), or the mean of these two numbers.  NMR spectroscopy coil manufacturers, on the other hand, are accustomed to specifying the length of the high-homogeneity region of their coils, which are generally some sort of saddle coil.  For high-resolution NMR, one is often interested in rms inhomogeneity below 5%, and the length of this region may be under 50% of the coil's overall length.

              Our Litzcages have (over a wide range of conditions) field profiles and B₁ homogeneity very similar to perfectly optimized 16-rung birdcages.  An optimized 16-rung shielded birdcage of 10 cm diameter d with 8 cm rung length, 10 cm overall length, 12 cm shield diameter, and 6 mm rung width will achieve ~10% rms inhomogeneity for a typical biological sample of 8 cm diameter over a length of 6 cm at frequency f up to ~100 MHz.  It is important to keep in mind that the field falls off with increasing z from the center only along the axis, while it increases near the edge of the sample.  On the z-axis, the field at the ends of the above sample will be ~20% below the central value.  The peak value near each rung at the center will be nearly 20% above the central value, while minimum value between rungs will be ~10% below the central value.  The mean field near the perimeter at the ends will be ~30% above the central value, but it falls off rapidly with decreasing radius.  Increasing the external shield diameter improves the homogeneity over the full surface (sides and ends) of the sample cylinder.

               At higher fd product, the relative field strength at the center of the sample increases.   At 200 MHz, the rms inhomogeneity for the above case will be ~15%, and at 400 MHz it will be ~20%.  Likewise, doubling the coil and sample dimensions at 100 MHz would also increase inhomogeneity to ~15%.

              For our CP Litzcages, we specify the rung length, and their homogeneous region will generally be 65-80% of this length, depending on fd.  For our linear litz coils, on the other hand, we specify the length of the region of 8% rms inhomogeneity, which is typically ~60% of the overall coil length.

              The table below summarizes the typical B₁ profile for a litzcage (or a highly symmetric 16-rung birdcage) of 10 cm diameter and 8 cm rung length, centered at the origin, inside a 12 cm shield.