Shimming, Part I
The Shimming of High Resolution NMR Magnets
As Told by a Couple of Nuts,
Virginia W. Miner
Woodrow W. Conover
Copyright © 1997 by Acorn NMR Inc. All rights reserved. Copies may be made for personal use and for educational purposes. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be sold or published in any form or by any means, or stored in any data base or retrieval system, without the prior written consent of Acorn NMR Inc.
This is the HTML version of the companion shimming manual for SAM, the NMR shimming simulation module within NUTS.
Table of Contents
Foreword In the olden days. Why is it called shimming?
Introduction What is shimming.
Equations for Common Room Temperature Shims Table showing field generated by common shims.
Sample Spinning Why samples are spun and the complications.
Basics What do we look at to shim.
Shim Interactions Procedure for adjusting shims with zero-, first- and second-order interactions.
A New Magnet Things which need to be checked when a magnet is installed.
Checking coil position A quick test for probe coil and shim coil alignment.
Before You Start To Shim Get off on the right foot.
Probe Coil Plot
A Shimming Procedure A systematic method of adjusting shims.
Symptoms of Inhomogeneity Lineshapes resulting from different axial gradients.
The Sample and Shimming End effects, particulates, dissolved material, radiation damping.
Probes and Shimming Probe materials, magnetic susceptibility correction, size of the probe coil.
RF Homogeneity Origin of different types of spinning sidebands.
Computer Shimming Things to be aware of in using automatic shimming.
In the beginning, the field homogeneity of large electromagnets was adjusted by mechanical alignment of the magnet pole faces. The more parallel the pole faces, the more homogeneous the magnetic field. The first step in the process of adjusting magnetic homogeneity was to adjust the position of the magnet’s pole faces by turning three large bolts which held the pole faces. Adjusting these bolts tilted the pole faces relative to each other with the aim of making the pole faces more parallel. If the bolts ran out of range, thin pieces of brass were placed between the magnet yoke and the pole pieces to move the pole pieces as parallel as possible. These thin pieces of brass were also placed in other strategic locations to make the pole faces parallel in a manner not addressed by the three adjustment bolts. The metal pieces were called shim stock and the seemingly endless process of placing and removing pieces of shim stock acquired the name “shimming“. Because tons of magnetic field pressure existed on the pole faces, the magnet had to be turned off to place and remove the shim stock. When the sample was spinning, the final part of adjusting magnetic homogeneity with these systems was to adjust a ratchet bolt which pulled together or pushed apart the tops of the magnet pole pieces to give a fine adjustment of the Y gradient. All of these processes were mechanical in nature. After these adjustments, the NMR instruments were typically capable of giving better than 0.2 Hz resolution. This is rather impressive when you consider that 0.2 Hz out of 60 MHz represents 3 parts per billion field homogeneity over the volume of the sample.
To increase the performance, reduce the difficulty of adjusting magnetic homogeneity and reduce the manufacturing difficulty of the magnets, an electronic “shimming” process was developed which used a series of small electromagnets having very specific magnet field contours. These small electromagnets are placed around the sample area. Each small electromagnet can be used to adjust the field in the area of observation to create more of or counteract existing types of magnetic gradients. A complete series of these electromagnets can be used to adjust the magnetic field homogeneity to a given level of purity depending on how many types of adjustment electromagnets are used. The process of adjusting the magnetic field homogeneity by adjusting the current in each of the small electromagnets retained the name shimming and the small electromagnets assumed the name “shims”.
At first only a few low order ( X, Y, and Z) electrical shims were used. As the fields became higher, magnet production became more difficult, and more and higher order electrical shims were added to maintain the same level of performance. These electrical shims are not 100% pure and have interactions with shims of a similar nature ( ZX creates some Z gradient and X gradient in addition to the intended ZX gradient ). Because of these interactions, the number of adjustments necessary to shim the magnet increases geometrically with the number of shims, not just linearly. In addition, the raw field encountered in superconducting magnets is usually worse than in electromagnets, so larger corrections are required. These two facts make the process of shimming superconducting magnets more difficult and the shimming process more important to obtain useful NMR spectra.
To obtain 0.2 Hz resolution requires ten times greater magnetic field homogeneity at 600 MHz than at 60 MHz. Therefore, in addition to the higher field superconducting magnets being more difficult to shim, shimming becomes more important to obtain the same results as the magnetic fields increase. Other aspects of an NMR instrument’s performance are also affected by shimming, such as the NMR signal’s lineshape, which is critical for achieving good solvent suppression. So the necessary evil of adjusting the small electromagnets, called shimming, remains very important in today’s NMR instrumentation.
Shimming a magnet for use in NMR is similar to many sports: mental attitude is a key to success. Shimming is often made more difficult than necessary by the operator’s belief that it is a “magic” process far too complex to understand. Successful shimming is a simple, but often very time-consuming, process. An organized and logical approach is key if the process is to be both fast and effective. Each shim or shim type generates symptoms in the NMR instrument’s performance indicating its misadjustment. An understanding of the relationship of each shim and these instrumental performance symptoms reduces shimming from a random knob turning task to a scientific procedure of adjustment and observation of effects.
Shimming is definitely a serial process. This means that things should be taken one step at a time; it does not mean, however, that there is one and only one defined process to be used. Instead of a “cookbook” approach to shimming where a defined stepwise procedure is followed, shimming should be approached like solving a murder mystery. In a murder mystery, there are many things which are common from one murder mystery to the next. The murderer needs a motive, the opportunity, etc. However, not every murder mystery is solved by the same stepwise procedure. In other words, the solution of a murder mystery has some generalized procedures and then becomes a search for clues. The process can be long and involved, but luckily the NMR instrument provides many clues to be followed. As will be discussed later, lineshape provides the clues to the solution of the mystery.
Shimming has some generalized procedures to be used when certain clues are observed. In addition to these procedures, there are tools available for use in the shimming process. Each tool is called upon as the conditions warrant, and each works in some cases, but not all. In addition, as the shimming process proceeds, additional clues suggest the use of other tools. The shimming process is a little like peeling an onion – removing one layer often reveals another layer underneath (and crying sometimes results).
The most common method of adjusting the homogeneity of an NMR magnet is the observation of an NMR signal. Since the natural line width of an NMR signal may be less than 0.1 Hz, then even for a 100 MHz NMR instrument a field homogeneity of one part per billion would be required to measure this line width. Very few test instruments have this precision. This means that the NMR instrument becomes the test instrument used to adjust itself.
An additional problem with the shimming process is that the observed NMR signal results from the integrated signal from the total volume of the observed sample, which may have many different resonant frequencies with different degrees of excitation arising from different positions in the sample. Visualize the NMR sample as a continuum of isolated mini-samples, each of which is infinitesimally small. Each mini-sample then generates a signal whose linewidth is determined by the T2 relaxation time of the sample and whose frequency results from the field value at that point. The intensity of the signal generated by each mini-sample would reflect the amount of excitation at that point. What the NMR operator observes is the sum of signals from all the mini-samples. In other words, the NMR signal is the total integrated signal over the total sample volume times each area’s degree of excitation. It is the integration of the NMR signal response which leads to a major difficulty in the shimming process. Any knowledge as to which part of the NMR sample is experiencing the magnetic inhomogeneity is lost in this integration process.
The NMR operator adjusts the field homogeneity for the NMR instrument with a set of electronic shims, each of which has its effects over a complex geometry. If positional information for each of the mini-samples were not lost in the integration process discussed above, the NMR operator would have much better clues as to which shim to adjust. There are, however, clues from the NMR signal which allow the NMR operator to narrow the selection of shims which probably need adjustment. These clues will be discussed later.
The shim gradients used to adjust the magnetic field homogeneity in superconducting magnets have the common names shown in the table on the next page. However, these shims have more complicated expanded equations describing their actions as indicated in the table. Although every different type of shim set has a slightly different set of expanded equations, the expanded equations for the shim gradients shown in the table are reasonable examples of the full gradient created by each shim coil. The equations are shown for interest and are not used in the shimming process to be described.
Equation for Field Generated
2z2 – (x2 + y2)
z[2z2 – 3(x2 + y2)]
8z2[z2 – 3(x2 + y2)]+3(x2 + y2)2
48z3[z2 – 5(x2 + y2)]+90z(x2 + y2)2
x[4z2 – (x2 + y2)]
y[4z2 – (x2 + y2 )]
Z(X2 – Y2)
z(x2 – y2)
In the early days of NMR, Bloch suggested that the effective homogeneity of the magnetic field can be improved in a simple way by providing a motion of the molecules within the sample. The rate of molecular motion necessary to accomplish this task is on the order of 4 Hz. This speed is easily obtainable by mechanical motion of the sample. Anderson and Arnold demonstrated the improvement by spinning a water sample about an axis coincident with the axis of the receiver coil. At rotational speeds in excess of 10 Hz, they reduced the halfwidth of the NMR signal by a factor of 17 and increased the amplitude by a factor of 7. The size of the improvement is proportional to the size of the field inhomogeneity along the axes averaged by the spinning process. As the magnetic field homogeneity increases, the improvement obtained by sample spinning decreases.
Spinning the NMR sample tube averages the field inhomogeneities along two axes but not along the axis about which the sample is spun. If the NMR operator could make a spherical sample and spin about the X, Y and Z axes simultaneously, shimming might become a lot easier. However, no simple mechanical means of preparing and spinning the sample to average all three axes has yet been devised. The effect of spinning in all three axes simultaneously can be seen when starting and stopping spinning on large diameter tubes. The turbulence created by starting and stopping causes sample mixing along the spinning axis. If the NMR operator watches the lock level of a spinning sample and suddenly turns off the spinner, the lock level will actually rise while the sample is mixing from the turbulence. The same effect can be seen when starting to spin where the lock level goes up to a higher level and fades back down to a final value between the non-spin value and its highest level. This is because turbulence when the spinner starts causes mixing of the sample, thereby effectively spinning about all axes simultaneously. The effect is most visible on large diameter tubes.
The spinning process divides the shim set into two different types: the type not averaged by spinning, or “on-axis” shims, and the type which are averaged by spinning, or “off-axis” shims. Adjusting the on-axis shims while spinning and the off-axis shims while not spinning can be used to “decouple” the different types of shims and simplifies the process.
Under some conditions of field inhomogeneity, spinning the sample produces an amplitude modulation of the NMR signal. This process gives rise to “spinning sidebands” on either side of the resonance signal. The sidebands occur at integer multiples of the spinning rate and have a tendency to become smaller as the spinning rate is increased. These properties can be used to help identify these spurious signals. For a more thorough discussion of the origins of different types of spinning sidebands, see the section on RF Homogeneity.
Proceed to Part II, Shimming Basics
Proceed to Part III, Symptoms of Inhomogeneity
Skip to Part IV, The Z1 Profile
Skip to Part V, Effect of Sample and Coil
Last updated: 01/22/03