Solenoidal Fields for Ion Beam Transport and Focusing
In this report we calculate time-independent fields of solenoidal magnets that are suitable for ion beam transport and focusing. There are many excellent Electricity and Magnetism textbooks that present the formalism for magnetic field calculations and apply it to simple geometries [1-1], but they do not include enough relevant detail to be used for designing a charged particle transport system. This requires accurate estimates of fringe field aberrations, misaligned and tilted fields, peak fields in wire coils and iron, external fields, and more. Specialized books on magnet design, technology, and numerical computations [1-2] provide such information, and some of that is presented here. The AIP Conference Proceedings of the US Particle Accelerator Schools [1-3] contain extensive discussions of design and technology of magnets for ion beams - except for solenoids. This lack may be due to the fact that solenoids have been used primarily to transport and focus particles of relatively low momenta, e.g. electrons of less than 50 MeV and protons or H- of less than 1.0 MeV, although this situation may be changing with the commercial availability of superconducting solenoids with up to 20T bore field [1-4]. Internal reports from federal laboratories and industry treat solenoid design in detail for specific applications. The present report is intended to be a resource for the design of ion beam drivers for Inertial Fusion Energy [1-5] and Warm Dense Matter experiments [1-6], although it should also be useful for a broader range of applications. The field produced by specified currents and material magnetization can always be evaluated by solving Maxwell's equations numerically, but it is also desirable to have reasonably accurate, simple formulas for conceptual system design and fast-running beam dynamics codes, as well as for general understanding. Most of this report is devoted to such formulas, but an introduction to the Tosca{copyright} code [1-7] and some numerical results obtained with it are also presented. Details of design, fabrication, installation, and operation of magnet systems are not included; here we are concerned with calculations that precede or supplement detailed design. Mathematical derivations are presented with only a moderate number of steps. While there is no claim of originality, except for various numerical approximations and a conceptual induction module design in section 20, many of the results and discussions are not readily available elsewhere. Our primary topic is axisymmetric solenoidal systems with no magnetic materials. These simplifying features allow useful analytical calculations, which occupy sections 2-13. Deviations from axisymmetry are considered in sections 14, 15, 21, 22, and 23 and the effects of magnetic materials are treated in sections 16-20. Since magnetic aberrations are mixed with geometric aberrations in computing ion orbits, section 22 on the ion equations of motion in an arbitrary field is included.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- Accelerator& Fusion Research Division
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 965351
- Report Number(s):
- LBNL-63716; TRN: US0903882
- Country of Publication:
- United States
- Language:
- English
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