By Bernard T. Merritt, Robert F. Post, Gary R. Dreifuerst, Donald A. Bender; October 28, 1994; Lawrence Livermore National Laboratory, UCRL-JC-119050 Introduction
For many years Klaus Halbach has been investigating novel designs for permanent magnet arrays, using ad vanced analytical approaches and employing a keen in sightinto such systems. One of his motivations for this research was to ﬁnd more e cient means for the utiliza tion of permanent magnets for use in particle accelera tors and in the control of particle beams. As a result of his pioneering work, high power free electron laser sys tems, such as the ones built at the Lawrence Livermore Laboratory, became feasible, and his arrays have been incorporated intoother particle focusing systems of various types. This paper reports another, quite di er ent, application of Klaus’ work, in the design of high power, high e ciency, electric generators and motors. When tested, these motor/generator systems display some rather remarkable properties. Their success de rives from the special properties which these arrays, which we choose to call “Halbach arrays,”possess. In August 1979, Klaus Halbach submitted a paper1 enti tled “Design of Permanent Multipole Magnets with Ori ented Rare Earth Cobalt Material.” In this paper, he presented a novel method of generating multipole mag netic ﬁelds using non intuitive geometrical arrange ments of permanent magnets. In subsequent publications,2,3 ,4 he further deﬁned these concepts. Of particular interest to one ofthe authors Richard F. Post was the special magnet array that gen erated a uniform dipole ﬁeld. In 1990 Post proposed the construction of an electric machine a motor/generator using a dipole ﬁeld based on Klaus Halbach’s array of permanent magnets. He further proposed that such a system should be employed as an integral part of “an electromechanical battery” EMB , i.e., a modular ﬂy wheel systemto be used as a device for storing electrical energy, as an alternative to the electrochemical storage battery. This paper reviews Halbach’s theory for the generation of a dipole ﬁeld using an array of permanent magnet bars, presents a simple analysis of a family of novel “ironless” electric machines designed using the dipole Halbach array, and describes the results obtained when they were testedin the laboratory.
The Dipole Array
Although electric machines can be constructed using multipole ﬁelds based on the techniques introduced by Klaus Halbach, the dipole ﬁeld o ers some unique ad vantages for the construction of a high speed electric machine. Figure 1 shows an end view of a dipole Halbach array. Shown in Figure 1a are the directions of magneti zation of the bars and in Figure 1b,one quadrant of the computed lines of force produced by the array. Note the highly uniform ﬁeld inside the array, and the near cancellation of the ﬁeld outside the array.
Figure 1a — Halbach Array
Halbach Festschrift Symposium, Berkeley, CA; February 3, 1995
-1.68 .36 -1.28
2.2 2.26 2.2 2.1
1.10 -1.06 1.55
-.82Figure 1b — Halbach Array Field Lines
Figure 2 — Halbach Array Measured Field Values
Except near the ends of the array, or very near its inner surface, the dipole ﬁeld inside a such an array is given by the expression derived by Halbach:
Construction of the Generalized Motor/Generator
The design of a motor/generator using a dipole Halbach array is simplicity itself. Furthermore,since there are no iron laminations used in the design the theoretical pre diction of the properties of such motor / generators is equally simple. In order to construct a motor/generator, all that is re quired is to insert a single or multi phase winding down the axis of the dipole ﬁeld and provide relative motion between the ﬁeld and the winding s . Relative rotation then generates an EMF in the...