Error field generation of solenoid magnets Page: 3 of 12
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THEORETICAL CALCULATIONS
Of course, the magnetic field on axis, generated by solenoids con-
sisting of current loops, can be calculated very simply by applying the
Biot Savart law,
dB = ^ 1 (dL x R) (1)
4tR3
around the loops and summing for the total field.
The complication arises when the current-carrying conductor
follows noncircular paths. A computer program was developed to ac-
cumulate the field, at any point, created by a multitude of straight
filaments representing the actual coil-winding conductors. This com-
puter code uses a method of computation developed for the MAGIC
program at General Dynamics Convair Division.1
Computer models were then developed to simulate the winding of
solenoidal coils. Two possible winding techniques were devised and set
up for computation with the code. A model was also developed to
simulate the field contributions made by the overhead buswork system
and the incoming leads.
COMPUTER MODELS
The first coil-winding case to be considered deals with the field
deviation which would be generated by winding the coils in a helical
fashion. The second case looks at a coil that is wound by what is re-
ferred to as the “joggled” method, which will be discussed later. In
comparing the two winding methods, joggle and helix, only the error
fields due to the coils themselves will be discussed (i.e., excluding the
leads and overhead buswork).
In each case, the magnetic model is divided into five sections
(Figure 2) with the following characteristics:
• Half of the 32nd layer from the center to the left flange (helical or
joggled)
• Pancake spiral from the 32nd to the first layer (actually consisting
of approximately 34 spiral turns because of the two-conductor-
width insulation between the 31st and 32nd layers)
• Main conductor pack consisting of 31 layers with approximately 39
turns/layer (helical or joggled)
3
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Saunders, J. L. Error field generation of solenoid magnets, article, January 1, 1982; United States. (https://digital.library.unt.edu/ark:/67531/metadc1067002/m1/3/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.