We have assembled a waterhyphen;cooled ironhyphen;free copper solenoid whose central magnetic field is constant to within one part in 105over a region 1 cm in diameter extending 12 cm along the axis of the magnet. The solenoid operates without the use of shim coils or current shunts. It achieves a central field of 15.7 kG for a current of 1150 A. In this article, we report on features incorporated in the design of the solenoid and the methods of field shaping used to obtain a very uniform central field region. The use in our design of multiple current elements has the advantage that it allows for great flexibility in obtaining a desired field shape. We describe in detail the method used to arrive at an initial guess for the optimal positioning of the coils as well as an iterative corrective procedure involving sequences of measurement, calculation, and adjustment that can be used subsequently to zero errors in the field shape. These general methods are easy to implement on a computer, yet they are powerful and appear to converge rapidly.
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