Field Strength Characteristics in Single-layer and Multi-layer Solenoids: Basic and Adaptive. The Zone of Uniformity

Abstract

The problem of identifying the executive zone of the solenoid, i. e. that of its median part with a length of [L], where the field strength H is almost constant, is solved in order to conduct research in it. According to the results of the diagnostics of the multilayer solenoids used (four, differing in length L), the acceptability of solving this problem is shown by adapting the well-known fundamental expression for H in a single-layer solenoid to a multilayer one: by means of a coefficient slightly greater than unity. It was found that, based on the requirement that the H value in the center of the solenoid be very close (with an underestimation of no more than 1-2%) to the potential value (in an infinitely long solenoid), the length-to-diameter ratio should be L/D ≥ 5-7. To determine [L], the current value of H on its coordinate characteristic is estimated, which indicates a noticeable (within acceptable limits, in particular, 3%) decrease in H compared to the potential one. The distance x = [x] from the end of the solenoid is determined, where, upon the requirement of field uniformity, such a decrease in H, for example, by more than ε = 5%, is hardly acceptable. It is shown that, regardless of the length L of the solenoids, the length values [x] of their lateral parts, where the field strength is significantly underestimated, are close, and the relative values [x]/L are subject to feedback from L/D. The dependences for [L] and [L]/L on L and L/D are obtained graphically and analytically.