Magnetic Force Calculation Between Circular Coils of Rectangular Cross Section With Parallel Axes for Superconducting Magnet

Abstract

Abstract-The electromagnetic force between two misaligned coils (coils with parallel axes) with uniform current density distribution and rectangular cross section based on the derived semi-analytical expressions was presented. Using the semi-analytical expressions for magnetic force between filamentary misalignment circular coils we calculate the propulsive and the transverse magnetic force. In order to verify the validity of the expressions, we use the filament method with Grover's formula to calculate the magnetic force for two coils with parallel axes. The results obtained by two methods are in a very good agreement. In this paper, the derivation of the semianalytical expressions and the calculation results of the magnetic force are introduced.

Magnetic Force Between Inclined Circular Loops (Lorentz Approach)

“…All results are in an excellent agreement as expected and the restoring and axial forces (F r and F a ) [15] correspond to the components F x and F z from this work respectively.…”

“…Filamentary circular coils are with parallel axes and the distance between planes in which they are positioned is c = 10 mm [15]. All currents are equal to 1 A.…”

“…In [15] we calculated the restoring and the axial magnetic forces for circular loops with parallel axes positioned in different planes.…”

“…The vast majority of this attention has been given to the purely coaxial geometries [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. More recently the focus has been shifted to calculation of the mutual inductance and magnetic force between circular coils with lateral and angular misalignments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Using the powerful numerical methods, such as Finite Element Method (FEM) and Boundary Element Method (BEM) [27,28], it is possible to calculate accurately and rapidly this important physical quantity.…”

Simple Method to Calculate the Force Between Thin Walled Solenoids

“…Yang and Hull present expressions to obtain force and torque between square loops [7]. Babic et al present formulas for the calculation of magnetic forces between: coaxial cylindrical magnets and thin coils [8], thick rectangular coils and thin walled solenoids [9], inclined circular coils [10], and misaligned thick coils with parallel axes [11]. Shiri and Shoulaie present a method that is useful to calculate the force between planar spiral coils [12], and also calculates the electromagnetic force distribution on a coil [13].…”