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In this paper, analytical relations for magnetic flux density components of helical toroidal coils (HTC) are presented. The numerical integrations resulting from these equations are done using the extended three-point Gaussian algorithm. The obtained results using numer-ical simulations coincide with the results of particle-in-cell (PIC) method. Th...
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... such as the Tokamak has suggested the use of an advanced coil with a helical toroidal structure [1]. The main reason for these suggestions is the ability to implement special target functions for this coil in comparison with other structures such as the toroidal, the solenoidal, and the spherical coils [2]. The structure of this coil is shown in Fig. 1. In this coil, the ratio of the major radius to the minor radius (A = R/a), the number of turns in a ring (N ), and the number of rings in a layer (υ) are called aspect ratio, poloidal turns (or pitch number), and helical windings, respectively. For example, the coil in Fig. 1 is composed of five helical windings (υ = 5) with nine ...
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... and the spherical coils [2]. The structure of this coil is shown in Fig. 1. In this coil, the ratio of the major radius to the minor radius (A = R/a), the number of turns in a ring (N ), and the number of rings in a layer (υ) are called aspect ratio, poloidal turns (or pitch number), and helical windings, respectively. For example, the coil in Fig. 1 is composed of five helical windings (υ = 5) with nine poloidal turns (N = 9). The inductance for-mulas show that parameters a, R, and N of the helical toroidal coil can be used as design parameters to satisfy special tar-get functions. With respect to the fact that each ring of the coil generates both toroidal and poloidal magnetic ...
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Citations
In this paper, equations for calculation of the self and mutual inductances of the Modular Toroidal Coil (MTC) applicable to Tokamak reactors are presented. The MTC is composed of several solenoidal coils (SCs) connected in series and distributed in the toroidal and the symmetrical form. These equations are based on the Biot-Savart and Neumanns equations, respectively. The numerical analysis of the integrations resulting from these equations is solved using the extended three-point Gaussian algorithm. Comparing the results obtained from the numerical simulation with the experimental and the empirical results confirms the presented equations. Furthermore , the comparison of the behavior of these inductances, when the geometrical parameters of the MTC are changed, with the experimental results shows an error of less than 0.5%. The behavior of the inductance of the coil indicates that the optimum structure of this coil with the stored magnetic energy as the optimization function is obtained when the SCs are located on the toroidal planes. At the end, the Finite Element Method (FEM) approach is employed to present an algorithm to study the three dimensional leakage flux distribution pattern of the coil and to draw the magnetic flux density lines of the MTC. The presented algorithm, due to its simplicity in analysis and ease of implementation of the non-symmetrical and three dimensional objects, is advantageous to the commercial software such as ANSYS, MAXWELL, and FLUX.
