The research of magnetic-field integration method based on linear-linear basis functions

In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a fractional integro-differential equation. The presented technique is based on the expressed basis functions and their fractional integral matrix together with the Gauss–Legendre integration method and the Lagrange multipliers algorithm. This approach converts the original problem into a mathematical programming one. Three examples are investigated numerically to verify the capability and reliability of the approach.

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FEM-simulation of superconducting linear acceleration system for pellet injection

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-209467 ◽

2020 ◽

Vol 64 (1-4) ◽

pp. 1469-1475

Author(s):

Teruou Takayama ◽

Takazumi Yamaguchi ◽

Ayumu Saitoh ◽

Atsushi Kamitani

Keyword(s):

Magnetic Field ◽

High Temperature ◽

Applied Magnetic Field ◽

Integration Method ◽

Fem Simulation ◽

Linear Acceleration ◽

Regularization Technique ◽

Acceleration Time ◽

Pellet Injection ◽

Improper Integrals

In order to simulate the high-temperature superconducting (HTS) linear acceleration (SLA) system for the pellet injection, the integration method of the applied magnetic field generated from the acceleration coil has been proposed. To this end, the regularization technique is used in the evaluation of the improper integrals, and simultaneously, a FEM code is developed for analyzing the shielding current density in an HTS film. In addition, the SLA system has been simulated using the code. The results of the computations show that the accuracy of the applied magnetic field is considerably improved. In this sense, the regularization technique is a useful tool. Also by locating the outer coil, the acceleration time during which the pellet speed reaches 5 km/s is about 3.5 times shorter than that of the only use of the inner coil. These results mean that the outer coil is effective in the improvement of the acceleration performance for the SLA system.

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Energy eigenvalues and bound-bound transitions of hydrogen atoms in a magnetic field using cylindrical basis functions

Computer Physics Communications ◽

10.1016/0010-4655(80)90004-1 ◽

1980 ◽

Vol 20 (2) ◽

pp. 221-235 ◽

Cited By ~ 1

Author(s):

S.M. Kara

Keyword(s):

Magnetic Field ◽

Basis Functions ◽

Hydrogen Atoms ◽

Energy Eigenvalues

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The use of curl-conforming basis functions for the magnetic-field integral equation

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2006.877159 ◽

2006 ◽

Vol 54 (7) ◽

pp. 1917-1926 ◽

Cited By ~ 43

Author(s):

Ozgur Ergul ◽

Levent Gurel

Keyword(s):

Magnetic Field ◽

Integral Equation ◽

Basis Functions ◽

Magnetic Field Integral Equation ◽

The Magnetic Field ◽

Field Integral

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Hydrogen atoms in the presence of a homogeneous magnetic field: a variational approach

Canadian Journal of Physics ◽

10.1139/p78-207 ◽

1978 ◽

Vol 56 (12) ◽

pp. 1545-1548 ◽

Cited By ~ 3

Author(s):

H. S. Brandi ◽

Belita Koiller

Keyword(s):

Magnetic Field ◽

Hydrogen Atom ◽

Excited States ◽

Three Dimensional ◽

Homogeneous Magnetic Field ◽

Basis Functions ◽

Variational Parameter ◽

Hydrogen Atoms ◽

Wide Range ◽

Free Hydrogen

We propose a variational scheme to obtain the spectrum of the hydrogen atom in the presence of an external homogeneous magnetic field. We use two different sets of basis functions to diagonalize the Hamiltonian describing the system, namely, the eigenfunctions of the free hydrogen atom and of the three-dimensional harmonic oscillator, both having their radial coordinates properly scaled by a variational parameter. Because of its characteristics, the present approach is suited to describe the ground state as well as an infinite number of excited states for a wide range of magnetic field strengths.

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