• Journal of the Korean Physical Society
• /
• 제73권10호
• /
• pp.1495-1501
• /
• 2018

We have developed an extended three-dimensional free-electron laser (3D FEL) code with source-dependent expansion to calculate the intensity of the radiation field and the spot size in a free-electron laser oscillator. The effect of the wiggler field errors was evaluated for the case of a planar wiggler generated by a magnet stack with parabolic shaped pole faces by using the extended three-dimensional equations in a free-electron laser oscillator based on the proposed FEL facility which is to be operated in the far-infrared and the infrared regions. The radiation spot size due to the wiggler field errors also have been analyzed for wiggler errors of ${\Delta}B/B=0.0$, 0.03, 0.06 and 0.09% at z = 1 m and z = 2 m. The effect of the diffraction of radiation field due to the wiggler field errors of ${\Delta}B/B=0.0$ and ${\Delta}B/B=0.09%$ at 200 passes was evaluated by using the extended 3D code that we developed. The variation of the curvature of the phase front and the effect of the radiation field intensity due to the wiggler field errors were also evaluated for B = 0.5 T and B = 0.7 T with the wiggler error of ${\Delta}B/B=0.09%$ at 200 passes and the results were compared to those of without errors. The intensity of the radiation, behavior of the radiation spot size and the variation of the curvature of the phase were highly sensitive to the wiggler error of ${\Delta}B/B$ > 0.09%, but were less sensitive to the wiggler errors for ${\Delta}B/B$ < 0.09% in a free-electron laser (FEL) oscillator based on the proposed FEL facility.

• 대한전기학회논문지
• /
• 제39권9호
• /
• pp.964-975
• /
• 1990

This paper aims at the design of high voltage electrode contour under specified field condition. Defining the contour with B-Spline curve, the number of contour variables can be reduced and very smooth electrode can be obtained. For the analysis of the electric field, Surface Charge Method which has advantages in practical model has been used. As an initial contour, the rod-plane gap has been used since the difference between maximum and minimum field value is relatively large. Various field conditions including uniform field condition are given to the end of the rod electrode. Under uniform field condition, authors designed an electrode whose field-deviation was under 0.5%. Finally, the relation between the curvature and field of the electrode has been checked, which showed that B-Spline curve is appropriate for the shape function.

• 대한수학회지
• /
• 제35권4호
• /
• pp.855-867
• /
• 1998

In the present paper, we introduce the notions of quaternionically planar curves and quaternionically projective transformations to the case of almost quaternionic manifold with symmetric affine connection. Also, we obtain an invariant tensor field under the quaternionically projective transformation, and show that a quaternionic Kahlerian manifold with such a vanishing tensor field is of constant Q-sectional curvature.

• Interaction and multiscale mechanics
• /
• 제2권1호
• /
• pp.1-14
• /
• 2009

This paper proposes an interaction field concept based on the field theory of plasticity. Relative deformation between two arbitrary scales, e.g., macro and micro fields, is defined which can be implemented in the crystal plasticity-based constitutive framework. Differential geometrical quantities responsible for describing dislocations and defects in the interaction field are obtained, based on which dislocation density and incompatibility tensors are further derived. It is shown that the explicit interaction exists in the curvature or incompatibility tensor field, whereas no interaction in the torsion or dislocation density tensor field. General expressions of the interaction fields over multiple scales with more than three scale levels are derived and implemented into the present constitutive equation.

• 대한수학회보
• /
• 제55권4호
• /
• pp.1273-1283
• /
• 2018

Let ($M,{\mathcal{F}}$) be a closed, oriented Riemannian manifold of a foliation ${\mathcal{F}}$ with a nonisometric transversal conformal field. Then ($M,{\mathcal{F}}$) is transversally isometric to the sphere under some transversal concircular curvature conditions.

• 대한수학회보
• /
• 제32권1호
• /
• pp.25-34
• /
• 1995

S. Tachibana [10] has defined a confornal Killing tensor in a n-dimensional Riemannian manifold M by a skew symmetric tensor $u_[ji}$ satisfying the equation $$ \nabla_k u_{ji} + \nabla_j u_{ki} = 2\rho_i g_{kj} - \rho_j g_{ki} - \rho_k g_{ji}, $$ where $g_{ji}$ is the metric tensor of M, $\nabla$ denotes the covariant derivative with respect to $g_{ji}$ and $\rho_i$ is a associated covector field of $u_{ji}$. In here, a covector field means a 1-form.

• 대한수학회보
• /
• 제42권2호
• /
• pp.279-294
• /
• 2005

We study a real hypersurface M satisfying $L_{\xi}S=0\;and\;R_{\xi}S=SR_{\xi}$ in a complex hyperbolic space $H_n\mathbb{C}$, where S is the Ricci tensor of type (1,1) on M, $L_{\xi}\;and\;R_{\xi}$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field e respectively.

• Kyungpook Mathematical Journal
• /
• 제62권2호
• /
• pp.333-345
• /
• 2022

We study *-Ricci solitons on non-cosymplectic (κ, µ)-acs (almost cosymplectic) manifolds M. We find *-solitons that are steady, and such that both the scalar curvature and the divergence of the potential field is negative. Further, we study concurrent, concircular, torse forming and torqued vector fields on M admitting Ricci and *-Ricci solitons. Also, we provide some examples.

• 대한수학회보
• /
• 제37권4호
• /
• pp.721-727
• /
• 2000

We study some spectral properties of the $\rho-Laplacian$ on quaternionic Kaehler manifolds.

• 대한수학회논문집
• /
• 제13권2호
• /
• pp.317-336
• /
• 1998

We study real hypersurfaces of a complex space form such that the Jacobi operator with respect to the structure vector field and the structure tensor $\phi$ on the real hypersurface commute.