Demagnetization factors for cylindrical shells and related shapes

Beleggia, Marco; Vokoun, D.; Graef, Marc De

doi:10.1016/j.jmmm.2008.11.046

Cited by 46 publications

(26 citation statements)

References 22 publications

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“…It is also physically satisfying that the result for the ring torus appears similar to the axial demagnetization factor for the ring of square cross section (see Beleggia et al 2009), the latter being the only other non-simply connected body characterized by a single aspect ratio. Note that the relationship for establishing the correspondence between the two bodies is given by a simple formula between their unique aspect ratios, α for the torus and σ for the square ring, with σ being the ratio of the inner and outer radii of the square ring: α = (1 − σ )/(1 + σ ), or conversely, σ = (1 − α)/(1 + α).…”

Section: (D) the Demagnetization Tensor Of A Torussupporting

confidence: 66%

Magnetostatics of the uniformly polarized torus

2009

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We provide an exhaustive description of the magnetostatics of the uniformly polarized torus and its derivative self-intersecting (spindle) shapes. In the process, two complementary approaches have been implemented, position-space analysis of the Laplace equation with inhomogeneous boundary conditions and a Fourier-space analysis, starting from the determination of the shape amplitude of this topologically non-trivial body. The stray field and the demagnetization tensor have been determined as rapidly converging series of toroidal functions. The single independent demagnetization-tensor eigenvalue has been determined as a function of the unique aspect ratio α of the torus. Throughout the range of values of the ratio, corresponding to a multiply connected torus proper, the axial demagnetization factor N z remains close to one half. There is no breach of smoothness of N z (α) at the topological crossover to a simply connected tight torus (α = 1). However, N z is a non-monotonic function of the aspect ratio, such that substantially different pairs of corresponding tori would still have the same demagnetization factor. This property does not occur in a simply connected body of the same continuous axial symmetry. Several self-suggesting practical applications are outlined, deriving from the acquired quantitative insight.

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Section: (D) the Demagnetization Tensor Of A Torussupporting

confidence: 66%

Magnetostatics of the uniformly polarized torus

2009

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“…Although the depolarization factors of some sample geometries has been theoretically calculated in free space by a number of researchers (see, for instance, [20], [22], and [23]), they are usually not applicable with reasonable accuracy in the CPM and they need to be determined by calibration procedures; typically, by measuring materials with known permittivity [24]- [27]. The term in (7) intends to remove wall losses in the perturbed cavity by assuming that the -factor of the walls remains the same when the specimen is introduced into the cavity.…”

Section: A Cpmmentioning

confidence: 99%

“…Equation (7) is then rewritten as (10) The QS perturbation analysis of samples contained in holders (such as the case of the cavity shown in Fig. 1) implies the analysis of three-phase media [23] and the precise knowledge of the permittivity and dimensions of the containers. However, the influence of sample holders in measurements is minimized by considering the cavity with the empty sample holder as the unperturbed situation [29].…”

Section: A Cpmmentioning

confidence: 99%

Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity

Catalá-Civera

Canós

Plaza-Gonzalez

et al. 2015

IEEE Trans. Microwave Theory Techn.

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Abstract-A microwave cavity and heating system for microwave processing and in situ dynamic measurements of the complex permittivity of dielectric materials at high temperatures ( 1000 C) has been developed. The method is based on a dual-mode cylindrical cavity where heating and testing are performed by two different swept frequency microwave sources. A cross-coupling filter isolates the signals coming from both sources. By adjusting the frequency bandwidth of the heating source and the level of coupling to the cavity, an automatic procedure allows for the establishment of a desirable level of heating rate to the dielectric sample to reach high temperatures in short cycles. Dielectric properties of materials as a function of temperature are calculated by an improved cavity perturbation method during heating. Accuracy of complex permittivity results has been evaluated and an error lower than 5% with respect to a rigorous analysis of the cavity has been achieved. The functionality of the microwave dielectric measurement system has been demonstrated by heating and measuring glass and ceramic samples up to 1000 C. The correlation of the complex permittivity with the heating rate, temperature, absorbed power, and other processing parameters can help to better understand the interactions that take place during microwave heating of materials at high temperatures compared to conventional heating.

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“…For the material and geometry parameters, we choose parameters representative of current CoCrPt based magnetic recording media: a hard cylinder radius of 1 R =3 nm and a height of 1 t =3,6,9,12,15 nm; the saturation magnetization of the soft material is twice that of hard material; and the coercivity of the hard cylinder is twice its saturation magnetization ( [ ] N represent the axial demagnetization factors for the cylinder and the shell, respectively [11]. Equations (6)(7)(8) were derived based on the integral form of the dipolar coupling factor, as discussed in [11] and [12].…”

mentioning

confidence: 99%

“…Equations (6)(7)(8) were derived based on the integral form of the dipolar coupling factor, as discussed in [11] and [12]. The demagnetization factors of cylinders and shells can be expressed as combinations of elliptic integrals [11,16].…”

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confidence: 99%

The influence of magnetostatic interactions in exchange-coupled composite particles

Vokoun¹,

Beleggia²,

Graef³

et al. 2010

J. Phys. D: Appl. Phys.

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Exchange-coupled composite (ECC) particles are the basic constituents of ECC magnetic recording media. We examine and compare two types of ECC particles: (i) core–shell structures, consisting of a hard-magnetic core and a coaxial soft-magnetic shell and (ii) conventional ECC particles, with a hard-magnetic core topped by a soft cylindrical element. The model we present describes the magnetic response of the two ECC particle types, taking into account all significant magnetic contributions to the energy landscape. Special emphasis is given to the magnetostatic (dipolar) interaction energy. We find that both the switching fields and the zero-field energy barrier depend strongly on the particle geometry. A comparison between the two types reveals that core–shell ECC particles are more effective in switching field reduction, while conventional ECC particles maintain a larger overall figure of merit.

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Demagnetization factors for cylindrical shells and related shapes

Cited by 46 publications

References 22 publications

Magnetostatics of the uniformly polarized torus

Magnetostatics of the uniformly polarized torus

Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity

The influence of magnetostatic interactions in exchange-coupled composite particles

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