The efficiency and the demagnetization field of a general Halbach cylinder

The maximum magnetic efficiency of a general multipole Halbach cylinder of order $p$ is found as function of $p$. The efficiency is shown to decrease for increasing absolute value of $p$. The optimal ratio between the inner and outer radius, i.e. the ratio resulting in the most efficient design, is also found as function of $p$ and is shown to tend towards smaller and smaller magnet sizes. Finally, the demagnetizing field in a general $p$-Halbach cylinder is calculated, and it is shown that demagnetization is largest either at $\cos 2p\phi=1$ or $\cos 2p\phi=-1$. For the common case of a $p=1$ Halbach cylinder the maximum values of the demagnetizing field is either at $\phi = 0,\pi$ at the outer radius, where the field is always equal to the remanence, or at $\phi = \pm \pi/2$ at the inner radius, where it is the magnitude of the field in the bore. Thus to avoid demagnetization the coercivity of the magnets must be larger than these values.Comment: 5 pages, 5 figure

Topology optimized permanent magnet systems

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. First, the Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown, albeit with an increase of 3.8 pp. in field inhomogeneity - a value compared to the inhomogeneity in a 16 segmented Halbach cylinder. Following this a topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111% for the chosen dimensions. Finally, a permanent magnet with alternating high and low field regions is considered. Here a $\Lambda_\mathrm{cool}$ figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.Comment: 10 pages, 10 figure

The lifetime cost of a magnetic refrigerator

The total cost of a 25 W average load magnetic refrigerator using commercial grade Gd is calculated using a numerical model. The price of magnetocaloric material, magnet material and cost of operation are considered, and all influence the total cost. The lowest combined total cost with a device lifetime of 15 years is found to be in the range \$150-\$400 depending on the price of the magnetocaloric and magnet material. The cost of the magnet is largest, followed closely by the cost of operation, while the cost of the magnetocaloric material is almost negligible. For the lowest cost device, the optimal magnetic field is about 1.4 T, the particle size is 0.23 mm, the length of the regenerator is 40-50 mm and the utilization is about 0.2, for all device lifetimes and material and magnet prices, while the operating frequency vary as function of device lifetime. The considered performance characteristics are based on the performance of a conventional A$^{+++}$ refrigeration unit. In a rough life time cost comparison between the magnetic refrigeration device and such a unit we find similar costs, the former being slightly cheaper, assuming the cost of the magnet can be recuperated at end of life.Comment: 17 pages, 17 figure

Dynamic rotor mode in antiferromagnetic nanoparticles

We present experimental, numerical, and theoretical evidence for a new mode of antiferromagnetic dynamics in nanoparticles. Elastic neutron scattering experiments on 8 nm particles of hematite display a loss of diffraction intensity with temperature, the intensity vanishing around 150 K. However, the signal from inelastic neutron scattering remains above that temperature, indicating a magnetic system in constant motion. In addition, the precession frequency of the inelastic magnetic signal shows an increase above 100 K. Numerical Langevin simulations of spin dynamics reproduce all measured neutron data and reveal that thermally activated spin canting gives rise to a new type of coherent magnetic precession mode. This "rotor" mode can be seen as a high-temperature version of superparamagnetism and is driven by exchange interactions between the two magnetic sublattices. The frequency of the rotor mode behaves in fair agreement with a simple analytical model, based on a high temperature approximation of the generally accepted Hamiltonian of the system. The extracted model parameters, as the magnetic interaction and the axial anisotropy, are in excellent agreement with results from Mossbauer spectroscopy

Elliptical double corrugated tubes for enhanced heat transfer

The thermal performance at constant pumping power conditions was numerically investigated in ellipse and super ellipse-based double corrugated tubes. A significant increase in thermal efficiency in double corrugated tubes is accompanied with a reasonable penalty in flow reduction for the cases modelled. An ellipse and a super ellipse-based double corrugated tubes were modelled at laminar fully hydraulically developed incompressible flow. Each base geometry was analysed holding either hydraulic diameter constant or the cross-sectional area constant. The pressure drop was normalized to the length of each modelled tube in order to maintain the pumping power. Thermal analysis was conducted under constant wall temperature boundary condition. The governing equations for non-isothermal flow were solved using the finite element method, and the results of the simulations were normalized to an equivalent straight tube. Numerical results predict a thermal efficiency enhanced by 400% maintaining 4.2 times lower volumetric flow rate in double corrugated tubes at the same pressure drop. The global performance evaluation criterion increases up to 14% for the double corrugated tubes with an ellipse-base and up to 11% for the tubes with super ellipse-base

Demagnetization factor for a powder of randomly packed spherical particles

The demagnetization factors for randomly packed spherical particle powders with different porosities, sample aspect ratios and monodisperse, normal and log-normal particle size distributions have been calculated using a numerical model. For a relative permeability of 2, comparable to room temperature Gd, the calculated demagnetization factor is close to the theoretical value. The normalized standard deviation of the magnetization in the powder was 6.0%-6.7%. The demagnetization factor decreased significantly, while the standard deviation of the magnetization increased, for increasing relative permeability.Comment: 4 pages, 4 figure