Radius Of Solenoid Research Articles

Concurrent Solenoid Design Optimization From Thermal and Electromagnetic Standpoints

This paper extends the previous effort by Gosselin and Bejan to optimize an electromagnet according to the constructal design approach. This paper pursues two objectives in the solenoid design: a constant Fabry factor of 0.16 and a minimum hot-spot temperature in the coil. In order to minimize the hot-spot temperature, cooling discs made of high thermal conductivity materials are inserted to transport heat to disc surfaces fixed at constant temperature (heat sink). Subsequently, two cooling disc configurations are investigated in this paper: discs with heat sinks on the outer surface and on both the inner and outer surfaces. A mathematical model for each configuration is presented and numerically verified using a commercial FEA software. These models are then used to examine the hot-spot temperature variation with respect to the number of cooling discs. In addition, optimal solenoid radius and length, as well as cooling disc volume, are determined for a range of fixed solenoid volumes; thereby, the ideal solenoid volume resulting in the minimum hot-spot temperature is found. In summary, the qualitative trend of the tradeoff between heat transfer and electromagnetic performances are analyzed, and the optimal design is deduced for the maximum performance from a combined standpoint.

Analysis of the magnetohydrodynamic heat shield system for hypersonic vehicles

During hypersonic flight, the weakly-ionized plasma layer post shock can be utilized for flow control by externally applying a magnetic field. The Lorentz force, which is induced by the interaction between the ionized air and the magnetic field, decelerates the flow in the shock layer. Consequently, the thickness of the shock layer is increased and the convective heat flux can be mitigated. This so-called magnetohydrodynamic (MHD) heat shield system has been proved to be effective in heat flux mitigation by many researchers.Different from the dipole magnet conventionally used in previous researches on MHD heat shield, a normal columned solenoid-based MHD thermal protection system model is built in this paper. The present numerical analysis is mainly based on the low magneto-Reynolds MHD model, which neglects the induction magnetic field. Hall effect and the ion-slip effect are also neglected here because an insulating wall is assumed. With these hypothesis, a series of axisymmetric simulations on the flow field of Japanese Orbital Reentry Experimental Capsule (OREX) are performed to analyze the influence of different externally applied magnetic fields on the efficiency of MHD thermal protection. First, based on the dipole magnet field, the influence of magnetic induction density is analyzed. Second， differences between the efficiency of MHD thermal protection under three types of magnetic field, namely dipole magnet, solenoid magnet, and uniform magnet field are compared. Finally, the influence of the geometric parameters of solenoid magnet on the MHD thermal protection is analyzed. Results show that, saturation effect exists in the process of MHD heat flux mitigation and it confines the effectiveness of MHD heat shield system. Thermal protection capabilities under three types of magnetic field are ranked from weak to strong as dipole magnet, solenoid magnet, and uniform magnet field. Under the same magnetic induction intensity at the stagnation point, first， the increase of solenoid radius improves its effectiveness in MHD thermal protection; second, the influence of solenoid length on the efficiency of MHD thermal protection is weak, indicating that the solenoid length can be optimized with the remaining two factors, namely the exciting current density and the total weight of solenoid magnet. Finally, the closer distance between the solenoid and stagnation point has negative influence on MHD thermal protection for the stagnation and the shoulder area of the reentry capsule.

Effect of vacuum polarization of charged massive fermions in an Aharonov–Bohm field

The effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm (AB) potential in 2+1 dimensions is investigated. The causal Green's function of the Dirac equation with the AB potential is represented via the regular and irregular solutions of the two-dimensional radial Dirac equation. It is shown that the vacuum current density contains the contribution from free filled states of the negative energy continuum as well as that from a bound unfilled state, which can emerge in the above background due to the interaction of the fermion spin magnetic moment with the AB magnetic field while the induced charge density contains only the contribution from the bound state. The expressions for the vacuum charge and induced current densities are obtained (recovered for massless fermions) for the graphene in the field of infinitesimally thin solenoid perpendicular to the plane of a sample. We also find the bound state energy as a function of magnetic flux, fermion spin and the radius of solenoid as well as discuss the role of the so-called self-adjoint extension parameter and determine it in terms of the physics of the problem.

Gradient-induced longitudinal relaxation of hyperpolarized noble gases in the fringe fields of superconducting magnets used for magnetic resonance

When hyperpolarized noble gases are brought into the bore of a superconducting magnet for magnetic resonance imaging (MRI) or spectroscopy studies, the gases must pass through substantial field gradients, which can cause rapid longitudinal relaxation. In this communication, we present a means of calculating this spatially dependent relaxation rate in the fringe field of typical magnets. We then compare these predictions to experimental measurements of 3He relaxation at various positions near a medium-bore 2-T small animal MRI system. The calculated and measured relaxation rates on the central axis of the magnet agree well and show a maximum 3He relaxation rate of 3.83×10−3s−1 (T1=4.4min) at a distance of 47cm from the magnet isocenter. We also show that if this magnet were self-shielded, its minimum T1 would drop to 1.2min. In contrast, a typical self-shielded 1.5-T clinical MRI scanner will induce a minimum on-axis T1 of 12min. Additionally, we show that the cylindrically symmetric fields of these magnets enable gradient-induced relaxation to be calculated using only knowledge of the on-axis longitudinal field, which can either be measured directly or calculated from a simple field model. Thus, while most MRI magnets employ complex and proprietary current configurations, we show that their fringe fields and the resulting gradient-induced relaxation are well approximated by simple solenoid models. Finally, our modeling also demonstrates that relaxation rates can increase by nearly an order of magnitude at radial distances equivalent to the solenoid radius.

Induced current and Aharonov-Bohm effect in graphene

The effect of vacuum polarization in the field of an infinitesimally thin solenoid at distances much larger than the radius of solenoid is investigated. The induced charge density and induced current are calculated. Though the induced charge density turned out to be zero, the induced current is a finite periodical function of the magnetic flux $\ensuremath{\Phi}$. The expression for this function is found exactly in a value of the flux. The induced current is equal to zero at the integer values of $\ensuremath{\Phi}/{\ensuremath{\Phi}}_{0}$ as well as at half-integer values of this ratio, where ${\ensuremath{\Phi}}_{0}=2\ensuremath{\pi}\ensuremath{\hbar}c/e$ is the elementary magnetic flux. The latter is a consequence of the Furry theorem and periodicity of the induced current with respect to magnetic flux. As an example we consider the graphene in the field of solenoid perpendicular to the plane of a sample.

Macroscopic Aharonov–Bohm effect in superconductors

The problems of the influence of the vector-potential field produced by a finite-radius solenoid on a superconducting medium outside the solenoid and on a hollow superconducting cylinder inside of which the solenoid is located are solved in the framework of the Ginzburg–Landau theory for type-II superconductors. The dependence of the magnetic flux in the solenoid on the surface current density in its winding is found, and it is shown that there exist regions of magnetic flux values that cannot be realized at any current density in the solenoid. In the case when the solenoid radius is significantly greater than the magnetic field penetration depth, this dependence has the form of a step function with a step height equal to the magnetic flux quantum and a width that is a “quantum of surface current density.” The change of the superconducting transition temperature in a cylinder outside the solenoid is found as a function of the surface current density in the solenoid.

Scattering of scalar and Dirac particles by a magnetic tube of finite radius

We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the z-components of the linear and the total angular momenta, and of one of the possible spin polarization operators. The spin structure of the solution is completely fixed independently of the radial distribution of the magnetic field which influences only the radial modes. We solve explicitly the radial equations for the uniform magnetic field inside a solenoid of finite radius and consider in detail the scattering of scalar and Dirac particles in this field. For particles with low energy the scattering cross section coincides with the Aharonov - Bohm scattering cross section. We work out the first-order corrections to this result caused by the fact that the solenoid radius is finite. At high energies we obtain the classical result for the scattering cross section.

MONTE CARLO EVALUATION OF THE AHARONOV-BOHM EFFECT

The electron propagator in the Aharonov-Bohm effect is investigated using the Feynman path integral formalism. The calculation of the propagator is effected using a variation of the Metropolis Monte Carlo algorithm. Unlike “exact” calculations, our approach permits us to include a nonvanishing solenoid radius. We investigate the dependence of the resulting interference pattern on the magnetic field as well as the solenoid radius. Our results agree with the exact case in the limit of an infinitesimally small solenoid radius.

Fermion-solenoid interactions: Vacuum charge and scattering theory.

Properties of the Dirac Hamiltonian for fermions in two space dimensions, interacting with a solenoid, are studied in the case of a finite solenoid radius and in the zero-radius limit. The asymmetric part of the Hamiltonian's spectral density is explicitly expressed in terms of the fermion's scattering phase shifts, and the convergence of the partial-wave expansion is examined. The spectral asymmetry, or equivalently the anomaly, is related to scattering amplitudes at high energy and can be easily evaluated using the eikonal approximation. A generalization to higher dimensions is briefly outlined.

Comments on the Born approximation in Aharonov-Bohm Scattering.

The cylindrically symmetric partial-wave amplitude for scattering of an electron on an impenetrable infinite solenoid of finite radius is studied for small magnetic-flux values and an electron wavelength much larger than the solenoid radius. The results of a recent study for the Born series expression of this amplitude is discussed.

Magnetic trapping in orbit

A toroidal solenoid in orbit can represent a magnetic trap for bodies carrying dipole moment. We find the dependence of the trap dimensions on the electrical parameters and the orbit height. There is no trap if the solenoid radius exceeds a certain value. Various trap dimensions are calculated for a non-spinning space station in Earth or Sun orbit. The trap dimension is nearly independent of the solenoid orientation so that the solenoid may be fastened to the station rigidly. If the solenoid radius is in the range of some meters, the trap dimension is one order of magnitude greater for a distant Earth orbit and two orders of magnitude for an orbit around the Sun at distances of the order of one AU. The calculations are performed for a non-superconducting solenoid. The trap can be used for simplifying the docking on of maintenance vehicles or building modules, as safety mechanism for crewmembers working in outer space, and for the collection of paramagnetic or ferromagnetic dust stopped by mechanical means.