Multipole Magnetic

The various sizes and types utilize single-bar, multifield, multipole magnets singly or in factory assembled bar-bundles. They are further designed for easy disassembly and cleaning in systems with existing corrosion build-up or iron content in the water. ... 

K. Halbach 1980, (Design of permanent multipole magnets with oriented rare earth cobalt material), Nud. Instrum. Meth. 169, 1-10. 

Magnetic (Natural) Multipoles. Magnetic dipole. In 1905 Langevin, when aiming at an explanation of Curie s law, i.e. of the temperature dependence of magnetic susceptibility in paramagnetics, attributed a priori and classically a permanent magnetic moment to the microsystems. 

Other postprocessing techniques allow the computation of the density of states/molecular orbital structure, local charges on atoms or fragments of the system, dipole and multipoles, magnetic properties, and the electrostatic potential. Energy minimization can also be performed in the presence of perturbations, such as external fields or imposed electrode... 

Plasma bucket A multipole magnetic field arrangement used to spread the plasma emerging from a plasma source into a downstream processing region. 

Halbach, K. (1980). Design of Permanent Multipole Magnets with Oriented Rare Earth Cobalt Material . Nuclear Instruments and Methods 169 (1) 1-10. 

For the sake of simplicity and a more instructive description, we shah restrict ourselves to the case of unpolarized single line sources of 7 = 3/2v / = 1/2 magnetic dipole transitions (Ml) as for example in Fe, which has only a negligible electric quadrupole (E2) admixture. It will be easy to extend the relations to arbitrary nuclear spins and multipole transitions. A more rigorous treatment has been given in [76, 78] and [14] in Chap. 1. The probability P for a nuclear transihon of multipolarity Ml (L=l) from a state I, m ) to a state h, m2) is equal to... 

These detectivity functions were derived for each magnetic sublevel by setting the population of one sublevel equal to f while setting the others to zero in Eq. (12), and then solving for the angular shape /detection( d) by transforming the multipoles to the probe frame and summing over K. 

Here p is the stellar dipole magnetic moment and M is the mass accretion rate through the disk. For this formula we assume a purely dipolar field higher multipoles weaken the dependence on M because the field is effectively stiffen... 

The X-ray source may be a conventional sealed tube or rotating anode generator or bending magnet synchrotron radiation and more recently the exploitation of multipole insertion devices such as wigglers and undulators represent great gains in source intensity. 

The above-mentioned nonlinear optical effects can be described by the perturbation of the electromagnetic held intensity under the electric dipole approximation. Actually, this approximation is broken in optical near-helds. Hence, a perturbation effect of multipole such as electric quadrupole or magnetic dipole should also be considered, although such a higher-order effect is normally negligible. Indeed, electric quadrupole contributions can be comparable with electric dipole contributions... 

Relative contributions of T-odd densities to a given mode should obviously depend on the character of this mode. Electric multipole excitations (plasmons in atomic clusters, E giant resonances in atomic nuclei) are mainly provided by T-even densities (see e.g. [19]). Instead, T-odd densities and currents might be important for magnetic modes and maybe some exotic (toroidal,. ..) electric modes. 

Pk in the form of the magnetic multipole transition operator in the longwave approximation. The T-even operators Qk are then obtained from the... 

Though the ESR Hamiltonian is typically expressed in terms of effective electronic and nuclear spins, it can, of course, also be derived from the more fundamental Breit-Pauli Hamiltonian, when the magnetic fields produced by the moving nuclei are explicitly taken into account. In order to see this, we shall recall that in classical electrodynamics the magnetic dipole equation can be derived in a multipole expansion of the current density. For the lowest order term the expansion yields (59)... 

In the usual texts a multipole expansion involving spherical Bessel functions and spherical vector harmonics is also introduced [16,23,23,26]. The fields from electric and magnetic dipoles correspond to the lowest-order terms ( =1) in the expansion. If we define dipole by this expansion then our toroidal antenna is an electric dipole. In any event, the fields away from the source are the same. This is perhaps a matter of consistency in definitions. 

As stated in an earlier paragraph, the sharp emission and absorption lines observed in the trivalent rare earths correspond to/->/transitions, that is, between free ion states of the same parity. Since the electric-dipole operator has odd parity,/->/matrix elements of it are identically zero in the free ion. On the other hand, however, because the magnetic-dipole operator has even parity, its matrix elements may connect states of the same parity. It is also easily shown that electric quadrupole, and other higher multipole transitions are possible. 

For quadrupole radiation, they estimate P 2x 10-9, whereas for magnetic-dipole radiation their result was P 2 x 10-8. The experimental values lie in the range of 10 7 to 10 5. From these estimates, one concludes that the probability of significant electric-quadrupole and higher-order-multipole radiation is very small indeed. The magnetic-dipole radiation is weak but probably is of some importance, particularly in cases where the electric-dipole emission is strictly prohibited. 

The symbol p is a transition moment operator, of which there are various kinds, namely, those corresponding to changes in electric or magnetic dipoles, higher electric or magnetic multipoles, or polarizability tensors. 

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