Inhomogeneous fields

The inhomogeneous field produces a trapping effect for ions so that, if an ion moves close to a pole, the field pushes it away and back toward the central axis. 

Hiirlimann and Venkataramanan [43] have derived the kernel for the inversion-recovery CPMG experiment in an inhomogeneous field ... 

Fig. 3.2.3 Example of areas that are not exploitable due to the inhomogeneous field at the outer parts of the object.

If we had taken a spatially inhomogeneous field Eq, the connection between the conductivity and the external electric field would be much more complicated than Eq. (113), due to the polarization of the medium.18 However, for q strictly equal to zero, the system remains spatially homogeneous and Eq. (113) holds. 

Besides a poorly resolved triplet structure in the EPR spectrum of 57Fe enriched two-iron ferredoxins266 at gz, no hf interactions are observed in all these iron-sulfur clusters. The distribution of principal axes of the g tensors gives rise to an inhomogeneous, field-dependent EPR linewidth, and obscures the resolution of ligand hfs265. This distribution, whose origin is not completely established, does not, however, prevent application of the ENDOR technique. 

The inhomogeneous field equation is not an identity, but an equation of the Yang-Mills type [6]... 

In the presence of matter (electrons and protons), the inhomogeneous field equation (32) can be expanded as given in Eqs. (52)-(54) and interprets the inverse Faraday effect self-consistently as argued already. Constitutive relations such as Eq. (55) must be used as in U(l) electrodynamics. 

The inhomogeneous field equation (32) in the Cartesian basis must be written in the static limit where... 

The IFE was inferred phenomenologically by Pershan [56] in terms of the conjugate product of circularly polarized electric fields, E x E = Em X e 2). In 0(3) electrodynamics, it is described from the first principles of gauge field theory by the inhomogeneous field equation (32), which can be expanded as... 

By way of introduction to the Noether currents and charges that exist in 0(3) electrodynamics, the inhomogeneous field of Eq. (32) can be considered in the vacuum (source-free space) and split into two particular solutions ... 

The Lagrangian (850) shows that 0(3) electrodynamics is consistent with the Proca equation. The inhomogeneous field equation (32) of 0(3) electrodynamics is a form of the Proca equation where the photon mass is identified with a vacuum charge-current density. To see this, rewrite the Lagrangian (850) in vector form as follows ... 

The existence of a vacuum current such as this is indicated in 0(3) electrodynamics by its inhomogeneous field equation... 

Since a small arbitrary inhomogeneous field must affect the correlations like small fluctuations from zero-field equilibrium, we may use Eq. (71) in Section III to linearize Eq. (32). 

Are the weak homogeneous fields present in most experiments sufficient to cause the observed lifetime lengthening, and if not, what is the relative importance of homogenous and inhomogeneous field effects ... 

Fig. 5.5 the Stem-Gerlach experiment, showing a beam of atoms splitting into two on passing Ihrough an inhomogeneous field generated by specially shaped pole pieces. 

Fig. 1.4. The force lines of a magnetic field Bn. (A) A weak, homogeneous field. (B) A strong, homogeneous field. (C) An inhomogeneous field with weak and strong field regions.

Finally, the inhomogeneous field equation in the vacuum becomes... 

The vacuum 0(3) and SU(2) field equations, on the other hand, are more complicated in structure and highly nonlinear. The 0(3) inhomogeneous field equation is given in Eq. (323) and must be solved numerically under all conditions. 

Consider the antisymmetric part of the Riemann tensor in Eqs. (647) by suitable contraction. In Eq. (647c), for example, the contraction is X = p. The result reduces to the 0(3) inhomogeneous field equation of electromagnetism in the form... 

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