Time-dependent magnetic field

The sensitivity of the NMR experiment is strongly dependent on the magnetic field used for the experiment, which precludes measurements at low field strengths with high sensitivity. A solution to this problem is to make the magnetic field time-dependent either by moving the sample from... 

Finally, we note that the nonrelativistic time-dependent CDFT, recently formulated by Vignale et al. ° does not include the coupling to external magnetic fields. Time-dependent CDFT is thus very different from static CDFT, which does include this coupling. 

To make the discussion concrete, suppose that a spin in a sample experiences a magnetic field due to a dissolved paramagnetic species. The size of the magnetic field will depend on the relative orientation of the spin and the paramagnetic species, and as both are subject to random thermal motion, this orientation will vary randomly with time (it is said to be a random function of time), and so the magnetic field will be a random function of time. Let the field experienced by this first spin be Fj(t). 

Maxwell s equation are the basis for the calculation of electromagnetic fields. An exact solution of these equations can be given only in special cases, so that numerical approximations are used. If the problem is two-dimensional, a considerable reduction of the computation expenditure can be obtained by the introduction of the magnetic vector potential A =VxB. With the assumption that all field variables are sinusoidal, the time dependence... 

Restraining a gaseous plasma from expanding and compressing is also a form of plasma modification. Two reasons for plasma confinement are maintenance of the plasma and exclusion of contaminants. Plasmas may be confined by surrounding material, eg, the technique of wall confinement (23). A second approach to confinement involves the use of magnetic fields. The third class of confinement schemes depends on the inertial tendency of ions and associated electrons to restrain a plasma explosion for a brief but usehil length of time, ie, forces active over finite times are required to produce outward particle velocities. This inertial confinement is usually, but not necessarily, preceded by inward plasma motion and compression. 

How must this theory be modified to describe the effect of the optical excitation The incident electric and magnetic X-ray fields are now pulses Ex(r, t) = Exo(t) exp[j(q r - Oxt)] and Hx(r, t) = Hxo(t) exp[/(q/r - Oxt)]. They still are plane waves with a carrier frequency Ctx, but their amphtudes Exo(t) and Hxo(t) vary with time. The same statement applies to the electron density n r, t), which also is time dependent. However, these variations are all slow with time scales on the order of 1/Ox, and one can neglect 5Exo(0/ 8Hxo(t)/8t as compared to iOxExo(t) and iTlxHxo(0- Detailed calculations then show that [17]... 

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

Kimira, T, Yoshino, M., Yamane, T, Yamato, M. andTobita, M. (2004) Uniaxial alignment of the smallest diamagnetic susceptibility axis using time-dependent magnetic fields. Langmuir, 20, 5669-5672. 

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