Nonuniform field

The desctiption of SF electtical properties needed for practical appHcations is more complex than knowledge of BDV. Corona-onset voltages (COV) must be considered, particularly for the more usual nonuniform fields. Figure 2 illustrates this for a point-to-plane electrode configuration, where extensive prebreakdown corona occurs before sparkover (36). 

FIG. 19-51 Solenoid-type magnets, (a) Nonuniform field, (h) Uniform field by use of return frame. 

Another hmitation to be considered is the volume that the DEP force can affec t. This factor can be controlled by the design of electrodes. As an example, consider elec trodes of cylindrical geometry. A practical example of this would be a cylinder with a wire running down the middle to provide the two electrodes. The field in such a system is proportional to 1/r. The DEP force is then Fdep VlE I =< 1/r, so that any differences in particle polarization might well be masked merely by positional differences in the force. At the outer cyhnder the DEP force may even be too small to affect the particles appreciably. The most desirable electrode shape is one in which the force is independent of position within the nonuniform field. This fisomotive electrode system is shown in Fig. 22-33. 

For particles, the maximum field intensity occurs at the particle surface and decays inversely with distance. This highly nonuniform field allows greater surface charge densities before breakdown takes place, depending on the curvature of the particle surface. Empirical studies reviewed in [18] ... 

Kulikovsky, A.A. (1997) Production of chemically active species in the air by a single positive streamer in a nonuniform field, IEEE Trans. PI. Sci. 25, 439-46. 

As a second example, consider a case in which the front of the body is irradiated by a nonuniform field of scattered radiation, the trunk is shielded by a protective apron on the front of the body, and the personal monitor value and tissue doses are as given in Table 1.3. The resulting values for He and E are 0.12 mSv and 0.05 mSv, respectively. In this case, the difference is caused primarily by the manner in which the remainder contribution is calculated (see Tables 1.1 and 1.2). Note also that a personal monitor located on the front at the neck outside and above the protective apron would have indicated a value of 1 mSv (see Table 1.3), which is a large overestimate of either He or . 

Irradiation of the front of the body by nonuniform field of scattered radiation, trunk shielded by protective apron on front of body. 

The setup for a Faraday experiment is represented schematically in Fig. 11.54. If a sample of mass in and specific susceptibility y is placed in a nonuniform field H that has a gradient in the x direction (SHISx) the sample will experience a force (/) along jc due to the gradient ... 

FIGURE 5.14 The force on a magnetic dipole in a nonuniform field depends on the orientation. Thus a beam of randomly oriented dipoles should fan out in a wide range of directions. 

Fano, U. (1964). Precession equation of a spinning particle in nonuniform fields, Phys. Rev., 133, B828-B830. 

MAGNETIC FORCE IN NONUNIFORM FIELDS PHASE ANALYSIS METHOD... 

Consider the situation where the local magnetic field at position r is the sum of a uniform field and a nonuniform field Bg(r, t), that is,... 

It follows that strong localized vortex motion may be generated by even slightly nonuniform fields, and the convective component of the convective diffusion equation (Eq. 20) becomes predominant, hi fact, a convincing argument may be put forward in favor of replacing Eq. 20 by the general vector equation... 

Two important cases of negative differential conductivity (NDC) are described by an iV-shaped or an -shaped j (F) characteristic, and denoted by NNDC and SNDC, respectively. However, more complicated forms like Z-shaped, loop-shaped, or disconnected characteristics are also possible [15]. NNDC and SNDC are associated with voltage- or current-controlled instabilities, respectively. In the NNDC case the current density is a singlevalued function of the field, but the field is multivalued the F j) relation has three branches in a certain range of j. The SNDC case is complementary in the sense that F and j are interchanged. In case of NNDC, the NDC branch is often but not always - depending upon external circuit and boundary conditions - unstable against the formation of nonuniform field... 

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