Skin depths

This paper compares experimental data for aluminium and steel specimens with two methods of solving the forward problem in the thin-skin regime. The first approach is a 3D Finite Element / Boundary Integral Element method (TRIFOU) developed by EDF/RD Division (France). The second approach is specialised for the treatment of surface cracks in the thin-skin regime developed by the University of Surrey (England). In the thin-skin regime, the electromagnetic skin-depth is small compared with the depth of the crack. Such conditions are common in tests on steels and sometimes on aluminium. 

At sufficiently high frequency, the electromagnetic skin depth is several times smaller than a typical defect and induced currents flow in a thin skin at the conductor surface and the crack faces. It is profitable to develop a theoretical model dedicated to this regime. Making certain assumptions, a boundary value problem can be defined and solved relatively simply leading to rapid numerical calculation of eddy-current probe impedance changes due to a variety of surface cracks. 

Three different specimens are considered here. Penetration depths range from 0.7 mm for aluminium to 0.15 mm for the steel block. For the experimental test frequencies used the electromagnetic skin depth is much smaller than the depth of the cracks for all the measurement considered. 

NDT inspection in the thin-skin regime is well adapted to finding the length of a surface slot or crack from eddy current data. With the electromagnetic skin depth smaller than the slot depth, the interaction between the eddy current induced in the test block and tbe slot is strong at the surface of the block. 

When tbe skin depth is of the same magnitude as the slot depth, the eddy current interaction with slot can lead to a deviation of currents that are able to pass under an inner defect, deeper in the block. In that case the interaction is not total, and the signal is smoothed. 

It enables first to explain the phenomena that happen in the thin-skin regime concerning the electromagnetic skin depth and the interaetion between induced eddy eurrent and the slots. Modelling can explain impedance signals from probes in order to verify experimental measurements. Parametric studies can be performed on probes and the defect in order to optimise NDT system or qualify it for several configurations. 

Phase lag = total depth of metal/skin depth, therefore phase lag is given by dV7t[Pg.321]

A typical mild steel tube has a skin depth of approximately 2mm at 300Hz. 

Dielectric losses arise from the direct capacitive coupling of the coil and the sample. Areas of high dielectric loss are associated with the presence of axial electric fields, which exist half way along the length of the solenoid, for example. Dielectric losses can be modeled by the circuit given in Figure 2.5.3. The other major noise source arises from the coil itself, in the form of an equivalent series resistance, Rcoii. Exact calculations of noise in solenoidal coils at high frequencies and small diameters are complex, and involve considerations of the proximity and skin depth effects [23],... 

It is perhaps useful to mentally picture the microwaves to travel through the waveguide like a water stream through a pipe. In reality, however, the transport is an electric phenomenon that occurs in a very thin layer of the waveguide s inside. The thickness of this layer is characterized by the skin depth parameter, 8, which depends on the used material and the frequency. For example, for the material copper and a frequency of 10 GHz the skin depth is 8 0.66 pm. While at the surface the amplitude of the electric field of the wave is maximal, at a depth of 8 the E is reduced by a factor e 1 0.37, and at a depth of a few 8 becomes negligibly small. Transmission of microwaves through a waveguide is essentially a surface phenomenon. 

Surprisingly, transparency to the laser light was observed in a 0.5 im thick plasma slab (much thicker than the skin depth) obtained by ultra-fast ionization of a plastic foil at a density orders of magnitude higher than nc [4]. The effect was observed at laser intensities corresponding to ao 1. Figure 8.1 shows the measurements of plasma transmittivity in that experiment vs. the intensity on target of a focused Ti Sa laser pulse (30 fs, 800 nm). 

There are some notable differences apparent in Fig. 11.14 between the extinction curves for aluminum spheres and those for water droplets. For example, av is still constant for sufficiently small aluminum particles but the range of sizes is more restricted. The large peak is not an interference maximum aluminum is too absorbing for that. Rather it is the dominance of the magnetic dipole term bx in the series (4.62). Physically, this absorption arises from eddy current losses, which are strong when the particle size is near, but less than, the skin depth. At X = 0.1 jam the skin depth is less than the radius, so the interior of the particle is shielded from the field eddy current losses are confined to the vicinity of the surface and therefore the volume of absorbing material is reduced. 

Figure 3.8 illustrates the photon-induced excitation of NO chemisorbed on Pt(lll) based on the scenario of substrate mediated excitation by hot electrons (see Section 4.8.1.1). Hot electrons (and hot holes) are created in the optical skin depth... 

As frequency increases, the current is forced out of the center of the conductor toward its periphery, a phenomenon known as the skin effect . A measure of the depth of penetration of the current into the conductor is the skin depth, defined as 8 = V(p/ir/p,), where / is the frequency and x is the conductor permeability (1.26 X 10 6 H/m for nonmagnetic conductors). For copper, the skin depth is 2 p,m at 1 GHz. When the skin depth is less than the conductor thickness, the line resistance becomes greater than the dc resistance. 

The skin effect resistance of a rectangular-cross-section line also depends on its aspect ratio. For a given cross-sectional area, as the ratio tlw approaches 1, the skin depth perimeter decreases and the resistance increases, as shown in Figure 10, in which the measured resistance is plotted as a function of frequency for lines of fixed cross-sectional area with different aspect ratios (52, 53). Unfortunately, the lines with high aspect ratios that are desirable for high wiring density and low dc resistance have a higher skin effect resistance compared with thin, wide lines. 

When modelling the nonlinear response from a metal surface, two source currents are involved. The first and most difficult to describe is the source current from the surface which extends only a few angstroms into the metal. This surface current has components parallel and perpendicular to the surface. The latter is most sensitive to the details of the surface but is also the most difficult to calculate because of the discontinuity at the interface and the rapidly varying normal component of the electric field there. The bulk current is the second and is calculated to extend on the order of the optical skin depth into the metal. 

The capacity of a cable to carry nonlinear loads may be determined as follows. The skin effect factor is calculated first. The skin effect factor depends on the skin depth, which is an indicator of the penetration of the current in a conductor. Skin depth (5) is inversely proportional to the square root of the frequency ... 

Skin Depth of Various Materials at Different Frequencies... 

Under the assumption that the fluid-solid interface appears locally flat if the viscous skin depth 5 is small enough, Johnson et al. [6] obtained the high-... 

Here, e = Ju jiuj = (1 — i)6/2 is the complex viscous skin depth parameter, and 4>, aoo, and C are purely geometrical parameters, respectively the porosity, tortuosity, and C = 2/A, where A is a pore size parameter characterizing transport properties of the porous material [6],... 

Where l is the length of the capillary, a is the radius of the capillary, Jo, is a Bessel function of the first kind and k = sj / r /poS) = 8, is the viscous skin depth, which is the distance at which the amplitude of the vorti-city (transverse) wave has attenuated by a factor of the natural logarithm e . Inserting (3) into (1) and using Poisson s equation for the charges distribution we can solve for the FDSP Helmholtz-Smoluchowski equation [Reppert et al., 2001],... 

In another, more recent study [58] 14C-tretinoin was intercalated in soybean lecithin labeled with 3H-phosphatidylcholine. The 3H/14C ratio in SC remained approximately constant, however, was lower in epidermis, and decreased steeply until a skin depth of approximately 200 pm was reached. The authors concluded that co-penetration of a drug-liposome bilayer is possible in the SC, but that based on the reduced 3H/14C ratio in deeper skin strata, drug and liposomal constituents diffuse separately in these layers. 

Equation (5.4) is valid as long as the skin depth is large in comparison to the mean free path of the electrons in the metal. This holds true in the microwave range at room temperature, for cryogenic temperature the surface resistance lies above the values predicted by Equation (5.4) and exhibits a f2 3 rather than a f1 2 frequency dependence (anomalous skin effect [7]). 

As an example, for copper with a room temperature conductivity of 5.8 x 107(O m) 1 the surface resistance at 10 GHz is 26 mil, the skin depth is 0.66 pm. Therefore, the Q of a cavity resonator with a geometric factor of several hundred is in the 104 range. However, for planar resonators like the ones shown in Figure 5.8 the G values are only a few Ohms leading to Q values of only a few hundred. This is too small for many filter and oscillator applications. 

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