Skin effect resistive losses

Resistive losses within the current-carrying conductors, i.e. within the electrical circuit itself, caused by the leakage flux (Figure 2.6), as a result of the deep conductor skin effect. This effect increases conductor resistance and hence the losses. For more details refer to Section 28.7. 

Current flowing in a cable produces PR losses. When the load current contains harmonic content, additional losses are introduced. To compound the problem, the effective resistance of the cable increases with frequency because of the phenomenon known as skin effect. Skin effect is due to unequal flux linkage across the cross section of the conductor which causes AC currents to flow only on the outer periphery of the conductor. This has the effect of increasing the resistance of the conductor for AC currents. The higher the frequency of the current, the greater the tendency of the current to crowd at the outer periphery of the conductor and the greater the effective resistance for that frequency. 

For example, for a 500kW 500pF unit with p s = 4 x 10-7Q Hz-1 2, Pe is 0.02W at 0.1 MHz and 7kW at 500 MHz. Therefore it is evident that below 1 MHz the major contribution to heat generation is dielectric loss, whilst at higher frequencies a significant proportion is due to electrode resistance, and that, because of the skin effect, this resistance cannot be reduced by making the electrodes or leads thicker than a small fraction of a millimetre. However, the thicker the electrodes and leads are the better is the heat transfer from the capacitor. 

Qualitatively different low-frequency, shielding,and skin effect losses were found depending upon the value of the classical skin depth for the transverse resistivity of the composite, in comparison with the twist length and conductor radius. This general set of solutions agrees with losses calculated for particular field situations... 

The transmission line model is composed of discrete resistors, inductors, capacitors and conductance. A length I of transmission line can conceptually be divided into an infinite number of increments of length Al dl) such that per-unit-length resistance R, inductance L, conductance G, and capacitance C are given. Each of the parameters R, L, and G is frequency-dependent. For example, R and L will change in value due to skin effect and proximity effect. G will change in value due to frequency-dependent dielectric loss [25]-[27]. From literature [24] we can get these four parameters ... 

Magnet coil losses represent the summation of resistive losses in each volume element of the coil. Each volume element dissipates electrical energy at a rate determined by the product of the volume resistivity of the conducting material and the square of current density, i.e., as pj . We will assume that either the current varies sufficiently slowly in time or that the conductors are sufficiently well subdivided that skin effects may be ignored. (This assumption is, however, not without its economic consequences.) The total energy dissipated by the coil is then simply the integral of pj over the volume of the magnet ... 

In 1973 Thiele and Malten [74] found in skin dermatitis, skin resistance, and water loss studies no negative effect using the sodium salt of a laurylpolyglycol ether carboxylic acid with 3.8 mol EO. 

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],... 

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