Energy-loss calculations

This is generally obtained by use of the integrated form of the mechanical energy equation with the frictional energy loss calculated by Eq. (65). Thus, the basic problem facing a design engineer is how to obtain numerical values for the friction factor /. 

Steady state acoustic response of the unit cell occurred for the composites considered after the passage of some five acoustic oscillations. Patterns of direct stress, and shear stress as shown in Figures 2 and 3 were obtained. As expected, the corners of the cavities concentrated the stresses. Viscoelastic energy loss calculations, not discussed here, also show that the corners of the cavities are concentrations of energy losses. 

To understand the basic difference arising from the linear and non-linear models with respect to the deduced effective charge values, we have performed energy loss calculations for partially stripped ions with two models (i) the linear DF model, and (ii) the present non-linear theory (NL). The linear calculations have been performed using equation (6) and using the DF obtained by Lindhard [13]. The electronic structure of the ions in both calculations was represented by the same Moliere-ion function. 

Fig. 10. Effective charge values, Z = Kon(v)/Sp(v)] for and Kr ions in carbon targets, obtained from energy loss calculations using the dielectric function (DF) and the non-linear (NL) models described in the text. The dotted lines separate the regions where Z > q and Z < q.

Not having enough space to summarize all of the recent work, we will give a couple of examples. A welcome new development is the integration of energy-loss calculations [79,87] with the stochastic Monte Carlo simulations of... 

Finally, the fundamental unit of concentration obtained by RBS is in atoms/cm or concentration in the sample-versus-bachscattering energy loss. To convert the profile of a backscattering peak into a depth profile it is necessary to assume a density for the material being profiled. For single-element films, such as Si, Ti, and W, an elemental density can be assumed for the film and an accurate thickness is obtained. In the case of multi-elemental films with an unknown density, a density for the film is calculated by summing the density of each element, normalized to its concentration. The accuracy of this assumption is usually within 25%, but for some cases the actual density of the film may vary by as much as 50%— 100% from the assumed density. It is useful to note that ... 

Future costs of replacement filters and energy are calculated according to the current value method. The final result for a 1 m /s filter with average pressure loss of 200 Pa may be as shown in Table 9.3, if the calculation is based on a 10-year period. 

The computation time for calculations of energy losses to the ground can be quite significant because of the three-dimensional heat conduction problem. Simplified methods are given in ISO/FDIS 13370 1998. ... 

Adamczyk (1976) is one of the few who tried to incorporate energy losses from the irreversible shock process into the calculation. He proposes to use the work done by gas volume in a process illustrated in Figure 6.12 and described below. 

The discrepancy may also be caused by the approximations in the calculation of the EEDF. This EEDF is obtained by solving the two-term Boltzmann equation, assuming full relaxation during one RF period. When the RF frequency becomes comparable to the energy loss frequencies of the electrons, it is not correct to use the time-independent Boltzmann equation to calculate the EEDF [253]. The saturation of the growth rate in the model is not caused by the fact that the RF frequency approaches the momentum transfer frequency Ume [254]. That would lead to less effective power dissipation by the electrons at higher RF frequencies and thus to a smaller deposition rate at high frequencies than at lower frequencies. 

The power dissipated at two different frequencies has been calculated for all reactions and compared with the energy loss to the walls. It is shown that at 65 MHz the fraction of power lost to the boundary decreases by a large amount compared to the situation at 13.56 MHz [224]. In contrast, the power dissipated by electron impact collision increases from nearly 47% to more than 71%, of which vibrational excitation increases by a factor of 2, dissociation increases by 45%, and ionization stays approximately the same, in agreement with the product of the ionization probability per electron, the electron density, and the ion flux, as shown before. The vibrational excitation energy thresholds (0.11 and 0.27 eV) are much smaller than the dissociation (8.3 eV) and ionization (13 eV) ones, and the vibrational excitation cross sections are large too. The reaction rate of processes with a low energy threshold therefore increases more than those with a high threshold. 

When a beam slows down in a target composed of more than one element, the energy loss can be calculated using Bragg s rule, which states that the total energy loss eAB in a compound AmB is given by... 

If the target is irradiated with particles of energy greater than there will be a defined depth below the surface where f a reaches fiar The corresponding Eb values may be calculated, and corrected for the energy loss in the outgoing direction on its way to the detector. 

---