Maxwellian source

The results for Pt(5 3 3) (Figs. 11 and 26) are consistent with the increased sticking probability observed for a Maxwellian source of H2 on Pt(9 9 7) over Pt(l 1 1) [81]. It also provides direct evidence for an additional channel to dissociative adsorption through step sites which was invoked to explain the enhanced rate of H2 + D2 exchange reaction at Pt(3 3 2) over that observed on Pt(l 1 1) surfaces investigated using a Maxwellian beam source [82]. 

X-ray spectroscopy has also been applied to the interpretation of solar spectra, which are emitted by solar flares. Now stellar objects are under investigation by X-ray satellites such as Chandra and XMM. Whereas the present X-ray telescopes are medium resolution devices, the next generation (Constellation-X, XEUS) will provide sufficient spectral resolution for detailed analysis. The spectra from distant object usually suffer from low statistics solar flares have low emission time and the observation time of stellar objects is limited. In addition, the electron distribution is not Maxwellian, in general, and some of the spectral lines may be polarized. Therefore, verified theoretical data are of great importance to interpret solar and stellar spectra, where they provide the only source of information on the plasma state. 

From these time-scales, it may be assumed in most circumstances that the free electrons have a Maxwellian distribution and that the dominant populations of impurities in the plasma are those of the ground and metastable states of the various ions. The dominant populations evolve on time-scales of the order of plasma diffusion time-scales and so should be modeled dynamically, that is in the particle number continuity equations, along with the momentum and energy equations of plasma transport theory. The excited populations of impurities on the other hand may be assumed relaxed with respect to the instantaneous dominant populations, that is they are in a quasi-equilibrium. The quasi-equilibrium is determined by local conditions of electron temperature and electron density. So, the atomic modeling may be partially de-coupled from the impurity transport problem into local calculations which provide quasi-equilibrium excited ion populations and effective emission coefficients (PEC coefficients) and then effective source coefficients (GCR coefficients) for dominant populations which must be entered into the transport equations. The solution of the transport equations establishes the spatial and temporal behaviour of the dominant populations which may then be re-associated with the local emissivity calculations, for matching to and analysis of observations. 

Miller and Kusch (3 ) determined the molecular composition of KI vapor by measurement of the velocity distribution of the molecules in the beam produced as the vapor effused through a small slit in a source. The analysis was based on an assumption that the velocity distribution within the oven is Maxwellian and that the vapor effuses through the ideal slit of kinetic theory. The velocity distributions of potassium and thallium atomic beams were found to be in excellent agreement with the theoretical distributions so the determination of the molecular composition of KI beams was tried. Using the derived equilibrium constants, we calculate the enthalpy change of the dissociation reaction by the 2nd and 3rd law methods. The results are presented in the following table. 

The function ffjl is derived analytically from the hard-sphere-collision integral, and readers interested in the exact forms are referred to Tables 6.1-6.3 of Chapter 6. One crucial issue is the description of the equilibrium distribution with QBMM. In fact, since the nonlinear collision source terms that drive the NDF and its moments to the Maxwellian equilibrium are approximated, the equilibrium is generally not perfectly described. The error involved is generally very small, and is reduced when the number of nodes is increased, but can be easily overcome by using some simple corrections. Details on these corrections for the isotropic Boltzmann equation test case are reported in Icardi et al. (2012). 

Fig. 8. Normalized residence time curves for ions of different mass accelerated to a fixed ion exit energy of 6.8 eV under conditions of a dc repeller field. Plotted is the relative ion intensity having a relative residence time greater than r/t, where t is the average residence time. Theory predicts that the shape of the curve is not mass-dependent, and experiment confirms this. The theoretical curve is computed for a Gaussian electron-beam distribution, with a full-width at half-maximum equal to the dimension of the slit through which the electron beam enters the source. Corrections resulting from the initial Maxwellian velocity distribution of the ions are ignored since they are negligible.

Plasma temperature. Generally, the concept of temperature is valid only for Maxwellian energy distributions, which cover most of plasmas but not all. In spite of this, quite often the plasma temperature is used also for plasmas of ion sources which are not in equilibrium. The ion temperatures (of z-times ionized ions) and electron temperature 7 are not necessarily equal and in the presence of magnetic field the temperatures parallel and perpendicular to the field may be different, especially for the electrons. It is usual to express the plasma temperature in electron volts (eV) using the relationship E= kT, where 1 eV corresponds to 11,600 K. Typical plasma electron and ion temperatures are several tens of electron volts. In some plasmas (e.g., ECR, see in Sect. 50.1.5.1), however, the T electron temperature can be several keVor higher. 

Spectral lamps that emit discrete spectra are examples of nonthermal radiation sources. In these gas-discharge lamps, the light-emitting atoms or molecules may be in thermal equilibrium with respect to their translational energy, which means that their velocity distribution is Maxwellian. However, the population of the different excited atomic levels may not necessarily follow a Boltzmann distribution. There is generally no thermal equilibrium between the atoms and the radiation field. The radiation may nevertheless be isotropic. 

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