Ion density

Assuming that the gas is electricaUy neutral over regions having dimensions larger than the Debye length, typicaUy of the order 10 m in an MHD generator, the electron and ion densities in the bulk of the gas are equal. 

Electrodes or Langmuir probes may be inserted into plasmas that are large enough (>1 cm) and relatively cool (<10 K). The net current to the probe is measured as a function of the appHed voltage. Electron temperatures, electron and ion densities, and space and wall potentials may be derived from the probe signals. Interaction of plasmas with soHd probes tends to perturb plasma conditions. 

High temperature is an important requirement for the attainment of fusion reactions in a plasma. The conditions necessary for extracting as much energy from the plasma as went into it is the Lawson criterion, which states that the product of the ion density and the confinement or reaction time must exceed 10 s/cm in the most favorable cases (173). If the coUisions are sufficiently violent, the Lawson criterion specifies how many of them must occur to break even. Conventional magnetic confinement involves fields of as much as 10 T (10 G) with large (1 m ) plasmas of low densities (<10 particles/cm ) and volumes and reaction times of about 1 s. If the magnetic flux can be compressed to values above 100 T (10 G), then a few cm ... 

To obtain the potential (jtaCr), we note that ( )2(r + mL) = ( )2(r) for any integer triple m, because this is simply a shifted sum over images. Thus ( )2(r) is a periodic function of r. Similarly, the source density p2, given by the sum of the co-ion densities over atoms... 

The original particle mesh (P3M) approach of Hockney and Eastwood [42] treats the reciprocal space problem from the standpoint of numerically solving the Poisson equation under periodic boundary conditions with the Gaussian co-ion densities as the source density p on the right-hand side of Eq. (10). Although a straightforward approach is to... 

FIG. 8 Density profiles p z) and running integrals n z) of the ion densities for cations (full lines) and anions (dashed lines) at three different surface charge densities in units of pC cm as indicated. Left NaCl solutions right CsF solutions. 

Fig. 8 (left) shows the ion density distributions of Na and CP in the vicinity of the metal electrode. Near the uncharged electrode there are no pronounced adsorption maxima. The density of Na (full line) is slightly increased in the range around z = 4.3 A between the first and second density... 

From the ion density profiles it is obvious that the surface charge is screened within less than 10 A. Thus, the thickness of the diffuse layer is of the same order of magnitude as the one derived from the Debye... 

Fig. 10 shows the radial particle densities, electrolyte solutions in nonpolar pores. Fig. 11 the corresponding data for electrolyte solutions in functionalized pores with immobile point charges on the cylinder surface. All ion density profiles in the nonpolar pores show a clear preference for the interior of the pore. The ions avoid the pore surface, a consequence of the tendency to form complete hydration shells. The ionic distribution is analogous to the one of electrolytes near planar nonpolar surfaces or near the liquid/gas interface (vide supra). 

Figure 1(a) shows the etch rates of niobium oxide pillar and Si film, and the etch selectivity of Si to niobium oxide as a function of CI2 concentration. The etch condition was fixed at coil rf power of 500 W, dc-bias to substrate to 300 V and gas pressure of 5 mTorr. As the CI2 concentration increased, the etch rate of niobium oxide pillar gradually decreased while Si etch rate increased. It indicates that the etch mechanism of niobium oxide in Cl2/Ar gas is mainly physical sputtering. As a result, the etch selectivity of Si film to niobium oxide monotonously increased. The effect of coil rf power on the etch rate and etch selectivity was examined as shown in Fig. 1(b). As the coil rf power increased, the etch rates of niobium oxide and Si increased but the etch rate of niobium oxide showed greater increase than that of Si. It is attributed to the increase of ion density with increasing coil rf power. Figure 1 (c)... 

As an electrolyte, Nafion 112 (Du Pont, Inc) membrane was pretreated using H2O2, H2SO4 and deionized water before ion beam bombardment. The prepared membranes with a size of 8 X 8 cm were mounted on a bombardment frame with a window size of 5 x 5 cm, equal to the active area of the test fuel cells, and dried up at 80 C for 2 hr. Then, the mounted membrane was brought in a vacuum chamber equipped with a hollow cathode ion beam source as described in the previous study [1]. Ion dose was measured using a Faraday cup. Ion density... 

A further result of the increase of power dissipation in the electrons has consequences for the plasma chemistry. Besides the increased ion densities, also the production of radicals will be increased, which may lead to higher deposition rates. 

It is observed that a decrease of the pressure (from p = 250 to 150 mTorr) mainly results in a decrease of the densities due to higher transport losses, and in an extension of the sheath due to a higher ion mobility. The electric field and the electron heating diminish slightly for lower pressure. The electron and Hj density, and consequently the HJ outflux, are much more influenced by the pressure decrease than the SiH+ and SiH ion densities and the SiH+ outflux. 

For one specific set of discharge parameters, in a comparison between the hybrid approach and a full PIC/MC method, the spectra and the ion densities of the hybrid model showed some deviations from those of the full particle simulation. Nevertheless, due to its computational advantages, the hybrid model is appropri-... 

The simulation of an electronegative gas discharge converges much more slowly than that of an electropositive discharge. This is mainly caused by tbe slow evolution of the negative-ion density, which depends only on attachment (to create negative ions) and ion-ion recombination (to annihilate negative ions), both processes with a very small cross section. In addition to the common procedures adopted in the literature [222, 223, 272, 273], such as the null collision method, and different superparticle sizes and time steps for different types of particle, two other procedures were used to speed up the calculation [224]. 

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