Slow ions in plasma wind tunnels

Abstract

Fig. 2 Convergence modes l/$ 2 A n+/ I = X / 1 / 6 2 A n I. simultaneous satisfaction of two criteria is recommended for terminating the iteration cycles. One criteria is that the change in deflections between two iterations (6 2 A (W) ), as measured by E nt be sufficiently small. The other criteria is that the change in strain energy (6(7) between two iterations be sufficiently small as compared to the strain energy (U) to assure that the stress changes are not of any engineering significance.i.e. E n <TOLl~ (maximum acceptable deflection error) 2 times the number of displacements (6a) 5U -< TOL2 -(maximum acceptable stress error U ratio) 2 where and (6b)It should be noted that the recommended iterative scheme is even more efficient when the modification increases the stiffnesses of the members. In this case the geometric matrix series solution represents an alternating series. This requires a large number of linear (oscillating) iterations to approach the solution, while the geometric series extrapolation requires a much smaller number of trial solutions. The recommended geometric solution isThe iterative algorithm consists of selecting a good initial guess as to the change in displacement (6A^_ 7 ) due to the structural modification (5K). The first initial guess is 6A 0 = AA 0 . Equation (4a) is then employed to determine values of dA n and dA n+} . The values of 6 2 A /7 , i d 2 A n+I , E n , E n+1 , and X are also calculated from Eqs. (5a) and (5c) and substituted into Eq. (7) to determine a new initial guess. This computational scheme is repeated as many times as required. The decision as to the acceptable accuracy of the last initial guess is based upon satisfaction of Eq. (6). It should be noted that the iterative scheme does not require the inversion of the stiffness matrix (K' 1 ). Any stiffness such as the main diagonal or upper triangle, which are easily inverted (F), may be utilized provided the norm ofFdK is less than one.The mode of convergence is schematically presented in Figs. 1 and 2. Figure 2 represents the Eq. (2d) solution of a one degree of freedom (invariant eigenvector) structure. Note that the value of 5 2 A n always decrease whenever X= \dK/K\<\.Q, guaranteeing convergence. A reduction in stiffness results in positive 6 2 A n , while an increase in stiffness causes an oscillation in sign and a slower convergence. Both solutions would be accelerated with the algorithm. Values of X> 1.0 result in nondecreasing values of 6 2 A W , indicating that Eqs. (2e) or (5b) should not be utilized for major increases of stiffness or an unstable structure. The increase of stiffness can be handled by an arbitrary magnification of the original stiffness (K 2 =fJiK I ), so as to result in X 72 =X /7 //i< 1.0.The algorithm assumes that the linear damaged structure has adequate strength to withstand the resulting calculated stresses, which are a known linear transformation of the displacements. If this is not justified, then the linear structure can be reanalyzed with a "pseudo load" (equal to the load ca...

Sur les ions lents dans une chambre de simulation du plasma ionosphérique

“…Ce plasma froid peut avoir une influence plus ou moins sensible sur les mesures, suivant sa densité et le type d'expériences menées. D'une façon générale, les expérimentateurs s'accordent souvent pour négliger cette influence si sa densité ne dépasse pas quelques pour-cent de celle du plasma dérivant [12]. Cependant, cette proportion est souvent difficile à mesurer directement, et il n'existe à notre connaissance, que peu de recherches relatives à ses variations avec les paramètres expérimentaux [1,4,13]. '…”

“…2.1.1 Le terme de source. -On fait l'hypothèse très largement admise [1,12,4,13], que les ions lents sont produits majoritairement par la réaction d'échange de charge résonnant :…”