Maxwellian average

Table 2. Exponent of the temperature dependence of the Maxwellian averaged nuclear cross section (middle column) for four different nuclear reactions, evaluated at a temperature of 1.5 107 K. The last column gives the Coulomb threshold energy.

A consequence of the steepness of both functions defining the Gamow-peak is an extreme sensitivity of the Maxwellian-averaged cross section to temperature ... 

This balance equation can also be derived from kinetic theory [101], In the Maxwellian average Boltzman equation for the species s type of molecules, the collision operator does not vanish because the momentum mgCs is not an invariant quantity. Rigorous determination of the collision operator in this balance equation is hardly possible, thus an appropriate model closure for the diffusive force is required. Maxwell [65] proposed a model for the diffusive force based on the principles of kinetic theory of dilute gases. The dilute gas kinetic theory result of Maxwell [65] is generally assumed to be an acceptable form for dense gases and liquids as well, although for these mixtures the binary diffusion coefficient is a concentration dependent, experimentally determined empirical parameter. 

By assuming that an ensemble average velocity equals a Maxwellian average velocity, we might introduce (2.374) into (2.368). In this way we get ... 

The interpretations of the velocity variables in the first and second terms on the RHS represent a severe problem due to a general lack of knowledge about the physics they represent. Besides, when the F quantity in the Maxwell equation is substituted by this relation and Maxwellian averaged, the resulting covariances consist of velocity quantities which are averaged in an inconsistent manner (Maxwellian- versus time-, volume-, or ensemble averaging). For this reason other somewhat ad hoc decomposition procedures have been defined intending to achieve more consistent closures for these terms. 

Maxwellian Averaged Cross Section Astrophysical Cross Seclions, averaged over a stellar neubon maxwellian spectmm characlerized by a thennal energy ol 30 keV, expressed In barns (10 cm, millibams (mb) or microbarns (pb). 

If an analytic fit to the measured cross-section data is available, the reaction rates (erv) (Maxwellian averages) can easily be calculated for weak plasma coupling approximation as... 

For strongly coupled plasmas, an appropriate enhancement factor must be introduced. O Figure 6.3 shows, again, for the most important fusion reactions, the energy dependence of the Maxwellian averaged fusion reaction rate. 

Here it was assumed that there are no ions other than the fuel ions present (i.e., no impurities and no helium ash), and that D and T are present in the optimal 50—50% mixture. Md, Mx, and e are the deuterium, tritium, and electron densities, respectively, and (crv) is the Maxwellian-averaged fusion reaction rate at the temperature T as given inO Chap. 6 of Vol. 1. 

H. J. Amster and J.B. Callaghan, KATE-1—A Program for Calculating Wigner-Wilkinsand Maxwellian Averaged Thermal Constants on the PHILCO-2000," WARD-TM-232 (October 1960). 

Thermal constants were obtained by using an S4 cylindrical cell transport code for the 7090 ffiM computer to calculate the thermal flux distribution in a cell. The cross seettons were Maxwellian averaged. 

The values of [av] are usually computed by averaging cross section and relative velocity over the maxwellian distribution of the reacting ions. As indicated earlier, super-thermal ions can be produced by both nuclear scattering and large angle coulombian collisions, with the fast fusion products, and this leads to increased values for [av]. In our calculations we shall use at first the maxwellian averaged values of the [av], and later discuss the consequences of the other effects. 

B. Estimated Conversion Ratio 2 This method only estimates the differential or local conversion ratio for those core positions where the cadmium ratio is known. Given the cadmium ratio, the resonance to thermal flux ratio can be calculated. If, in addition, the U effective resonance integral, a, is calculated ( 100 b), and the thermal Maxwellian averaged cross sections are known (U = 2.34 b and = 485 b), the conversion ratio is given by... 

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