Maxwellian flux

If Coo > c. the flow of molecules of A is toward the particle and if c < c, vice versa. The result given above was first obtained by Maxwell (1877) and (12.12) is often called the Maxwellian flux. Note that as c is the molar concentration of A, the units of Jc are moles per time. On the contrary, the units of J A are moles per area per time. 

Column 5 Westcott g -factor for 300 K Maxwellian flux distribution. 

Ej is the neutron energy where the Maxwellian flux and the i/e tail intersect,... 

The diffusion coefficients and ages were calcul.ated 1)V a numerical integration procedure [8]. The fast diffusion constant, />i, and the Fermi age, T, are ba.sed on a /E flux distrihution, and the slow diffusion constant, L>2, is based on a Maxwellian flux distribution. 

The addition of constraints to the equations of motion have also been used to produce thermostats at surfaces which control the flux of heat in and out of the substrate. For example, Riley et al. have proposed a velocity reset procedure which regulates atomic motion by coupling the current velocity of each atom with a velocity chosen from a Maxwellian distribution . In a similar scheme, Agrawal et al. have added a friction term to atomic velocities which depends in part on the difference between the current temperature of the surface region and that desired for the substrate . This approach was... 

Applying the local Maxwellian distribution function (2.225), explicit expressions can be obtained for the heat flux, q and the pressure tensor P. 

Appl3ung the Enskog perturbation method we intend to describe the prop>-erties of gases which are only slightly different from equilibrium. Only under these conditions will the flux vectors be about linear in the derivatives so that the formal deflnitions of the transport coefficients apply. In this limit the distribution function is still nearly Maxwellian, and the Boltzmann equation can be solved by a perturbation method. The resulting solutions are then used to obtain expressions for the heat and momentum fluxes and for the corresponding transport coefficients. 

The small size of the moderators also means that all neutrons of the same energy are created within a very short period of time, the pulse width. Short pulse widths, ca 10 ps, are essential for good energy resolution ( 3.4). Targets are often surrounded by several moderators, these run at temperatures optimised to produce peak neutron flux at different energies. Water moderators (300 K) produce peak fluxes at ca 200 cm, methane (112 K) ca 70 cm and dihydrogen (20 K) ca 40 cm. The flux distribution, J E-), of the ISIS moderators is shown in Fig. 3.7. In the Maxwellian region ( 3.1.1.2), the distribution is described by ... 

Fig. 3.7 Flux distribution from the ISIS moderators in the Maxwellian region, the points are experimental measurements, the lines are from Eq. (3.3).

Another consequence of the much smaller mass of electrons compared to ions is the formation of a so-called sheath over any material surface in contact with the plasma. When a surface is first exposed to the plasma, the surface receives a much higher electron flux compared to the positive ion flux. For a Maxwellian velocity distribution of the particles, the flux due to particle i striking the surface is given by [15]... 

Based on the principle of microscopic reversibility ("detailed balance of fluxes"), the angular and kinetic energy distribution directed towards the surface, Eq. (27), and that of the molecules leaving the surface are the same in thermal equilibrimu The angular distribution of molecules leaving the surface are thus slightly peaked in the direction of the surface normal and the velocity distribution is Maxwellian. 

Here, and are, respectively, the nondimensionalized radial and transverse components of velocity, f is the distribution function for the species being described, and f is the local Maxwellian distribution. Charging of spherical aerosol particles of radius a by gaseous ions is modeled by solving the equation with the surface of the sphere placed at r = a and the force appropriately chosen. The distribution function must then be integrated over r = a to give the ion flux. 

The evaporation coefficient o is the ratio of the evaporating particle flux to the particle flux of a Maxwellian distribution function in thermal equilibrium with the surface ... 

An obvious advantage can be seen to using 4>o since cross section tables usually give a list of (To values and since it is necessary to know the temperature corresponding to the Maxwellian velocity in order to determine other fluxes and cross sections. Often, the neutron temperature is not known, and this lack of knowledge is reflected in the uncertainty in any cross section measurement if the species in question is not known to obey the 1/v law in and near the thermal region. In any case, it is customary to measure the thermal flux with a 1/v absorber of known cross section and then to use the same flux for determining an unknown cross section. 

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