Momentum coupling coefficient

V. Aquilanti, S. Cavalli, and D. De Fazio, Angular and hyperangular momentum coupling coefficients as hahn polynomials. J. Phys. Chem., 99 15694-15698, 1995. 

To analyze the performance of the polymer films for LPTs, the target momentum was measured by the torsion balance and used to calculate the momentum coupling coefficient, Cm. This quantity is defined as... 

In Fig. 100 the momentum coupling coefficients at various laser fluences of the carbon-doped triazene polymer and of a carbon-doped PVA are shown. The triazene polymer reveals higher coupling coefficients and, more importantly, a quite well defined threshold for a maximum Cm. In Fig. 101 the specific impulses, Isp, at various laser fluences are shown. 

Fig. 100 Momentum coupling coefficients (impulse/laser energy) at various fluences for the carbon-doped polymers. Optical density at 935 nm 0.9, film thickness 65 jim, PET substrates. REPRINTED WITH PERMISSION OF [Ref. 222], COPYRIGHT (2001) Elsevier Science...

The designed polymers also have superior properties for applications in the near-IR. The carbon-doped triazene polymer shows higher values of Cm and Isp as compared to a commercial polymer (PVA). The well-defined threshold for the momentum coupling coefficient is an important aspect for the application of polymers in laser plasma thrusters. 

The first step in reducing the MBPT expressions into a form suitable for numerical evaluation is a decomposition of the Coulomb integrals Uy w into sums of products of angular momentum coupling coefficients and radial integrals. To accomplish this decomposition, we first expand the kernel of the Coulomb integrals l/ri2 as... 

A potential application of polymer laser ablation concerns the propulsion of small satellites (1-10 kg) used in space science [86]. Laser plasma thrusters, LPTs, operating with small, powerful diode lasers emitting in the near-infrared wavelength range (930-980 nm) have been proposed. Polymers intended to serve as fuel for a thruster are required to possess a large momentum coupling coefficient, C, defined by Eq. (9-3) ... 

Let us now consider the overlap between the spherical and the Stark basis. For the latter, the momentum space eigenfimctions, which in configuration space correspond to variable separation in parabolic coordinates, are similarly related to alternative hyperspherical harmonics [2]. The connecting coefficient between spherical and 5 torA basis is formally identical to a usual vector coupling coefficient (from now on n is omitted from the notation) ... 

Spin-coupled wavefunctions have also recently been used in a critical appraisal of local density approximations in small molecules and for a comparison of the effects of bond formation on electron densities in momentum space and in position space. An example of a momentum space-orbital is shown in Fig. 12 for at 3.75 bohr in the range of R where the spin-coupling coefficients are undergoing large changes. The obvious diffraction effects are greatest in this region a detailed interpretation of momentum-space orbitals is presented in Ref. 81. 

Because of the conservation of the total angular momentum (J = j -f-1), we have to search for a proper combination of spherical harmonics. Introducing then the coupling coefficients of quantum mechanical angular momenta (the Clebsch-Gordan coefficients), we obtain a bipolar harmonic... 

Matrix element expressions depend on the coupling scheme which is adopted for nuclear spins / and rotational angular momentum /, and are developed conveniently in terms of vector-coupling coefficients [64Tha, 67Hiit]. 

The form of Eq. (5.9) models a retum-to-isotropy effect due to fluctuating interfacial momentum coupling and reduces the turbulent viscosity from that predicted by the single-phase model. The turbulence energy exchange rate coefficient Ey is given by... 

Overall the results show that the wall force field penetration depth is an additional length scale for gas flows in nano-channels, breaking dynamic similarity between rarefied and nanoscale gas flows solely based on the Knudsen and Mach numbers. Hence, one should define a new dimensionless parameter as the ratio of the force field penetration depth to the characteristic channel dimension, where wall effects cannot be neglected for large values of this dimensionless parameter. Additionally, the calculated tangential momentum accommodation coefficients for a specific gas-surface couple were found to be constant regardless of different base pressure, channel height, wall velocity, and Knudsen number. Results of different gas-surface couples reveal that TMAC is only dependent on the gas-surface couple properties and independent of the Knudsen number. 

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