Adiabatic Region Research Articles

Theoretical solutions for low-Péclét-number thermal-entry-region heat transfer in laminar flow through concentric annuli

Exact temperature solutions and theoretical Nusselt curves, valid for Péclét numbers ranging from 1 to ∞, were obtained for thermal-entry-region heat transfer for laminar flow through concentric annuli, subject to a step jump in wall heat flux at z = 0. To allow for the effect of axial conduction, which is significant at low Péclét numbers, the inlet fluid temperature was taken to be uniform at z = −∞, and the first twenty eigenconstants were computed for the adiabatic region (−∞ < z ⩽ 0) and the heated region (0 ⩽ z < ∞), separately. By constructing two sets of orthonormal functions from the non-orthogonal eigenfunctions, the series expansion coefficients were then determined such that both the temperatures and longitudinal temperature gradients for the two regions match at z = 0. The temperature solutions corresponding to the limiting case of N pe = ∞ show excellent agreement with those reported by Lundberg et al. [4], who analyzed the entry-region problem by neglecting axial conduction.

Resonant Charge Exchange of the Negative Ions in Slow Collisions with Atoms

The resonant single-charge-transfer process for negative ions, ${A}^{\ensuremath{-}}+A\ensuremath{\rightarrow}A+{A}^{\ensuremath{-}}$, is considered at low energies. The exact asymptotic behavior of the energy separation $\ensuremath{\Delta}(R)$ of the symmetrical and antisymmetrical states of the quasimolecule ${A}_{2}^{\ensuremath{-}}$ is determined. In the adiabatic region, the transition probability of charge-exchange processes is determined by $\ensuremath{\Delta}(R)$. The general results are used to calculate cross sections for ${A}^{\ensuremath{-}}+A\ensuremath{\rightarrow}A+{A}^{\ensuremath{-}}$ reactions where $A$ is H, Na, K, Rb, and Cs. Comparison is made with the experimental data and with the calculations of other authors.

Exact stationary solution of a Fokker-Planck-equation for multimode laser-action

The stationary solution of a Fokker-Planck equation describing the statistics of a multimode laser below, at and above threshold in the adiabatic region is given. Both the saturated gain and the frequency shifts may be power-dependent.

Single-Electron Capture and Loss Cross Sections for 2-50-keV Hydrogen Atoms Incident upon Hydrogen and the Inert Gases

The single-electron capture and loss cross sections ${\ensuremath{\sigma}}_{0,\ensuremath{-}1}$ and ${\ensuremath{\sigma}}_{01}$ for 2-50-keV hydrogen atoms incident upon hydrogen molecules and inert-gas atoms have been measured directly by observing the growth of the fast-collision products (i.e., the fast primary $\mathrm{H}_{1}^{}{}_{}{}^{0}$ which have changed charge) with the target-gas number density. In ${\mathrm{H}}_{2}$, He, Ne, and Ar, the present values of ${\ensuremath{\sigma}}_{0,\ensuremath{-}1}$ and ${\ensuremath{\sigma}}_{01}$ generally confirm previous measurements, with the notable exception that in ${\mathrm{H}}_{2}$ the low-energy values of ${\ensuremath{\sigma}}_{01}$ are as much as 30% smaller (at 2 keV) than the values of McClure. In Kr and Xe there are no previous measurements of ${\ensuremath{\sigma}}_{0,\ensuremath{-}1}$, while the only previously reported values of ${\ensuremath{\sigma}}_{01}$ are smaller than the present values by as much as a factor of 3. For a hydrogen-gas target, the present measurements do not show any large subsidiary peaks. The use of an electrostatic field, prior to the collision cell, to quench possible excited states in the primary $\mathrm{H}_{1}^{}{}_{}{}^{0}$ atom beam is shown to have only a very small effect upon the measured cross sections. Both ${\ensuremath{\sigma}}_{01}$ and ${\ensuremath{\sigma}}_{0,\ensuremath{-}1}$ are found to increase in value with increasing atomic number for all the inert gases. The low-energy (adiabatic) region is extended down to 2 keV, where it is seen that ${\ensuremath{\sigma}}_{01}$ rises exponentially with increasing relative velocity of the colliding particles.

Mass spectrometer sampling through a small hole in the adiabatic flow region

Mass spectrometer sampling through a small hole in the adiabatic flow region

Mass spectrometer sampling through a small hole in the adiabatic flow region: M. Barber, et al., Proc. Roy. Soc., 274 (1358), 293–305

Mass spectrometer sampling through a small hole in the adiabatic flow region: M. Barber, et al., Proc. Roy. Soc., 274 (1358), 293–305

The change in the action integral for nearly adiabatic systems

The asymptotic method for calculating the change in the action integral for a one-dimensional linear system, with discontinuous derivative in a parameter, is extended to include two varying parameters. This allows for the treatment of relativistic systems in which the mass, as well as the force, varies. The limits of validity of the asymptotic expansion are discussed and it is shown by an example that the number of valid terms of the expansion can be quite limited in practical cases. A particular variation of parameters which insures that the expansion is valid to the same number of terms for all times during the variation is treated in detail. It is shown by an exact calculation, for a particular variation of this type, that the asymptotic series gives the correct change in action. The results are quite useful for the design of a nearly adiabatic transition region, such as the bunching section of a linear accelerator.

Mass spectrometric sampling through a small hole in the adiabatic flow region

This paper describes a simple theoretical treatment of sampling by a mass spectrometer through a pinhole at pressures for which the mean free path of the molecules is small compared with the diameter of the hole. An expression has been derived which relates the ion beam intensity to the partial pressures of the components of a mixture on the high-pressure side of the sampling pinhole. Experiments have been carried out to test the validity of the theoretical expression; its applications to the analysis of chemically reacting and other systems have also been discussed.

Microwave Absorption and Emission in the Atmosphere of Venus.

The radio-astronomical observations of Venus are analyzed in terms of a model atmosphere and the known microwave absorbing properties of CO2 and 1120. The model atmosphere is taken to consist of an adiabatic region with a temperature gradient of 9.0 K/km and an isothermal region with a scale height of 6 86 km and a temperature of 285 K. The surface temperature is assumed to be 580 K The centimeter and millimeter radio data require surface pressures between 10 and 30 terrestrial atmospheres on the basis of the assumed model and atmospheric compositions of 75 per cent CO2, 22-25 per cent N2, and 0-3 per cent 1120.

Inelastic Ion-Atom Collisions

Ion-atom charge exchange cross sections of incident ion velocity v in the adiabatic region are shown to be proportional to exp (−K′a|ΔE|/v) energy defect ΔE. Maximum cross sections of the negative ion-atom detachment collision and certain other inelastic ion-atom collisions are shown to be proportional to the maximum kinetic energy available for internal excitation, ½μv2, where μ is the reduced mass of the system. The semiempirical prediction of cross-section energy dependence is discussed.

Ionization by positive ions

We describe a method of measuring the ionization cross-section of atoms by positive ions, in which electrons are collected from single collisions of an ion beam passing through a gas at low pressures. Secondary electrons formed by the collisions of ions with surfaces are suppressed. Measurements are given for twenty-three cases, over energy ranges of ~ 5 to ~ 40 keV (§ 1) and ~ 100 to ~ 3 keV (§2). The cross-sections do not appear to conform to the simple adiabatic theory, but the size of cross-section in the adiabatic region appears to depend upon the reduced mass of the system.

Experiments on the Propagation of Plane Sound Waves in Tubes I: The Adiabatic Region: II: The Transition Region

I. An experimental investigation using an acoustic interferometer with a magnetostriction source is described. Results on attenuation and velocity in tubes of radius 0.013 cm and upwards, from 10 to 20 kc/s, and for a variety of tube materials and gases are given. These confirm modified Kirchhoff's formulae. II. The velocity and attenuation of plane sound waves in tubes of radius 0.02 cm have been measured in the transition region between adiabatic and isothermal flow.