Maxwellian Temperature Research Articles

Quantum Theory of Energy Loss by Test Ions to Plasma

A fully quantum theoretical calculation is carried out for the average energy loss rate by test ions released in a plasma. The calculation is based on the divergence-free kinetic theory of Kihara and Honda. The rate is given in terms of several auxiliary functions which may be evaluated numerically for a given test ion once the Maxwellian temperatures and densities of each plasma species (electrons and ions) are specified. The examples considered earlier by Sigmar and Joyce are re-evaluated and the accuracies of their approximate calculations are found to be generally quite good. Several new quantitative results are presented.

Collisional and Landau damping of ion-acoustic waves in a two electron temperature plasma

Propagation of low-amplitude ion-acoustic waves at low frequencies is studied in a DP-machine with a plasma exhibiting two maxwellian electron temperatures. Damping rate and phase velocity are found in agreement with a linear kinetic theory including two electron temperatures, the total damping consisting of exponential Landau decay and a small collisional contribution.

Pulse pileup effects on plasma electron temperature measurements by soft X-ray energy analysis

The electron temperature of hot plasmas is conveniently derived from bremsstrahlung spectra obtained by pulse-height analysis using a lithium-compensated silicon detector. Time-resolved temperature measurements require high counting rates, with ultimate rate limited by pulse pileup. To evaluate this limit, spectral distortion due to pileup and consequent effects on temperature determination are investigated. Expressions for disto Maxwellian temperature and pileup fraction for both square and triangular pulse shapes. A comparison of temperatures obtained from distorted spectra with actual values indicates that measurements with less than 10% error can be made in the absence of line radiation, even from spectra containing 40% pileup.

252Cf neutron irradiation facilities

An activation facility has been designed for the accomodation and safe-handling of up to 50 mg of 252Cf neutron source. The absolute values of thermal, epithermal and fast neutron fluxes were determined by the foil activation method using In, Dy, Au, Al and Fe detectors, and compared with other experimental results and theoretical estimations. The Maxwellian temperature and average energy of 252Cf neutron spectrum have been determined.

Fission neutron spectrum of 252Cf

Average cross sections for the unmoderated spontaneous fission neutron spectrum of 252Cf have been measured for 10 different threshold reactions by activation method. On the basis of the measured data and of the excitation functions the Maxwellian temperature for 252Cf neutron spectrum has been deduced and a value of T = 1.41 ± 0.02 MeV was found between 2.5 and 15 MeV. The temperature has been determined also from the average energy which was deduced from the age of epithermal neutrons in water measured by gold foil. The high 〈σ〉 values obtained by the low threshold reactions and the age method confirm the assumption on the excess of neutrons in the low energy region of the spectrum.

Ion momentum and energy transfer rates for charge exchange collisions

The rates of momentum and energy transfer have been obtained for charge exchange collisions between ion and neutral gases having arbitrary Maxwellian temperatures T i and T n and bulk transport velocities c i and c n. The results are directly applicable to the F-region of the ionosphere where O + - O charge is the dominant mechanism affecting ion momentum and energy transfer.

Hot Ion Production in a Modified Penning Discharge

Ions with Maxwellian energy distributions and kinetic temperatures up to seven keV have been observed in a modified Penning discharge. Investigation of the plasma revealed two distinct spoke-like concentrations of charge, consisting respectively of ions and electrons, rotating with different velocities in the sheath between the plasma and the anode ring. Theoretical expressions are derived for the frequency of the ion and electron spoke rotation, for the ion kinetic temperature resulting from the ion spoke velocity, and for the ion heating efficiency. An extensive series of experimental measurements were made to check these theoretical expressions, and approximate agreement was obtained. It is shown that the ion kinetic temperature in the modified Penning discharge scales according to the relation Vi ~ Vani1/4/B1/2 where Va is the applied anode voltage, ni is the ion density in the sheath, and B is the magnetic field strength. The observed data demonstrate that the ion heating efficiency can be as high as several tens of percent.

Fission Temperatures as a Function of the Average Number of Neutrons from Fission

Terrell proposed, in 1959, a relationship between the mean energy of a fission spectrum and the average number of neutrons resulting from fission. Using the relationship between the mean energy of fission neutrons and the Maxwellian temperature of the fission spectrum, his relationship can be written as where is the average rmmber of neutrons from the fission process excluding any prefission neutrons from the n, n’f and n, 2nf modes of fission.We have used a weighted least squares method to obtain values for a and b from available experimental determinations of Tm or its equivalent. The values we obtain are a = 0.353, b = 0.510. We have also fit the relationship obtaining values for c and d of 0.997 and 0.125, respectively. The goodness-of-fit criteria are essentially the same for the two representations. Terrell’s relationship was derived from theoretical considerations, but there is no theoretical basis for the linear representation.

High-Field Energy Distribution, Mobility, and Diffusion of Heavy Holes inp-Germanium

A novel approximation scheme for hot-carrier distribution functions is introduced and employed in a calculation of the high-field mobility and diffusion coefficients of heavy holes in $p$-Ge at 77\ifmmode^\circ\else\textdegree\fi{}K. It is assumed that the heavy-hole band has an isotropic and momentum-independent effective mass, and that the holes are scattered elastically by acoustic phonons and inelastically by optical phonons. Interaction with the light-hole and split-off bands is neglected. The principal results of the calculation are as follows: Over the decade $1 \mathrm{kV}/\mathrm{cm}<E<10 \mathrm{kV}/\mathrm{cm}$ the mobility obeys the power-law relation $\ensuremath{\mu}\ensuremath{\propto}{e}^{\ensuremath{-}0.8}$. The diffusion tensor is moderately anisotropic with ${D}_{\mathrm{II}}>{D}_{\ensuremath{\perp}}$, but neither coefficient departs greatly from the zero-field diffusion constant, 250 ${\mathrm{cm}}^{2}$/sec, in the field range up to 35 kV/cm. The calculation method makes use of a parametrized model of the distribution function which characterizes the energy dependence of its angular average by two distinct Maxwellians intersecting at the optical-phonon energy, but which makes no a priori assumptions about the angular dependence of the distribution function. Solution for the Maxwellian temperatures is effected by means of a special set of "anisotropy balance equations." These equations involve only the isotropic part of the distribution function and may be used to obtain the parameter values of any parametrized energy distribution, of which the present model is but a special case. Following a procedure originally outlined by Wannier, a derivation of these equations is given first for isotropic scattering and a spherical, constant mass, as required for the $p$-Ge calculation. An alternative method is used to derive a more general set of balance equations valid for scattering probabilities of the form $P(|\mathrm{k}\ensuremath{-}{\mathrm{k}}^{\ensuremath{'}}|)$ and spherical bands of arbitrary dispersion law. An error-estimate criterion is formulated. This criterion permits evaluation of the influence on calculated transport quantities of distribution-function parametrizations with one additional parameter.

Pb208(n, γ)Cross Sections by Activation between 10 and 200 keV

The $^{208}\mathrm{Pb}(n, \ensuremath{\gamma})^{209}\mathrm{Pb}$ activation cross section has been measured in the energy range relevant to stellar nucleosynthesis. A large-area, low-background $\ensuremath{\beta}$-ray counting system was developed to obtain sufficient sensitivity. Information on the radiative widths of the known resonances below 120 keV was derived. The cross-section average found for the Maxwellian temperature distribution assumed for a stellar interior ($kT=30$ keV) is $\frac{1}{3}$ mb. This value is quite compatible with expectations based on current nucleosynthesis theory.

Charge exchange and ion diffusion for thermal nonequilibrium conditions

The ion-neutral diffusion coefficient for resonance charge exchange has been obtained directly from Boltzmann's equation for conditions of separate ion and neutral Maxwellian gas temperatures. With application to the problems of O +−O and H +−H diffusion it is found that there is little effect upon the F 2-region maximum since T i $ ̃ T n . At higher altitudes, where T > T n to a significant degree, the present diffusion coefficient becomes substantially larger than previous expressions based upon a condition of thermal equilibrium between ion and neutral gases.

GaP Surface-Barrier Diodes

Surface-barrier diodes have been formed by depositing vaporized metals onto chemically cleaned GaP. Detailed studies of diodes made with gold on p-type GaP show that current flow is by the Schottky emission of hot holes from the gold over the barrier at the metal-semiconductor interface. The barrier properties deduced from the current-voltage properties were checked by capacitance-voltage and photoresponse studies. With the junction biased in avalanche breakdown, electrons were emitted through the gold film into vacuum, and were studied as a function of junction bias, film thickness, and retarding potential. It was found that the distribution of hot electrons in GaP has a Maxwellian temperature of 0.8 V, and that the attenuation length for 4.7- to 9-V electrons in gold is 130±40 Å.

Spatial Dependence of Thermal-Neutron Spectra and the Interpretation of Thermal Utilization Measurements

Experimental determinations of the thermal utillzation factor (f) are discussed, and effects on f of neutron temperature differences between fuel and moderator are considered. It is noted that even though the Maxwellian temperature difference may be as high as 200 deg , consideration of the slowing- down component of the spectrum and of the poor thermalization of the neutrons invalldates the Maxwellian calculation. The error in f caused by neglect of the temperature difference is concluded to be negliglble. (T.F.H.)

Effective Cadmium Cutoff Energies

Effective cutoff energies for point 1/υ absorbers inside of spherical and cylindrical cadmium filters have been calculated for thermal reactor neutrons. The neutron spectrum was assumed to consist of a Maxwellian plus a 1/E component, and the parameters varied were the thickness of filter, the Maxwellian temperature, and the Maxwellian to 1/E flux ratio. Because of the sensitivity of the effective cutoff to Maxwellian flux parameters for thin filters it is recommended that filter thicknesses of about 40 mils be used. Forty-mil filters show effective cutoffs at about 0.50 to 0.55 ev for temperatures up to about 500°A (or about 0.045 ev). Effective cutoff energies for boron filters were also calculated for purposes of comparison.