Measured detonation velocities of a variety of C–H–N–O explosives agree with values predicted from the equation D = 1.01φ1 / 2(1 + 1.30ρ0), where φ = NM1 / 2Q1 / 2, with an average absolute error of ∼1%. The H2O–CO2 arbitrary assumption of detonation product compositions is used in the calculation of N, the number of moles of detonation gases per gram of explosive; M, the average molecular weight of these gases; and Q, the chemical energy of the detonation reaction.
The collective motions of a fully ionized cold plasma in a uniform external magnetic field are treated by standard small amplitude theory. Finite temperature and collision effects are neglected. Specializing the analysis to a neutral plasma of uniform unperturbed density containing electrons and ions of one species, one obtains a dielectric tensor and dispersion relation which is a special example of results previously given by Aström. A detailed discussion of the exact dispersion relation is given for the entire frequency spectrum, and completeness theorems are presented with the aid of scalar potentials representing the electromagnetic field quantities. It is found that when the Alfvén dielectric constant α = 4πn(m + M)c2/B02 becomes comparable in magnitude to the ion-to-electron mass ratio, the plasma space charge may play an important role in determining the nature of collective oscillations. In particular, if the axial wavelength of the perturbation is sufficiently large, the singularities of the effective dielectric constant become displaced from the neighborhood of the particle cyclotron frequencies to hybrid frequencies, which, in the limit of high plasma density, become equal to the geometric mean of the cyclotron frequencies and the plasma frequency, respectively. The last two sections discuss particle orbits in idealized oscillatory modes and simplified boundary value problems associated with plasma resonance.
The development of a strong hydromagnetic disturbance traveling perpendicular to an initially uniform magnetic field in a cold plasma is investigated by numerical integration of the equations of motion. The disturbance is driven by an electric field applied at a fixed plane surface which coincides with the initial boundary of the plasma. If the Mach number of the resulting disturbance is less than two, no crossing of particle orbits occurs. The disturbance then consists of a growing train of almost independent hydromagnetic pulses progressing into the undisturbed plasma at a speed somewhat in excess of the shock velocity which would be calculated from classical theory. The magnitudes of the vacuum magnetic field and the vacuum-plasma interface velocity are, however, almost identical to the predictions of classical theory. These results, as well as the observed pulse spacing, can be understood in terms of a two-region model of the disturbed portion of the plasma together with the assumption that the pulses are accelerated by mutual interaction until their spacing substantially exceeds their width.
Numerical calculations are made of a strong one-dimensional disturbance traveling perpendicular to a magnetic field in a fully ionized and collisionless plasma. When the Alfvén-Mach number Mh is greater than 2, orbit crossings of the ions occur, which rapidly leads to thermalization perpendicular to the magnetic field if the crossings are extensive (Mh > 3). The thermalization approximates the behavior of a classical hydromagnetic shock, with a shock-front thickness roughly equal to the distance the shock front travels in one-half an ion gyration time. This length is somewhat greater than the ion gyration radius. The structure of the front is found to be strongly time dependent, and undergoes large fluctuations in an ion gyration period. It is argued that when the ion-electron mass is large, the magnetic forces tend to suppress electron orbit crossings. This results in relatively cold electrons in the shocked region, with the ions obtaining nearly all of the thermal energy. A relationship between the longitudinal electrostatic potential difference across the shock front and mass flow in the plane of the front is derived on the basis of a simplified model and is found to be in qualitative agreement with the numerical results. The range of applicability of the calculations to real plasmas is discussed.
The flow following the impact of a plane detonation front, in a condensed organic explosive, on a rigid piston is obtained by a finite difference procedure. The equation of state E = Pv/(γ−1) is used for the gaseous explosion products with γ equal to 2.5, 3.0, and 3.5. Explicit formulas for the piston motion are obtained analytically for γ = 3. The effects of the detonation parameters and the explosive-mass to piston-mass ratio on the terminal velocity of the piston and on the energy transmitted to the piston are described. For γ = 2.5 to 3.5, the terminal velocity of the piston depends almost entirely on the chemical energy released in the explosion and on the explosive-mass to piston-mass ratio; i. e., for a fixed chemical energy, the total energy transmitted to the piston is insensitive to the form of the detonation wave.
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