Plasmas Created in the Interaction of Antiprotons with Atomic and Ionized Hydrogen Isotopes. Suggested Fuels for Space Engines

The main objective of the present work is to investigate the properties of plasmas created by injecting a thermalized beam of antiprotons in two types of media. The first is hydrogen, deuterium, or tritium atoms localized in palladium crystals. The second medium is composed of protons, deuterons, or tritons localized in a magnetic cavity. Particularly, it is demonstrated that huge amounts of energy are released in both cases which could be used as fuels for space shuttle engines. A novel mathematical scheme is employed to calculate the energy yields in real space at different incident energies of the antiprotons.


Introduction
With the discovery of antiprotons (p) by Chamberlain et al. [1] at Fermilab in the fifties of the preceding century, the ultimate proof of possible formation of antiparticles in laboratory was rigorously confirmed. Consequently, Dirac's theory of holes [2] was acknowledged [3] as one of the fundamental theories of particle physics. The interest in the formation of cold antiprotons was demonstrated through the development of the "Low Energy Antiproton Ring (LEAR)" at CERN [4], in the early eighties of the preceding century which led in 1995 to the forma-tion of the first antiatom in laboratory, namely the ANTIHYDROGEN by the ATHEN experiment [5] [6] (For more study about Antihydrogen see [7] [8] [9]). Other interesting experiments were performed after the development of the ATRAP machine at CERN ( [10] [11] [12]) most of them seeking on the one hand, the production of large number of antihydrogen atoms, protoniums and protonium ions [13]. On the other hand, efforts were made to test the behavior of antimatter from the gravity point of view [14]. Recently, several applications of matter-antimatter interactions at low energy were explored ( [15] [16] [17]).
Experimental investigations of plasmas involving antiprotons were carried out at the AEgIS, (for a review see [18] [19]). In this case nonneutral plasmas were studied in detail [20]. Formation of Matter-antimatter plasma, particularly high energetic electron-positron plasms, was also proposed as plausible explanation for the mysterious radiation emitted from pulsers. The motive of the present work is the experimentally confirmed fact that matter-antimatter annihilation occurring by magnetically confined plasma releases much higher energy per unit mass comparative to any other source of propulsion [20] (For a comprehensive account on plasma theory and applications see [21]- [28]).
Our present work is concerned with two problems. The first is the formation of plasma through the interaction of antiprotons with highly populated hydrogen, deuterium or tritium atoms localized in a material host (e.g., palladium crystal). The second problem is to study plasmas formed by injecting a beam of antiprotons in a magnetic trap filled with protons, deuterons, or tritons.
The main objective of our investigations is to show that huge number of energies could be released from the plasmas created in both cases. Particularly, the employment of this plasma as fuel for engines of space shuttles is strongly emphasized.
The present paper falls in other three sections followed by a complete list of references mentioned in the text. The next section deals with the mathematical formalism of our problems. In Section 3 the results of our calculations are displayed and discussed. In Section 4 the main conclusions drawn from our investigations are presented. The paper concludes with the list of references mentioned in the text.

Mathematical Formalism
The present section is split into two parts, the first is devoted to the treatment of antiproton-atom plasmas and the second deals with the antiproton-nucleon plasmas.
For simplicity, it is assumed that the fluid of particles is forming an ideal gas.
Hence, the pressure of each stream is defined by n α are, respectively, pressure, the temperature, and density of the particle gas, whilst k B is Boltzmann constant. The model is explained by the fluid equations.
The continuity equation for particles is given by.
The equation of motion for particle has the form.
Poisson's equation is expressed by where m α ; u α ; and q α denote, respectively, the mass, velocity and charge of the particle α in the stream. φ is the electrostatic potential and the index i refers to H + ; D + ; or T + . The fluid system of Equations (1) ω is the plasma frequency of particle and n 0 is the equilibrium density, and is the acoustic wave speed and T e is the electron temperature respectively. Thus, the normalized system is described by the equations. and Hence, the solution of kdv Equation (8) and the first order perturbation of velocity and density of particle are given by Journal of High Energy Physics, Gravitation and Cosmology where,  , where p α , T α , and n α stand, respectively, for the pressure, temperature, and density of particle stream, whilst k B is Boltzmann constant. The model is explained by the following system of equations. The continuity equation the equation of motion with α = P − , P, D, T) and Poisson's equation where m α , u α , and q α are the mass, velocity, and charge of the particle α. φ is the electrostatic potential and the index i refers to P, D, or T.
The Plasma system of Equations (1) is the acoustic wave speed and T e is the electron temperature respectively. Thus, the normalized system is described by. and Hence, the solution of kdv Equation (8) and the first order perturbation of the velocity and density of the particle are given by

Results and Discussion
As shown in tables. The following values of particle masses have been employed in the present work.

Conclusion
The