Enhanced beam of protons in plasma gas for three systems (tokamak, Z-pinch and ICF)

: The interaction of fast beam of proton impinging on a plasma target is treated theoretically, since in general the number density of the beam ions n b is much smaller than the electron density n e of the plasma target. The interaction between proton clusters (collective and individual) with plasma gas is evaluated using the dielectric dispersion function Vlasove formalism both for single and correlated protons. In present work interaction clusters for proton on three different systems (tokamak, Z-pinch and inertial confinement fusion (ICF)) were used at different thermal energy (1000, 20 and 300) (a.u) and densities of proton (10 13 , 10 18 and 3x10 22 ) cm -3 at three velocities (1,7.5 and 35) a.u. to study the effect of these parameters. Found that collective excitations give a small contribution to the energy loss of single ions, We obtain the best beams of the protons in the system (ICF) and at high rates (0,0.2,0.4,0.6) increase with increasing density. This gives a good beam of plasma proton use in different applications such as metal alloying, surface treatment, implantation, surface analysis, sputtering, determination of geometrical structures of polyatomic ions in addition give information about a variety of atomic-collision phenomena.


2-Energy loss of correlated ions in plasma
The Energy loss of ions penetrating dense p1asmas is given by equations of stopping power ≡ − / , [5] when a point particle move in medium as plasma with charge Ze and velocity , described by a dielectric function in form wave vector and frequency , [6,7] Where ° the dielectric function in medium of plasma define as,  is the density of plasma electron and T is the electron temperature, and atomic unit will be given in atomic units.
( ) = ( ) + ( ) (5) Where Plasma dispersion function ( ) start from derivation of the longitudinal electron capability for a nonrelativistic thermal electron gas. In this paper using this formula to study and to describe movement the individual and collective clusters ions in plasma. [9] Therefore Eq.(2) becomes, Rewrite Eq.(1) by taking the imaginary part of dielectric function given in Eq.(8) as: And stopping power given in Eq.(1) becomes,

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To evaluated the energy loss of single ion move in medium as plasma using the dielectric formula and integrate first on variable k, According to Bohm and Pines theory the first part is the individual mode ( < < ) and the second part in the collective mode (0 < < ). Where = = 1⁄ , To avoid logarithmic divergences in this integral for large k, a cut off ( ≡ 1⁄ ) must be introduced. The origin of this cut off is due to the limit of applicability of the dielectric approach to treat short-range interactions. [10] The stopping power has been solved numerically taking in the consideration an approximation for low and high velocity. A program Baida-for has been written in Fortran-90 for numerical solution, and a copy of program is a vailable in [to sumite on].

International Letters of Chemistry, Physics and Astronomy Vol. 61
The expression to transition between both cases: In low velocity the electron-ion collisions controlling where the short-range excitations only take place, so use the approximation = ≪ 1 to the dielectric function [12].

3-Interference effect on the energy loss
The energy loss of a pair of charges in correlated motion (dicluster) shows some significant differences with the case of uncorrelated particles discussed before. These differences come from interference effects in the simultaneous interactions of both particles with the medium [13], and internuclear distances of several atomic units, the interferences are generally more important for the collective -interaction terms. Therefore, the role of collective terms in this case must be carefully reevaluated.
The stopping power of a dicluster can be expressed as follows: [14 ] ( )is the interference function.
In terms of stopping power 0 , defined in eq. (1) and the interference function ( ) given by [15], , one can rewrite it as follows: The integration over the variable may be performed analytically. After some algebra, one can express the function ( ) as a single integral.

4-Systems a. Tokamak system:
A tokamak as shown in Fig.(2) is a device using a magnetic field to confine a plasma in the shape of a torus. Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape. Such a helical field can be generated by adding a toroidal field and a poloidal field. In a tokamak, the toroidal field is produced by electromagnets that surround the torus, and the poloidal field is the result of a toroidal electric current that flows inside the plasma. This current is induced inside the plasma with a second set of electromagnets. [16] The fusion reactions in the plasma spiraling around a tokamak reactor produce large amounts of high energy neutrons. These neutrons, being electrically neutral, are no longer held in the stream of plasma by the toroidal magnets and continue until stopped by the inside wall of the tokamak. [17] b. Z-pinch The Z-pinch is an application of the Lorentz force as shown in Fig(3), in which a current-carrying conductor in a magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, Z-Pinch physics considered in the development of a simplified Z-Pinch fusion thermodynamic model to determine the quantity of plasma, plasma temperature, rate of expansion, and energy production to calculate parameters and characterize a propulsion system. [16] (a) (b) [19] 68 ILCPA Volume 61

C. ICF system
In inertial confinement fusion (ICF) is shown in Fig.(4), a high density, low temperature plasma can be obtained during the compression phase, so minimizing the energy needed for compression. If the final temperature reached is low enough, the electrons of the plasma can be degenerate. In this case, bremsstrahlung emission is strongly suppressed and ignition temperature becomes lower than in classical plasmas. [7]. The obvious interest of using the heaviest ions in drivers for compressing ICF targets makes it desirable to also consider atomic clusters with arbitrarily large mass 1. The production of clusters and their internal properties have been given a certain attention recently from the inertial thermonuclear fusion point [20]. The comparison between three systems is shown in table (1). velocities (1, 7.5 and 3.5)

Fig.(4) Show the ICF system [20]
International Letters of Chemistry, Physics and Astronomy Vol. 61

DISCUSSION
The theory of heavy-ion stopping power is developed as a basis of the influence of the individual and collective clusters on the stopping in plasma, this stopping gives full concept on interactions the ions in plasma gas. We adopted use the dispersion function of dielectric formal in plasma and evaluated the equations numerically and analytical by using a software Compaq visual Fortran v6.6 for linking and executing programs. We study the ions stopping power for various classical and quantum plasma parameters, such as the number density, velocities, electron temperature, interference effect and effective range (b max ). And the basic factor between two cases (classical and quantum) the parameter k max . Figure (1) displays the results of analytical values for equations stopping that translator format forms. Where (F1) represent the individual excitations at high velocity in this case the Debye screening modified as the dynamical screening distance because the wake potential behind moving ion.
At low velocity (L) represent the collective excitations in this case Debye screening represent by effective range (b max ) , both cases the parameter k max and k min controls on stopping in plasma.
This study showed the individual excitations are best in the stopping from the collective excitations. Where the short-rang collisions control in high velocity that represents the quantum values. At low velocity close electron-ion collisions is the dominant and here shows the influence Coulomb potential.
Figures (5, 6 and 7) show the interference function at different velocities and internucler distance r 12 , the difference between three systems (ICF, Z-pinch and tokamak) come from interference effect, this factor its more important in low velocity so the affective appear on collective interaction than individual. So the effect of density on the stopping where the number of folds increases with increase density because the relationship between the frequency and density in stopping equation (30). As well the contribution of collective modes increases with plasma density and decreases with temperature.

CONCLUSIONS
In presented work a stopping power of proton clusters penetrating plasma has been where studied numerically and analytical for group of parameters in classical dielectric to evaluated the interference effect and study the cut off k max in quantum dielectric we arrive: 1-At low velocity the collective interactions are controlled than individual. 2-Coulomb effect appear in low velocity (classical dielectric). 3-Interference effect is very important when the distance between tow ions similar or equal to Debye length ( ). 4-Contribution of collective modes decreases with temperature and increases with density on shown through the increasing of folds.