CRITICAL VELOCITY OF PROJECTILE ION IN HELIUM PLASMA

ABSTRACT

In recent years, there has been growing interest in studying the properties of plasma, which is found both in astrophysical objects (neutron stars, white dwarf comets, nebulae, etc.) and in facilities for thermonuclear fusion. To maintain a nuclear fusion reaction, it must be periodically heated. This article investigates the speed of the incident particle, at which the interaction will be most effective.

АННОТАЦИЯ

В последние годы возрастает интерес к изучению свойств плазмы, которая присутствует как в астрофизических объектах (нейтронные звезды, кометы белых карликов, туманности и др.), так и в установках для термоядерного синтеза. Для поддержания реакции ядерного синтеза его необходимо периодически нагревать. В данной статье исследуется скорость налетающей частицы, при которой взаимодействие будет наиболее эффективным.

Keywords: projectile ion, stopping power, loss of energy, critical velocity, thermonuclear fusion

Ключевые слова: налетающий ион, тормозная способность, потеря энергии, критическая скорость, термоядерный синтез.

Let us consider a plasma, which consists of three kinds of particles, a hydrogen ion, a helium ion, and electrons. To determine the plasma stopping power, we use the formula (source 1), which, after integration over the directions of the wave vector, takes the form

                                                (1)

To carry out numerical calculations of plasma energy losses, we will use the following dimensionless parameters: - density parameter, which is the ratio of the average distance between plasma particles and the Bohr radius , where , ,  ,  are the concentrations of electrons and ions of the first and second grades,  in this case . - coupling parameter, determined by the ratio of the interaction energy of pairs to the kinetic energy . In the case of the interaction of electrons , an electron with ions; ions to each other .

blue line – energy loss in three-component plasma; black line - energy loss in hydrogen plasma; red line - energy loss on electronic component.

Figure 1.  proton energy Loss  in a three-component helium-hydrogen plasma at

It can be seen from this figure that, at low velocities, the loss of proton energy is mainly due to deceleration by ions. As for the drag on electrons, it is negligible at low velocities and slowly increases with increasing velocity of the test proton, slowly reaching a maximum and slowly decreasing with a further increase in the velocity. This figure also shows the dependences of the proton energy losses on electrons, in an electron-proton two-component plasma, and the losses during its deceleration in a three-component plasma. From figure 2.1. It follows that proton deceleration in a three-component plasma occurs more efficiently than in an electron-proton two-component plasma. Undoubtedly, the deceleration efficiency and the quantitative values of proton energy losses depend on the ratio of the fractions of plasma ions.

2. Critical velocity of a proton in a semi classical, helium-like plasma

The energy loss on the plasma components will be more efficient at the so-called critical velocity, at which the losses on the ionic components of the target become equal to the losses on the electrons.

If at other speeds the stopping power of the plasma was less than at the critical speed, then the critical speed determines the optimal speed of the test particle, at which its energy is transferred to the entire system.

The total energy loss can be written as the sum of losses on all plasma components: , where  - energy loss on electrons, , - losses on ions of the first and second grade, respectively, then the critical velocity is determined from the fulfillment of the condition  or  .

At the figure 2 it’s shown a three-dimensional 3D dependence of the critical velocity of a semi classical plasma on the density parameter and the coupling parameter Г=0,1;0,5;0,9

Figure 2. The critical velocity of the incident proton in units of the thermal velocity of electrons depending on Г and  at

Figure 3. Critical velocity of the incident proton in units of the thermal velocity of electrons depending on  for fixed Г=0.1;0.5;0.9, at

Figure 3 shows the dependences of the critical velocity on the density parameter for fixed values of the coupling parameter Г=0.1;0.5;0.9.

Figure 4. Critical velocity of the incident proton in units of the thermal velocity of electrons depending on Г, for fixed = 0.1; 0.5; 0.9,   at

Figure 4 shows the dependence of the critical velocity on the coupling parameter Г for fixed values of the density parameter  . From these graphs it can be seen that, at values of Г =0.5; 0.9, the critical velocity increases monotonically with increasing ,  its value slowly increases with decreasing coupling parameter Г at . With a further decrease in the coupling parameter (Г=0.1), a feature appears in the dependence of the critical velocity on , namely, at , the critical velocity rapidly increases and reaches its maximum value at  . With further growth , the value of the critical velocity rapidly drops to a value of the order of  . An increase in the critical speed with increasing  , i.e. with a decrease in the plasma density and with a decrease in the coupling parameter, it can be explained by the fact that the plasma temperature plays a significant role in the deceleration of the proton in the considered helium-hydrogen plasma, i.e. The chaotic motions of plasma particles are significant in comparison with the interaction effects, since the coupling parameter decreases with decreasing density and also decreases with increasing temperature.

As for the singularities at  and , this is apparently due to the approximation of the thermal velocity of electrons to their orbital velocity, i.e. the formation of a quasi-bound state, in which the interaction of a proton with plasma electrons becomes more efficient.

Summary

Using the example of semiclassical plasma, the effective use of plasma bombardment to maintain thermonuclear fusion is shown. In the future, these data can be used to calculate deceleration in real installations with nonideal plasma.

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