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UNIVERSUM:
ТЕХНИЧЕСКИЕ НАУКИ
июнь, 2023 г.
POWER, METALLURGICAL AND CHEMICAL ENGINEERING
CRITICAL VELOCITY OF PROJECTILE ION IN HELIUM PLASMA
Bekbolat Tashev
PhD,
Abai Kazakh National Pedagogical University, Republic of Kazakhstan, Almaty E-mail: bekbolat.tashev@gmail.com
Meruert Abdrakhman
Doctoral thesis student, Abai Kazakh National Pedagogical University, Republic of Kazakhstan, Almaty E-mail: m.meruert.1995@mail.ru
КРИТИЧЕСКАЯ СКОРОСТЬ НАЛЕТАЮЩЕГО ИОНА В ГЕЛИЕВОЙ ПЛАЗМЕ
Ташев Бекболат Аханович
PhD,
Казахский Национальный педагогический университет имени Абая,
Республика Казахстан, г. Алматы
Абдрахман Меруерт Муратцызы
докторант PhD,
Казахский национальный педагогический университет имени Абая,
Республика Казахстан, г. Алматы
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 . * 2
kinds of particles, a hydrogen ion, a helium ion, and parameters: r = I 3 13 mee - density parameter,
electrons. To determine the plasma stopping power, we 5 \A7rn
use the formula (source 1), which, after integration over f *
the directions of the wave vector, takes the form a = \ — 13 which is the ratio of the average distance
a =.
4жп J
dE e1 dk kv° 1 between plasma particles and the Bohr radius — = —j f — f dcc Im-— (1) ^1
dx 70 J к s(a,к) a5 =--, where, n = nx + n2, ne = zxnx + z2n2
To carry out numerical calculations of plasma т"е
energy losses, we will use the following dimensionless n , n,n? are the concentrations of electrons and ions
Библиографическое описание: Tashev B., Abdrakhman M.M. CRITICAL VELOCITY OF PROJECTILE ION IN HELIUM PLASMA // Universum: технические науки : электрон. научн. журн. 2023. 6(111). URL: https://7universum.com/ru/tech/archive/item/15682
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UNIVERSUM:
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июнь, 2023 г.
of the first and second grades, zx = 1, z2 = 2 in this
e2zz ■
case . r =-— - coupling parameter, determined
akBT
by the ratio of the interaction energy of pairs to the kinetic
energy KBT. In the case of the interaction of electrons Z = z2 = — 1, an electron with ions z. = 1, z . = 1,2; ions to each other zx = 1, z2 = 2.
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 a = 0,1
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: S = S1 + S2 + Se,
where S - energy loss on electrons, S , S - losses on
ions of the first and second grade, respectively, then the critical velocity is determined from the fulfillment
of the condition S — Se = Se or S = 2Se.
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 r and r at a = 0,1
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Figure 3. Critical velocity of the incident proton in units of the thermal velocity of electrons depending on rs
for fixedr=G.1;G.S;G.9, at a = 0,1
Figure 3 shows the dependences of the critical velocity on the density parameter for fixed values of the coupling parameter T=0.1;0.5;0.9.
Figure 4. Critical velocity of the incident proton in units of the thermal velocity of electrons depending on r,
for fixed rs = 0.1; 0.5; 0.9, at a = 0,1
Figure 4 shows the dependence of the critical velocity on the coupling parameter T for fixed values of the density parameter r = 5,10, 15 . From these graphs it
can be seen that, at values of T =0.5; 0.9, the critical velocity increases monotonically with increasing rs, its value slowly increases with decreasing coupling parameter T at rs < 12 . With a further decrease in the coupling parameter (T=0.1), a feature appears in the dependence of the critical velocity on rs , namely, at r > 12, the critical velocity rapidly increases and reaches its maximum value at r -15. With further growth r > 15, the value of the critical velocity rapidly drops to a value of the order of v v - 0,3 . An increase in
p ,crit '
the critical speed with increasing rs , 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
References:
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 r - 0,1 and 18 > r > 12,
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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UNIVERSUM:
ТЕХНИЧЕСКИЕ НАУКИ
июнь, 2023 г.
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