# Effect of Laser Radiation on the Dynamics of Active Brownian Macroparticles in an Extended Plasma-Dust Monolayer

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## Abstract

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## 1. Introduction

## 2. Statement of the Problem and Details of Modeling

_{d}—particle charge, r—the distance between two neighboring particles, λ

_{D}—Debye shielding radius, which was assumed to be equal to the mean distance between particles. l

_{p}corresponds to the parameters of the simulation of such systems and is close to actual experimental data [1]. One of the key parameters of the dusty subsystem is the effective nonideality parameter Γ*, which is determined from the following relation [18,19]:

_{a}is the concentration of buffer gas atoms, m

_{a}is the mass of buffer gas atoms, c

_{a}is the velocity of buffer gas atoms, r

_{p}is the radius of a dusty macroparticle. For the coefficient δ, a value of 1.22 was chosen, which corresponds to an intermediate value between the ideal reflecting surface at δ = 1 and the surface of the ideal heat insulator at δ = 1.442 [20]. Note that in this case, the force${L}_{i}$ is specified as a normal random variable with variance $\sqrt{2{k}_{B}T/\gamma dt}$, where dt is the simulation time step. It is assumed that the forces acting in the vertical direction counterbalance each other. The system is kept within the considered region by specifying potential walls at the boundaries; in the equation of motion term is responsible ${F}_{conf}$—the force from the border of the area (confinement). In the case under consideration, the potential trap is specified by applying mirror boundary conditions. In addition, the particles are affected by a random force ${F}_{i}^{\mathit{t}\mathit{p}}$, associated with the effect of thermophoresis under the heating effect of laser radiation on the metal surface of the particle, which is proportional to the density of the light flux [17]. The heated surface of the particle leads to the fact that neutral atoms of the buffer gas transfer a greater momentum upon collision with a particle than upon collision with a “cold” particle. In our case, it is assumed that the system is uniformly illuminated by laser radiation, so that the surface of all particles is simultaneously and uniformly heated. Thus, this force is responsible for the activity of the particles. In this work, the magnitude and direction of this force is set randomly with uniformly distributed values of the modulus and angle of rotation of the force vector, and the maximum value of the force is selected so as to provide the desired effective parameter of the nonideality of the dust subsystem, since an increase in force causes an increase in the effective temperature of the dust subsystem. The modulus of its average value is further denoted as $\overline{F}$. Thus, the equations of motion of particles in the system are as follows:

^{−9}g. The charge on the particles was taken as equal to 10,000 electron charges, which corresponds to the data of many works, see, for example, [5]. The determination of the effective nonideality parameter Γ* was carried out by calculating the radial distribution function of particles (pair correlation function) using the method described in [21]. The studies were carried out for different values of the initial effective nonideality parameter Γ*

_{0}, as well as for different values of the average force $\overline{F}$ caused by the heating of the particle surface by laser radiation. After “switching on” the force $\overline{F}$, the system was held for 50 s in order to come to a stationary state, which was characterized by a fairly stable average kinetic energy of the dust subsystem. Figure 2 shows the trajectories of particles obtained in 0.3 s for different values of the force $\overline{F}$ and the initial effective parameter of nonideality Γ*

_{0}= 300. As expected, with an increase in the force $\overline{F}$, an increase in the intensity of the kinetic motion of the particles (effective temperature) of the system is observed. In this case, if $\overline{F}$= 10 fN, we have Γ* ≈ 200, if $\overline{F}$ = 20 fN, we have Γ* ≈ 50, and if $\overline{F}$ = 40 fN, we have Γ* ≈ 15.

## 3. Obtained Data, Their Analysis and Discussion

_{0}, the effect of the external force will manifest itself less because of the high initial average kinetic energy of the particles. It can be seen that under the action of a thermophoretic force on a dusty system for the root-mean-square displacement of particles in such a system, there are regions corresponding to the ballistic, transient, and diffusion regimes. Moreover, the transient regime is more pronounced at the minimum value of the acting thermophoretic force.

**v**(0) are taken to be those velocities that the particles acquire 50 s after the “switching on” of the force $\overline{F}$.

_{i}## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Sample Availability

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**Figure 2.**Particle trajectories in 0.3 s. Initial Γ*

_{0}= 300, (

**a**) $\overline{F}$ = 10 fN; (

**b**) $\overline{F}$ = 20 fN; (

**c**) $\overline{F}$ = 40 fN.

**Figure 3.**(

**a**) Mean square displacements of particles at Γ*

_{0}= 100 и 500, and with different values of thermophoretic force $\overline{F}$. (

**b**) Mean square displacements of particles at the initial value of the effective parameter of nonideality Γ*

_{0}= 500 and various values of thermophoretic force .

**Figure 4.**Scheme for calculating the linear displacement of a particle along and perpendicular to the direction of the initial velocity.

**Figure 5.**Average linear displacements along the vector of initial velocities for particles with a metal coating in a plasma-dust monolayer at different power levels of the acting laser radiation.

**Figure 6.**Dependence of the maximum values of the average linear displacements of active particles in a plasma-dust monolayer along the vectors of the initial velocities on the steady-state effective parameter of nonideality of the system.

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**MDPI and ACS Style**

Fairushin, I.I.; Vasiliev, M.M.; Petrov, O.F.
Effect of Laser Radiation on the Dynamics of Active Brownian Macroparticles in an Extended Plasma-Dust Monolayer. *Molecules* **2021**, *26*, 6974.
https://doi.org/10.3390/molecules26226974

**AMA Style**

Fairushin II, Vasiliev MM, Petrov OF.
Effect of Laser Radiation on the Dynamics of Active Brownian Macroparticles in an Extended Plasma-Dust Monolayer. *Molecules*. 2021; 26(22):6974.
https://doi.org/10.3390/molecules26226974

**Chicago/Turabian Style**

Fairushin, Ilnaz Izailovich, Mikhail Mikhailovich Vasiliev, and Oleg Fedorovich Petrov.
2021. "Effect of Laser Radiation on the Dynamics of Active Brownian Macroparticles in an Extended Plasma-Dust Monolayer" *Molecules* 26, no. 22: 6974.
https://doi.org/10.3390/molecules26226974