On the Influence of Magnetic Field on the Probability of Diffusing Particle Capture by Absorbing Traps
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
On the Influence of Magnetic Field on the Probability of Diffusing Particle Capture by Absorbing Traps V. E. Arkhincheeva,b a
Laboratory of Applied Physics, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, 700000 Vietnam bFaculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, 700000 Vietnam e-mail: [email protected] Received September 17, 2018; revised September 17, 2018; accepted October 8, 2018
Abstract—The influence of a magnetic field on the capture of diffusing particles into traps is considered. It is shown that the survival probability for particles in a medium with adsorbing traps in a magnetic field depends on the magnetic field strength; expressions for temporal asymptotic forms of the survival probabilities in media with traps in a magnetic field are derived. The magnetic field influence on the survival probability is determined by a change in the curvature of diffusion trajectories due to rotation of particles in the magnetic field under the action of the Lorentz force. DOI: 10.1134/S1063776119020018
1. INTRODUCTION The problem of random walks of particles in media with traps has been studied in various publications [1– 4]. Mathematical description of this problem was formulated in [3, 4] and in [5, 6]. This problem has a large number of applications, such as diffusion of vacancies in crystals with impurity centers and random walks with memory. The diffusion problem for a medium with randomly distributed traps is a classical model for diffusion-controlled chemical reactions [7–12]. The following main results were obtained. In the studied problem for a medium with traps, there appears a new parameter, viz., time tc = 1/Dc2 of diffusion over a distance on the order of mean distance lc = 1/c between traps (for 1D case), where D is the diffusion coefficient and c is the concentration of absorbing traps; for this reason, the asymptotic forms of the particle survival probability at short times t ≪ tc [3] and long times t ≫ tc [4] are different. The effect of electric field on the capture of particles in traps was studied in [13–15]. Let us briefly recall how the electric field is introduced in the diffusion problem. It is performed in the standard manner as anisotropy in the direction of diffusion. Accordingly, the drift velocity in electric field E is v = μE, where μ is the particle mobility. Therefore, the force exerted by the electric field has the standard form F = qE. The inclusion of electric field into the diffusion problem leads to drift with velocity v and the emergence of another new parameter, viz., “field time” tE ∝ D/v 2 . Over time intervals on the order of the field
time, the drift displacement becomes equal to the diffusion displacement: v 2tE2 ∝ DtE [16, 17]. It has been shown recently that the particle survival probability over long times t ≫ tE, which is exponential by nature, also depends on the field time [18]: 1/3 t (1) W (t, E ) ∝ W0 exp −C . t E In
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