The 15 reference contexts in paper G. Bondarenko G., V. Kristya I., D. Savichkin O., P. Żukowski, Г. Бондаренко Г., В. Кристя И., Д. Савичкин О., П. Жуковский (2018) “Моделирование распыления поверхности катода ионами и быстрыми атомами в таунсендовском разряде в смеси аргон-ртуть с зависящим от температуры составом // Simulation of cathode surface sputtering by ions and fast atoms in Townsend discharge in argon-mercury mixture with temperature-dependent composition” / spz:neicon:pimi:y:2018:i:3:p:227-233

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    7769
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    Devices and Methods of Measurements. 2018, vol. 9, no. 3, рр. 227–233. DOI: 10.21122/2220-9506-2018-9-3-227-233 228 In different types of gas discharge illuminating lamps, the mixture of argon and mercury vapor is used as the background gas
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    [1, 2]
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    . The argon atom number density in it does not depend on the temperature, whereas the mercury atom number density is decreased under its reduction. The most intensive sputtering of the cathode surface in the discharge proceeds directly after the lamp ignition, because its lifetime in the continuous operation mode exceeds considerably that in the periodic turning
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    8191
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    The most intensive sputtering of the cathode surface in the discharge proceeds directly after the lamp ignition, because its lifetime in the continuous operation mode exceeds considerably that in the periodic turning on and off mode
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    [3]
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    . The mercury ion flow density near the cathode surface at the stage of lamp turning on should increase with the ambient temperature due to rising of the mercury atom number density in the discharge volume.
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    Moreover, in the argon-mercury mixture, besides of the direct ionization of gas atoms by electrons, ionization of mercury atoms by metastable exited argon atoms takes place (the Penning reaction)
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    , which also increases the mercury ion number density. Therefore, at quite small mercury content in the mixture, its ions can make a significant contribution to the lamp electrode sputtering.
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    9186
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    The distributions of ions and fast atoms by energy in gas discharges, as well as the cathode sputtering by them, were studied in a number of works both experimentally and theoretically. However, only discharges in pure noble gases or their mixtures with temperature-independent composition were usually investigated in them
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    . For the discharge in the argon-mercury mixture with the temperaturedependent composition and under the existence of the Penning ionization of mercury atoms, though, this question was studied insufficiently.
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    9557
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    For the discharge in the argon-mercury mixture with the temperaturedependent composition and under the existence of the Penning ionization of mercury atoms, though, this question was studied insufficiently. The distributions of ions of the mixture components by energy in the low-current discharge was calculated only in
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    on the basis of the approximation of continuous slowing down of mercury ions in argon without taking into account the stochastic nature of ion-atomic collisions. Besides, the energy spectrum of fast atoms, generated under the charge exchange and elastic scattering of ions on slow argon atoms, which can contribute substantially to the cathode sputt
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    9980
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    Besides, the energy spectrum of fast atoms, generated under the charge exchange and elastic scattering of ions on slow argon atoms, which can contribute substantially to the cathode sputtering, was not found in
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    [16]
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    . In this work, a model describing the ion and fast atom motion in the low-current (Townsend) discharge in an argon-mercury mixture, based on the Monte Carlo method, is used. The energy distributions of ions and fast atoms at the cathode surface are calculated and their contributions to its sputtering are found as functions of the mixture temperature.
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    10850
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    large transverse dimensions be filled with a mixture of argon with density nAr and saturated mercury vapor with density nHg, and the voltage U sufficient for ignition of the Town-send discharge is applied to it. If the z-axis is directed along the normal to the electrode surfaces, then, since the space charge is rather small in such discharge
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    , the electric field in all points is parallel to axis z and its strength is equal to E = U/d. Electrons generated in the discharge gap under the ionization of atoms of the mixture components are accelerated by the field in the direction of the anode, and ions are accelerated to the cathode, colliding with neutral atoms.
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    11305
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    Electrons generated in the discharge gap under the ionization of atoms of the mixture components are accelerated by the field in the direction of the anode, and ions are accelerated to the cathode, colliding with neutral atoms. Simulation of their transport is fulfilled in this work on the basis of the hybrid discharge model
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    [17, 18]
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    . At the first stage, motion of primary electrons (emitted from the cathode and produced in electron-atomic collisions) is calculated using the Monte Carlo method, whereas the ion and metastable excited atom motion, in order to reduce the calculation time, is described on the basis of their macroscopic transport equations.
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    Between collisions with slow atoms the fast atoms move rectilinearly and uniformly. Since the relative content of mercury in the discharge at the stage of lamp ignition is usually small (nHg/nAr = 10−5 − 10−2)
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    [6, 18]
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    , only collisions of ions and fast atoms with argon atoms can be taken into account. The trajectory of each fast heavy particle is calculated starting from the point of its formation by solving the equation of its motion sequentially at each time step Δt.
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    14802
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    Whether the particle collides with an atom in such section, its type, as well as the direction of motion and energy ε of the particle after the collision, are determined from the corresponding formulas of the collision theory with using of random numbers
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    [12]
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    . The energy dependencies of the cross sections of argon ion charge exchange on argon atom and isotropic elastic scattering of argon ion and atom on argon atom, taken from [19], are used, as well as the cross section of isotropic elastic scattering of mercury ion on argon atom, found using of the argon and mercury atom gaskinetic radii.
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    15006
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    The energy dependencies of the cross sections of argon ion charge exchange on argon atom and isotropic elastic scattering of argon ion and atom on argon atom, taken from
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    [19]
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    , are used, as well as the cross section of isotropic elastic scattering of mercury ion on argon atom, found using of the argon and mercury atom gaskinetic radii. The trajectory of each ion is calculated until it reaches the cathode, and the trajectory of each fast atom is calculated until it reaches the cathode or its energy becomes less than 10 eV, since such atoms do
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    15777
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    As a result of calculations, the energy distribution functions of ions and fast atoms fAr+ (d,ε), fHg+ (d,ε) and fAr (d,ε) at the cathode surface are formed. Using them, the effective (averaged over particle energies) coefficients of the cathode surface sputtering by each type of particles are found, defined by expressions
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    : where Y(ε), Y(ε) and Y(ε) = Y(ε) are the yields of cathode material sputtering by argon and mercury ions and fast argon atoms with energy ε, εtAr and εtHg are the corresponding threshold sputtering energies, e is the elementary charge.
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    16865
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    It was considered to be filled with a mixture of argon and mercury, in which the number density of argon atoms was assumed to be constant and equal to nAr = 6.6·1022 m−3, which corresponds to its pressure p = 266 Pa at the room temperature, whereas the mercury atom number density was dependent on the temperature T
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    [18]
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    . The discharge voltage was equal to 200 V, so that value of the reduced electric field strength E/n in the discharge was 3·10−18 Vm2 (where n = nHg + nAr). In the process of simulation, trajectories of 106 argon and mercury ions were calculated with using of the coordinates of their generation, found taking into account the calculated distributions of
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    19074
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    In Figure 3, the temperature variation of the flow densities of atoms, sputtered from the tungsten cathode surface by different types of particles, obtained with using of expressions (1), (2) and the experimental dependencies YAr+ (ε) and YHg+ (ε)
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    [20]
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    , are shown. It can be seen that at low temperatures near –30 °C the main contribution to the cathode sputtering make fast argon atoms generated by argon ions.
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    argon ions and fast argon atoms, arising in collisions of argon ions with slow argon atoms, do not depend on the temperature, whereas the flow densities of mercury ions and fast argon atoms, produced by them, grow rapidly with temperature due to rising of the mercury content in the mixture by three orders of value at a temperature increase from –30 °C to +30 °C
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    [18]
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    . Figure 2 – The energy spectra of ions and fast atoms at the cathode surface. Designations are the same as in Figure 1 The calculated energy distributions of argon ions, mercury ions and fast argon atoms at the cathode surface are presented in Figure 2.
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