4. The model of the plasma-dynamical filter for micro-droplets eliminations

Now the vacuum-plasma technologies are widely used in erosion plasma sources, such as cathodic arc and laser-produced plasma, for thin films synthesis, and coatings with control properties. However, the micro-droplets present in the formed ion plasma flow restrict the applicability of this method of film synthesis. The micro-droplets component of erosion for the majority of metals is an essential part of general losses of the cathode material in a vacuum-arc, comparable with ion component. Therefore, for prevention of effect of micro-droplets on a substrate, it is necessary to eliminate droplets. The formation and propagation of microdroplets, and also the mechanisms of decreasing of their effects on quality and rate deposition films and coatings were investigated in detail in works [22–26]. It is known from several approaches micro-droplets density reduction in ion plasma flows. Therefore, proposed methods do not provide the complete solution of the problem of micro-droplets elimination.

In paper Anders [26], the conclusion has been formulated that micro-droplets cannot be evaporated in the arc plasma flow without additional energy source. A new approach to the elimination or reduction of micro-droplets from the dense metal plasma flow based on the use of a cylindrical electrostatic PL configuration to generate an energetic radial electron beam within the low-energy ion plasma flow has been proposed and described in [27, 28]. The pumping of energy into arc plasma flow by the self-consistently formed radial beam of highenergy electrons for evaporation of micro-droplets could serve as additional energy source. The beam is formed by double layer, appeared in a cylindrical channel of the novel plasmaoptical system in crossed radial electrical and longitudinal magnetic fields. Here we detailed describe the model of device for filtering dense plasma flow from micro-droplets.

### 4.1. Model approach

where R(r,rj

z-axis in both direction.

3.3. Conclusion remarks

(left) and 340(right).

) – usual standard PIC – core, that characterizes particle size and shape and charges

distribution in it. After that, the Poisson equation was solved, and new electric field distribution was found. Since electrons are magnetized we consider their movement in radial plane only, thus can solve for electrons one-dimensional hydrodynamic equations on each layer at z separately. Solve it we find electron density, calculate electric field on each layer and correct particle trajectories. After that, the procedure was repeated again. Modeling time is large enough for establish of ion multiplication process. The formation of the sufficient number of ions is possible due to magnetic field presence, which isolates anode from the cathode. Ions practically do not feel the magnetic field action and move from anode to the axis, where create a space charge, first in the center of the system. Electrons move along the magnetic field strength line, but due to collisions with neutrals, they start moving across the magnetic field. An internal electric field is formed, which slow down the ions and pushes out them from the volume along system axis. Figure 13 shows results of modeling high-current mode (Ua = 1.2 kV, pressure 0.15 Pa, and magnetic field at the axis is 0.03 T). Figure 13a shows how the ions number to axis increases when ionization process is steady-state. One can see that number of ions increase not only to axis but also along axis from center to edge too. Figure 13b shows ion space charge distribution for different time step. One can see that ions create space charge in center of the system first, but then under electric field action they leave center and move along

282 Plasma Science and Technology - Basic Fundamentals and Modern Applications

First, the original approach to use plasma accelerators with closed electron drift and open walls for creation cost-effective low-maintenance plasma device for production converging toward axis accelerating ion beam was described. Based on the idea of continuity of current transferring in the system are found exact analytical solutions describing electric potential distribution along acceleration gap. It was shown that potential distribution is parabolic for different operation modes as in low-current mode as well as in high-current quasi-neutral plasma mode and cannot depend on electron temperature. It is found under conditions that everything electrons originated within the gap by impact ionization only, and go out at the anode due to mobility in transverse magnetic field, the condition full potential drop in the accelerating gap corresponds to equality gap length to the anode layer thickness. In case when the gap length less than anode layer thickness potential drop is not completed. For case when the gap length more than anode

Figure 13. (a) Ions number dependence on r and z (r = 0,z = 0–center of the system); (b) ion space charge for time step 70

We will consider electrostatic PL configuration through which a low-energy arc ion plasma flow passes. Figure 14 shows experimental device (left) and simplified model (right). A dense arc plasma flow with micro-droplets is propagated from the cathodic arc source and passes

Figure 14. (a) Schema of the experimental set-up, (b) simplify model (Δ–spatial layer in which the strong radial electrical field is supported).

process and electrons multiplication. The potential distribution is found by solving Poisson

density we can use expression: ne = ne0� exp.(eφ/Te), where ne0 – electron density of quasineutral plasma. For simplicity, we did not take into account the plasma heating and used finite Te and Ti at the first stage. For all particles in the calculation box, the motion equations solve and find new positions and velocities. Part of the ions reaches the cathode and knocks out γelectrons from it. We took them into account for Poisson equation solving too. We also take into account their ability to ionize when acquiring energy exceed the ionization energy. Very soon (in real time it corresponds to 1.6–2.5 μs) the potential jump near cathode is formed (see

One can see that size of the potential jump layer is very small (about 5�10�<sup>7</sup> cm, so it is <<rLe), thus electric field formed in the layer is large enough to accelerate the electrons to high-energy in the layer and force them to move toward the axis. We assumed the initial energy of emitted electron is 5 eV. Initial electrons move along magnetic field line as it shown in Figure 16a. However, due to appearance strong electric field in the layer, the average electron energy increases. It begins to exceed 10 eV at field strength is about 100 V/cm, and when electric field strength reaches about 500 V/cm it exceeds 100 eV. At such energies, the secondary electrons acquire the ability to ionize neutrals with the new secondary electrons appearance. As results, an avalanche-like ionization begins. Electrons move toward the axis and can accumulate there (see Figure 16b)). Note that application of the plasma lens to the transport of low-energy

<sup>¼</sup> 0. For electron

Modeling of Novel Plasma-Optical Systems http://dx.doi.org/10.5772/intechopen.77512 285

equation (see Eq.(7)). Ion density we find from the continuity equation: div ji

Figure 15. (a) Initial copper plasma flows, (b) potential distribution for time step 50.

Figure 16. Trajectories of the emission electrons depends on time (a) Nt = 40, (b) Nt = 80.

Figure 15b).

through diaphragm into the plasma-optical system. A part of the micro-droplets settles on the diaphragm, which is at the beginning of plasma-optical system, and remaining ones along with the flow propagate through the system.

The system consists of a cylinder (central electrode) of length L and diameter D on which the negative voltage U 1–3 kV is applied, and a pair of external ring grounded electrodes arranged symmetrically to the central electrode. The system is in the magnetic field of a short coil or permanent magnets. When arc plasma flow reaches the zone of the magnetic field action, it penetrates into the flow. The magnetic field must satisfy to the condition: rLe << D << rLi, where rLe, rLi – are the electron and ion Larmour radiuses. In such a magnetic field the electrons are magnetized, and ions are not magnetized. A dense plasma flow propagating inside the cylinder creates a thin wall layer Δ with a large radial electric field Er. The magnetic field lines are equipotential inside flow, and electrical field, which created is similar to magnetic field lines. Because of the electrons of the flow are magnetized, they in the magnetic field are displaced to axis and prevent radial expansion of the flow. The density of flow increases with increasing of the magnetic field near axis, so control by magnetic field we can control by flow, keeping it from expansion.

High-energy electrons appear near the inner cylindrical surface by secondary ion-electron emission at this surface bombardment by peripheral flow ions. In result, the fast electrons beam created with current density jeb = γjis in near-wall layer (γ – secondary ion-electron emission coefficient).This electron beam injected from near-wall layer to plasma flow axis can serve as additional effective energy source for micro-droplet elimination.

#### 4.2. Modeling and results

The modeling of high-energy radial electron beam formation was the first task of our consideration. For simulation, we used PIC-method with Boris scheme, analogically to previous section. The copper plasma flows transport through the plasma lens with applied potential 3 kV on the central electrode and magnetic field about 300–400 E was considered. Figure 15a shows initial plasma flow. The peripheral ions of flow collide with the inner wall of the central electrode and emitted electrons. The Monte-Carlo method was used for modeling emission

Figure 15. (a) Initial copper plasma flows, (b) potential distribution for time step 50.

through diaphragm into the plasma-optical system. A part of the micro-droplets settles on the diaphragm, which is at the beginning of plasma-optical system, and remaining ones along

Figure 14. (a) Schema of the experimental set-up, (b) simplify model (Δ–spatial layer in which the strong radial electrical

The system consists of a cylinder (central electrode) of length L and diameter D on which the negative voltage U 1–3 kV is applied, and a pair of external ring grounded electrodes arranged symmetrically to the central electrode. The system is in the magnetic field of a short coil or permanent magnets. When arc plasma flow reaches the zone of the magnetic field action, it penetrates into the flow. The magnetic field must satisfy to the condition: rLe << D << rLi, where rLe, rLi – are the electron and ion Larmour radiuses. In such a magnetic field the electrons are magnetized, and ions are not magnetized. A dense plasma flow propagating inside the cylinder creates a thin wall layer Δ with a large radial electric field Er. The magnetic field lines are equipotential inside flow, and electrical field, which created is similar to magnetic field lines. Because of the electrons of the flow are magnetized, they in the magnetic field are displaced to axis and prevent radial expansion of the flow. The density of flow increases with increasing of the magnetic field near axis, so control by magnetic field we can control by

High-energy electrons appear near the inner cylindrical surface by secondary ion-electron emission at this surface bombardment by peripheral flow ions. In result, the fast electrons beam created with current density jeb = γjis in near-wall layer (γ – secondary ion-electron emission coefficient).This electron beam injected from near-wall layer to plasma flow axis can

The modeling of high-energy radial electron beam formation was the first task of our consideration. For simulation, we used PIC-method with Boris scheme, analogically to previous section. The copper plasma flows transport through the plasma lens with applied potential 3 kV on the central electrode and magnetic field about 300–400 E was considered. Figure 15a shows initial plasma flow. The peripheral ions of flow collide with the inner wall of the central electrode and emitted electrons. The Monte-Carlo method was used for modeling emission

serve as additional effective energy source for micro-droplet elimination.

with the flow propagate through the system.

284 Plasma Science and Technology - Basic Fundamentals and Modern Applications

field is supported).

flow, keeping it from expansion.

4.2. Modeling and results

process and electrons multiplication. The potential distribution is found by solving Poisson equation (see Eq.(7)). Ion density we find from the continuity equation: div ji <sup>¼</sup> 0. For electron density we can use expression: ne = ne0� exp.(eφ/Te), where ne0 – electron density of quasineutral plasma. For simplicity, we did not take into account the plasma heating and used finite Te and Ti at the first stage. For all particles in the calculation box, the motion equations solve and find new positions and velocities. Part of the ions reaches the cathode and knocks out γelectrons from it. We took them into account for Poisson equation solving too. We also take into account their ability to ionize when acquiring energy exceed the ionization energy. Very soon (in real time it corresponds to 1.6–2.5 μs) the potential jump near cathode is formed (see Figure 15b).

One can see that size of the potential jump layer is very small (about 5�10�<sup>7</sup> cm, so it is <<rLe), thus electric field formed in the layer is large enough to accelerate the electrons to high-energy in the layer and force them to move toward the axis. We assumed the initial energy of emitted electron is 5 eV. Initial electrons move along magnetic field line as it shown in Figure 16a. However, due to appearance strong electric field in the layer, the average electron energy increases. It begins to exceed 10 eV at field strength is about 100 V/cm, and when electric field strength reaches about 500 V/cm it exceeds 100 eV. At such energies, the secondary electrons acquire the ability to ionize neutrals with the new secondary electrons appearance. As results, an avalanche-like ionization begins. Electrons move toward the axis and can accumulate there (see Figure 16b)). Note that application of the plasma lens to the transport of low-energy

Figure 16. Trajectories of the emission electrons depends on time (a) Nt = 40, (b) Nt = 80.

discharge at low-pressure. Use of plasma lens configuration in this way was elaborated, explored and developed some cost efficiency, low-maintenance plasma devices for ion treatment, and deposition of exotic coatings with given functional properties. These devices make using permanent magnets and possess considerable flexibility with respect to spatial configuration. They can be operated as a stand-alone tool for ion treatment of substrates, or as part of integrated processing system together with cylindrical magnetron sputtering system, for coat-

Modeling of Novel Plasma-Optical Systems http://dx.doi.org/10.5772/intechopen.77512 287

The research described has shown a principal possibility of a positive space charge cloud creation for negative charged particle beam focusing. It was demonstrated that possible create a positive space charge due to the magnetic electron insulation and reach strong focusing electric field, which sufficient for creation of short-focus elements to be used in systems for manipulating intense beams of negative ions and electrons. The further development of focusing properties of these devices demands study of intense negatively charged particle beams

The simulations and experimental results demonstrate the high-efficiency of the electrostatic PL for focusing and manipulating wide aperture, high-current, low-energy, heavy metal ion plasma flow. These results open up new attractive way for further development and application erosion plasma sources for synthesis of exotic films and coatings with given functional properties. Some preliminary theoretical and experimental studies [27–29] have been carried out, providing confidence and optimism that the proposed idea for micro-droplet elimination

[1] Morozov A. Focusing of cold quasi-neutral beams in electromagnetic fields. Doklady of

This work was support by Grant NASU No PL-18 and No P-13\_18.

\* and Alexey Goncharov<sup>2</sup>

2 Institute of Physics NAS of Ukraine, Kiev, Ukraine

1 Institute for Nuclear Research NAS of Ukraine, Kiev, Ukraine

the Academy of Sciences of the U.S.S.R. 1965;163(6):1363

\*Address all correspondence to: ilitovko@ukr.net

ing deposition.

passing through the systems.

has good potential for success.

Acknowledgements

Author details

Iryna Litovko<sup>1</sup>

References

Figure 17. Influence radial electron beam on beam focusing: (a) trajectories of cu + beam; (b) space charge density in the beam.

high-current ion beam can improve the delivery of plasma flow to a substrate, as well as providing micro-droplet removal via the fast electrons within the lens region.

We considered the transport aspect and effect of fast electrons on transport characteristics lowenergy ion plasma beam. Figure 17 shows results of modeling transport copper ion beam with current 100A through plasma lens with presence of fast electrons in the volume. One can see that accumulation high-energy electrons on the axis and their space charge can provide additional compensation and focusing of the high-current ion beam.

#### 4.3. Conclusion remarks

A new approach was proposed for the elimination of micro-droplets from the dense metal plasma, based on evaporation and thus removal of micro-droplets from the arc plasma by energetic electrons within the electrostatic PL. These electrons are generated self-consistently by secondary emission in the near-wall plasma layer from the internal surface of the lens central electrode and serves to evaporate, and thus remove micro-droplets from the plasma flow. The experiments [29] demonstrate the effectiveness of the electrostatic PL for focusing and manipulating wide-aperture, high-current, low-energy, streaming metal ion plasma flows. In these experiments, the self-sustained focusing of high-density, wide-aperture, low-energy ion plasma flow was observed. It has been shown that the presence of fast electrons in the volume of the plasma lens both improves the propagating ion plasma flow toward the substrate and introduces additional energy for effective evaporation and elimination of micro-droplets from the plasma flow.
