2.3. Negative charge particle beams focusing on space charge plasma lens

Ar + ions trajectories in different time step. The calculation continued until reaching a selfconsistent solution. The calculation time comprised 10<sup>5</sup> sec. For that time the stationary state

The model was applied for calculating the lens volume based on the local area with diameter of 80 mm and a height of 50 mm. In our simulations, we considered Ar<sup>+</sup> and Xe+ ion beams with maximal energy from 1 to 3 keV and total current of 20 mA that moved in the magnetic field. Magnetic field is similar to the experimental one and changes from 0.07 T near electrodes to 0.01 T on the system axis. The results of the calculations of the potential distribution when steady-state dynamical equilibrium is reached for Ar<sup>+</sup> ions with maximal energy 1.2–2.4 keV are shown in Figure 3. One can see that with ions energy increasing, the spatial distribution shape changes markedly. Whereas maximum of potential for ion beam's energy 0–1.5 keV (see left Figure 3) is double-humped situated in the coaxial region around the axis, the maximum

The same result we can see with ion mass increasing (see Figure 4). The maximum of potential for Ar + ion beam (Figure 4 left) is in the coaxial region around the axis, but the maximum for

Figure 3. Potential distribution in plasma lens midplane for Ar + ion beam with total current 20 mA and Emax = 1.2 keV

Figure 4. Potential distribution for Ar+ ion beam (left) and Xe+ ion beam (right) with total current 20 mA and

of the lens operation was achieved.

for energy 0–2.4 keV (right) is single-humped onto the axis.

272 Plasma Science and Technology - Basic Fundamentals and Modern Applications

2.2. Simulation results

(left) and 2.4 keV(right).

Emax = 1.4 keV.

We investigated transport electron beam with energy from 5 to 20 keV through the plasma lens. As first step was solved equations for ion's part and as result – obtaining stable positive charge cloud inside plasma lens. Next step was launch e-beam through the lens with cloud. For correct description, we must solve equations for ions and electrons parts together, so we must include electron motion equations in our consideration and modify Poisson equation to form:

$$\frac{1}{r}\frac{d\varphi}{dr} + \frac{d^2\varphi}{dr^2} + \frac{d^2\varphi}{dz^2} = 4\pi e(n\_e + n\_{eb} - n\_i) \tag{7}$$

For simulation high-current electron beam transport need also taking into account the space charge of the particle and the magnetic self-field that may affect the dynamic beam particles in addition to the external fields. The possibility of ionization residual gas by electron beam is necessary taking into account also.

Equations of motion for electrons are solving by current tubes of variable width with central trajectory. A shape of trajectories in an electromagnetic field is calculated using Boris scheme [11]. A space charge beam density is calculated using equation of continuity: div(reve) = 0.A self-consistent solution can be found by repeated solving of Poisson equation, motion equations for all particles, and re-determination of the space charge distribution on every time step. An iteration method with relaxation was used for faster convergence.

Numerical simulations results show clearly that for electron beam current less than 1A the electrostatic beam focusing occurs [12, 13]. The results of simulation for space charge plasma lens and magnetic lens (ML) with the same magnetic field are shown in Figure 5. The comparison shows that beam compression is stronger, and beam divergence is less in PL case than in ML case. The experimental results [12, 13] confirm our simulations. The lens can be used even more effectively for negative ions beam focusing. The simulation results for H-beam with passing through plasma lens and magnetic lens with the same magnetic field are shown in Figure 6. One can see that lens effectively compresses H-ions beam, whereas the magnetic lens does not focus it at all.

However, it should be noted, some part of cloud ions can be captured by a beam and carried away from the cloud. It is positive for beam transport, but as a result of this, cloud potential decreases, and its focusing properties deteriorate. It is not critical for electron beams with current up to 1 A, because a new Ar + ions come to the cloud and renew its focusing properties.

Figure 5. Electron beam (Eb = 10 keV, Ib = 0.2A) passing through the positive space charge plasma lens (left) and magnetic lens (right).

Figure 6. Trajectories of H-ions beam (Eb = 10 keV, Ib = 0.01A) passing through the positive space charge plasma lens (left) and magnetic lens (right).

However, for beam current of about or more 1 A the potential maximum in the positive space charge region decreases (from 580 to 210 V for Ieb = 1 A), the distribution is getting doublehumped and electrostatic focusing destroyed (see Figure 7 top).

It is due to that some part of ions comes out from cloud with the propagating electron beam and their number grows with beam current increasing [13]. A significant part of cloud particles carry out by e-beam along beam line, and ions are continuing to come in cloud from electrodes cannot support renewal processes. Thus cloud potential decrease and it distribution changes from one-hump to two-humps. Note that if it corresponded to case when beam space charge density a bit exceeds to space charge cloud density is possible to improve plasma lens electrostatic focusing property by increasing energy and current density Ar + ions beam that creates positive space charge cloud. Figure 7 (down) shows potential distribution by electron beam propagating for increasing Ar + ions beam current from 20 up to 60 mA. One can see potential distribution come back to one-peak form and focusing properties of plasma lens recovered.

of the beam provides. However, even in this case use of PL is useful since it improves e-beam transport, providing additional compensation of beam space charge and decreasing beam divergence. Note that taking into consideration an ionization residual gas by electron beam

Figure 8. Electron beam trajectories (Eb = 10 keV, Ib = 10A) and positive charge cloud potential distribution created by Ar + ions beam with maximal energy 2.4 keV and current I = 100 mA. Magnetic field twice as much compared with

Figure 7. Electron beam trajectories (Eb = 10 keV, Ib = 1A) and positive charge cloud potential distribution created by

Modeling of Novel Plasma-Optical Systems http://dx.doi.org/10.5772/intechopen.77512 275

Ar + ions beam with maximal energy 2.4 keV and current I = 20 mA(up) and I = 60 mA(down).

The research described has shown a principal possibility of creation of a positive space charge in the cylindrical anode layer accelerator due to a positive ion flow that converges onto its axis. This makes possible to develop a plasma lens with essentially under-compensated positive

do not lead to essential changing in simulations of final results.

2.4. Conclusion remarks

previous case.

However, the positive space charge cloud quickly destroys with further increasing of electron beam current when beam space charge density significantly exceeds space charge cloud density, (see Figure 8) and it is not possible to renew electrostatic focusing properties anymore. In this case, for an electron beam with current on the order of tens of ampere for which the beam space charge density much more than space charge plasma lens the only the magnetic focusing

#### Modeling of Novel Plasma-Optical Systems http://dx.doi.org/10.5772/intechopen.77512 275

Figure 7. Electron beam trajectories (Eb = 10 keV, Ib = 1A) and positive charge cloud potential distribution created by Ar + ions beam with maximal energy 2.4 keV and current I = 20 mA(up) and I = 60 mA(down).

Figure 8. Electron beam trajectories (Eb = 10 keV, Ib = 10A) and positive charge cloud potential distribution created by Ar + ions beam with maximal energy 2.4 keV and current I = 100 mA. Magnetic field twice as much compared with previous case.

of the beam provides. However, even in this case use of PL is useful since it improves e-beam transport, providing additional compensation of beam space charge and decreasing beam divergence. Note that taking into consideration an ionization residual gas by electron beam do not lead to essential changing in simulations of final results.

#### 2.4. Conclusion remarks

However, for beam current of about or more 1 A the potential maximum in the positive space charge region decreases (from 580 to 210 V for Ieb = 1 A), the distribution is getting double-

Figure 6. Trajectories of H-ions beam (Eb = 10 keV, Ib = 0.01A) passing through the positive space charge plasma lens (left)

Figure 5. Electron beam (Eb = 10 keV, Ib = 0.2A) passing through the positive space charge plasma lens (left) and magnetic

It is due to that some part of ions comes out from cloud with the propagating electron beam and their number grows with beam current increasing [13]. A significant part of cloud particles carry out by e-beam along beam line, and ions are continuing to come in cloud from electrodes cannot support renewal processes. Thus cloud potential decrease and it distribution changes from one-hump to two-humps. Note that if it corresponded to case when beam space charge density a bit exceeds to space charge cloud density is possible to improve plasma lens electrostatic focusing property by increasing energy and current density Ar + ions beam that creates positive space charge cloud. Figure 7 (down) shows potential distribution by electron beam propagating for increasing Ar + ions beam current from 20 up to 60 mA. One can see potential distribution come back to one-peak form and focusing properties of plasma lens recovered.

However, the positive space charge cloud quickly destroys with further increasing of electron beam current when beam space charge density significantly exceeds space charge cloud density, (see Figure 8) and it is not possible to renew electrostatic focusing properties anymore. In this case, for an electron beam with current on the order of tens of ampere for which the beam space charge density much more than space charge plasma lens the only the magnetic focusing

humped and electrostatic focusing destroyed (see Figure 7 top).

274 Plasma Science and Technology - Basic Fundamentals and Modern Applications

lens (right).

and magnetic lens (right).

The research described has shown a principal possibility of creation of a positive space charge in the cylindrical anode layer accelerator due to a positive ion flow that converges onto its axis. This makes possible to develop a plasma lens with essentially under-compensated positive space charge. The lens will be used for focusing and manipulating beams of negatively charged particles. The value of positive charge potential formed at the axis and the steady state of the space charge depending on plasma dynamical parameters of the system are determined experimentally [12, 13]. Electric field value reaching 600–1000 V/cm realized under experimental condition is determined. Such electric field strength is sufficient for creation of short-focus elements to be used in systems for manipulating intense beams of negative ions and electrons. Experimental results [14] demonstrate an attractive possibilities application positive space charged plasma lens with magnetic electron insulation for focusing and manipulating wide-aperture high-current no relativistic electron beams. For relatively low-current mode for which electron beam space charged less than positive space charged plasma lens, it realizes electrostatic focusing is passing electron beam. In case of high-current mode, when electron beam space charge much more than space charge plasma lens the lens operates in plasma mode to create transparent plasma accelerating electrode and compensate space charge propagating electron beam. The lens magnetic field in this case uses for effective focusing beam.

In experiment was demonstrated a perspective applications of positive space charged PL with magnetic electron insulation for focusing and manipulating wide aperture high-current no relativistic electron beams (Eb = 16 keV; Ib = 100 A) [14]. Particularly, it was shown experimentally that under focusing these beams maximal compression factor was up to 30x, and beam current density at the focus was about 100 A/cm<sup>2</sup> .
