Simulation of laser-plasma focusing using taper solenoid

A laser ion source can produce ion beams of various elements, including high melting point metals. Owing to its ability to switch beams rapidly by loading multiple solid targets, we are developing a laser ion source to implement it in a 400 kV ion implanter, which requires a wide range of ion species. Although a laser ion source offers above advantages, most of the plasma is lost in an ion source due to the generation of the beam from a part of the diffused plasma with a broad angular distribution. To suppress this loss and enhance beam intensity, we employ a linear solenoid to increase the amount of plasma reaching the extraction electrode by suppressing the three-dimensional plasma diffusion. However, the linear solenoid cannot suppress the loss of plasma near the target as the plasma spreads three-dimensionally from the plasma generation point. Therefore, by placing a taper solenoid near the target, it is possible to suppress the diffusion of plasma immediately after its generation and to transport most of the generated plasma to the extraction electrode. In this paper, we present the results of plasma trajectory calculations using the particle-in-cell method by the plasma simulations involving taper solenoids.


Introduction
A laser ion source (LIS) is suitable for producing various ions from solid samples.Takasaki Ion Accelerators for Advanced Radiation Application is developing LIS for implementing it in the 400-kV ion implanter [1][2][3].A LIS has the advantage of being able to provide ion beams of a wide range of elements, including high melting point metals.Additionally, it can rapidly change beams by loading multiple solid targets.The beam current for ion implantation is an average current of the order of pµA.To achieve this, a high-frequency repetitive laser operation is required because LIS produces pulsed ion beam.Recent studies have demonstrated that a repetition frequency of 1 kHz can produce an average current of the order of µA during experiments on carbon plasma generation [3].Although increasing laser energy can result in higher current output, this approach is less economical as it consumes more target material.However, a low laser energy may result in insufficient beam current required for the ion implanter.It is desirable to operate a LIS at as low laser energy as possible in term of the size and cost of the laser system.The plasma produced by laser irradiation on the target diffuses three-dimensionally, and only a fraction of the plasma is utilized as an ion beam.To enhance the beam intensity it is effective to focus the plasma.A typical example of plasma focusing technique is the using of a linear solenoid, which has been reported to increase the beam intensity by several orders of magnitude [4][5][6].However, it is difficult to place a linear solenoid close to the target surface because the laser is directed at the target from a certain angle.It is impossible to focus the diffusing plasma when a linear solenoid placed away from the target, and plasma loss increases in the LIS chamber.Therefore, we propose a more efficient approach to plasma transport by placing a taper solenoid magnet close to the target surface.Taper solenoids, also known as flux concentrators, have been used successfully for positron collection at SLAC [7][8].In positron collection systems, there are two types of flux concentrators: the quarter wave transformer (QWT) and the adiabatic matching device (AMD) [7][8].The AMD, using a taper solenoid, has a wide energy acceptance range due to the nonadiabatic changes in the magnetic field.Moreover, the taper shape of the solenoid results in a strong magnetic field at the target surface while keeping it weak at the solenoid's exit, thereby reducing plasma diffusion at the exit.Furthermore, the taper angle is wider than or equal to the angle of injection of the laser so that it does not interfere with the laser injection.In this study, we presented simulation results for ion and plasma trajectory and assessed the efficiency of plasma transport using the taper solenoid.

Simulation results
Figure 1 illustrates the experimental setup and the geometry of the taper solenoid used in the simulation.The taper solenoid is intended to be installed in the existing LIS system.The opening halfangle of the taper solenoid was set to 25 degrees, which was the same as the incident angle of the laser.The length of the taper solenoid was set to 200 mm based on the structure of the vacuum chamber.The simulation results are compared with different conditions in terms of transport efficiency (TE), which is defined as equation ( 1).In our setup, an ion beam is extracted from the plasma entering the beam extraction hole by an electrostatic field.Accordingly, it is necessary to transport the plasma efficiently to the extractor electrode hole.
The diameter of the extractor electrode hole is 10 mm, and TE is defined as the ratio of ions passing through this hole to the total number of ions initially generated.The position of beam extraction electrode was set at 968mm from the target.An overview of the simulation conditions is summarized in Table 1.The plasma diffusion angle of the generated plasma is assumed to be 50°, corresponding to the opening angle of the taper solenoid.We employed experimental values for plasma velocity while setting the plasma density at 10 16 m -3 due to the performance of the calculation hardware.
First, we investigated whether the taper solenoid effectively focused the plasma emanating from the target surface by simulating simple conditions involving ions alone without Coulomb interaction.The simulations were performed using CST STUDIO SUITE [9].These simulations were conducted under the same conditions, except for magnetic flux density, as detailed in Table 1.The results are presented   in Figure 2, where the x-axis depicts the maximum magnetic field at the narrow end of the taper solenoid.Notably, TE was enhanced by nearly 40% with taper solenoids only.This outcome signifies that ~40 times more ions can be transported compared to a scenario without focusing.It was found that the diverging ions can be focused by using a taper solenoid under the condition without Coulomb interaction.
Next, the results of the plasma transport simulation considering Coulomb interactions are discussed.
The software used in this study is Vism12.1 [10], which employs the Particle-in-Cell (PIC) algorithm to analyze the motion of charged particles.In Figures 3, 4 and 5, we present four cases: (i) without solenoid, (ii) taper solenoid only, (iii) linear solenoid only, and (iv) a combination of taper and linear solenoids.A Linear solenoid produces almost constant magnetic field within the solenoid.On the other hand, a taper solenoid produces a peak-shaped magnetic field with a maximum at the narrow end.
Combining taper and linear solenoid, the peak-shaped magnetic field and the constant magnetic field are connected without falling to zero gauss.In free plasma expansion with no magnetic field, the TE was only 0.7% (case (i)).In case (ii), we observed that increasing the magnetic field suppressed the plasma diffusion near the target.However, regardless of the magnetic field strength, plasma diffused at the exit of the taper solenoid, indicating that the taper solenoid alone is insufficient for efficient plasma transport.The TE in this case was ~0.1% lower than that in the absence of a magnetic field.In case (iii), increasing the liner solenoid magnetic field focused the plasma in it.On the other hand, a  Taper solenoid: 彵 � � G part of the plasma with large divergence angle was not effectively focused.Here, the maximum TE reached ~5%.To address these limitations, we combined the taper solenoid with the linear solenoid in case (iv).This combination effectively suppressed plasma diffusion at the taper solenoid exit, resulting in a TE of ~8%.When the magnetic field in the linear solenoid reached around 330 Gauss, plasma was effectively collimated within it, and the TE improved by a factor of 10 compared to the case (i).
Furthermore, since it was found that the plasma was diverging at the TE measurement point in the center of the diagnostic chamber, the TE at the exit of the linear solenoid (z = 826 mm) was evaluated as shown in figure 6.It was found that 35% of the ions was transported, which was ~45 times more than in the case (i).In conclusion, we have found that the high-efficiency transport of plasma was achieved by combining the tapered solenoid and the linear solenoid.

Summary
We have simulated plasma transport using a taper solenoid to achieve highly efficient transport of the produced plasma in the LIS.Simulations involving only ions (without considering Coulomb interactions) demonstrated that employing a taper solenoid alone increased ion transport by ~40 times compared to without magnetic field conditions.However, considering Coulomb interactions in plasma simulations, it became evident that the taper solenoid alone could not efficiently transport the plasma as it diffused at immediately after the tapered solenoid exit.However, a more efficient plasma transport is achievable by combining the taper solenoid with the linear solenoid.In this configuration, the TE improved by a factor of ~8 times, as it suppressed the plasma diffusion at throughout plasma drift space.Furthermore, ~45 times ions could be transported by adjusting the calculated TE position to the exit of the linear solenoid.These results suggest that positioning the extraction electrode near the linear solenoid exit could enhance ion extraction considerably.In conclusion, our simulations support the effectiveness of taper solenoids for efficient plasma transport.In the future, further (iv) (iii) (ii) (i)

Figure 1 .
Figure 1.(a) is experimental setup and (b) is cross-sectional view of the taper solenoid.

Figure 2 .
Figure 2. Ion simulation results of CST STUDIO SUITE.

Table 1 .
Two dimensional plasma Particle-In-Cell(PIC) simulation setup