# One-Body Capillary Plasma Source for Plasma Accelerator Research at e-LABs
## 4 Capillary Discharge Plasma Source for Active Plasma Lens  
In this study, we investigated the feasibility of utilizing a capillary gas cell as a source for a plasma lens. The plasma lens is an attractive method of focusing electron beams  
Figure 4: Experimental setup for a laser wakefield electron acceleration. The 150 TW laser system and a helium-filled capillary gas cell of 7 mm length are used. Figure 5: **(a)** False color images of the accelerated electrons on the LANEX 2 and **(b)** normalized charge as a function of electron energy. **(c)** The plasma profile was set similarly to the CFD simulation result. The PIC simulation results at three different positions are represented in **(d–f)**. The red lines in left of the bottom panels are the spectral density in terms of beam energy. through the creation of a radially symmetric field, as reported in previous studies [13; 14; 15]. Our approach involved the use of a pulsed, high-voltage (HV) discharge system to generate a gas discharge plasma, as is depicted in Figure 6a. The HV discharge was triggered by a thyratron switch (MA2440B, E2V) and powered by a DC power supply (EH50R02, Glassman) capable of providing up to 50 kV. All circuit components, depicted by the dashed line in Figure 6a, were installed in a metal box for radiation shielding. The gas pressure and injection were controlled by a vacuum regulator (3491A, [PERSON], Irving, TX, USA) and a solenoid valve (6013A, [PERSON], Ingelfingen, Germany), respectively. The capillary cell employed was 15 mm long, with a diameter of 1 mm, and was fitted with holey copper electrodes, which were mounted at each end with PEEK cover plates, as shown in Figure 1b. Helium gas was introduced into the capillary at a constant pressure of 300 mbar and a high voltage of 10 kV. The operation and synchronization of the gas injection and high voltage systems were managed by a delay generator (DG645, SRS). The generated capillary discharge plasma is shown in Figure 6a. The current was monitored during the discharge using a current transformer (7795, Pearson Electronics, Palo Alto, CA, USA), and is depicted in Figure 6b. The current increased to 140 A after an initial breakdown phase of approximately 100 ns. Assuming a cylindrical coordinate, the distribution of the magnetic field corresponding to the measured current can be calculated using the Ampere's law, as follows:  
\[B_{\theta}(r)=\frac{\mu_{0}}{r}\int_{0}^{r}J(r^{\prime})r^{\prime}dr^{\prime}, \tag{2}\]  
where \(B_{\theta}\) is the azimuthal magnetic field, \(\mu_{0}\) is the magnetic permeability of vacuum, and \(J(r)\) is the current density within \(r<R\) (\(R\) is the capillary radius). The current density, \(J(r)\), is a varying function along the radius, \(r\), which can be derived by the assumption of a plasma temperature difference between the center (\(r=0\)) and the capillary wall (\(r=R\)) [32]. It is anticipated that the \(B_{\theta}\) exhibits a non-linear profile as a result of the varying current density. Figure 7a shows the current density and the azimuthal magnetic field along the radius at the discharge current of 140 A in a 1 mm diameter capillary. The magnetic field gradient around the center was determined to be 97 T/m. To validate the beam focusing capabilities in the discharge capillary, the PIC simulations were performed using Equation (2), and the numerical, dispersion-free field-solver was employed to minimize the numerical Cherenkov noise [31]. The simulation range was at a capillary length of 15 mm, and the beam size calculation was then followed using the Twiss matrix. The Twiss parameters for an input electron beam were \(\beta_{r}=10\) m; \(\alpha_{r}=7\); a normalized emittance, \(\epsilon_{Nr}=0.5\) um mrad; the  
Figure 6: (**a**) Schematic diagram of the pulsed, high-voltage discharge system. The pulsed, HV discharge system and a 15 mm, helium-filled capillary discharge plasma are shown in the inner photographs. (**b**) The current profile, with a peak current of 140 A, was obtained by applying the voltage of 10 kV.