Characterization of plasma-discharge Capillaries for Plasma-based Particle Acceleration

Novel particle accelerators based on plasma technology allow a drastic reduction in size, due to the high accelerating field established inside plasmas, which are created and confined by specific devices. Plasma Wakefield Acceleration experiments are performed at the SPARC_LAB test facility (Laboratori Nazionali di Frascati - INFN) by using gas-filled capillaries, in which the plasma formation is achieved by ionizing hydrogen gas through high voltage pulses. In this work, the characterization of gas-filled plasma-discharge capillaries is presented. Several geometrical configurations are tested, including capillaries with different channel shapes and arrangement of inlets positions for the gas injection. Such configurations are designed in order to enhance the uniformity of the plasma density distribution along the plasma channel, which is necessary to improve particle beam acceleration. Plasma sources are characterized by means of the spectroscopic technique based on the Stark broadening method, which allows to measure the evolution of the plasma density profile along the channel. In addition, the CFD software OpenFoam is used to simulate the dynamics of the neutral gas during the filling of the capillary.


Introduction
Plasma-based electron beam acceleration experiments are performed at SPARC LAB test facility, in the framework of EuPRAXIA project, by using gas-filled discharge capillaries to create and confine plasmas [1,2,3,4].Capillaries are designed and characterized at Plasma Lab facility both experimentally and by fluid simulations [5,6,7,8].Different geometrical configurations and experimental settings are tested to enhance the reproducibility, uniformity and shot-to-shot stability of the plasma, necessary to improve the accelerated beams quality [9].

Experimental setup
The experimental apparatus of Plasma Lab facility is constituted by synchronized systems for the gas injection, plasma formation and characterization, as depicted in Fig. 1.Tested gas-filled discharge capillaries are installed inside a vacuum chamber, in which a pressure of 10 −6 mbar is established by means of three primary scroll pumps and one turbo-molecular pump.Capillaries are filled with hydrogen gas by means of a gas injection system.Hydrogen gas is produced through electrolysis by means of a hydrogen generator and it is injected inside the capillary at a pressure of 10-50 mbar, set by a mechanical regulator.An electro-mechanical valve controls the gas injection at a frequency between 1-10 Hz for about 5 ms, to preserve the vacuum inside the chamber.An electrical circuit delivers kV-range µs short pulses to a couple of copper electrodes attached to the capillary extremities, in order to ionize the neutral gas inside the capillary channel and produce the plasma [10].The electrical circuit is synchronized with the gas injection valve by means of a delay generator (Stanford Research DG535), which allows to ignite the plasma when the capillary is completely filled with hydrogen.Plasma density measurements are performed through the spectroscopic analysis of plasma-emitted light, which is guided through an optical line and collected into an imaging spectrometer (SpectraPro 275).
Hydrogen emission lines of the Balmer series, H α (656.3 nm) and H β (486.1 nm), are selected by a diffraction grating and lines broadening is measured to recover the electron plasma density, exploiting the direct proportionality between the broadening of the hydrogen spectral lines ∆λ 1/2 and the electron plasma density N e , according to the Stark effect [11]: Spectral images, acquired by an intensified CCD camera (Andor Istar 320) equipped with the spectrometer, allow to reconstruct the longitudinal electron plasma density profile inside the capillary channel.Furthermore, the camera is synchronized with the electrical circuit to measure the plasma density profile evolution at different delays after the electrical discharge.

Experimental testing
3D-printed capillaries tested at Plasma Lab are made of VeroClear, a rigid and transparent plastic material.Various geometrical configurations are designed to improve the plasma uniformity and stability.In this paper we present the characterization of 3 cm long 1 mm diameter capillaries, having different inlets arrangements and channel shapes, as described in Fig. 2.  Voltage pulses of 7 kV are applied at 1 Hz to tested capillaries, resulting in the onset of plasma currents of 380 A. A delay of 7 ms is set between the gas valve closure and the voltage discharge, so that once hydrogen is injected, the pumping system restores a high vacuum level outside the capillary before the plasma is produced.This synchronization setup replicates the one used in SPARC LAB for particle acceleration experiments.Measured longitudinal plasma density profiles are depicted in Fig. 3, regarding capillary configurations with uniform channel shape and two inlets located at different positions.Results highlight the dependence of the density profile on the inlets arrangement, with higher uniformity for closer inlets (9 and 12 mm) compared to inlets at higher distance (15 and 24 mm).
On the other hand, concerning the effect of the channel shape, a cigar shape (with 1.3 mm inner diameter and 1 mm outer diameter) determines a more uniform profile compared to a   uniform channel shape, while a tapered channel with conical ends (having 1 mm inner diameter and 2 mm outer diameter) provides density ramps that can be controlled to improve the matching between the accelerated particle bunch and the plasma.Moreover, time resolved measurements of the average plasma density show that the temporal evolution is not affected by the inlet configuration, as reported in Fig. 4.

Numerical Analysis
3D fluid simulations are performed with the CFD software OpenFoam [12] to analyze the neutral hydrogen gas dynamics during the filling of the capillary.SonicFoamART solver is employed to simulate the gas in turbulent transient sonic regime.The experimental testing is reproduced in fluid simulations by setting a gas injection pressure of 20 mbar for 5 ms (electro-mechanical valve opening time) and closing the inlet for the following 7 ms (time interval between valve closure and electrical discharge).OpenFoam is limited to describe only neutral gas dynamics, therefore electrical discharge and plasma expansion are not included in simulations.However this analysis provides useful information regarding the hydrogen distribution inside the capillary before the plasma formation and how it relates to the plasma density distribution as well.Hydrogen density distributions reported in Fig. 5 show that a distance of 12 mm between the two inlets entails an axial density profile with two peaks and a central plateau, while a distance of 15 mm determines a more curved profile, peaked at the channel center.the configuration with 15 mm spaced inlets is characterized by a gas flow directed outward from the channel center, leading to a curved density profile.On the other hand, the capillary with 12 mm spaced inlets has a gas flow that is still directed from the inlets to the center, meaning that the channel is not completely filled with the gas.Therefore simulation results suggest that a different synchronization between injection valve and electrical discharge is required to obtain similar density profiles with different capillary geometry, i.e. the discharge must be applied earlier for configurations with higher inlet spacing.

Conclusion
In this paper we presented the design and characterization of gas-filled plasma discharge capillaries.Experimental results proved the ability to control the plasma distribution inside these sources through a proper design of the geometry, in terms of inlets arrangement and channel shape.Fluid simulations provided a theoretical support to the experiments, giving insight on the effect of the source geometry on the neutral gas dynamics.

Figure 1 :
Figure 1: Plasma Lab experimental setup (a) Two inlets spaced 9 mm, uniform channel (b) Two inlets spaced 12 mm, uniform channel (c) Two inlets spaced 15 mm, uniform channel (d) Two inlets spaced 24 mm, uniform channel (e) One central inlet, channel with conical ends (f) One central inlet, cigar-shaped channel

Figure 2 :
Figure 2: Tested 3D-printed capillaries (a) Plasma density profiles for two inlets capillaries with uniform channel (b) Plasma density profiles for one inlet capillaries with various channel shapes

Figure 3 :
Figure 3: Longitudinal plasma density profiles 1600 ns after the electrical discharge for capillaries with different channel shapes and inlets arrangements.Arrows indicate the inlet positions in the different configurations, while blue rectangles represent the electrodes at the capillaries ends.

Figure 4 :
Figure 4: Time evolution of the average plasma density inside the channel for different configurations.
(a) Section view of hydrogen density distribution inside a capillary with two inlets with 15 mm spacing (b) Axial hydrogen density profiles for capillaries having two inlets with 12 mm and 15 mm relative distance.Arrows indicate inlets positions.

Figure 5 :
Figure 5: 2D and axial hydrogen density distributions (a) Section view of axial flux distribution inside a capillary with two inlets with 15 mm spacing (b) Axial hydrogen flux profiles for capillaries having two inlets with 12 mm and 15 mm relative distance.Arrows indicate inlets positions.