Low jitter parabolic profile low density plasma channel in 3D printed gas filled capillary

In recent years, plasma channel research had undergone immense development due to its potential and applications in the electron acceleration field. In particular, capillary discharge had been shown to act as a useful method to produce plasma channels for several possible applications. The capillary discharges were used for laser wake field acceleration (LWFA) up to energy of several Gev (Gonsalves et al 2019). In addition the capillary discharges used as a plasma lens for transporting and improving energy spread during beam-driven plasma acceleration (Pompili et al 2021). In laser-driven plasma acceleration the plasma channel enables the guiding laser to sustain its intensity for distances greater than the Rayleigh length, since they act as an effective plasma composed wave guide.

So far, electron acceleration using high intensity lasers have not been able to provide electron beams with high enough quality such as standard accelerators. The improvement of electron beams accelerated by high intensity lasers can be done by injecting electrons with a low energy spread and high brightness produced by a standard accelerator into a capillary discharged generated plasma channel. This sort of operation demands a high-quality synchronization between three separate systems: plasma channel generation, high intensity laser insertion (guiding laser) into the plasma channel and the electrons injection. Additional methods for control of the accelerated electron beam quality were proposed (Gupta et al 2007, Gopal and Gupta 2017).

LWFA scheme has shown to accelerate electrons up to high energies (Sprangle et al 2002, Faure et al 2004, Geddes et al 2004, Mangles et al 2004, Faure et al 2006, Leemans et al 2006, 2014), using capillary plasma channel. The LWFA method includes a guided laser pulse inside a plasma channel created in a capillary, where the produced wake field accelerates the electrons. Other methods of guiding a high-intensity laser pulse in a plasma wave guide were developed (Lemos et al 2018, Qin et al 2018). The technique, as simple as it might seem, has its limitations and difficulties. These include, the necessity of high precision, for the synchronization between the plasma generation, the incident ultra–short high intensity laser , the injection of the electrons, dephasing of electrons away from the wake field, etc. Another crucial requirement would be, the on-axis density minimum for the plasma channel, required for optical guiding (Durfee et al 1995, Ehrlich et al 1996, Kaganovich et al 1999, Levin et al 2006, Gonsalves et al 2007, Bobrova et al 2013).

In this letter, we demonstrate ignition of the capillary discharge plasma with a jitter on the scale of 1 ns. This level of high precision opens a hatch into the possibility of sufficient synchronization between the plasma channel, high intensity laser and other auxiliary systems (e.g injectors). We demonstrated the optical guiding of an 84 MHz oscillator laser using a straight and curved plasma channels in order to show the level of precision within the plasma ignition, and guiding window supported by the parabolic profile plasma channel. This in turn will be sufficient for synchronization with the above mentioned auxiliary systems (Luo et al 2018, Zigler et al 2018). The use of curved capillaries will enable the insertion of additional laser pulses into the primary channel were the electrons are accelerated.

Our method to produce and confine the plasma is based on a gas–filled capillary (Spence and Hooker 2001, Bobrova et al 2002). The onset of the plasma ignition is triggered by an external laser, that is the laser trigger technique with the consideration of nitrogen/hydrogen gas inside the capillary(Levin et al 2006). In particular, two electrodes are mounted at both ends of the capillary, that are connected to a high-voltage driver source, which is used to ionize the neutral gas injected into the capillary (nitrogen/hydrogen mixture). In addition to the high voltage applied to the electrodes, a laser pulse is synchronized with the high voltage spike in order to encourage the discharge ignition. It is achieved by a 50 mJ 1064 nm laser of 10 ns pulse width. The triggering laser produces the first free electrons, that in turn, initiates an avalanche mechanism by ionizing the molecules of the neutral gas (Palchan et al 2007).

The discharge represents the current that effectively closes an electrical circuit (figure 1(a)), so the plasma ignition acts as a switch for that circuit. The current is measured using a Rogowski coil connected to an oscilloscope (figure 1(b)). The jitter (the variation in latency of the current) is calculated as the standard deviation of the difference measurement between the igniting laser and the current signal.

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In the second part of the experiment, we aligned an 0.8 μm Ti:Sa oscillator laser operating at 84 MHz using the plasma channel produced in 3D printed gas filled capillary, acting as a curved plasma channel (Zigler et al 2018). A photo–diode (figure 2, P.D2) placed behind the capillary measured the intensity of the transmitted oscillator light passing through it. P.D1 was used to send a fiducial signal to the oscilloscope to check whether the plasma ignition is synchronized with the igniting laser (figure 2, P.D1).

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For the LWFA system to efficiently accelerate electrons, the high intensity laser beam must be guided over many Rayleigh lengths. We accomplish this by guiding the laser pulse in a plasma channel with parabolic, on axis, low electron density distribution. In the case where one does not use plasma, the effective length the laser beam is confined and wherein the electron can get accelerated is approximately twice the Rayleigh length, and corresponds to the guiding laser parameters. However, if one were to use a parabolic profile plasma density, the acceleration length could reach up to the plasma channel length. The parabolic profile density distribution is one where the plasma is enriched at the sides and diluted at the center. This way the plasma channel acts as a graded–index fiber, which keeps the laser beam collimated for the length of the channel, maintaining the electron acceleration potential.

The timing and duration of the parabolic density profile of the plasma is derived from measuing the guided laser signal transmitted through the capillary in the presence of the plasma channel. The signal amplitude, calibrated to the transmission efficiency, tells us how efficient the plasma channel is, and how well does the channel guide the laser. The efficiency is determined by the percentage of the laser that passes through the capillary (Zigler et al 2018).

The characteristic duration of the produced plasma was about 1 μs and the maximum voltage was 16 V, which corresponds to a current of 160 A, (figure 3). Figure 4 depicts the current measurement of the accumulation of 50 consecutive ignitions performed at constant time intervals. The inset of figure 4 depicts the initial current rise caused by the plasma ignition for the same 50 ignitions where the time axis is in scale of nanoseconds. Thus, we derive that the jitter in plasma ignition is approximately on the scale of several nanoseconds. The time resolution is evaluated taking into consideration both the oscilloscope sampling rate and the prior to ignition electrical components jitter. Overall, we evaluate the jitter to be ${\tau }_{\mathrm{jitter}}\approx 1\pm$ 0.36 ns. This implies that, we can determine the timing in which to ignite the plasma channel relative to the high intensity (and the related wake) laser, with no concerns of shooting too early or too late with respect to the plasma channel. Also, we deduce that our system over all its components is relatively stable and reliable.

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To estimate the timing and duration of the parabolic density profile, we guided a 0.8 μm Ti:Sa oscillator laser at frequency of 84 MHz, (a pulse every 12 ns), and observed the guided laser signal. In addition to the timing and duration we examined the factor within which the guidance efficiency is determined.

Therefore, we measured the optical signal for different parameters: applied voltage, laser power and injected gas pressure. Analysis show, that the main parameter that increases the efficiency of the guiding is, the applied voltage. Figure 5 depicts a single guiding measurement. The green line is the oscillator laser signal as recorded by the photo-diode (P.D2). The figure also shows the discharge current (blue) as measured by Rogowski coil and the maximal peak 24 V. The measured voltage is translated into current when multiplying it by the Rogowski coil A/V factor. In addition, the figure reveals the segment in time in which we consider that a parabolic profile was present. One can see that the 'best' transmission duration is approximately on the scale of 100 ns. Also, we see that the timing seems to be synchronized with the maximal value of the current (a good indication of correlation between the phenomenon). Furthermore, using more precise analysis we assess the mean duration of the density profile to be ${\tau }_{\mathrm{channel}}\approx 300\,\mathrm{ns}$ and with a maximal transmission achieved approximately at 350 ns after the plasma channel has been generated. Figure 6 depicts the correlation between the guiding and the applied voltage. It is clearly shown that as we increase the applied voltage, we achieve better guiding, up to 80% transmission efficiency, reaching saturation above 8 kV. This indicates that the density profile is deeper and gets closer to the desired profile. The most efficient guiding achieved, is for applied voltages that range between 8 to 10 kV. An additional phenomenon to remark is that the oscillator pulse-train is blocked by the plasma in later stages of the discharge. In this part of the plasma lifetime the capillary waveguide is not operating. The plasma functions as a medium that refracts the radiation in some uncontrolled way to the capillary plastic walls, thus less light is collected by the photodetector. The system approaches the state prior to the ignition after the plasma is diffused into the vacuum chamber.

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To validate that the parabolic profile does exist at the time segment in which we observe the guiding, we performed temporally resolved plasma spectroscopy measurements. For this purpose, we imaged the capillary entrance on the slit of Acton Research Corp spectrometer coupled to an Andor ICCD camera.

The measurement is based on the effect of Stark broadening for the H_α  = 656.28 nm line of hydrogen in the Balmer series. The electron density was derived from correlation to the full width half maximum (FWHM) of the broadened line. Assuming cylindrical symmetry we get the diameter of the formed plasma waveguide:

$$\begin{eqnarray}&&{n}_{e}\left[{10}^{18}\,{\mathrm{cm}}^{-3}\right]={\left(\displaystyle \frac{{\rm{\Delta }}{\lambda }_{1/2}}{\gamma \left({n}_{e},{T}_{e}\right)}\right)}^{3/2},\end{eqnarray} \tag{ 1 }$$

where n_e is the plasma density and ${\rm{\Delta }}{\lambda }_{1/2}$ is the FWHM of H_α . The γ parameter can be calculated numerically and experimentally; for our system it is 5.4.

We scan measurements of the density over the entire duration of the plasma by sequential gating of the ICCD at various times. Due to signal to noise ratio consideration, each measurement duration was conducted over a 40 ns segment. It was clear that at times before and after the parabolic profile, the density showed a constant flat profile. However, at the time corresponding to the maximal transmission of the oscillator signal (as was described above) we were able to observe the parabolic profile and measure the plasma density alongside with a good assessment for the width of the plasma channel. Figure 7 depicts a characteristic measurement of the plasma density over the radius. The black line represents a parabolic density profile, which tells us that at the center the density is proportional to the parabolic profile. We note that the width of the channel is about 70 μm and the lowest density measured is roughly half of the averaged density at the sides of the capillary.

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In conclusion, we measured our plasma channel system's jitter for the ignition of the plasma channel. We have verified the existence and repeatability of a plasma channel, formed in a gas–filled capillary. The laser triggered, plasma ignition was found to be highly effective and with a low jitter. The measured jitter was ${\tau }_{\mathrm{jitter}}\approx 1\,\mathrm{ns}$. We have found the timing and duration of the formed plasma channel with respect to the plasma lifetime. It was shown that the channel occurs repeatedly at the same temporal segment of the plasma discharge lifetime. The measured duration was ${\tau }_{\mathrm{channel}}\approx 300\,\mathrm{ns}$, and the optimal guiding window is about 100 ns, more than an order of magnitude greater than the jitter. This allows to simplify the synchronization of the timing between the guiding laser, possible electron injection and the plasma channel, with high quality of precision and consistency.

Acknowledgments

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