Abstract
Keywords
1 Introduction
Capillary discharge plasma waveguides[1,2], also used as active plasma lenses, allow control over laser pulse diffraction[3] and particle bunch divergence[4–7]. They are typically used to guide laser pulses and focus electron bunches, but may also prove useful in a ‘plasma telescope’ configuration to change laser system focal spot sizes without lengthy transport lines. Optical pulses are focused as a result of the waveguide’s radial variation of the plasma electron density[8]; charged particle bunches are focused by the magnetic field associated with the current[5]. Capillary plasma waveguides are compact, provide a strong gradient (or focusing)[9], and have a high damage threshold[10]. They allow for modification of the spot size evolution of intense particle beams and laser pulses and are thus of interest for many applications, including plasma wakefield acceleration[11–14], high harmonic generation[15–18], and X-ray lasing[19,20]. In this paper, we concentrate on waveguide properties that are mainly relevant for laser pulse propagation. Specifically, we measure the transverse electron density profile with sufficient accuracy to discuss the effect of non-parabolic contributions for applications, as well as the stability of the channel shape and position. These parameters are of great importance for the aforementioned applications.
In gas-filled capillary discharge waveguides, the plasma is created by a discharge inside a capillary that is initially filled with neutral gas. The current ionizes the gas and heats the plasma. At the same time the plasma is cooled at the capillary walls, leading to a radial variation of the plasma electron density, also called a plasma channel[21,22]. The channel profile can be expressed as
There is no current method to measure pulse evolution inside the waveguide; experiments are typically guided by calculations and simulations and require precise knowledge of the channel properties. Radial profiles of capillary discharge waveguides have been measured using longitudinal and transverse diagnostics[21,24–26]. Although interferometry measurements revealed non-parabolic profiles[21,25], the precision was not sufficient to discuss potential effects on guiding. Higher precision was enabled by centroid oscillation measurements, but did not reveal non-parabolic profiles[24]. In this paper, we reveal for the first time non-parabolic contributions to the channel profile from centroid oscillation measurements. We show that these contributions are negligible when the pulse is approximately matched to the waveguide. However, for non-matched applications (e.g., when waveguides are used in a plasma telescope configuration) these contributions need to be taken into account.
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Figure 1.Schematic overview of the experimental setup. The pulse propagates from right to left. The distance along the capillary is and downstream the capillary is . Optical lenses have the following focal lengths: L, –10 cm; L, 40 cm; L, 150 cm; L, 100 cm; L, 60 cm.
Applications require reproducible waveguide parameters. For example, the reproducibility of particle bunches accelerated in laser-driven plasma wakefield accelerators (LPAs) is defined by the reproducibility of the wakefield, which is a product of all parts that are involved. Acceleration of high-quality bunches requires every component to be well controlled and stable, i.e., the plasma and the drive bunch or pulse. In this paper, we characterize the plasma to understand the sources of variations. We show that the matched spot size
2 Experimental setup
Figure 1 provides a schematic overview of the experimental setup. We used a laser probe pulse to characterize the plasma channel properties. The pulse was produced by the front end of the BErkeley Lab Laser Accelerator (BELLA) petawatt laser system[27]. Light leaking through a mirror downstream the regenerative amplifier was transported to the experimental area by a single mode optical fiber (see Figure 1). After transport, the pulse had a central wavelength of
The transverse, time-integrated laser pulse profile was imaged with a charged-coupled-device (CCD) camera, as shown in Figure 1. The camera had 1626 × 1236 pixels and a resolution of 0.935
Figure 2.Examples of experimentally measured transverse pulse intensity distributions: left, at vacuum focus; center, at the capillary exit plane when the pulse propagated in the 40 cm long capillary #4; right, at the capillary exit plane when the pulse propagated in vacuum. Blue lines show the horizontal and vertical projections of the camera images. Red dotted lines show the results of Gaussian fits of the projections. The left and middle plots are on the same linear color scale; the color scale of the right plot is enhanced by a factor of 10.
The plasma was created by a discharge current in a gas-filled capillary. The capillary bulk material was either sapphire
Capillary | Material | Diameter | Length (cm) | ||
---|---|---|---|---|---|
#1 | Sapphire | 650 | 9 | (1.6–13) | 105–75 |
#2 | Sapphire | 830 | 20 | (0.7–6.6) | 180–115 |
#3 | MGC | 2000 | 20 | (0.65–2.4) | |
#4 | MGC | 830 | 40 | (1.5–6.6) | 180–115 |
Table 1. Overview of capillary parameters and operation range.
Electrodes were located at each end of the capillary. Switching capacitors charged to
As summarized in Table 1, plasma waveguides of length 9–40 cm were analyzed. Producing shorter channels is typically straightforward. To the best of the authors’ knowledge, 40 cm is the longest discharge capillary waveguide that has been demonstrated. In the context of laser-driven plasma wakefield acceleration, reaching 10 GeV electron energy gain in a single stage requires an on-axis plasma electron density lower than
Capillary #3 has a diameter of 2000
3 Experimental results
3.1 Measurement of the matched spot size
Figure 2 shows examples of transverse pulse intensity distributions measured when using the 40 cm long capillary #4: the left image shows the pulse at the capillary entrance (which is also the location of the focal point); the right image shows the central section of the pulse after 40 cm of vacuum propagation (root-mean-square (rms) spot size
We estimated the waveguide energy transmission
Plasma channels focus laser pulses due to a radially varying refractive index. The profile is defined by the radial plasma electron density distribution
Measuring the pulse centroid position at the capillary exit
Figure 3(a) shows the measured relation of
Figure 3.Reconstructed radial plasma electron density profile. (a) Measurements of the centroid position of the guided pulse at the capillary exit as a function of the parallel capillary offset with respect to the laser propagation axis (green markers). Error bars (standard deviation of the individual measurements) are not visible because they are smaller than the marker size. The blue line shows a linear fit to the data; it is solid over the measurement range and dashed outside (assuming the continuation of a parabolic channel outside the measurement range). (b) Calculated relative change of the radial plasma electron density (green markers) compared with one-dimensional NPINCH simulation results (gray line). The blue line corresponds to the result of the fit shown in panel (a).
In Figure 3(a),
We performed horizontal and vertical centroid oscillation measurements for all capillaries over the accessible density range. Values for
3.2 Waveguide parameter reproducibility
Applications and multi-shot measurements require channel properties to be stable and reproducible from discharge to discharge. Parameters such as the channel central axis, the focusing strength, or the on-axis plasma electron density are demanded to be repeatable from event to event and stable over long timescales. For example, variations in the matched spot size change the pulse evolution inside the waveguide as well as the pulse divergence downstream. To evaluate waveguide parameter variations, we observed their effects on the probe pulse. We also decided to use a combination of capillary length
We chose capillary #1 (9 cm length[38]) together with an initial neutral gas density of
Figure 4(a) compares variations of the guided pulse centroid position at the capillary exit (orange) with those of the incoming pulse at the capillary entrance (blue). The pulse centroid was defined as the location of the peak of the Gaussian fit to the projections. Deviations from the centroid reference
Figure 4.(a) Pulse centroid position variations , where is the measured pulse center and the average value of all measurements; (b) spot size deviations , where is the rms pulse size and the average value of all measurements. The figure shows the running average of 100 measurements (solid line) as well as their standard deviation (error-band) for capillary #1. Measurements for the incoming pulse at the capillary entrance are shown in blue and those for the guided pulse at the capillary exit in orange. (c) Correlation between and the timing jitter between the discharge and the probe pulse () for an initial neutral gas density of atoms/cm for capillary #2. The green dashed line shows the result of a linear fit.
From the data presented in Figure 4(a) we calculated the standard deviation of all measurements. Variations of the incoming pulse
The rms spot size variation
We performed the same set of measurements for capillaries #2 and #4. There was no measurable increase in
We found that for capillaries longer than 20 cm, part of the increase in spot size variations could be explained by timing jitter between the discharge and the laser pulse arrival time (
For our laser pulse input parameters and the minimum matched spot size of capillary #3
3.3 Observation of higher order contributions to the transverse channel profile
The excellent reproducibility of the waveguide is a prerequisite for applications, e.g., to produce stable electron bunches from an LPA. Together with a reproducible probe pulse it also enabled measurements of the transverse channel profile with unprecedented precision. Figure 5(b) shows a centroid oscillation measurement for the 2000
Figure 5.Reconstructed radial plasma electron density profile. (a) Measurements of the centroid position of the guided pulse at the capillary exit (green markers) as a function of the parallel capillary offset with respect to the laser propagation axis . Error bars (standard deviation of the individual measurements) are not visible as they are smaller than the marker size. The blue and red solid (within the measurement range) and dashed (outside the measurement range) lines show the calculated centroid oscillation scan result corresponding to the density profiles of the same color on the right. (b) Calculated relative change of the plasma electron density as a function of radial position for a parabolic channel (blue line), a channel with an component (red line) compared with the result from NPINCH simulations (gray line).
The blue line in Figure 5(a) shows a linear fit (according to Equation (6)) to the centroid oscillation result. It does not provide a good description of the measurement for
Figure 5(a) shows that adding an
Figures 3(b) and 5(b) show that the central regions (
Figure 6.Waterfall plot of the simulated pulse intensity evolution downstream the capillary exit . The red dashed line shows the rms spot size from Gaussian fits to the intensity distribution from the simulations for a parabolic channel using (red). The green line shows the measured evolution of the rms size of the pulse after guiding. The blue line shows the pulse evolution downstream the vacuum focus.
Figure 7.(a) Simulation result of the laser pulse intensity evolution along the capillary #3 in a plasma telescope configuration, using the channel profile according to
4 Implications of parameter reproducibility and non-parabolic channel contributions for applications
4.1 LPAs
When using waveguides in the context of laser-driven plasma wakefield acceleration the matched spot size
To confirm that the radial profile measured in Section 3.1 is consistent with the evolution of the pulse exiting from the waveguide, propagation simulations were performed. The pulse mode was retrieved from a Gerchberg–Sexton algorithm on the measured fluence evolution along the propagation axis
In Section 3.2 we demonstrated the excellent reproducibility of the waveguide parameters that control pulse guiding (second term on the right-hand side of Equation (2)). For capillary #2, the matched spot size was repeatable to 0.1%. Changing the matched spot size by
LPAs additionally require reproducibility of the on-axis plasma electron density
The two major components of LPAs are the laser and the plasma. Our measurement results highlight that discharge plasma waveguide parameter variations are small compared with typical variations of the pulses produced by LPA laser systems. Thus, increased laser pulse parameter reproducibility is essential to achieve significant improvements in the reproducibility and stability of particle bunches, consistent with the findings of Ref. [44].
4.2 Plasma telescopes
Waveguides could also be used as ‘plasma telescopes’: for the right combination of capillary length and matched spot size the pulse exits from the plasma after half a spot-size oscillation, changing it from
To understand how the
We simulated pulse propagation with INF&RNO, using the reconstructed input pulse and the NPINCH channel profile from Figure 5. Figure 7(a) shows the pulse evolution inside the capillary and Figure 7(b) downstream the capillary exit. The transverse pulse intensity distribution downstream the capillary exit showed higher-order modes, qualitatively similar to the experimental measurements; the pulse peak intensity as well as its spot size oscillated as different modes came in and out of focus. Figures 7(c)–7(e) compare transverse pulse intensity distributions 20 cm downstream the capillary exit. Figure 7(c) is the experimentally measured distribution; Figure 7(d) was obtained from simulations when using a model of the input pulse; and Figure 7(e) from simulations when using a transversely Gaussian input pulse. Figures 7(c)–7(e) all show the same ‘ring’ features, even when the input pulse is a perfect Gaussian (Figure 7(e)); the ‘ring’ features are therefore a result of the pulse experiencing the non-parabolic contributions of Equation (7). These initial experiments highlighted that research and development will be required before capillary discharge waveguides can be used as plasma telescopes for applications that require a Gaussian mode.
Figure 7(f) shows the simulated transverse pulse intensity distribution 20 cm downstream the capillary exit for a pulse (
5 Conclusions and summary
We evaluated the reproducibility of plasma channels formed by discharges in gas-filled capillary waveguides and obtained precise measurements of their radial plasma electron density distributions. Variations of the waveguide central axis were below the 1
Measurements of the transverse waveguide profiles revealed non-parabolic contributions to the radial channel profile that were in excellent agreement with MHD simulation results. We have demonstrated that non-parabolic effects influenced pulse propagation for non-matched waveguide applications, such as plasma telescopes. However, when the pulse was approximately matched to the waveguide, their effects were negligible.
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