Sources and space–time distribution of the electromagnetic pulses in experiments on inertial confinement fusion and laser–plasma acceleration

Abstract

When high-energy and high-power lasers interact with matter, a significant part of the incoming laser energy is transformed into transient electromagnetic pulses (EMPs) in the range of radiofrequencies and microwaves. These fields can reach high intensities and can potentially represent a significative danger for the electronic devices placed near the interaction point. Thus, the comprehension of the origin of these electromagnetic fields and of their distribution is of primary importance for the safe operation of high-power and high-energy laser facilities, but also for the possible use of these high fields in several promising applications. A recognized main source of EMPs is the target positive charging caused by the fast-electron emission due to laser–plasma interactions. The fast charging induces high neutralization currents from the conductive walls of the vacuum chamber through the target holder. However, other mechanisms related to the laser–target interaction are also capable of generating intense electromagnetic fields. Several possible sources of EMPs are discussed here and compared for high-energy and high-intensity laser–matter interactions, typical for inertial confinement fusion and laser–plasma acceleration. The possible effects on the electromagnetic field distribution within the experimental chamber, due to particle beams and plasma emitted from the target, are also described.

This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 2)’.

1. Introduction

The interaction of high-energy and high-power lasers with matter produces broadband particle and electromagnetic radiation. In particular, a significant portion of the incoming laser energy is transformed to powerful transient electromagnetic pulses (EMPs) mainly in the range of radiofrequencies and microwaves [1]. Such fields depend on laser energy and intensity and they are so powerful to potentially represent a danger for any electronic device placed inside or even outside the experimental vacuum chamber. In [1], a map of the maximum values for the EMP electric fields, normalized at 1 m distance from target, is given for different regimes of laser interaction with matter. The highest fields are reported for high-energy (tens-hundreds joules) and short-pulse (picosecond) facilities and can reach the MV m⁻¹ order. Moreover, in these cases, EMP intensities are scaled with laser energy and intensity and are thus expected of higher values for future laser facilities with improved performances. For this reason, understanding the origin and the actual time distribution of these electromagnetic fields is of key importance for the development of suitable mitigation schemes for the safe operation of existing laser facilities for inertial confinement fusion and laser–plasma acceleration. This is of course an even more severe issue for future lasers with higher energy and power. On the other hand, the comprehension of these mechanisms can potentially enable the future use of these high fields in new applications. In figure 1, a typical EMP signal is shown.

Figure 1.

Typical EMP signal detected by a D-dot probe in an experiment at the Vulcan laser facility, with λ = 1053 nm, ∼400 J energy, ∼1 ps duration and ∼10²¹ W cm^–2 intensity for a parylene-N plastic foil of a few hundred nanometre thickness. (Online version in colour.)

This was detected by means of a D-dot probe [2] placed inside the experimental chamber during an experiment at the Vulcan facility, where a laser pulse with characteristics λ = 1054 nm, ∼400 J energy, ∼1 ps duration, ∼10²¹ W cm⁻² intensity and contrast greater than 10¹⁰ on a nanosecond time scale was directed on a parylene-N plastic foil of a few hundred nanometre thickness.

Several sources of these transient fields have been recognized during the last years, but the actual comparison among them in a single experiment is still an open issue. In this paper, we discuss the features of these sources. The overall distribution of the EMP field is the composition of the contributions coming from each of them, but is also affected by the time-varying nature of the environment created by the laser–matter interaction of high intensity. The importance of this topic for present and future laser facilities for inertial confinement fusion was the reason to present it at the Hooke Discussion ‘Prospects for high gain inertial fusion energy', held at The Royal Society in London on the 2 and 3 March 2020.

2. Neutralization current due to electron emission

The interaction of a high-power laser pulse with a solid target leads to the acceleration of target electrons at energies that can be larger than one hundred MeV, depending on the intensity of the focused laser light [3]. They are followed by slower ions, and the transient net charge on target is thus positive [4–6]. Depending on the laser energy and intensity, this charge can be up to the microcoulomb order of magnitude, and this fast charging can induce high neutralization currents on the surface of the vacuum chamber flowing through the target stalk [4]. The stalk thus radiates as an $\lambda /4$ antenna [7], and, due to its physical dimensions, the emitted EMP fields have frequencies up to several GHz [4,6].

In figure 2a, a scheme representing this source of emission is given. The target is placed on a holder and the neutralization current is indicated by the red arrow. In figure 2b, we show an example of the field intensity associated with the emitted 100 keV electron bunch at two different time instants with respect to the moment of interaction, obtained by means of particle-in-cell (PIC) simulations on a spherical chamber of 1.5 m diameter. At the time instant t₁ = 4 ns, the bunch of hot electrons has completely left the target, which becomes positively charged, and the neutralization current travels through the stalk to the chamber surface. At t₂ = 10 ns, the electron bunch has completely reached the chamber surface, and also quasi-stationary resonating oscillations are established on the stalk.

Figure 2.

(a) Scheme of the source emission due to the neutralization current flows through the stalk as electrons are extracted from the target because of the laser interaction. (b) Snapshots of a PIC simulation of the process for 100 keV electron bunch and 1.5 m chamber diameter. (Online version in colour.)

Because of the long wavelengths, comparable to or larger than the typical dimension of the experimental vacuum chamber used in these experiments, the radiated EMPs normally have near-field features [7] and local plane-wave approximations, suitable instead at larger distances from target, cannot be applied here effectively. The electric field is expected to have thus comparable radial and transversal components, and the intensity to scale as $\sim r^{-\alpha }$, with r being the radial distance from the stalk and $\alpha <2$. This mechanism is recognized to be one of the main sources of EMP fields when laser pulses with duration up to tens of picosecond and kilojoule energies are used to irradiate solid targets [1,5]. This was validated experimentally at laser energies of approximately 100 mJ, with tens of femtosecond laser pulses, at 10¹⁹ W cm⁻² [4,6]. In figure 3a, it is shown a typical result of measurement and simulation of the neutralization current in that experiment.

Figure 3.

(a) Comparison of the neutralization current wave form between the simulations and the experimental data achieved at the Eclipse laser with 80 mJ, 50 fs, approximately 10¹⁸ W cm⁻². Reprinted with permission from [4]. Copyright 2014 by the American Physical Society. (b) Comparison of signals got by SWB antenna and neutralization current in experiments at PALS laser, with 350 ps pulse. Reprinted with permission from [9]. Copyright 2014 by ENEA. (Online version in colour.)

Laser pulses of picosecond duration are capable of driving neutralization currents up to $J\sim 100\text{ kA}$, leading to emitted electric fields exceeding the MV m⁻¹ order of magnitude at a distance of 1 m from the laser–plasma interaction point [1,5]. For nanosecond laser pulses, this emission mechanism has lower efficiency [6], but currents of the 4 kA order were anyway effectively measured in experiments at the PALS facility $(E=600\text{ J },\hspace{0.17em}\tau =300\text{ ps})$ where strong $\lambda /4$ antenna-like EMP emission was detected [8], and effectively associated with the measured current [9]. Figure 3b shows the comparison between measurements of neutralization currents and EMP signals detected by a super-wideband (SWB) antenna in that experimental campaign.

3. Plasma surface-sheath oscillations

Hot electrons are generated at the front surface of a thin foil target due to the interaction with intense short-pulse lasers. Some of these electrons pass through the target and are ejected from its rear surface, generating a strong charge separation on this side. This is capable to ionize the hydrocarbon impurities present on the rear surface and subsequently lead to the acceleration of these ions in the well-known process called Target Normal Sheath Acceleration [10]. In addition, the transient motion of such sheath leads to the classical emission of electromagnetic radiation [11], as depicted in figure 4a.

Figure 4.

(a) The formation process of a sheath on the rear side of the target, as a consequence of the laser–target interaction and the associated electromagnetic emission. (b) Typical signal detected in experiments where the Flame laser (35 fs, ∼10¹⁸ W cm⁻², energies up to a few joules) was focused on 0.7 µm thick commercial razor blade. Figure 4b is reprinted from [12] under Creative Commons license. (Online version in colour.)

The duration and the consequent spectral features of this process are related to the electron ejection from the target, and thus to the specific laser–plasma interaction, i.e. to the laser pulse regime and to the volume and geometry of the ionized region. Electromagnetic radiation with a bandwidth of several tens of GHz [12] and up to the terahertz level [13] has been demonstrated by tailored measurements. In figure 4b, a typical emission is shown for experiments performed at the Flame facility with laser pulses of 35 fs, ∼10¹⁸ W cm⁻² intensity and maximum energy of a few joules, focused on a stainless steel sharp target (0.7 µm thick commercial razor blade) [12]. Fields up to the MV m⁻¹ order, with Gaussian time-profile and 3 dB band up to 40 GHz, were there measured at 6 mm from target. For this mechanism, the wavelengths of the emitted fields are typically small in comparison with the dimension of the vacuum chambers that are used for these experiments, and far-field conditions are easily met. Since the current is normal to the target surface, the emission is as from a horizontal dipole and is represented in figure 5 in the xz and yz planes.

Figure 5.

The far-field emission geometry of the structure constituted by the target and its holder, in the xz plane (a), and in the xy plane (b). (Online version in colour.)

4. Transient charged layers due to photoionization

The interaction of intense lasers with matter can generate a notable amount of UV, X and γ rays. When these photons impinge on the surfaces of objects exposed, they produce the photoemission of electrons, causing the consequent positive charging of the irradiated surfaces and the generation of a sheath. A scheme of this phenomenon is represented in figure 6.

Figure 6.

The scheme illustrating the creation of a zone of charge separation due to photoionization produced by UV-X-γ radiation impinging on the surface of an object. (Online version in colour.)

This scheme is more effective for UV-X radiation rather than γ, which is weakly interacting with materials. On dielectric surfaces, it creates and sustains sheaths for a time duration related to the plasma emission from the target. In general, this EMP source is of interest whenever objects are located close enough to the interaction point, and normally the associated field intensity strongly decreases with the distance from target. These fields may have a broad spectrum in experiments with short laser pulses. If the exposed objects are instead conductive and connected to the chamber surface, a transient current can be also generated on the object surface, which then behaves as an antenna, similarly to what discussed in §2.

This phenomenon was first observed for objects exposed to nuclear explosions, and called system-generated EMP [14]. In that case, the ionizing electromagnetic radiation was generated by the nuclear bursts and was in the X-γ region.

This EMP source was observed in experiments at the ABC laser and estimated in the hundreds kV m⁻¹ order of magnitude at a distance of approximately 10 cm from a thick Al target interacting with laser pulses of 3 ns duration, tens of joules energy, and focused intensities up to 5 × 10¹⁴ W cm⁻² [15,16]. Further experiments on the PALS laser (400 J, 300 ps, ∼10¹⁶ W cm⁻²) showed intense fields due to this mechanism [17].

5. Deposition/secondary emission of particles on surfaces

Charged particles accelerated in laser–target interactions propagate in the vacuum and eventually reach the surfaces of objects placed inside the experimental chamber. They may be thus either implanted in dielectrics, or accumulated in conductors, and the related fields are generated as in classical capacitors (figure 7a).

Figure 7.

(a) A scheme of the laser-accelerated particles emitted from the target impinging on an object inside the experimental chamber, modelled here as a disc, charging it and generating an electric field. The secondary electrons emitted by the disc are here also included (b) The electric fields for different shots by the D-Dot probe placed behind the focusing parabola in the Vulcan experiment. Figure 7b is reprinted from [18] under Creative Commons license. (Online version in colour.)

This occurs for both incoming electrons and ions. Electrons of low energy may also generate, on the same surfaces, secondary electron emission, which plays a relevant role in the ‘local' charging process [18]. This is more effective for the lower energy component of the electron spectrum. Moreover, when the charge is collected on conductive surfaces physically connected to the chamber walls, a current can be generated. This is another source of EMPs, similar to the classical antenna discussed in §2. When these charged particles eventually reach the chamber wall, the accumulated charge is distributed equally on the latter, thus driving transient surface currents which are also a source of radiation.

For an expanding particle beam, more charges can be accumulated on the same surface S when this is closer to the target. The electrical field associated with a surface charge σ is E = σ/(2ε₀), where ε₀ is the electrical permittivity in vacuum. So larger fields will be obtained at shorter distances from the target. On the other hand, up to microcoulomb charges can be emitted in experiments with energetic lasers, and this can lead to high fields even at large distances from the target. Moreover, if the charged surface is close to one of the conductive chamber walls, possible at large distances from the target, a charge of the opposite sign will be induced on the latter, and a configuration similar to a parallel-plate capacitor may be obtained [18]. The field between the plates will be increased (doubled, in an ideal parallel-plate capacitor), and that outside the two-plate region will be thus decreased or neutralized. Indeed, the maximum potential energy in the capacitor cannot be larger than the energy of the incoming charged particles, and this imposes an upper limit to the accumulated charge and to the associated electric field.

The first experimental observation of these transient electromagnetic fields was reported in [18] for experiments performed at the Vulcan Petawatt laser, with laser pulses of λ = 1054 nm, ∼400 J energy, ∼1 ps duration and ∼10²¹ W cm⁻² intensity on parylene-N plastic foil. The fields were detected by means of a D-dot probe placed behind a glass mirror at a distance ∼2 m from the target. Some measurements, performed for different target thickness and laser energy, are shown in figure 7b. The large emitted charge produced fields in the MV m⁻¹ range even at a large distance from the target, with rise time of a few tens of ns and an associated bandwidth in the order of tens of MHz, due to ion deposition [18]. In the case of electron deposition, the rise times may be much shorter and thus the associated bandwidths larger. In the same measurements, the EMP contribution due to the neutralization current flowing through the target holder, described in §2, is also visible as an amplitude modulation of the detected signal, with amplitude decreasing with time and lasting for a few hundreds of nanosecond. It is found to be much smaller than the field due to charge accumulation, which is explained by its large dependence on the target distance.

6. Quasi-static electric wakefields from charges accelerated by laser–matter interaction

Charges accelerated from the target in laser–matter interaction propagate in vacuum at a constant velocity. They thus do not emit waves, but they indeed carry an electromagnetic field with them [11]. This field can be detected also at locations not precisely in the path of the particle beam, but anyway rather close to it, and its intensity decreases with the distance from the particle bunch and from the target. If these charged bunches pass close to a conductor, they can induce a charge displacement on it, and then currents. These wakefields can be generated by both electron and ion bunches. Figure 8 shows a schematic drawing of the wakefields associated with charges in motion from the target after laser–matter interaction.

Figure 8.

Schematic drawing of the wakefields generated by the particles in motion from the target after laser–matter interaction. (Online version in colour.)

Measurements of wakefields due to hot electrons with energies up to 10 MeV have been reported in [19] for experiments with the Flame laser and with pulses of 35 fs duration, intensity up to approximately 10¹⁸ W cm⁻² and energy of 4 J. Wakefields due to ion bunches were reported in [15,16] where a 3 ns laser pulse with ∼40 J energy and ∼5 × 10¹⁴ W cm⁻² intensity was used. In both of these experiments, electro-optical techniques were used to diagnose these fields in different configurations. The wakefields coming from these beams can reach intensities of hundreds of kV m⁻¹ near the direction of maximum particle emission, and their strength should be significantly dependent on the distance to the accelerated beam.

7. Configuration of the electromagnetic pulse field distribution inside the experimental chamber

As discussed so far, there are several mechanisms that lead to the generation of intense transient electromagnetic fields as a consequence of the laser–matter interaction. The associated fields, each with its own features and space distribution, superimpose in the interior region of the vacuum chamber where the laser–plasma interaction occurs. Table 1 presents a summary of main characteristics of the electromagnetic fields due to each of those mechanisms.

Table 1.

Characteristics of the EMP sources.

field source	distribution	intensity decreasing from	max fields	max temporal duration	max frequency range
neutralization current	vertical monopolar antenna	target $\sim r^{-\alpha }$ with $\alpha <2$	Several MV m−1	100s ns	10s GHz
surface-sheath oscillations	horizontal dipolar antenna	target $\sim r^{-2}$	MV m−1	some ps	10s GHz to THz
charged layers due to photoionization	close to surfaces exposed to UV-X-γ	target and from exposed surfaces	MV m−1	some ns	10s GHz
wakefields of accelerated charges	close to the charged particle beams	charged particle beams and target	∼MV m−1	10s ns	100s GHz
particles on surfaces	close to surfaces, even far from the target	exposed surfaces and target	MV m−1	10s ns	approximately 10s MHz to GHz

Fields generated by the neutralization current and by the plasma surface-sheath have their maximum close to the target. Even if these mechanisms are efficient radiators and may emit a large part of the overall EMP energy, their fields rapidly decrease with the distance from the source. On the other hand, the other contributions, that should in principle carry a smaller part of the overall EMP energy, can produce fields much more intense in regions close to the surfaces exposed to particle and electromagnetic ionizing radiation emitted from the target, or close to charged particle bunches. As mentioned in §5, the fields due to the accumulation of charges, on a collector approximately 2 m far from the target, can be several times stronger than the EMP fields caused, in the same experiment, by the neutralization current and the plasma surface-sheath [18]. It is important to take this into account when positioning electronic devices within the experimental chamber. The distance from target is thus not the only critical parameter to consider.

In order to have a suitable picture of the overall field distribution within the experimental chamber, it is of high importance to develop numerical codes capable to deal with all these EMP contributions. It is really not straightforward, and requires the precise knowledge of each object present within the chamber. This is a significant issue, since in typical experiments the number and the position of objects change on a shot-to-shot basis. Moreover, it is necessary to have a clear and complete description of the fields emitted by each of the source mechanisms, although their characterization in different laser regimes is still far to be complete.

A significant issue to consider whenever modelling the overall EMP distribution is that the internal region of the vacuum chamber is an environment that changes over time, because of particle emission from the target, and cannot be thus considered as a time-invariant homogeneous medium. Electrons, ions and plasma, generated at the interaction point, gradually fill up space in the chamber, and their presence can effectively influence the propagation and spatial distribution of the EMP fields. The electron density has a maximum of approximately 10²¹–10²² cm⁻³ at the target, close to the critical density associated with the wavelength of the laser radiation, and decreases to negligible values in proximity of the chamber walls. So, a large gradient of concentration is present in the chamber during and after the interaction.

Hot electrons emitted from the target are followed by slower ions, in bunches that can be considered quasi-neutral [20]. Thus, the electron spatial distribution over time in these bunches can be related to the associated ion distribution: $n_e(\mathit{r},t)\sim (Z_{\text{eff}}\text{/}e)n_i(\mathit{r},t)$, being $n_e(\mathit{r},t)$ and $n_i(\mathit{r},t)$ the electron and ion densities at the position r and at the time t after the laser–target interaction, respectively, Z_eff the effective ion charge state and e the electron charge. The associated spatial distribution of the plasma frequency is determined by the formula:

$${\omega }_p(\mathit{r},t)=5.64\times {10}^4\sqrt{n_e(\mathit{r},t)},$$ 7.1

where n_e is in cm⁻³ and ${\omega }_p$ is in rad s⁻¹ [20]. From this equation, the critical plasma electron densities associated with EMP waves in the (0.1; 3) GHz range lay in the ≈10⁸ to ≈10¹¹ cm⁻³ interval. Figure 9a shows the ion charge density over the radial distance DOF (Distance Of Flight) from target, at 8 ns and 20 ns after the end of the laser pulse in an experiment where a Pb foil was irradiated with an intensity of 3 × 10¹⁶ W cm⁻² at the PALS laser facility.

Figure 9.

(a) Example of ion charge density over the radial direction (DOF, distance of flight)) at 8 and 20 ns after the end of laser pulse, in an experiment with the PALS laser on a Pb foil irradiated at intensity 3 × 10¹⁶ W cm⁻². (b) Reflection of EMP waves emitted by the neutralization current mechanism by the bunch of charged particles emitted from the target. (Online version in colour.)

According to figure 9a, these electron densities can be easily obtained in wide regions within an experimental chamber typical for these experiments, and for a time interval of several tens to hundreds of nanosecond after the laser shot. A particle cloud with critical density for a given wave can potentially behave as a reflective medium. This space–time distribution of the critical electron density may cause, in each region of space, a reflection of waves having frequencies equal or lower than the critical one in that region. Since the EMP duration is comparable with the duration of the plasma occurrence within the chamber, it follows that the expanding plasma would affect the distribution of the EMP emissions. Moreover, since the plasma configuration also changes over time [20], this can lead to multiple wave reflections at different time instants. Figure 9b shows a scheme where EMP waves emitted by the neutralization current mechanism described in §2 are reflected by a bunch of plasma emitted from target. A thorough description of the electromagnetic pulses generated in laser–matter experiments should thus include the influence of the emitted particle beams on the propagating waves.

8. Conclusion

In this paper, we explored and compared several sources of transient electromagnetic fields in the radiofrequency-microwave regime generated in the laser–matter experiments with high-energy and high-intensity lasers. Depending on the position within the chamber, local mechanisms can generate EMPs more intense than those produced by the central sources. We have also shown that to have a complete view of the electromagnetic field distribution within the experimental chamber it is necessary to take into account the interaction of these electromagnetic waves with charged particles emitted from the target because of the laser interaction.

Full understanding and modelling of these intense fields is a primary topic for the correct operation of the modern laser facilities, and a breakthrough-enabling issue for future laser facilities, where higher laser energies and intensities will produce higher EMP levels and thus more serious associated problems.

Nevertheless, there are also several promising applications of these huge fields that can become a reality [1], if the source mechanisms will be fully characterized.

Data accessibility

Several figures are reported from the references, and correctly cited in the associated captions. The datasets of new data in figures 1 and 9a are available as electronic supplementary material.

Authors' contributions

F.C. prepared the first draft of the paper which was then extended and revised by the other authors. All the authors contributed to its final form and editing.

Competing interests

We have no competing interests.

Funding

This work has been carried out within the framework of the EUROfusion Consortium and funded from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement no. 633053. Part of this work was realized within the project 19-02545S with financial support from the Czech Science Foundation. The views and opinions expressed herein do not necessarily reflect those of the European Commission.