Effect of transverse magnetic field on hot electron and ion fluxes generated by laser interactions with disc-double-coil targets

Abstract

Success of hitherto experiments carried out on PALS using disc-coil (DC) targets irradiated by 1ω and 3ω beam of the PALS laser, in which magnetic fields of axial geometry with respect to the laser beam axis and induction above 5T were generated, initiated a complementary research directed on creation of magnetized plasma jets in a magnetic field with transverse geometry of force lines in relation to the laser direction. This configuration is important for implementation of inertial fusion by magnetic implosion. In order to understand the influence of the transverse magnetic field on the emission parameters of hot electrons (HE) and ions from the ablation plasma, innovative disc-coil targets (DCT-DC) were used, consisting of a Cu disk coupled with a system of two coils. Comprehensive diagnostics included 2D and 1D space-time resolved imaging of the Cu Kα line emission, a multichannel magnetic electron spectrometer was used to measure the angular distribution of the HE energy spectra. Ion collectors, target current probes, X-ray spectroscopy, and plasma visualization in the soft X-ray range using a 4-frame X-ray camera were used as additional diagnostics. To characterize the plasma streams created under Cu-discs irradiation by laser beams and to determine the regions with electron density corresponding to the most probable mechanisms of the HE generation, were defined by 3-frame complex interferometry. Numerical simulations of experimental results based on the three-dimensional PIC code EPOCH provided a basic insight into mechanisms of HE propagation in a transverse magnetic field. The performed experiments demonstrated that the presence of the transverse magnetic field leads to a spatial broadening of the HE emitting region and to an increase of the HE energy, both in the backward and forward direction from the target. The increased fluxes of higher energy HEs observed at 1ω irradiated targets agree with results of simulations.

Introduction

An occurrence of the electron density and temperature gradients in a laser-produced plasma with external magnetic fields can cause drift motion or rotation of the plasma. Therefore, understanding the interaction of high energy density electron fluxes with external magnetic field is a challenge for upgraded laser-driven secondary sources of energetic particles and radiation. In laboratory experiments, a magnetic flux density in the kilo-Tesla strength is required to reveal the influence of external B-fields on the produced plasma under conditions of high-energy density plasma. Currently, there are several ways to generate such strong B-fields in close proximity to the laser-produced plasma using high-power lasers. When the laser beam interacts with the target, a current up to the level of 10-kA flows between the ground to the target. This current is driven by the positive charge created on the target due to the escaped thermal and hot electrons^1,2. Insertion of miniature coils into the target-ground circuit allows to generate a very strong magnetic field inside the coils. The size of these coils, their location relative to the expanding plasma, and the magnitude of the return target current offer a variety of conditions for interaction of the external B-field with the expanding plasma. The progress in manufacturing of advanced target systems consisting of disc and coils supports a design of experimental configurations coupling a strong external B-field with the laser produced plasma, where the B-field axis is perpendicular to the expansion vector of the plasma ablation. The anticipated reduction and an increase of the plasma production and expansion due to the action of the external B-field can significantly affect all plasma parameters. We note that the expanding plasma is not affected by the external B-field only, but also by self-generated B-fields resulting from perturbations or filamentations caused by hydrodynamic instabilities^3,4,5.

Hitherto research initiated within the PALS iodine laser system experiments has confirmed the possibility of generating an axial magnetic field above 5 T by irradiating the disc-coil target with the 1 st or 3rd harmonic frequencies of the laser beam with an energy of approximately 0.5 kJ. Considering the scheme for realization of inertial fusion by magnetic implosion of laser targets⁶, it seems that such magnetic field is sufficient to achieve an induction level of several kilo-Tesla in the compressed core of the fuel target due to advection. Similar strong magnetic fields are promising for realizing the magnetic inertial fusion because they reduce the energy losses in the direction perpendicular to the magnetic field lines, thus limiting the fusion of α particles to the region of the compressed core and the formation of so-called hot spots incipient thermonuclear ignition.

The success of previous studies generating magnetic fields coaxial with axis of the 1ω or 3ω laser beam incident on DC targets^7,8 became the motivation to undertake research on creation of magnetized plasma jets with magnetic field geometry transverse to the laser direction. This idea was tested on targets shown in Fig. 1b, which facilitate creation of the magnetized plasma expanding transversely to the magnetic field lines.

To understand the effect of the transverse magnetic field on hot electron (HE) and ion emission, routine diagnostics available at PALS were used, allowing both visualization of HE emission and quantitative assessment of their temperature and energy. The principal diagnostic methods represent the 2D and 1D space-time resolved imaging of the Kα₁ line emission from Cu targets and measurements of angular distribution of the emitted HEs using a multi-channel magnetic electron spectrometer. Further supporting diagnostics included a grid collector system measuring the ion emission parameters, return current measurements through the target coil system associated with the HE emission, as well as a 4-frame X-ray pinhole camera allowing for visualization of the process of interaction of the ablation plasma with the transverse magnetic field generated by the DCT-DC target coils. A particularly useful diagnostic was multi-frame interferometry identifying the regions of critical density n_e−cr, 0.25n_e − cr, and 0.1n_e − cr, necessary to define the initial conditions for numerical simulations with the EPOCH code⁹.

Experimental and theoretical investigations of the influence of laser-driven strong, quasi-static magnetic fields on the evolution of laser-generated plasmas performed at the PALS Laser Facility complement experiments undertaken in this field at other laser facilities reported in¹⁰. The review¹⁰ presents potential problems with diagnostic analyses that can lead to overestimation of the magnetic fields generated from laser-driven coils. At the PALS Laser Facility, we use optical complex polaro-interferometry of magnetized plasma and accurate diagnostics of the return target current driving the coils producing transversal magnetic field to have a consistent picture for these diagnostics. For numerical simulations, additional insights into the mechanisms of hot electron propagation in a transverse magnetic field were provided by data from measurements of CuKα emission lines and energy spectra of hot electrons escaping from the plasma and causing the target current.

The paper is structured as follows: In section II the experimental set-up is presented including description of the target construction and diagnostics used. Section III includes results of diagnostic measurements and their discussion. In section IV, the results of 3D numerical simulations demonstrating influence of the transverse magnetic field on the HE emission are shown. General conclusions of the performed studies are discussed in section V.

Experimental setup

The experimental set-up for studies of the transverse magnetic field effect on the expansion of the ablative plasma, created from DCT-DC targets, Fig. 1b, accompanied by the electron and ion emission, is presented in Fig. 1a. The target complex consists of two coaxially arranged coils connected to a copper disk, which is irradiated by a laser. The return target current passing through the coils induces a magnetic field in the coils with a geometry of the lines of force perpendicular to the direction of the laser beam irradiating the disc. To vary the intensity of the magnetic field, discs with coils of different diameters (φ_coil = 1 and 1.5 mm) and different distances of the coils from the disc (d = 0.8 and 1.2 mm) were used.

Fig. 1

Experimental setup: (a) a scheme of the diagnostics configuration in the experimental chamber, (b) DCT-DC target construction for creating a magnetized plasma stream in a transverse magnetic field and the way of irradiating it with a laser beam.

The influence of the transverse magnetic field on emission parameters of hot electrons (HE) and ions from the ablation plasma was investigated by interaction of the fundamental 1ω (wavelength λ₁ = 1315 nm, energy E_L ≈ 500 J, pulse duration τ_L ≈ 350 ps) and the frequency tripled radiation 3ω (λ₃ = 438 nm, E_L ≈ 200 J) of the PALS laser beam with Cu foil targets. In both cases the laser beam was smoothed by a random-phase-plate and then focused to a minimum radius of r_L= 50 μm.

A complex diagnostic system used facilitated the measurements of:

• space - time distribution of electron density in ablative plasmas using a 3-frame interferometric system^11,12,13,

• return target current flowing between the ground and target through the coil, using current probes^14,15,

• HE deposition inside the targets based on x-ray 2D space resolved¹⁶ or 1D space-time resolved imaging¹⁷ of the Cu Kα₁ line emission complemented by high-resolution Cu K-shell emission spectroscopy¹⁸,

• angular distribution of HE energy spectra emitted outside the target using a multichannel magnetic electron spectrometer¹⁹,

• ion emission parameters using grid collectors²⁰, and.

• visualization of the process of a magnetized plasma jet creation in the range of soft X-ray radiation, using a 4-frame X-ray camera^11,21.

The location of all diagnostics in the interaction chamber is schematically shown in Fig. 1a. Control shots with “bare” Cu discs were performed, allowing us to identify the impact of the B-field in the measurements.

Results of measurements

Interferometry results

To characterize the process of forming plasma jets created by irradiating targets with the 1 st and 3rd harmonic of the PALS iodine laser a 3-frame polaro-interferometer utilizing the Ti: Sa laser with a pulse duration of about 40 fs was used. This system allows to register 3-frame sequences of complex interferograms with an adjustable interval between individual frames. Three interferograms with a temporal interval of 300 ps between the frames allowed to cover the range from t = − 500 ps up to about t = 1000 ps, as defined by the first frame delay vs. the main laser beam maximum. The interferometric measurements give information on the space-time electron density distributions the ablation plasma generated by irradiating Cu disks with 1ω and 3ω, necessary for determining the initial conditions of numerical simulations modelling the influence of the magnetic field on the emission parameters of hot electrons. The key task is to determine the locations of the regions of critical density n_e−cr, 0.25n_e − cr, and 0.1n_e − cr, corresponding the two most probable mechanisms responsible for HE generation: (i) Stimulated Raman Scattering (SRS) and (ii) Two Plasma Decay (TPD).

In order to obtain information on the location of the above-mentioned critical density areas, two time sequences of interferograms obtained by irradiating Cu disks with 1ω and 3ω PALS iodine lasers were analysed, as shown in Figs. 2a and 3a respectively. The fringes brightening visible in complex interferograms are related to the Faraday effect, and their occurrence in the upper or lower half of the interferogram depends on the direction of the initial rotation of the polarizer in the polaro-interferometer system. In the case of clockwise rotation, the brightening occurs in the lower half of the interferogram, while in the counterclockwise direction, it occurs in the upper half. To obtain information about the space-time electron density distributions, the methodology presented in¹² was used, in which the phase distributions, depending on the quality of the interferogram, are obtained by Fourier analysis or the maximum fringe method. FFT is used to abelize the phase distributions. In our case, the subject of abelization were the averaged phase distributions obtained by the maximum fringe method using two halves of the interferogram.

The plasma expansion process in the case of irradiation of Cu disk with a 1ω PALS iodine laser is illustrated by the space-time electron density distributions, the linear-scale density distributions and axial concentration profiles obtained on their basis shown in Fig. 2, while the plasma expansion process created when irradiating the disks with a 3ω laser is illustrated in Fig. 3.

As Fig. 2b reveals, in the case of 1ω the electron density distributions show the spherical character of the plasma expansion, in contrast to the 3ω illumination where the axial nature of the expansion dominates. In the case of 1ω, the electron density distributions are characterized by a clearly smaller axial range compared to 3ω, which is confirmed by the linear density distributions (Figs. 2c and 3c). Moreover, in the case of 1ω the electron density distributions have a depression on the axis (visible on the axial profiles - Fig. 2d) in contrast to the distributions for 3ω, characterized by a maximum density on the axis (visible in Fig. 3d). In the case of 3ω the maximum electron density on the axis is several times higher than in the case of 1ω.

Fig. 2

(a) Sequence interferograms and (b) space time electron density distributions illustrating the plasma expansion process created by irradiating Cu disk with a 1ω iodine laser and obtained on their basis: (c) linear concentration distributions and (d) axial electron density profiles.

To obtain information on the location of the critical density regions, the method described in⁸ was used, which consisted in fitting the exponential function: n₀exp(-z/L), where n₀ is the density at a location corresponding to the original position of the front surface of the target and L is the scale-length. The exponential function fitted is based on two points: the first corresponding to the experimentally measured electron density at the point where the plasma becomes opaque and the second corresponding to the density of the solid state for Cu and the position z = −20 μm (to account for the resulting crater). Such fitted function was treated as an approximate description of the electron density profile of the plasma in the region where it is opaque and was used to determine the locations of the regions of critical density n_e−cr, 0.25n_e − cr, and 0.1n_e − cr,. The obtained results for the selected shots in the case of Cu-discs irradiation by 1ω are presented in Table 1, while Table 2 presents the results for 3ω. Based on the data from Tables 1 and 2, the dependence of the critical density position: n_e−cr, 0.25n_e − cr and 0.1n_e − cr as a function of the expansion time of the plasma created by 1ω and 3ω laser was obtained, which is illustrated in Fig. 4a and b, respectively.

Fig. 3

(a) Sequence interferograms and (b) space time electron density distributions illustrating the plasma expansion process created by irradiating Cu disk with a 3ω iodine laser and obtained on their basis: (c) linear concentration distributions and (d) axial electron density profiles.

Table 1 Position of areas with density: the n_e−cr, n_e−cr/4, n_e−cr/10 relative to the Cu-disc surface for different plasma expansion times, in the case of irradiation their by a 1ω PALS iodine laser.

Table 2 Position of areas with density: the n_e−cr, n_e−cr/4, n_e−cr/10 relative to the Cu-disc surface for different plasma expansion times, in the case of irradiation their by a 3ω PALS iodine laser.

By performing linear regression of the data, the critical density position: 0.25n_e-cr and 0.1n_e-cr was determined for t = 0 ps. The position of 0.25n_e-cr for t = 0 together with the parameters of the corresponding exponential function are required to define the initial conditions of numerical simulations modeling the influence of the magnetic field on the emission parameters of HE. In connection with the above, for the numerical simulation presented in section IV, as the most appropriate positions were chosen at z = 129 μm corresponding to 0.25n_e-cr in the case of 1ω and at z = 119 μm for 3ω, while for 0.1n_e-cr, both positions remain the same (z = 150 μm) for both harmonics.

Fig. 4

Dependence of the critical density position: 0.25n_e − cr and 0.1n_e − cr as a function of expansion time of the plasma created by: (a) 1ω and (b) 3ω iodine laser PALS.

It should be emphasized that the information obtained from interferometric measurements about the expansion character of the ablation plasma created by the 1ω and 3ω beams turned out to be very helpful for the interpretation of the angular distributions of energy and temperature HE obtained using a multi-channel magnetic electron spectrometer, which are presented in Section III.C.

Current probe measurements

The purpose of measuring the return target current flowing between the ground and target through the DCT-DC shield coil is to determine the magnetic field distribution generated by the DCT-DC shield coil system, which is necessary for numerical simulations using the EPOCH code. The measurement results of the time profiles of the return target current flowing through the DCT-DC coils are shown in Fig. 5.

Fig. 5

Time profiles of the return target current flowing through the coil system of the DCT-DC target.

The kiloampere return target current flowing between the target and the grounded interaction chamber was measured using inductive target current probe specially developed for this purpose¹⁴. The waveform of the return current j_T(t) was calculated by integrating the the probe output voltage (U_TB) as $\:{j}_{T}\left(t\right)=-\frac{1}{M}\int\:{U}_{TB}dt$, where M is the mutual inductance between the probe inductive loop and the return current conductor (target stalk); M ≈ 0.6 nH. The loop probe was placed near the target stalk, and both were shielded by a Faraday cage against EMP interference.

As results from the comparison, the time profiles of the current pulses are very similar for all DCT-DC target constructions and both laser wavelengths. The differences concern the maximum current amplitude, which is about 4 times higher in the case of 1ω compared to the illumination of the shields by 3ω. In particular, the current peak maximum at 1ω can exceed 3 kA (see Fig. 5a), whereas in the case of 3ω, the peak current maximum varies between 250 and 700 A (see Fig. 5b). We note that the current in coils with a diameter of Φ_coil = 1.5 mm is lower than in coils with a diameter of Φ_coil = 1 mm. It could be caused by higher inductance, which is proportional to the area enclosed by the conductor. This higher inductance increases the coil’s impedance and thus reduces the current. Assuming that the coils have a Helmholtz-like configuration and neglecting the wire diameter (50 μm), we can estimate the magnetic field at the center along the coil axis using a simple formula

$$\:B=\:\frac{{\mu\:}_{0}{I}_{coil}{\left(\frac{{\varPhi\:}_{coil}}{2}\right)}^{2}}{\left[{\left(\frac{{\varPhi\:}_{coil}}{2}\right)}^{2}+{\left(\frac{{L}_{c}}{2}\right)}^{2}\right]}$$

(1)

Here, L_c is the axial distance between the coils, and the coil current I_coil corresponds to half of the current measured by the inductive target current probe^14,15, since the probe measures the sum of the currents from both coils (see Fig. 1b). According to this formula, at 1ω the peak magnetic field approaches approximately 1 T and 0.8 T for Φ_coil = 1 mm and Φ_coil = 1.5 mm, respectively. At 3ω, the peak magnetic field is approximately 0.15 T and 0.1 T for Φ_coil = 1 mm and Φ_coil = 1.5 mm, respectively. Such magnetic fields are sufficient to affect the emission of electrons with the temperatures of 110 keV and 32 keV for the 1ω and 3ω, respectively. The full width at half maximum (FWHM) is of about 2 ns, which is about 6 times longer the laser pulse duration. The long-lasting target current and thus the long-lasting transverse magnetic field is the cause of the long duration of the XUV emission, as mentioned in the chapter devoted to the 4-frame X-ray pinhole camera measurements.

In conclusion, it should be emphasized that the measurements of the magnetic field induction in the DCT-DC disk coil system using current probes are consistent with the measurements of the magnetic field induction in the DCT-STCM disk using the Faraday effect in the TGG crystal, obtained in earlier experiments at PALS^7,8. In contrast to the results presented in¹⁰, which compared three different methods of measuring the magnetic field in the capacitor disks with a coil under the same experimental conditions, each method gives different results, namely: proton radiography − 95 T, B-spot probes − 600 T and Faraday rotation − 450 T. Such large differences in field measurements depending on the method used raised concerns about the reliability and applicability of these methods in the PALS experiment. For the above reasons, the method of measuring the magnetic field in DC targets using a target current probe was chosen as a straightforward and sufficiently reliable tool for conducting the research presented in this article.

X-ray imaging and spectroscopy of HE-induced Cu Kα line emission

The influence of the transverse magnetic fields generated at DCT-DC targets on the HE energy population and deposition inside the laser irradiated targets was studied by high-resolution x-ray spectroscopic methods analysing the HE-induced Cu K-shell line emission. The efficiency of the laser energy conversion into the HE energy including its absolute dose and spatial distribution along the target surface was characterized by time integrated 2D space resolved Cu Kα₁ imaging¹⁶. The information on the HE duration and delay vs. the laser pulse maximum was obtained from 1D space-time resolved imaging¹⁶. Both systems were equipped with spherically bent crystals of quartz (422), the data were recorded using the imaging plate or x-ray streak camera, respectively.

A comparison of 2D space resolved images of the HE-induced Cu Kα₁ emission obtained by 1ω and 3ω laser irradiation of targets with different coil diameters Φ and different distances d between the coil and the Cu disc is presented in Fig. 6. The detailed reproducibility of images recorded by using the 1ω radiation (Fig. 6a) is reduced due to a limited number of available laser shots but the characteristic features of these records are well demonstrated. All images taken at DCT-DC targets display an enhanced Cu Kα₁ emission from the disc rim. The size of the central brightly emitting spot is increased compared to the emission from the bare Cu disc, which means that the radial distribution of the Kα emission is broadened in the presence of the magnetic field. The spatially integrated signal proportional to the generated HE dose and the laser to HE conversion efficiency are also considerably larger (see Table 3). The visualized positions of the magnetic field generating coils are ascribed to the Cu Kα₁ fluorescence due to the plasma corona radiation and the particle fluxes streaming from the target. The images recorded by irradiating the targets with the 3ω laser beam (Fig. 6b) are characterized by a lower Cu Kα₁ emissivity in accordance with the decreased coupling factor Iλ² where I is the laser intensity and λ the relevant wavelength. Consequently, the generated HE dose and the laser to HE conversion are also reduced (see Table 4). On the other hand, the FWHM size of the Cu Kα₁ emitting area is considerably larger compared to the 1ω case. This phenomenon observed at both bare Cu and DCT-DC targets can tentatively be ascribed to diverse focusing conditions of the random phase plate smoothed 3ω radiation but alternatively also to an enhanced lateral transport and deposition of the laser energy along the target surface. Finally, this could beintroduced by nonlinearities, which arise from strong laser-plasma coupling, make the system more sensitive to even small changes in the focusing conditions, and lead to larger changes in electron transport through the plasma.

The more pronounced increase of the FWHM size of the Cu Kα₁ emitting area due to the action of the coil-generated electromagnetic field relates to interplay between the enhanced characteristic energy of the emitted HEs and their deflection at the coil-induced magnetic field. These results were confirmed by numerical simulations (see section IV).

Fig. 6

Comparison of 2D space resolved images of the HE-induced Cu Kα₁ emission from the plasma created at DCT-DC targets with coils of different diameters Φ positioned at variable distances d from the Cu disk irradiated by: (a) 1ω and (b) 3ω PALS laser beam. On the right side, the reconstructed records of the time integrated Cu Kα₁ emission from the bare Cu discs are shown.

The 2D space resolved images shown in Fig. 6a, b are supplemented by detailed spatial profiles of the HE-induced Cu Kα₁ intensity distribution at the target surface in the horizontal plane (Fig. 7). The presented graphs demonstrate that in the case of the 1ω laser irradiated bare Cu targets (i.e., not affected by an additional magnetic field), the FWHM width of the Kα₁ emission is almost twice as small as the FWHM width observed in the case of 3ω irradiation. The presence of the transverse magnetic field results in lower-level of the Kα emission, both when irradiating the DCT-DC discs by 1ω and 3ω laser pulses. The influence of the magnetic field on the space and time integrated Cu Kα₁ emission is larger for discs with a smaller coil diameter and a smaller distance between the coil and the Cu disc, which is in line with expectations.

Fig. 7

Horizontal cross-sections derived from the Cu Kα₁ intensity distributions shown in Fig. 6 characterize diversity of HE energy deposition in DCT-DC targets irradiated by 1ω and 3ω laser beam.

A more detailed quantitative information on these shots including the FWHM values of the HE-induced spatial profiles in the horizontal and vertical cross-sections, space-integrated signal Σ_signal recorded on the imaging plate, corresponding dose of HEs created close to the surface of irradiated Cu discs and the laser-HE energy conversion are surveyed in Tables 3 and 4. We note that the absence of X-ray streak camera data in Table 3 for the last 3 shots was due to a camera problem.

The displayed characteristics include the laser shot identification, energy and pulse duration, spatial extent of the HE-induced Cu Kα₁ emission, time and space integrated HE signal, its recalculation to the HE dose and the laser to HE energy conversion efficiency. The 1D space-time resolved imaging provides information on FWHM duration, spatial extent and temporal delay of the HE action vs. the laser maximum.

Table 3 HE emission parameters from DCT- DC targets irradiated by 1ω PALS laser: (1) FWHM extend (horizontal and vertical), µm, (2) signal, ph/IP, (3)HE doze, J, (4) conversion, % (5) HE FWHM duration, ps, (6) HE FWHM extent, µm, (7) HE/laser delay ps.

These data derived from 2D space resolved images are complemented by characteristics of the HE interaction with targets measured using the 1D space-time resolved imaging. The most important finding following from these data is that the presence of transverse magnetic fields increases the HE energy deposition in the Cu target material. The found FWHM values of the temporal HE action are always longer than those of the laser pulse duration. The values measured for 1ω laser shots are shorter than those observed in 3ω shots. Here we note that the increased duration of the 3ω laser induced signal may consist in a stronger contribution of the corona emission which is negligible for 1ω case. The found FWHM values of the HE spatial extent are systematically smaller compared to analogous data derived from 2D imaging. An explanation of this inconsistency may partly follow from diverse angles of Cu Kα₁ observation, as the time integrated and time resolved images were recorded at angles of 29º and 55º vs. the target surface, respectively. The decisive factor however consists in a much better spatial resolution of 1D imaging (at the level of 3.22 μm as recalculated to the source position), whereas the resolution of the 2D imaging is limited by resolution of the imaging plater used (at the level of 40 μm).

Table 4 HE emission parameters from DCT- DC targets irradiated by 3w of iodine PALS laser: (1) FWHM extend (horizontal and vertical), µm, (2) signal, ph/IP, (3)HE doze, J, (4) conversion, % (5) HE FWHM duration, ps, (6) HE FWHM extent, µm, (7) HE/laser delay ps.

The last important parameter derived from the 1D space resolved imaging is the temporal delay between the maxima of the Cu Kα₁ emission and the laser pulse. At bare Cu disc targets, this delay is practically zero, whereas at DCT-DC targets the found delay values are always negative, i.e. the maximum of HE-induced Cu Kα₁ emission precedes the laser maximum. This earlier culmination of the HE energy deposition inside the targets can be ascribed to an advanced action of the transverse magnetic field. A full explanation of all these effects, however, requires further investigation, both experimental and theoretical. An increased deposition of hot electrons in laser irradiated targets due to transversal magnetic fields produced near the target surface was confirmed by advanced x-ray spectroscopy²². The Johann type spectrometer equipped with the quartz (223) crystal spherically bent to a radius of 150 mm observed the Cu K-shell emission from 1ω laser-irradiated targets at an angle of 39º vs. the laser axis, as shown in Fig. 1a. The time integrated spectra were again recorded on absolutely calibrated imaging plates with magnification M = 0.4. An example of the spectra recorded at different type targets irradiated by 1ω is depicted in Fig. 8, the bound-bound transitions corresponding to different ionization states are identified. The covered photon energy range 7950–8500 eV surveys the Cu emission at bulk electron temperatures ranging from a cold target material to the hot corona plasma. The analysis of the HE action was limited to the Cu Kα group in the photon energy window of 8020–8100 eV including M-shell charge states emission, as these states exist only for bulk electron temperature lower than ~ 200 eV. This temperature is too low to ionize the inner-shell of mid-Z elements, and, consequently, x-ray lines are mostly induced by HEs²³. Based on collisional-radiative code FLYCHK calculations²⁴, the increase in the Kα group emissivity integrated over the range of 8020–8100 eV is directly proportional to a magnetic field affected fraction of HEs interacting with the target. Compared to bare Cu disc, the emissivity observed at DCT-DC targets grows by a factor up to 1.6 which agrees reasonably well with conclusions of the 2D space resolved imaging data displaying HE deposition increase by a factor up to 1.46.

Fig. 8

Magnetic field affected Cu M-shell charge states emission from DCT-DC and bare Cu discs.

To resume this section, the quantitative analysis of the monochromatic HE-induced Cu Kα₁ images and high-resolution Cu K-shell spectra recorded at different configurations of DCT-DC targets irradiated by 1ω and 3ω PALS laser allowed to obtain information on:

• HE energy deposition in the target center and rim,

• conversion efficiency of the laser into the HE energy,

• spatial extension profiles of the magnetic field affected HE emission, and.

• temporal profiles of the HE emission including a delay between the maxima of the Cu Kα₁ emission and the laser pulse.

Multi-channel magnetic electron spectrometer

The measurements were carried out using a multichannel electron spectrometer described in the paper¹⁷, which recorded HE spectra at angles: −65^o, −44 ^o, −25 ^o, 0 ^o, 23 ^o and 48 ^o in the horizontal plane in relation to the main laser beam, Fig. 1a. The aim of the measurements was to obtain information on the influence of the transverse magnetic field on the angular distributions of energy and temperature of hot electrons (HE) emitted from the magnetized plasma created using DCT-DC targets of the construction shown in Fig. 1b as a result of irradiating them with a 1ω and 3ω PALS iodine laser beam focused to a minimum radius of r_L=50 μm. The basis for obtaining information on the distributions of HE energy and temperature are the energy spectra from individual channels of the multichannel spectrometer, obtained for different constructions of DCT-DC targets irradiated by 1ω and 3ω PALS iodine laser presented in Fig. 9. The spectra reveal the influence of the transverse magnetic field on the angular distribution of HE energy as a function of the PALS iodine laser wavelength, the coil diameter, and its distance from the Cu-disc. This refers to the HE emissions observed at an angle of 0^o to the laser beam. In the case of 1ω, the HE energy range is more than three as large compared to 3ω.

Fig. 9

The energy spectra from individual channels of the multichannel spectrometer, obtained for different constructions of DCT-DC targets irradiated by 1ω (a) and 3ω (b) PALS iodine laser.

Fig. 10

Angular distributions of the number of particles per unit solid angle, maximum energy and HE temperature obtained for DCT-DC targets with a coil of different diameter and a distance d = 0.8 mm from the Cu disc in the case of irradiation by: (a) 1ω and (b) 3ω PALS iodine laser.

Regarding the angular distribution: all data as the number of particles per unit solid angle, the maximum energy and HE temperature obtained for DCT-DC targets with a coil of different diameter and a distance of d = 0.8 mm from the Cu disk, irradiated by 1ω and 3ω PALS laser are shown in Fig. 10, while in Fig. 11 the above distributions are shown for a larger distance of d = 1.2 mm. First of all, it should be emphasized that in the case of free plasma expansion, the angular HE flux distributions reflect the spherical plasma expansion in the 1ω case and the axial expansion in the 3ω case, as demonstrated by the electron density distributions presented in Section III.A. In the case of 1ω, Fig. 10a, the HE flux value on the axis is only several times higher than the HE flux value outside the central region (for angles <−2^o and > + 2^o), which results from the depression of the electron density distribution on the axis related to the spherical expansion, in contrast to 3ω, Fig. 10b for which the HE flux on the axis is over an order of magnitude higher than in the region outside the central region, which is caused by the maximum electron density in the central region caused by the axial expansion.

Fig. 11

Angular distributions of the number of particles per unit solid angle, maximum energy and HE temperature obtained for DCT-DT targets with a coil of different diameter and a distance d = 1.2 mm from the Cu disc in the case of illumination by: (a) 1ω and (b) 3ω PALS iodine laser.

The external magnetic field causes changes in the HE flux, very noticeable near the axis in the angle range from − 20^o to 20^o, but also changes in the HE energy and temperature in the entire observed angle range, depending on the irradiation of the DCT-DC 1ω or 3ω laser. In the case of 1ω and 3ω and for the coil with a smaller radius and a smaller distance between the coil system and the Cu disc, both the HE energy and temperature are clearly higher in the whole range of observation angles compared to the free expansion. In the case of 1ω the HE energy reaches a maximum value on the axis of about 850 keV, and the corresponding HE temperature is 110 keV, while for 3ω, both the HE energy and temperature are much lower and are: HE energy of about 320 keV and temperature 32 keV respectively.

For larger coil diameters and larger distances between the coil system and the Cu disc, Fig. 11, the HE emission parameters are correspondingly smaller.

Measurements of ion emission parameters using grid collectors

The aim of the ion measurements was to obtain information on the influence of the transverse magnetic field on the ion expansion process, using grid collectors arranged in the vertical plane at different angles to the main laser beam, see Fig. 12. An additional measurement system, designed to capture the ion beam declination in terms of the spatial shift of the maximum of dose distribution absorbed by the radiochromic film, was also implemented to confirm presence of the magnetic field (Fig. 13).

Fig. 12

Geometry of the measurement of the ion beam shift recorded on the image plate.

Due to the direction of the current flow through the coil, positively charged particles were expected to deflect their trajectory vertically in the direction of higher angles, following the scheme on Fig. 12. The RCF camera that was mounted at the 45^o consisted of the aluminum housing with 1 mm wide vertical slit and a RCF stripe mounted inside. The entrance of the slit was covered with 3 μm thick Al foil in order to filter out the heavier ions and protons of energy lower than 200 keV. As displayed on the Fig. 13, for 3ω laser beam shots on DCT-DC targets during which the device was installed, the distribution of absorbed dose was visibly shifted along the slit length, compared to the shots performed on Cu disk targets, exhibiting significantly higher signal for the positions along the X axis corresponding to the bigger angles.

Fig. 13

Results of RCF camera measurements, displaying a tendency of shifting the maximum of registered signal away from the laser propagation axis and increasing the absorbed dose at higher angles when DCT-DC targets were used (61,239–61,243). Vertical lines show example of displacement of signal maximum based on comparison of averaged signal for flat targets and signal from shot 61,243.

The spatially resolved ion charge density map shown in Fig. 14 was derived from time-resolved ion currents measured using²⁰ grid collectors placed vertically in the front of the target, as shown in Fig. 12. The maps were calculated for the time 0.7 µs that has elapsed since the laser interacted with the target¹¹. Figure 14(a) shows a comparison of the angular distribution of ion charge density from the DCT-DC target system (left half of the image) with the free emission of ion created from the Cu-discs (right half of the image) irradiated by the 1ω laser beam, while Fig. 14b shows the results for 3ω laser beam. The charge density distributions clearly demonstrate the influence of the transverse field on the nature of the ion expansion depending on the irradiation of the DCT-DC targets by 1ω and 3ω PALS iodine laser. In the case of the 1ω laser, the presence of the perpendicular magnetic field forces the ion stream to expand axially in the central area and causes radial emission in the outer areas as demonstrated by Fig. 14a. For the 3ω laser the situation is reverse, the magnetic field restricts the axial expansion of ion in the central area, and enhances the radial expansion of ions in the outer regions as shown in Fig. 14b. Quantitatively, such an influence of the magnetic field is confirmed by the angular distributions of total charge of ions emitted at given angle for 1ω and 3ω obtained from the angular distributions of charge density shown in Fig. 15a and b, respectively.

As it results from the presented dependencies, in the case of 1ω the influence of the magnetic field concerns the entire range of angles and is greater than the ion charge corresponding to the case without a magnetic field. In the central region in the range of angles: 0^o−30^o, the charge decreases, whereas for angles outside the central region greater than 30^o, the charge increases. However, when the 3ω pulse is used, only the latter is observed, whereas the collectors placed in the 0–30^o range exhibit visible drop in the signal intensity.

It should be emphasized that the observed effect of the transverse magnetic field on the expansion of ions formed by DCT-DC targets illuminated by 1ω and 3ω iodine lasers is in good agreement with the measurements of HE emission parameters using a multi-frame magnetic electron spectrometer presented in the III-C paragraph.

Fig. 14

Comparison of the angular density distributions of ions emitted from DCT-DC targets with a double coil (left side of the image) with the distributions corresponding to bare Cu disks (right side of the image) in the case of irradiation by: (a) 1ω and (b) 3ω PALS iodine laser after 0.7 µs from irradiation.

Fig. 15

Comparison of the angular charge distributions of ions emitted from DCT-DC targets with a coil of different diameter and different distance “d” from the Cu disk (red line) with the distributions corresponding to free expansion from bare Cu disks (black line) in the case of irradiation with: (a) 1ω and (b) 3ω PALS iodine laser.

4-frame x-ray pinhole camera measurements

A four-frame x-ray camera with an exposure time of 1 ns and an inter-frame separation of 3 ns was used to record the plasma emission in the XUV and soft x-ray spectral ranges between 10 and 10 000 eV^11,18,21. Sequences of x-ray images illustrating the process of plasma formation in the DCT-DC targets with a coil of different diameter and positioned at different distances from the Cu disk in the case of irradiation by the 1ω laser beam focused to minimal focal spot radius are presented in Fig. 16, while x-ray images registered in the case of the 3ω are shown on Fig. 17. The plasma dynamics was observed over a relatively long period of up to 10 ns. Please note that the maximum XUV and soft x-ray emission appears about 2–5 ns after the laser-target interaction.

Fig. 16

(a) and (b) time sequences of images illustrating the formation of a magnetized plasma stream in the soft X-ray range in DCT-DC targets with a coil of different diameter (Φ_coil) and positioned at different distances from the Cu disk (d) in the case of irradiation by 1ω PALS iodine laser. (c) X-ray images illustrates the free expansion of plasma (without a magnetic field) from the Cu disk.

Fig. 17

(a) and (b) time sequences of images illustrating the formation of a magnetized plasma stream in the soft X-ray range in DCT-DC targets with a coil of different diameter (Φ_coil) and positioned at different distances from the Cu disk (d) in the case of irradiation by 3ω PALS iodine laser. (c) X-ray images illustrates the free expansion of plasma (without a magnetic field) from the Cu disk.

The X-ray image sequences in Fig. 16 and Fig, 17 clearly demonstrate the influence of the transverse magnetic field on the limitation of the axial expansion of the plasma jet created by DCT-DC targets as a function of the PALS laser wavelength and its intensity as a function of the coil diameter and their distance from the Cu disk. In contrast to the free emission of a plasma stream from a Cu disk, Fig. 16c and Fig.17c, the plasma expands into a cone as expected, while the presence of a magnetic field, Fig. 16ab and Fig. 17ab, clearly restricts the axial expansion, which demonstrates the self-illumination of the plasma in the region between the disk surface and the axis of the coil system.

Numerical simulations of the transverse magnetic field influence on the HE flux generated from DCT-DC targets

In order to better understand the influence of the transverse magnetic field generated from the DCT-DC target on the hot electron flux, numerical simulations were carried out. These simulations concerned the expansion of HE (> 54 keV) in the external EM field of the coils with diameter of 1 mm. The distance of the coils from the disc (d) was equal to 0.8 mm. The simulations were performed using an appropriately modified three-dimensional (3D3V) particle-in-cell EPOCH code⁹. The modification allowed for placing a constant current, corresponding to that in the coils, in the appropriate places of the computational space. Then, as a result of the code operation (solving Maxwell’s equations), this current is converted into the electric and magnetic field of the coils. The value of this current was determined based on the current probe measurements (see section III.B). The actual simulation of HE propagation begins when the magnetic and electric fields associated with the coils stabilize within the computational space. In the simulations, in addition to the interactions of HE with the EM field of the coils, the interactions between hot electrons and the interaction of HE with other particles, such as thermal electrons, protons or copper ions were also taken into account. In particular, the influence of fields generated by charged particles on the motion of other charged particles was taken into account. Both the HE flux propagating in the direction consistent with the laser beam propagation direction (forward) and in the opposite direction (backward) were studied. The initial velocities and directions of motion of the hot electrons were determined based on the results of measurements carried out using a multichannel electron spectrometer (see section III.D) using a dedicated Monte Carlo code. The HEs started from a location where the plasma density is equal to 0.25 n_e−cr. This location was determined based on interferometric measurements (see section III.A).

Figure 18 shows spatial distributions of the magnetic (x component; a, b, e, f) and electric (z component; c, d, g, h) fields for the case with coils (a, c, e, g) and the reference case without coils (b, d, f, h) and for 1ω (I_L=1.9*10¹⁶ W/cm²) (a, b, c, d) and 3ω (I_L=6.7*10¹⁵ W/cm²) (e, f, g, h) of the PALS iodine laser. The presented distributions refer to the z-y plane being a cross-section along x = 0 (in the middle between coils), where the z direction corresponds to the direction of laser pulse propagation, and time t = 3 ps, where t = 0 corresponds to the beginning of the simulation. The magnetic field is non-uniform and is divided into two parts: the field coming from the coils and the field generated by charged particles such as HE, thermal electrons, protons or copper ions. There is a clear difference in the strength of the coil’s magnetic field (generated by coil’s current) between the 1ω and 3ω cases. Between the coils, the value of this field reaches 0.735 T for the first harmonic (Fig. 18a) and 0.14 T for the third harmonic (Fig. 18e) of the PALS laser. This is due to the significantly larger current flowing in the coils in the 1ω case compared to the 3ω situation. Non-uniformities in the coil’s magnetic field cause electric fields generated by the coils. Such fields are the strongest in the regions close to the coil’s wire, where the changes of the B field in space are the highest. However, also in the center between the coils electric field generated by the coil are present (Fig. 18c, g).

Fig. 18

Spatial distributions of magnetic (a, b, e, f) and electric (c, d, g, h) field strengths in the z–y plane, where z is the direction of the laser axis (the beam propagates towards negative z values), for 1ω (a, b, c, d) and 3ω (e, f, g, h) of PALS iodine laser. t = 3 ps (t = 0 corresponds to the beginning of the HE propagation simulation).

Comparison of two-dimensional hot electron density distributions for different simulation time steps and for the case with coils (d, e,f) and without coils (a, b, c) are shown in Figs. 19 and 20. Figure 20 presets the results for the first harmonic while Fig. 20 shows the results for the third harmonic of the PALS laser. Both figures show the influence of the coils’ magnetic field on the HE propagation. This influence consists in deflecting the backward (towards positive z values) propagating flux downwards (towards negative y values). This influence is higher for the 1ω case due to the stronger magnetic field of the coils. Moreover, this influence is higher for more advanced phases of hot electron flux propagation (t = 14 ps). This is due to the longer time of interaction of the B field with the hot electron flux, including the interaction with a larger number of slower HEs that later reached the areas of the stronger field.

Fig. 19

2D distributions of hot electron density in the y–z plane parallel to the laser beam axis in various phases of the HE expansion. (a, b, c)—target without the coils; (d, e, f)—target with the coils. The case of irradiation by 1ω PALS laser.

Fig. 20

2D distributions of hot electron density in the y–z plane parallel to the laser beam axis in various phases of the expanding HE. (a, b. c)—target without the coils; (d, e, f)—target with the coils. The case of irradiation by 3ω PALS laser.

In order to better understand the influence of the electromagnetic field generated by the coils on the propagation of hot electrons in both the forward (towards negative z values) and backward (towards positive z values) directions, a 2D distributions of the energy fluence in the x-y plane and their cross sections along x and y axis were performed. For the purpose to avoid large energy fluence fluctuations, the prepared cross-sections have a finite thickness of ± 0.2 mm. Figures 21 and 22 show the results for the backward beam and for z = 1.5 mm, where z = 0 corresponds to the plane intersecting the centers of the coils. Figure 21 shows the results for the first harmonic of the PALS laser, while Fig. 22 shows the results for the third harmonic of this laser. Both for the 1ω and 3ω cases, as in Figs. 19 and 20, the HE beam deviation is visible. The value of this deviation is higher for the first harmonic case. Moreover, it is visible that for 1ω the recorded energy fluences are higher in the case with the coil than without it. This effect is negligible for 3ω. These results are confirmed by the values of the energy of the backward hot electron flux (integral over the fluence distribution). For the first harmonic of the PALS laser, these values are equal to 3.49 mJ for the case with coils and 1.09 mJ for the case without coils. In turn, for the third harmonic of this laser, these values are equal to 0.133 mJ (with coils) and 0.132 mJ (without coils), respectively. The above results concerning the increase in the HE beam energy are qualitatively consistent with the experimental results, especially in the case of 1ω. Figure 10 shows that for 1ω and a coil diameter of 1 mm we have an increase in both the particle fluence of hot electrons, their maximum energy and temperature compared to the case without coils. This increase is observed for almost all tested angles in the case of the particle fluence and all tested angles in the case of maximum energy and temperature. This confirms the increase in the HE beam energy observed in the simulation results for the case with a coil compared to the case without a coil for 1ω. In the case of 3ω the experimental data are not so clear. Fig, 10 shows that both in the case of particle fluence of HE and hot electron temperature their values for the case with coils are higher or lower than for the case without coils depending on the angle. Moreover, particular fluences are usually lower for the case with coils, while HE temperatures are usually higher for this case.

Fig. 21

2D distributions of energy fluence in the x–y plane for the HE flux propagating backward in the case of a target without a coil (a), and with a coil (b). Bottom graphs present HE flux cross-sections along x (c) and y (d) axis taken at distances 1.5 mm from the plane intersecting the centers of the coils. The case of irradiation by 1ω PALS iodine laser.

Fig. 22

2D distributions of energy fluence in the x–y plane for the HE flux propagating backward in the case of a target without a coil (a), and with a coil (b). Bottom graphs present HE flux cross-sections along x (c) and y (d) axis taken at distances 1.5 mm from the plane intersecting the centers of the coils. The case of irradiation by 3ω PALS iodine laser.

Analogous results to those presented above but for the forward HE flux and a x-y plane corresponding to the surface of the target (z=−0.8 mm) are presented in Figs. 23 and 24. For the forward beam, no beam deflection is visible. Moreover, the influence of the electromagnetic field generated by the coils on the central part of the beam is negligible for both the 1ω and 3ω cases. However, the situation changes at the edges of the beams. Here, an increase in fluence is visible for the case with coils for both harmonics of the PALS laser. Moreover, for the cross-sections along the x axis, fluence maxima are visible in the regions where the coils fragments are located closest to the target surface. Finally, it is worth noting that the observed increases in fluence are higher for 1ω where the magnetic and electric fields generated by the coils are stronger. The energy of the forward hot electron flux for the first harmonic of the PALS iodine laser are equal to 13.46 mJ for the case with coils and 3.18 mJ for the case without coils. In turn, for the third harmonic of this laser, these values are equal to 0.161 mJ (with coils) and 0.136 mJ (without coils), respectively. The results concerning the HE-induced Cu Kα emission line (see section III.C) show a broadening of the emission areas for the case with coils, which may be a confirmation of the above simulation results.

The important reason for the increase in the energy of the hot electron flux for 1ω and for the forward 3ω HE flux is an increase in the energy of single electrons. Figure 25 shows the energy spectra for both studied harmonics of the PALS iodine laser and for the forward and backward fluxes. It is visible that the presence of the fields generated by the coils contributes to the appearance of a high-energy tail both in the case of electrons flying to the target and those flying in opposite direction. The reason for the appearance of this tail is the interaction of electrons with the electric field generated by the coils (see Fig. 18c, g). These fields are stronger for the 1ω case hence the observed higher energy and number of electrons forming the discussed tail in this case.

Fig. 23

2D distributions of energy fluence for the HE flux in the x–y plane propagating forward in the case of a target without a coil (a), and with a coil (b). Bottom graphs present HE flux cross-sections along x (c) and y (d) axis taken at target plain. The case of irradiation by 1ω PALS iodine laser.

Fig. 24

2D distributions of energy fluence for the HE flux in the x–y plane propagating forward in the case of a target without a coil (a), and with a coil (b). Bottom graphs present HE flux cross-sections along x (c) and y (d) axis taken at target plain. The case of irradiation by 3ω PALS iodine laser.

The increase of the maximum energy of hot electrons in the case with coils relative to the case without coils is visible in the experimental results for the 1ω case Figs. 9a and 10a. Unfortunately, the high-energy tails observed in the simulation results are not visible in the experimental results due to the electrons energy being outside the measurement range of the detectors (< 2 MeV). Additionally, the number of electrons creating the discussed tails is usually small, which additionally complicates the measurements.

The effect of this state of affairs is the visible higher increase in beam energy (both forward and backward) relative to the case without coils, for 1ω compared to 3ω. Additionally, it is worth noting that the discussed fields have the highest values in the region of the coil wire. Hence the biggest differences in fluence between the cases with and without coils are visible at the edges of the beams. The discussed effect is best seen in the case of forward beams where the greatest increases in fluence are visible in places where the coils wires are located closest to the target. In the last cases, the increase in fluence in the mentioned places is also caused by the reversal of ions, originally moving in the backward direction, by the coil magnetic field, back towards the target.

These effects discussed in this section require further investigation. In particularly, there is a lack of information about the forward HE flux in the source and in general our assumption that initial HE fluxes in both directions are equal, may be unjustified. For this reason, the presented results of simulation should be used only for qualitative analysis not for quantitative comparison with the experiment.

Fig. 25

Energy spectra for backward beam (a, c) recorded for z = 1.5 mm and forward beam (b, d) recorded on the target plane. Results for 1ω (a, b) and 3ω (c, d).

Conclusions

The ongoing development of a strong external magnetic field for experiments with magnetized laser-driven plasmas with high energy density is based on a hybrid strategy. This consists of two methods of powering the external magnetic field. The standard method uses an external coil power supply, while the self-powered coil method uses a return target current neutralizing the target polarization. This current flows from the ground through the coil to the target creating a strong magnetic field in close proximity to the irradiated target and the plasma produced. Changing the configuration of the disc-coil target system, which consists of a target foil and one or two coils, allows varying both the intensity of the magnetic field produced and its orientation. In this experiment, we used a system of two coils generating a magnetic field whose vector is perpendicular to the direction of the laser beam irradiating the target disk. To vary the intensity of the magnetic field, discs with coils of different diameters and different distances of the coils from the disc were used. The peak magnetic field reached a value of ≈1 T in the 1ω experiment and ≈0.15 T in the 3ω experiment.

The design of the target system allowed the use of a femtosecond 3-frame polaro-interferometer, which provides information on the evolution of the electron density distribution in space-time during the interaction of the laser with the plasma produced on a Cu disk. Using this interferometer, we determined the locations of the critical density n_e−cr regions, and the locations of 0.25n_e − cr and 0.1n_e − cr regions being related to the two most probable mechanisms responsible for HE generation, such as stimulated Raman scattering and two plasma decays.

The 2D imaging of the Cu Kα line emission induced by hot electrons revealed that the presence of a magnetic field increases the HE energy released in the Cu target material. The conversion of laser energy to HE energy does not show a significant dependence on the laser wavelength. The experiment revealed that the integrated HE emission time for both harmonics is clearly longer in the presence of a transverse magnetic field compared to the free expansion of the plasma. Moreover, The effect of this magnetic field on the K-alfa emission is clearly evident before the laser peak. Measurements of the energy spectra of the runaway hot electrons also revealed that both the HE energy and the temperature are clearly higher compared to free expansion. We note that the effect of the transverse magnetic field on the ion emission from the plasma created on the DCT-DC target is in good agreement with measurements of the HE emission parameters.

Significant properties of the produced plasma were revealed by measuring the return target current and X-ray emission with a 4-frame pinhole camera. The transverse magnetic field caused the return current to be prolonged by several nanoseconds. Although the FWHM of the laser pulse duration was only 350 ps, the FWHM of the target current duration increased up to 2 ns, and the pulse duration at 0.1 of the current maxima up to about 9 ns. Also, plasma dynamics observed using XUV and soft X-rays lasted up to about 10 ns. It is important to focus attention on the fact that the maximum emission of XUV and soft X-rays appears with a delay of up to 2–5 ns after the interaction of the laser with the target.

In order to better understand the influence of the transverse magnetic field generated from the DCT-DC target on the hot electron flux, the (3D3V) particle-in-cell simulations were performed. The initial conditions of these simulations were define based on the energy spectra of HE recorded by the multi-channel magnetic spectrometer, the information about position of the 0.25n_e − cr region, and the current probe measurement results. The influence of coils fields on both the forward and backward propagating HE flux were studied. It has been shown that the presence of the field generated by the coils causes an increase in the fluence and total energy of the hot electron beams propagating in both studied directions. This result is consistent with the experimental results. It has also been shown that the observed increases are related to the increase in the energy of individual electrons accelerated as a result of interaction with electric fields that are part of the electromagnetic fields generated by the coils and are present mainly in the regions close to the wires forming the coils. In particular, within the HE energy spectra for the cases with coils, the formation of long high-energy tails is visible. These tails are not visible in the experimental results due to measurement limitations of the used detectors. Due to the limitations of the conducted simulations related, among others, to the lack of information about the forward HE flux in the source, further studies of the discussed phenomena are necessary.

In conclusion, the presented experimental and theoretical studies of a self-powered laser generator for a strong transverse magnetic field provide new results relevant to ICF studies, both for 1ω and 3ω iodine laser radiation.