The synthesis of approximately half of the atomic nuclei heavier than iron is theorized to occur via the rapid neutron-capture process (r-process) in astrophysical environments of extreme temperature and density. While such temperature and density are unlikely to be recreated in the lab, a broadly-recognized goal is to develop experiments to study the nuclear scattering and excitation dynamics of multi-neutron capture, which is estimated to require neutron fluxes greater than 10²² cm⁻² s⁻¹ [1]. Beyond nuclear astrophysics, fast neutrons produced in a compact, ultra-short pulse source, would have wide ranging applications including high energy density physics [2], materials science [3], and medical research [4]. For this reason, high-flux neutron sources remain an important subject of research and development. Laser-driven neutron sources in particular are a promising approach [5], having already achieved much higher peak neutron fluxes than fission reactors ( ∼ 1 0 15 /cm²/s) or spallation ( ∼ 1 0 17 /cm²/s) sources in laboratory experiments, potentially in a more compact facility [6].

The highest neutron yields achieved by laser-driven sources are from inertial confinement fusion (ICF) [7] experiments. The most successful shots at the National Ignition Facility (NIF) produced > 1 0 15 neutrons in less than a nanosecond [8] suggesting that neutron fluxes greater than 10²⁴/cm²/s are achieved just outside the cm-long hohlraum. However, ICF user facilities like OMEGA [9] or the NIF [10] are too large to be available for smaller-scale nuclear physics studies with neutrons for the foreseeable future.

The advent of ultrahigh intensity lasers thanks to chirped pulse amplification [11] has enabled the production of neutrons in a much more compact arrangement [3, 12–24]. Several schemes have been tested on laser systems ranging in scale from millijoules [22] to kilojoules [3]. Among them, the most promising method is the ion-driven neutron source approach [20] because of its comparatively high efficiency and neutron yield. Experiments have demonstrated a directional peak yield of up to 1 × 10¹⁰ n/sr/shot [19]. The scheme is usually employed in “pitcher-catcher” configuration, where the laser interacts with a thin ( ∼µm) pitcher target to accelerate ions, typically protons or preferably deuterons. These ions then interact with a cm-scale, low-Z “catcher” target, beryllium-9 [18], lithium-7 [25] or deuterated plastic [23], undergoing nuclear reactions and producing neutrons in the process. Using break-out afterburner acceleration in the relativistic transparency regime [19], this method could achieve an overall laser-to-neutron energy conversion efficiency of ∼ 6 × 1 0 8 n/J compared to ∼ 4 × 1 0 8 n/J for TNSA acceleration driven laser-neutron generation, ∼ 4 × 1 0 6 n/J for laser-electron driven neutron source [24], and only ∼ 1 0 5 n/J for laser-cluster fusion neutron source [17].

We report on a novel approach to laser-driven neutron generation. For the first time in a petawatt laser facility, cryogenic deuterium jet targets were used to efficiently generate neutrons. These targets offer several advantages over the deuterated plastic foils used in previous experiments [16, 18, 19, 26], including near-critical electron density allowing access to the relativistic transparency regime and potential for high repetition rate target preparation [27]. The thin, above critical density target results in efficient ion acceleration ( ∼ 10 % of laser energy transferred to ions), and the higher yield ( ∼ 1 0 13 /shot) and energy deuteron beam produces a higher yield of neutrons in the pitcher-catcher configuration. We find higher neutron yields detected in the bubble detectors than can be explained by deuteron-converter interactions. E other sources and simulating the laser-plasma interaction, we consider the most plausible explanation is that, in addition to being efficiently accelerated out of the target, deuterons in the target are volumetrically heated and produce a significant number of neutrons by the d (d,n)³He reaction. The deduced fusion neutron yield is consistent with simulation estimates and, considering the small source size ( ≲ 100 µm), suggests a route to the ultra-high fluxes required for r-process studies.

The experiment was carried out at the Texas Petawatt laser [28] facility at the University of Texas at Austin. The experimental setup is depicted in Figure 1. The 1057 nm Nd:Glass laser delivered 90–140 J, 140 fs laser pulses to irradiate the deuterium jet targets. Using an f/3 off-axis parabolic mirror, the laser beam was focused to a spot size of 6 µm full-width half-maximum (FWHM) to an average encircled laser intensity of > 1 0 21 W/cm². A plasma mirror was installed 5 cm before the target to remove pre-pulses and steepen the rising edge of the main pulse (see temporal profile in Appendix A), reaching a contrast ratio of > 1 0 5 at 10 ps before the arrival of the main beam. The plasma mirror reflectivity was estimated to be approximately 80%.

The deuterium jet was made by a cryogenic microjet system developed at SLAC [29, 30]. Deuterium gas is liquified and held at 19–21K in a copper source assembly cooled by a continuous-flow helium cryostat. The liquid deuterium enters the chamber through a 2 × 40 µm rectangular aperture and rapidly solidifies a few 100 µm from the nozzle by evaporative cooling. The resulting cryogenic deuterium jet is a relatively flat planar sheet of width 15 µm between two 5 µm diameter cylindrical columns, as illustrated in Figure 1A, running at a speed of 50–100 m/s into vacuum [31]. At this temperature, the density of the deuterium is expected to be n _d ≃ 6 × 10²² cm⁻³. The jet-laser overlap was monitored and adjusted using two orthogonal probe imaging systems.

Either a radiochromic film (RCF) stack or a Be converter was placed downstream of the laser forward direction. The RCF stack consisted of alternating layers of aluminum foil, copper sheets and calibrated RCF films [32] of different thicknesses to measure the deuteron beam divergence profile and rough spectrum. The precise composition of the stack is given in Appendix B. The 2.7 × 2.3 cm² RCF stack was centered on the laser axis 4.5 cm behind the target. It had a centered 5 mm diameter hole providing line of sight for a Thomson parabola spectrometer (TPS). The TPS was analyzed in conjunction with the RCF stack to provide an absolutely calibrated, high resolution measurement of the deuteron beam energy spectrum. A second TPS and an electron spectrometer were respectively located 30° and 36° counter clockwise from the laser axis. The high voltage setting on the TPS was not turned on during the measurements since the irradiated target introduces a significant load on the vacuum system resulting in pressures which cause electrical arcing in the TPS thereby corrupting the signal recorded on the imaging plate. However, a previous experiment which utilized differential pumping to separate the TPS from the vacuum chamber, demonstrated that other ion species are negligible compared to the main source because of the high purity of the deuterium gas (D₂, 99.6% + HD, 0.4%) used to create the cryogenic deuterium jet target [33].

In addition to measuring the energy-resolved spatial distribution of the deuteron beam, the RCF stack also acts as a neutron converter where laser-accelerated deuterons produce neutrons via breakup reactions. We also investigated enhancing neutron production by installing a 1 × 1 × 5 cm³ Be converter centered on the laser axis at a distance of 2.7 cm. Due to its light atomic weight and high (d,n) reaction cross section, the Be converter is expected to produce a higher neutron yield than the RCF stack. The beryllium converter was housed in an aluminum casing with a 100 µm thick aluminum window on the side facing the laser-plasma interaction. This shields the beryllium from the transmitted laser pulse, while still allowing the majority of MeV-energy deuterons to pass through.

A neutron time of flight (n-TOF) detector was used to measure the neutron energy spectrum 4.5 m away from the target chamber center (TCC) and 110° away from the laser propagation direction, which was the only available line-of-sight given the radiation shielding. The n-TOF consists of a fast plastic scintillator (EJ-200), a photomultiplier (XP2020) and a fast-digital oscilloscope (TDS5104). The strong x-ray signal from the laser target interaction was shielded by a 32.5 mm thick Cu plate to reduce the decay signal width (FWHM) to below 25 ns. The thickness is chosen to ensure the neutron signal remains greater than the x-ray-generated background, which thereby served as a time reference for the neutron energy analysis. The response function of the scintillator was measured beforehand and the width (FWHM) was found to be around 10 ns per volt. For our setup, this would introduce a 10% uncertainty in the energy measurement and it affects the low energy range less than the high energy range. Ten bubble detectors [34] were positioned in the laser plane at various angles around the target chamber (−177° – 90° from target normal, to measure the fast neutron flux at the detector position. The bubble detectors’ sensitivities varied between 2–2.5 bubbles/mrem. Distances of the bubble detectors were measured using the front of the Be converter or the front of the RCF stack as a reference point as our analysis, presented in the following sections, suggests this is the primary source of neutrons.

A typical deuteron energy spectrum measured at 0 and 30° from the laser forward direction, as well as the reconstructed average spectrum from the dose recorded on each RCF film are shown in Figure 2A. Note that the absolute flux was calculated using the energy-dependent image plate calibration from [35] in conjunction with doses extracted from the RCF films in the laser forward direction. The deuteron spectrum follows a semi-Maxwellian distribution, indicative of a TNSA-dominated regime [31], with a cut-off energy of 50 MeV (shot 11,557) at 0 deg. Consistent with a previous study using planar cryogenic hydrogen jets [31], the deuteron beam is comprised of two main components which are attributed to the planar central region and cylindrical rims of the cryogenic jet. The former produces a conical beam with a half-angle decreasing from approximately 20° at the lowest energies to less than 10° near the cut-off energy (Figure 2B). The latter produces a near azimuthally symmetric deuteron emission with similar confinement along the jet axis as illustrated in Figure 2C.

The neutron yield was measured using the bubble detector array and the neutron spectrum measured using the n-TOF detector for 3 consecutive shots. For shots 11,555 and 11,557, deuterons were impinging on the RCF stack as shown in Figure 1A, while for shot 11,569, the Be converter was implemented in the setup replacing the RCF, see (b).

Absolute neutron numbers at the location of the bubble detectors were calculated by converting bubble counts to dose in mrem using the manufacturer provided sensitivity of the individual detectors. Dosages (mrem) were then converted to neutron flux (n/sr) using the conversion relation provided in [18] and the distances of the detectors to the RCF or converter. Figure 3A shows the calculated neutron flux as a function of angle with respect to laser forward direction for the three recorded shots. The error bars shown in the plot are a combination of the statistical error of the measurement ( N / N ) and the response fluctuation of the bubble detector across its sensitivity range. This response dependent error (19%) is determined by calculating the standard deviation of the response measurement conducted by [18] across an energy ranging from 0.3 to 32 MeV. Calculated fluxes across the three shots ranged from (5.2 × 10⁸–2.9 × 10⁹) n/sr. As seen in Figure 3A the neutron fluence distribution is predominantly isotropic with two broadened peaks visible at −150 and 30°. Monte Carlo simulations described in the next section show that the peak at 30° is due to the forward-directed conical-beam component of the deuteron distribution described above. Averaging over the detected neutron flux for all shots and integrating over 4π, in the same way as previously published works, we obtain a total neutron yield of ∼ 2 × 1 0 10 n/shot. Note that due to the lack of neutron flux measurements outside of the laser propagation plane, this number can be viewed as the ideal case and as an upper bound to the actual on-shot neutron yield. Future measurements will give more insight into the neutron flux distribution outside the laser plane. Even though the flux we calculate is based on the important assumption of isotropy in 4π, the estimate still agrees within error bars with Monte Carlo simulation described below.

Figure 3B shows the raw neutron traces acquired by the n-TOF detector for all three shots (11,555, 11,557 and 11,569). The spectra were extracted first by subtracting the signals corresponding to the x-rays from the overall time of flight signals, which is accomplished by fitting the X-ray peak with a skewed Gaussian model f x = A e α μ − x + α σ 2 2 1 − erf μ − x + α σ 2 2 σ (1) with the center of the peak μ, the standard deviation σ, the amplitude A, the fit factor α and the error function erf. As an example the gamma peak decay fit for shot 11,557 is displayed in Figure 3B as the light blue curve. We fit the decay line after the first 16 ns to avoid the interference of the fast decay process, corresponding to the very sharp peaks at time zero. Then the neutron signal was converted from the time domain to energy domain (dV/dt → dV/dE) by setting a 10% threshold on the X-ray peak to determine the laser-target interaction time. Figure 3C shows the three different spectra as a function of energy in MeV and the neutron signal in terms of V/MeV. By allowing systematic uncertainties in the x-ray signal subtraction, we estimated the error on the neutron spectrum to be less than 10%.

In shot 11,555, the spectrum is monotonically decreasing with an endpoint energy E _n ≃ 15 MeV, consistent with simulations of deuteron break-up on Be, Al in the chamber walls and other experimental apparatus. In shots 11,557 and 11,569, we identify two distinct peaks, one around 2.7 MeV for 11,557 and 3.2 MeV for 11,569, the other broader and peaked around 6 MeV, suggesting two populations of neutrons with different origins.

Combining a thin, several micron-scale cryogenic deuterium target with a petawatt-class laser, we obtained a total deuteron yield of 10¹³/shot with efficient ∼ 8 − 10 % energy transfer from the laser. This high deuteron yield supported a high neutron yield ≳ 10¹⁰ and efficiency of 10⁸ neutrons/J, comparable to previously published highest neutron yields from laser-driven sources. With 10¹⁰ neutrons produced by the forward-directed beam in the beryllium catcher, fluences > 1 0 9 /cm² would have been achieved, primarily in the beam direction in the catcher. Accounting for the nanosecond delay between faster and slower deuterons in the beam, we infer that fluxes exceeding 10¹⁸/cm²/s were obtained at the catcher. If the catcher could be placed closer to the ion source, millimeters away instead of centimeters, this flux could be enhanced by at least an order of magnitude, if not more. Deuteron break-up on Be and Al experimental apparatus explains a majority but not all the observed neutron yield. Identifying the remaining neutrons as derived from d (d,n)³He fusion reactions in the laser-irradiated deuterium jet, we infer a fusion neutron yield (10⁷ n/J) and high peak flux ( > 1 0 22 n/cm²/s) near the plasma. As a consequence of the much higher neutron contribution from break-up, a signal of fusion was not clearly identifiable in the neutron spectrum. The double peak feature in two observed neutron spectra is currently not fully understood. In future experiments, multiple neutron time-of-flight detectors should be employed to allow coincidence-based background rejection to determine if the second, higher energy peak is due to a physical neutron signal or not. In case this peak represents a real signal, a multiple detector setup also enables extraction of additional information about the location of the source of the signal.

The neutron flux inferred to originate from in-target fusion is almost a million times higher than the laser-ion driven method (10¹⁷ n/cm²/s) [26] as well as conventional neutron source like spallation sources (10¹⁷ n/cm²/s) and fission reactors (10¹⁵ n/cm²/s) [6]. Additional experiments with improved diagnostics (multiple TOF spectrometers and yield measurements out of plane) are necessary to confirm both the yield and d (d,n)³He nature of the source. We anticipate that a thicker target could suppress high energy deuteron emission without significantly reducing the neutron yield. If harnessed and controlled in the right setup, this high peak flux can enable experiments up to now infeasible, for example, the study of the nuclear cross sections and excitation dynamics essential to the r-process [49], responsible for the creation of heavy elements. The key requirement for this research is an extremely high flux of neutrons to allow successive neutron absorption at a rate faster than the decay time. A laser-driven neutron source such as described here introduces additional technical challenges to designing a multi-neutron capture experiment, not least because of the high energy particle and radiation background from the nearby laser-plasma interaction. Future work can stabilize this mechanism as a neutron source and improve the design to begin addressing these challenges. A future multi-beam facility could irradiate a target of interest using two or more laser-driven fusion neutron sources with ultrahigh neutron flux in precision intervals down to ps. This method has potential to significantly increase the peak neutron flux with the next-generation lasers such as 10 PW Extreme Light Infrastructure [50] and multi-PW Apollon laser [51].