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High-order harmonics are ubiquitous in nature and present in electromagnetic, acoustic, and gravitational waves. They are generated by periodic nonlinear processes or periodic high-frequency pulses. However, this periodicity is often inexact, such as that in chirped (frequency-swept) optical waveforms or interactions with nonstationary matter -- for instance, reflection from accelerating mirrors. Spectra observed in such cases contain complicated sets of harmonic-like fringes. We encountered such fringes in our experiment on coherent extreme ultraviolet generation via BISER, and could not interpret them using currently available knowledge. Here, we present a comprehensive theory based on interference of harmonics with different orders fully explaining the formation of these fringes, which we call alloharmonics. Like atomic spectra, the complex alloharmonic spectra depend on several integer numbers and bear a unique imprint of the emission process, which the theory can decipher, avoiding confusion or misinterpretation. We also demonstrate the alloharmonics in simulations of gravitational waves emitted by binary black hole mergers. Further, we predict the presence of alloharmonics in the radio spectra of pulsars and in optical frequency combs, and propose their use for measurement of extremely small accelerations necessary for testing gravity theories. The alloharmonics phenomenon generalizes classical harmonics and is critical in research fields such as laser mode locking, frequency comb generation, attosecond pulse generation, pulsar studies, and future gravitational wave spectroscopy., 29 pages, 9 figures, 3 tables

1. Introduction Burst Intensification by Singularity Emitting Radiation (BISER) [1] is the emission of coherent traveling waves by multi-stream flow singularities. Such singularities can be produced in relativistic plasma by high-power lasers, resulting in very bright coherent x-ray emission [2],[3]. 2. Experimental We have recently performed an experiment on BISER coherent x-ray generation with the Astra Laser at the CLF RAL, UK. We extensively optimized the experimental conditions, namely the plasma density and profile, and laser spot [4] and pulse, making use of substantial beam time. This resulted in a ~2 orders of magnitude higher BISER brightness compared to earlier experiments with 10 TW lasers. 3. Results In this presentation we discuss results from two soft x-ray spectrographs: a three-channel flat field spectrograph [5] in the forward direction (channels at −0.6, 0, and 0.8°) operating in the 17-34 nm range and a normal-incidence imaging spectrograph [6] in a 10° off-axis direction operating in the 12.4-20 nm range. Under optimum conditions, both spectrographs showed μJ and higher BISER pulse energies per shot in the corresponding spectral ranges and within their acceptance angles. This implies multi-100 μJ BISER pulses in the entire spectral range and within the full angular width. Acknowledgement We acknowledge support from the Astra Laser Group and the CLF Target Fab, Mechanical, and Electrical. Financial support: JSPS Kakenhi JP 19KK0355 and 19H00669, CLF, Russian Science Foundation (20-62-46050), IAP RAS, ELI-Beamlines, MŠMT by the project "Advanced Research Using High Intensity Laser Produced Photons and Particles" (CZ.02.1.01/0.0/0.0/16_019/0000789), High Field Initiative (CZ.02.1.01/0.0/0.0/15_003/0000449) from the European Regional Development Fund, and the QST Director Fund 創成的研究 #20. References [1]A. S. Pirozhkov, T. Zh. Esirkepov et al., "Burst intensification by singularity emitting radiation in multi-stream flows," Sci. Rep. 7, 17968 (2017). [2]A. S. Pirozhkov, et al. "Soft-X-Ray Harmonic Comb from Relativistic Electron Spikes" PRL 108, 135004 (2012). [3]A. S. Pirozhkov, et al., "High order harmonics from relativistic electron spikes" NJP 16, 093003 (2014). [4]A. S. Pirozhkov, et al. "Laser Requirements for High-Order Harmonic Generation by Relativistic Plasma Singularities," Quantum Beam Sci. 2, 7 (2018). [5]D. Neely, et al., "A multi-channel soft X-ray flat-field spectrometer," AIP Conf. Proc. 426, 479 (1998). [6]A. N. Shatokhin, et al., "High-resolution stigmatic spectrograph for a wavelength range of 12.5-30 nm," Opt. Express 26, 19009 (2018)., OPIC-2022 (ALPS-2022)

Burst Intensification by Singularity Emitting Radiation (BISER) [1] is the phenomenon of extremely bright coherent wave emission (constructive interference, N^2 effect) by singularities of multi-stream flows. High-power femtosecond lasers can produce such flows and corresponding relativistic plasma singularities in underdense plasma; these singularities emit very bright coherent x-rays [2]-[3]. We have recently performed an experiment on BISER coherent x-ray generation with the Astra Laser in the CLF RAL, UK. We observed BISER coherent soft x-rays with two spectrographs: a three-channel flat field spectrograph [4] in the forward direction (channels at -0.6, 0, and 0.8°) operating in the 17-34 nm range and a normal-incidence imaging spectrograph [5] in a 10° off-axis direction operating in the 12.4-20 nm range. Both spectrographs, in addition, provided data on the angular distribution of the BISER radiation. We took advantage of an extensive experiment term and long daily laser operation hours to optimize the laser (in particular, focal spot, which is a necessary prerequisite for BISER [6], and pulse width) and the experimental conditions (in particular, the density profile). These resulted in ~2 orders of magnitude enhancement in BISER photon number, providing >10^11 photons and >μJ energies per pulse in each channel at 7 TW laser power, the result which could previously be obtained at >100 TW laser power only. We acknowledge support from the Astra Laser Group and the CLF Target Fab, Mechanical, and Electrical. Financial support: JSPS Kakenhi JP 19KK0355 and 19H00669, CLF, Russian Science Foundation (20-62-46050), IAP RAS, ELI-Beamlines, the Ministry of Education, Youth and Sports of the Czech Republic by the project "Advanced Research Using High Intensity Laser Produced Photons and Particles" (CZ.02.1.01/0.0/0.0/16_019/0000789), and the QST Director Fund 創成的研究 #20. [1] A. Pirozhkov, T. Esirkepov et al., "Burst intensification by singularity emitting radiation in multi-stream flows," Sci. Rep. 7, 17968 (2017). [2] A. S. Pirozhkov et al. "Soft-X-Ray Harmonic Comb from Relativistic Electron Spikes" PRL 108 135004 (2012) [3] A. S. Pirozhkov et al., "High order harmonics from relativistic electron spikes" New J. Phys. 16, 093003 (2014). [4] D. Neely et al., "A multi-channel soft X-ray flat-field spectrometer," AIP Conf. Proc. 426, 479 (1998). [5] A. Shatokhin et al., "High-resolution stigmatic spectrograph for a wavelength range of 12.5-30 nm," Opt. Express 26 19009 (2018). [6] A. S. Pirozhkov, et al. "Laser Requirements for High-Order Harmonic Generation by Relativistic Plasma Singularities," Quantum Beam Sci. 2, 7 (2018)., Annual meeting of the JSAP

Ultra-high intensities open a way towards Terawatt and potentially Petawatt gamma-ray pulses in the so called Gamma Flare regime. We performed our first experiment towards this regime with the J-KAREN-P laser operating at intensities close to 10^22 W/cm^2. In this presentation I will overview the experiment, including very bright hard x-ray generation (sub-MeV to a few-MeV spectral range), high-order harmonic generation (30 to 70 eV), and multiple additional diagnostics revealing information on preplasma (properties of reflected 1st, 2nd, and 3rd harmonics and back-reflection). I will compare these results with the integrated HD and PIC simulations., OPTO-2021 Symposium on Photon and Beam Science

We describe our experiment performed with the J-KAREN-P laser at the intensity approaching 10^22 W/cm^2. In particular, we present the results obtained with hard x-ray (0.1-3 MeV) spectrographs comprising 10 scintillators and a method to reconstruct the x-ray spectra., 3rd International Conference on Nuclear Photonics (NP2020)

At PW-class laser facilities pulse intensities of the order of 10^21 – 10^22 W/cm^2 can be reached by focusing high quality laser beams to spots of a few microns size. Under such conditions, during fs- time intervals a huge amount of optical energy is concentrated into a tiny volume and by the interaction with solid targets creates a plasma with high energy density. Such plasma can be sources of non-linear phenomena, among known and predicted by theory there is the acceleration to high energy of protons, ions, electrons and neutrons, generation of HOH and gamma-flare, creation of exotic states of hollow ions and WDM. The observed phenomena are defined by the type of target, laser energy and strongly depend on the prepulse condition. Achieving highly ionized states for elements with medium Z allows to effectively perform x-ray diagnostics of plasma parameters and preplasma conditions by means of high-resolution spectroscopy based on the analysis of spectra of H-like and He-like ions. Here we l present a review on the recent results on application of x-ray spectroscopic diagnostics of plasmas generated in the interaction of J-KAREN-P ultra-high intensity laser pulses with solid and clusters targets under conditions of different intrinsic laser contrast and under the cases of specially incorporated prepulse for controlled preplasma formation. Plasma parameters were evaluated by means of time integrated x-ray spectroscopic measurements and kinetic modeling using the code PrismSPECT. Certain line intensity relations, including the relations (Ly_a / He_b), (Ly_a / Ly_a satellites), relation between Ly_a satellites, as well as broadening and the shape of line, were used as the main tools for evaluation of plasma parameters. Each of the tools has preferred dependences on plasma electron temperature, electron density, electric and magnetic field strength. Four types of experiments are under consideration., 3rd International Conference on Nuclear Photonics NP2020

We present multi-diagnostic results from laser-plasma experiment at ~10^22 W/cm^2, including optical and high-order harmonics, back-reflection, soft x-rays, keV x-rays, and sub-MeV to MeV x-rays, simultaneously with important laser parameters. We discuss methods to find at-focus target position and compare intensity dependences., OPTICS & PHOTONICS International Congress 2021

After recent upgrade of the Petawatt-class J-KEREN-P laser system the experiments with on-target relativistic intensity up to 10^22 W/cm^2 (pulse energy ~10 J, pulse length ~40 fs, focal spot down to 1.5 um) are routinely carried out at KPSI, QST. In general, for solid targets the plasma formation threshold is of ~10^10-10^12 W/cm^2, therefore the long ASE prepulse, short and ultrashort pedestal intensity crucially impact the formation of plasma conditions and the observed phenomena. It was demonstrated that there exists a strong dependence of the degree of Fe ionization on a laser prepulse, and that an effective generation of energetic, multiply-charged moderate- and high-Z ions can be driven only with laser pulses of ultra-high contrast. Here we report on the new experiments performed at J-KAREN-P laser with the tailored plasma density profile created by specially incorporated prepulse. For the prepulse the ~1/100 of the main pulse power was picked up and delivered to the target with controlled sub-nanosecond time interval prior to the main pulse. The prepulse was focused: (1) on the front of a stainless steel foil for the formation of downstream preplasma with conditions aiming the efficient generation of x-ray flare and high-order harmonics (experiment led by A.S. Pirozhkov); and (2) on the rear-side of a 4-Chlorosterene foil mimicking upstream preplasma, which has the necessary density profile for collisionless shock ion acceleration, when the main pulse is irradiated (experiment led by Y. Fukuda and Y. Sakawa). For both experiments, we present the detailed analysis of plasma parameters provided by means of high-resolution x-ray spectroscopic methods, based on emission characteristics of plasma in the spectral range of Ne-like Fe and H-like Cl ionization states, respectively., International Conference on High Energy Density Sciences (HEDS2021)

Recently it was shown that injection of gas preliminary cooled down to cryogenic temperatures is a promising way to produce micron-scale clusters. For example, in hydrogen clusters with the size up to ≈2 μm were produced via a conical nozzle at 25 K, 6 MPa. Micron scale clusters can be also created with another pre-cooled gases, for example Ar or Kr, but for other temperature values. So large clusters diameter value becomes comparable with a waist width of a laser beam produced by the J-KAREN-P laser facility. As a result, an experimental case can occur, when most of the laser energy is absorbed in a single cluster. Such situation can be considered as an interaction of a laser pulse with matter, state of which is close to solid-state. In the presentation plasma X-ray spectra features indicating the described case of high-intensity laser and large-scale-cluster interaction are discussed. They were observed experimentally during irradiation of cryogenic (T = 140 K – 220 K) Ar flows by ultra-intensive (I = 10^22 W/cm^2) femtosecond laser pulses generated by the J-KAREN-P laser. Registered X-ray spectra of produced plasma contains Ar XVIII Ly-α and Ar XVII He-α of comparable intensities. It should be noted that the Ar XVIII Ly-α line has been for the first time observed in laser-matter interaction experiments. It indicates that the density of irradiated matter is high enough to provide a rate of impact ionization process, which is sufficient to create a significant amount of H-like Ar ions. It is a challenge to reach such condition for a pure gas or small clusters. Thus, the observed spectra are considered as an evidence of a large micron cluster existing in the beam waist region., International Conference on High Energy Density Sciences (HEDS2021)

Generation of bright sources of hard and soft x-rays is one of the most promising applications of high-power lasers. We report on our first experiment on achieving ultra-high on-target intensities, reaching efficient conversion of laser radiation to hard x-rays (towards the "Gamma Flash" regime [1-3]), and generating intense high-order harmonics [4]. Our international team (Japan, Czech Republic, Russia, UK) used the J-KAREN-P laser facility at KPSI QST, Japan [5-8] and irradiated solid targets with intensities close to 1022 W/cm2. We employed a broad range of diagnostics, including laser, plasma, secondary radiation (from NIR to MeV x-rays) and particle (e-, p+) diagnostics, and controlled the preplasma scale length, which is a critical parameter for both hard x-ray [1,3] and harmonic generation [4]. Here we overview the experiment and dedicated simulations, and show first results on hard x-ray and harmonic generation, x-ray spectroscopy, and preplasma analysis. We thank the J-KAREN-P laser operation group. We acknowledge financial support from ELI-Beamlines, High Field Initiative Project (CZ.02.1.01/0.0/0.0/15\_003/0000449) from the European Regional Development Fund, JSPS JP 17F17811 and 19H00669, QST-IRI, and QST Director Funds 創成的研究#16 and #20. [1]T. Nakamura, et al., Phys. Rev. Lett., 2012, 108 195001. [2]C. P. Ridgers, et al., Phys. Rev. Lett. 2012, 108, 165006. [3]K. V. Lezhnin, P. V. Sasorov, G. Korn, and S. V. Bulanov, Phys. Plasmas, 2018, 25, 123105. [4]U. Teubner and P. Gibbon, Rev. Mod. Phys., 2009, 81, 445. [5]A. S. Pirozhkov, et al., Opt. Express, 2017, 25, 20486. [6]H. Kiriyama, et al., Opt. Lett., 2018, 43, 2595. [7]H. Kiriyama, et al., Opt. Lett., 2020, 45, 1100. [8]H. Kiriyama, et al., Crystals., 2020, 10, 783., International Conference on X-Ray Laser 2020

We present an overview of our recent experiment on achieving ultra-high on-target intensities, reaching efficient conversion of laser radiation to hard x-rays ("Gamma Flash"), and generating intense coherent soft x-rays (high-order harmonics). Our international team used the J-KAREN-P laser facility at KPSI QST and irradiated solid targets with intensities close to 1022 W/cm2. We employed a broad range of diagnostics, including laser, plasma, secondary radiation (from NIR to MeV x-rays) and particle (e-, p+) diagnostics, and controlled preplasma using several laser contrast modes and artificial prepulse. In this presentation we overview the experiment and simulations dedicated to it, and show first results on hard x-ray and harmonic generation, x-ray spectroscopy, and preplasma analysis., Opto-2020 Symposium on Photon and Beam Science

We performed our first experiment on achieving ultra-high on-target intensities, reaching efficient conversion of laser radiation to hard x-rays ("Gamma Flash"), and generating intense coherent soft x-rays (high-order harmonics). Our joint team used the J-KAREN-P laser facility inat KPSI QST and irradiated solid targets with intensities close to 1022 W/cm2. We employed a broad range of diagnostics, including laser, plasma, secondary radiation (from NIR to MeV x-rays) and particle (e-, p+) diagnostics, and controlled preplasma using several laser contrast modes and artificial prepulse. In this presentation we overview the experiment and simulations dedicated to it, and show first results on hard x-ray and harmonic generation, x-ray spectroscopy, and preplasma analysis., 2020 Autumn JPS Meeting

Efficient generation of ~MeV x-rays in the Gamma Flare regime [1],[2] in preplasma via the nonlinear Thomson/inverse Compton scattering mechanism [3] is one of the most promising and expected high-power laser applications. The hard x-rays are generated by Bremsstrahlung as well, while the electrons go through the target [4],[5], which also includes multiple passes (refluxing) [5],[6]. Simulations predict that at high intensities the preplasma x-rays dominate; however, at intensities available now, Bremsstrahlung dominates, so that the Gamma Flare mechanism is not yet demonstrated experimentally. We describe our experiment performed with the J-KAREN-P laser [7]-[9], with the emphasis on data from the scintillator-based hard x-ray spectrographs [10] (0.1 – 1 MeV) and Compton spectrograph [11] (2 – 10 MeV), and our efforts to distinguish the generation mechanism. We thank the J-KAREN-P laser operation group. We acknowledge financial support from ELI-Beamlines, JSPS JP 19H00669, and QST Director Funds 創 成的研究 16 and 創成的研究 20. [1] T. Nakamura, et al., "High-Power γ-Ray Flash Generation in Ultraintense Laser-Plasma Interactions," Phys. Rev. Lett. 108, 195001 ( 2012). [2] C. P. Ridgers, et al., "Dense Electron-Positron Plasmas and Ultraintense γ rays from Laser-Irradiated Solids," Phys. Rev. Lett. 108, 165006 (2012). [3] K. V. Lezhnin, P. V. Sasorov, G. Korn, and S. V. Bulanov, "High power gamma flare generation in multi-petawatt laser interaction with tailored targets," Phys. Plasmas 25, 123105 (2018). [4] D. Wu, et al., "Characteristics of X/γ-ray radiations by intense laser interactions with high-Z solids: The role of bremsstrahlung and radiation reactions," Matter Rad. Extremes 3, 293-299 (2018). [5] J. Vyskočil, O. Klimo, S. Weber, "Simulations of bremsstrahlung emission in ultra-intense laser interactions with foil targets," Plasma Phys. Control. Fusion 60, 054013 (2018). [6] D. R. Rusby, et al., "Effect of rear surface fields on hot, refluxing and escaping electron populations via numerical simulations," High Pow. Las. Sci. Eng. 7, e45 (2019). [7] A.S.Pirozhkov, et al., "Approaching the diffraction-limited, bandwidth-limited Petawatt," Opt. Express 25, 20486 (2017). [8] H. Kiriyama, et al., "High-contrast high-intensity repetitive petawatt laser," Opt. Lett. 43, 2595 (2018). [9] H. Kiriyama, et al., "Experimental investigation on temporal contrast of pre-pulses by post-pulses in a petawatt laser facility," Opt. Lett. (accepted). [10] D. R. Rusby, et al., "Novel scintillator-based x-ray spectrometer for use on high repetition laser plasma interaction experiments," Rev. Sci. Instr. 89, 073502 (2018). [11] S. Singh, et al., "Compact high energy x-ray spectrometer based on forward Compton scattering for high intensity laser plasma experiments," Rev. Sci. Instr. 89, 085118 (2018)., OPTICS & PHOTONICS International Congress 2020

High power laser systems are an attractive driver for compact energetic ion sources. We demonstrate repetitive acceleration at 0.1 Hz of proton beams up to 40 MeV from a reeled tape target irradiated by ultra-high intensities up to 5 × 1021 Wcm 2 and laser energies ≈ 15 J using the J-KAREN-P laser system. We investigate the stability of the source and its behaviour with laser spot focal size. We compare the scaling of proton energy with laser energy to a recently developed analytical model, and also demonstrate that it is possible to reach energies up to 50 MeV on a single shot with a lower laser energy ≈ 10 J by using a thinner target, motivating development of high repetition targetry suitable for thinner targets.

Motivated by the development of next-generation heavy-ion sources, we have investigated the ionization and acceleration dynamics of an ultraintense laser-driven high-Z silver target, experimentally, numerically, and analytically. Using a novel ion measurement technique allowing us to uniquely identify silver ions, we experimentally demonstrate generation of highly charged silver ions (Z= 45+2−2 ) with energies of >20 MeV/nucleon (>2.2 GeV) from submicron silver targets driven by a laser with intensity 5 × 1021 W/cm 2 , with increasing ion energy and charge state for decreasing target thickness. We show that although target pre-expansion by the unavoidable rising edge of state-of-the-art high-power lasers can limit proton energies, it is advantageous for heavy-ion acceleration. Two-dimensional particle-in-cell simulations show that the Joule heating in the target bulk results in a high temperature (∼10 keV) solid density plasma, leading to the generation of high flux highly charged ions (Z= 40−2 +2, 10 MeV/nucleon) via electron collisional ionization, which are extracted and accelerated with a small divergence by an extreme sheath field at the target rear. However, with reduced target thickness this favorable acceleration is degraded due to the target deformation via laser hole boring, which accompanies higher energy ions with higher charge states but in an uncontrollable manner. Our elucidation of the fundamental processes of high-intensity laser-driven ionization and ion acceleration provides a path for improving the control and parameters of laser-driven heavy-ion sources, a key component for next-generation heavy-ion accelerators.

New regime of high-order harmonic generation by relativistic-irradiance multi-TW fs lasers focused onto gas jet targets is discussed. The laser induces multi-stream relativistic plasma flow resulting in the formation of density singularities. Here we analyse the dependence of harmonic yield on the focal spot quality and derive the required laser parameters for efficient harmonics generation.

We present here a new diagnostics based on using LiF crystal detectors that are able to perform measurements an intensity distribution of X-rays beams with diameters ranging from some microns up to some centimeters with high spatial resolution (~1 micron). in situ, 3D visualization of SACLA XFEL focused beam profile along propagation, including propagation inside photoluminescence solid materials, is demonstrated.

By using of high-resolution X-ray spectroscopic measurements and kinetic simulations, we demonstrate that the energy of femtosecond laser pulses is efficiently converted to X-ray radiation and produces exotic states in solid density plasma regions. It is shown that exotic hollow multicharged ions states can be obtained and studied not only by ultra-intense X-ray radiation of XFEL, but also upon using optical laser technology. We have concluded that observable features of the hollow-ion spectra are sensitive to such plasma parameters as density, temperature, hot-electron fraction, and intensity of X-ray pumping radiation and could be used for effective diagnostics of warm dense matter parameters.