Spin and orbital angular momentum of an optical beam are two independent parameters that exhibit distinct effects on mechanical objects. However, when laser beams with angular momentum interact with plasmas, one can observe the interplay between the spin and the orbital angular momentum. Here, by measuring the helical phase of the second harmonic 2ω radiation generated in an underdense plasma using a known spin and orbital angular momentum pump beam, we verify that the total angular momentum of photons is conserved and observe the conversion of spin to orbital angular momentum. We further determine the source of the 2ω photons by analyzing near field intensity distributions of the 2ω light. The 2ω images are consistent with these photons being generated near the largest intensity gradients of the pump beam in the plasma as predicted by the combined effect of spin and orbital angular momentum when Laguerre-Gaussian beams are used.
In this work using three-dimensional particle-in-cell simulations and analytical considerations we demonstrate intense high-order plasma surface harmonics carrying a time-varying orbital angular momentum (OAM) -- the self-torque. We show that by using two laser beams with different OAMs $l_1$ and $l_2$ and a certain delay between each other and shooting them obliquely on an overdense plasma target, one can generate harmonics with OAM spanning $nl_1$ to $nl_2$, where $n$ is the order of the harmonic. Such intense self-torqued harmonics can offer new possibilities in ultrafast spectroscopy.
We report the enhancement of individual harmonics generated at a relativistic ultra-steep plasma vacuum interface. Simulations show the harmonic emission to be due to the coupled action of two high velocity oscillations -- at the fundamental $ω_L$ and at the plasma frequency $ω_P$ of the bulk plasma. The synthesis of the enhanced harmonics can be described by the reflection of the incident laser pulse at a relativistic mirror oscillating at $ω_L$ and $ω_P$.
Harmonic generation in the limit of ultra-steep density gradients is studied experimentally. Observations demonstrate that while the efficient generation of high order harmonics from relativistic surfaces requires steep plasma density scale-lengths ($L_p/λ< 1$) the absolute efficiency of the harmonics declines for the steepest plasma density scale-length $L_p \to 0$, thus demonstrating that near-steplike density gradients can be achieved for interactions using high-contrast high-intensity laser pulses. Absolute photon yields are obtained using a calibrated detection system. The efficiency of h…
Lorentz invariant scalar functions of the magnetic field are defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the {\it potential magnetic field} introduced by R. Hide in Ann. Geophys. 1, 59 (1983) on the line of Ertel's theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the Eulerian-Lagrangian variable mapping. In addition the adopted procedure allows us to formulate Alfvèn theorem for the conservation of the magnetic flux through a surface comoving with the plasma in a Loren…
The hybrid Stimulated Raman Scattering - Two Plasmon Decay instability had shown to play the dominant role for plasma waves excitation and energy absorption at interaction of very intense femtosecond obliquely incident $p$-polarized laser pulse (intensity $10^{17}-5\cdot10^{19}$ W/cm$^2$) with a steep gradient ($L\sim λ$) plasma near the quarter critical surface, i.e. within the typical for modern experiments conditions. The plasmons are excited as two wave packets confined near this surface with very wide $\approx ω_0/c$ spatial spectra along its normal. Hence, phase matching conditions for 3…
A scheme for generating intense high-harmonic optical vortices is proposed. It relies on spin-orbit interaction of light when a relativistically-strong circularly polarized laser pulse irradiates a micro-plasma-waveguide. The intense laser field drives a strong surface wave at the inner boundary of the waveguide, which leads to high-order harmonic generation as the laser traveling inside. For a circularly polarized drive laser, the optical chirality is imprinted to the surface wave, which facilitates conversion of spin angular momentum of the fundamental light into orbital angular momenta of t…
We analyse the kinematic properties of a plasma electron hole: a non-linear self-sustained localized positive electric potential perturbation, trapping electrons, that behaves as a coherent entity. When a hole accelerates or grows in depth, ion and electron plasma momentum is changed both within the hole and outside it, by an energization process we call jetting. We present a comprehensive analytic calculation of the momentum changes of an isolated general one-dimensional hole. The conservation of the total momentum gives the hole's kinematics, determining its velocity evolution. Our results e…
The ideal CGL plasma equations, including the double adiabatic conservation laws for the parallel ($p_\parallel$) and perpendicular pressure ($p_\perp$), are investigated using a Lagrangian variational principle. An Euler-Poincaré variational principle is developed and the non-canonical Poisson bracket is obtained, in which the non-canonical variables consist of the mass flux ${\bf M}$, the density $ρ$, three entropy variables, $σ=ρS$, $σ_\parallel=ρS_\parallel$, $σ_\perp=ρS_\perp$ ($S_\parallel$ and $S_\perp$ are the two scalar entropy invariants), and the magnetic induction ${\bf B}$. Conser…
In this work we numerically study a self-guiding process in which ionization plays a dominant role and analyze its effect on high-order harmonic generation (HHG) in gases. Although this type of self-guiding --- termed as plasma-core induced self-guiding in previous works --- limits the achievable cut-off by regulating the intensity of the laser beam, it provides favorable conditions for phase matching, which is indispensable for high-flux gas high-harmonic sources. To underline the role of self-guiding in efficient HHG, we investigate the time-dependent phase matching conditions in the guided …
It is shown that a vorticity, constructed from spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that obeys the standard vortex dynamics. Expressions for the quantum or spin vorticity, and for the resulting generalized helicity invariant are derived. Reduction of the rather complex spinning quantum system to a well known and highly investigated classical form opens familiar channels for the delineation of physics peculiar to dense plasmas spanning solid state …
Vector beam, with a spatial nonuniform polarization distribution, is important for many applications due to its unique field characteristics and novel effects when interacting with matter. Here through three-dimensional particle-in-cell simulations, we demonstrate that intense vector beams in the extreme-ultraviolet to x-ray spectral region can be generated by means of high harmonic generation (HHG) in the relativistic regime. The vector features of the fundamental laser beam can be transferred to the higher frequency emission coherently during the extreme nonlinear HHG dynamics from relativis…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD). Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, can furnish this gap in the lower levels of the model hierarchy. In the present work, we develop low-dimensional Galerkin plasma models which preserve global conservation laws by construction. This additional model structure enables physics-constrained machine learning algorithms that can …
Experimental data compiled over five decades of dense plasma focus research is consistent with the snowplow model of sheath propagation, based on the hypothetical balance between magnetic pressure driving the plasma into neutral gas ahead and wind pressure resisting its motion. The resulting sheath velocity, or the numerically proportional drive parameter, is known to be approximately constant for devices optimized for neutron production over 8 decades of capacitor bank energy. This paper shows that the validity of the snowplow hypothesis, with some correction, as well as the non-dependence of…
The influence of surface plasma waves (SPW) on high harmonic generation (HHG) from the interaction of intense lasers with overdense plasma is analyzed. It is shown, that the surface waves lead to the emission of harmonics away from the optical axis. These off-axis harmonics violate the parity selection rules found from 1D models. Further, our investigations in the highly relativistic regime point towards the existence of a new SPW generation process.
Second-harmonic emission at a frequency that is twice the laser frequency is an important diagnostic for nonlinear laser-plasma interaction. It is forbidden for centrosymmetric materials such as the bulk of sapphire. The symmetry, however, can be broken by dielectric discontinuities as a result of plasma generation inside a solid dielectric. In the present work, we explore the basic characteristics of experimentally observed second-harmonic emission during focusing a femtosecond Bessel beam inside sapphire. We employ three-dimensional particle-in-cell simulations and the Helmholtz wave equatio…
High harmonic generation by relativistically intense laser pulses from overdense plasma layers is surveyed. High harmonics are generated in form of (sub-)attosecond pulses when the plasma surface rebounds towards the observer with relativistic velocity. Different cases are considered. The "relativistically oscillating mirror" (ROM) model, describing the most typical case, is analyzed in detail. The resulting harmonic spectrum is usually a power law with the exponent -8/3 [baeva2006relativistic], but possible exceptions due to "higher order γ-spikes" are considered. It is shown that under certa…
We report for the first time on the anticorrelated emission of high-order harmonics and energetic electron beams from a solid-density plasma with a sharp vacuum interface$-$plasma mirror$-$driven by an intense ultrashort laser pulse. We highlight the key role played by the nanoscale structure of the plasma surface during the interaction by measuring the spatial and spectral properties of harmonics and electron beams emitted by a plasma mirror. We show that the nanoscale behavior of the plasma mirror can be controlled by tuning the scale length of the electronic density gradient, which is measu…
When the nature of a magnetosonic pulse propagating in a bounded magnetized plasma slab is successively transformed from compression to rarefaction and vice-versa upon reflection at a plasma-vacuum interface, both the energy and the longitudinal electromagnetic (EM) momentum of the plasma-pulse system are found to oscillate between two states. Simple analytical models and particle-in-cell simulations show that these oscillations are associated with EM radiation to and from the surrounding magnetized vacuum. For partial reflection supplemental losses in total pulse energy and mechanical momentu…
A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa- Mima equation, but does not conserve enstrophy, and, as a result, exhibits a forward cascade of energy, to small scales. The inertial-range energy spectrum is argued to be shallower than a -11/3 power law, as compared to the -5 law of the Hasegawa-Mima enstrophy cascade. This property, confirmed here by direct numerical simulations of the fluid system, may help explain the fluctuation spectrum observed in gyrokineti…
Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects…
Plasma high harmonics generation from an extremely intense short-pulse laser is explored by including the effects of ion motion, electron-ion collisions and radiation reaction force in the plasma dynamics. The laser radiation pressure induces plasma ion motion through the hole-boring effect resulting into the frequency shifting and widening of the harmonic spectra. Classical radiation reaction force slightly mitigates the frequency broadening caused by the ion motion. Based on the results and physical considerations, parameter maps highlighting optimum regions for generating a single intense a…
The mechanism of harmonic generation in both O and X-mode configurations for a magnetized plasma has been explored here in detail with the help of Particle-In-Cell (PIC) simulations. A detailed characterization of both the reflected and transmitted electromagnetic radiation propagating in the bulk of the plasma has been carried out for this purpose. The efficiency of harmonic generation is shown to increase with the incident laser intensity. Dependency of harmonic efficiency has also been found on magnetic field strength. This work demonstrates that there is an optimum value of the magnetic fi…
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not, respectively. The relativistic cold laser-plasma equations, describing the interaction between an intense laser field with a cold relativistic electron plasma, provide a useful set of equations amenable to both variational formulations. The derivation of conservation laws by Noether method proceeds from the Noether equation, whose form depends on the variational form…
Generation of electromagnetic radiation near the second harmonic of the plasma frequency during the injection of an electron beam into a rippled-density plasma channel is investigated using both analytical theory and particle-in-cell simulations. The generating scheme is based on nonlinear interaction of the most unstable beam-driven potential plasma wave with its satellite arising due to scattering on the longitudinal modulation of plasma density. Resulting superluminal oscillations of electric current in a finite-size plasma channel radiate electromagnetic waves via the same mechanism which …
The power of second harmonic electromagnetic emission is calculated for the case when strong plasma turbulence is excited by a powerful electron beam in a magnetized plasma. It is shown that the simple analytical model of strong plasma turbulence with the assumption of a constant pump power is able to explain experimentally observed bursts of electromagnetic radiation as a consequence of separate collapse events. It is also found that the electromagnetic emission power calculated for three-wave interaction processes occurring in the long-wavelength part of turbulent spectrum is in order-of-mag…
We introduce two-color counterrotating circularly polarized laser fields as a new way to spectrally control high harmonic generation (HHG) from relativistic plasma mirrors. Through particle-in-cell simulations, we show that only a selected group of harmonic orders can appear owing to the symmetry of the laser fields and the related conservation laws. By adjusting the intensity ratio of the two driving field components, we demonstrate the overall HHG efficiency, the relative intensity of allowed neighboring harmonic orders, and the polarization state of the harmonic source can be tuned. The HHG…
Semi-analytic expressions for the electron cyclotron emission (ECE) shape function are developed for arbitrary high harmonics. The integrand of the ${m}^{\mathrm{th}}$ harmonic ECE shape function is fitted with the readily-integrable test function which is parameterized by plasma temperature $T_e$, harmonic number $m$ and emission angle $θ$. Semi-analytic formulae for high harmonic ECE emissivity are obtained by integrating the test integrand with the fitting parameters gained from the regression analysis as well as the inductive studies for arbitrary cases. The developed expression matches th…
The effects of second harmonics of the density and temperature perturbations on the linear Geodesic Acoustic Mode (GAM) frequency and non-linear generation of the GAM are investigated, using a fluid model. We show that the second harmonics contribute to the frequency through the density gradient scale length and the wave number of the GAM. In addition, the linear frequency of the GAM is generally increased by coupling to the higher harmonic.
In [I.R. Khairulin et al., submitted to Phys. Rev. Lett.] we propose a method for amplifying a train of sub-femtosecond pulses of circularly or elliptically polarized extreme ultraviolet (XUV) radiation, constituted by high-order harmonics of an infrared (IR) laser field, in a neon-like active medium of a plasma-based X-ray laser, additionally irradiated with a replica of a fundamental frequency laser field used to generate harmonics, and show the possibility of maintaining or enhancing the ellipticity of high-harmonic radiation during its amplification. In the present paper we describe this p…
Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field terms. Equations for the fields are given by functional derivatives. The symmetry through the Hamiltonian with time and toroidal angle invariance of the geometry lead to energy and toroidal momentum conservation. In various levels of ordering against fluctuation amplitude, energetic consistency is exact. The role of this in underpinning of conservation laws…
The laser interaction with an electron-positron-ion mixed plasma is studied, from the perspective of the associated high-order harmonic generation. For an idealized mixed plasma which is assumed with a sharp plasma-vacuum interface and uniform density distribution, when it is irradiated by a weakly relativistic laser pulse, well-defined signals at harmonics of the plasma frequency in the harmonic spectrum are observed. These characteristic signals are attributed to the inverse two-plasmon decay of the counterpropagating monochromatic plasma waves which are excited by the energetic electrons an…
We report results from a series of PIC simulations carried out to investigate the interaction of intense laser light with overdense plasma and in particular, aspects of the harmonic emission spectrum generated in these interactions. Recent observations of emission in this range by Watts et al. (2002) show emission above the 20th harmonic extending to the 37th with conversion efficiencies of order 10^-6 with this spectrum showing distinct, if variable, modulation of between two and four harmonics. This spectral feature proved highly sensitive to the incident intensity, with more pronounced modu…
Visible or near infra-red light can be manipulated to produce bursts of coherent extreme ultraviolet (XUV) or X-rays via the relativistic high-order harmonic generation process when a laser irradiates a solid plasma target. The intensity of the spectral components of the reflected signal decays with increase of harmonic order and the efficiency of this non-linear process largely hinges on how prompt this decay is. This is governed by the conditions of the laser-plasma interaction for which various models have been proposed. At relativistic intensities, a spectrum exhibiting a power-law decay w…
The Eulerian variational principle for the Vlasov-Poisson-Ampère system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to obtain the momentum conservation law and the symmetric pressure in a more direct way than using the translational and rotational symmetries of the system. Next, the Eulerian variational principle is given for the collisionless drift kinetic equation, where particles' phase-space trajectories in given electromagnetic fields are described by Littlejohn's guiding cente…
In present paper, we describe a theoretical model of generation of harmonic emissions of type III solar radio bursts. The goal of our study is to fully take into account the most efficient physical processes participating in generation of harmonic electromagnetic emission via nonlinear coupling of Langmuir waves in randomly inhomogeneous plasma of solar wind ($l+l^{'} \rightarrow t$). We revisit the conventional mechanism of coalescence of primarily generated and back-scattered Langmuir waves in quasihomogeneous plasma. Additionally, we propose and investigate another mechanism that generates …
Ultrafast extreme ultraviolet (XUV) sources with a controllable polarization state are powerful tools for investigating the structural and electronic as well as the magnetic properties of materials. However, such light sources are still limited to only a few free-electron laser facilities and, very recently, to high-order harmonic generation from noble gases. Here we propose and numerically demonstrate a laser-plasma scheme to generate bright XUV pulses with fully controlled polarization. In this scheme, an elliptically-polarized laser pulse is obliquely incident on a plasma surface, and the r…
A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is dev…
Three-wave interactions in plasmas are described, in the framework of kinetic theory, by the quadratic response tensor (QRT). The cold-plasma QRT is a common approximation for interactions between three fast waves. Here, the first-order thermal correction (FOTC) to the cold-plasma QRT is derived for interactions between three fast waves in a warm unmagnetized collisionless plasma, whose particles have an arbitrary isotropic distribution function. The FOTC to the cold-plasma QRT is shown to depend on the second moment of the distribution function, the phase speeds of the waves, and the interact…
We investigate the generation of broadband terahertz (THz) pulses with phase singularity from air plasmas created by fundamental and second harmonic laser pulses. We show that when the second harmonic beam carries a vortex charge, the THz beam acquires a vortex structure as well. A generic feature of such THz vortex is that the intensity is modulated along the azimuthal angle, which can be attributed to the spatially varying relative phase difference between the two pump harmonics. Fully space and time resolved numerical simulations reveal that transverse instabilities of the pump further affe…
High harmonic generation due to the interaction of a short ultra relativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultra relativistic similarity theory we show that the high harmonic spectrum is universal, i.e. it does not depend on the interaction details. The spectrum includes the power law part $I_n\propto n^{-8/3}$ for $n<\sqrt{8α}γ_{\max}^3$, followed by exponential decay. Here $γ_{\max}$ is the largest relativistic $γ$-factor of the plasma surface and $α$ is the second derivative of the surface velocity at this moment. The high ha…
A particle-in-cell (PIC) simulation study is performed to investigate the discharge asymmetry, higher harmonic generations and electron heating mechanism in a low pressure very high frequency capacitively coupled plasma (CCP) excited by a saw-tooth like current waveform. Two current densities, 50 A/m2 and 100 A/m2 are chosen for a constant gas pressure of 5 mTorr in argon plasma. The driving frequency is varied from 13.56 MHz to 54.24 MHz. At a lower driving frequency, high frequency modulations on the instantaneous sheath edge position at the grounded electrode are observed. These high freque…
Particle-in-cell (PIC) plasma simulations are a productive and valued tool for the study of nonlinear plasma phenomena, yet there are basic questions about the simulation methods themselves that remain unanswered. Here we study one such question: energy and momentum conservation by PIC. We employ both analysis and simulations of one-dimensional, electrostatic plasmas to understand why PIC simulations are either energy or momentum conserving but not both, what the role of numerical stability is in non-conservation, and how do errors in conservation scale with the numerical parameters. Conservin…
An alternative mechanism is proposed for the generation of harmonics of the electron plasma frequency due to the development of explosive instability in a system of interpenetrating electron and proton flows in the solar atmosphere. The efficiency of the new mechanism in comparison with the earlier discussed mechanisms involving multistage processes of nonlinear interaction of waves in plasma is determined. It is shown that the development of explosive instability can lead to the excitation of the second and third harmonics of the plasma frequency with comparable amplitudes.
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result of increasing contribution of harmonics and may be used in theoretical studies of processes involving nonlinear plasma waves.
Observations made in dusty plasma experiments suggest that an ensemble of electrically charged solid particles, confined in an elongated trap, develops structural inhomogeneities. With narrowing the trap the particles tend to form layers oriented parallel with the trap walls. In this work we present theoretical and numerical results on the structure of three-dimensional many-particle systems with screened Coulomb (Yukawa) inter-particle interaction in the strongly coupled liquid phase, confined in one-dimensional harmonic trap, forming quasi-2D configurations. Particle density profiles are cal…
A relativistic electron beam propagating through plasma induces a return current in the system. Such a system of counterstreaming forward and return current is susceptible to host of instabilities out of which Weibel remains a dominant mode for destabilizing the system. Weibel instability has been widely investigated in simulations, experiments, as well as, analytically using fluid and kinetic treatments. A purely growing mode like Weibel instability can also be understood by using conservation theorems and energy principle analysis. An electrostatic analog to the Weibel instability, two strea…
