Recurrent spatio-temporal structures in presence of continuous symmetries

When statistical assumptions do not hold and coherent structures are present in spatially extended systems such as fluid flows, flame fronts and field theories, a dynamical description of turbulent phenomena becomes necessary. In the dynamical systems approach, theory of turbulence for a given system, with given boundary conditions, is given by (a) the geometry of its infinite-dimensional state space and (b) the associated measure, that is, the likelihood that asymptotic dynamics visits a given state space region. In this thesis this vision is pursued in the context of Kuramoto-Sivashinsky system, one of the simplest physically interesting spatially extended nonlinear systems. With periodic boundary conditions, continuous translational symmetry endows state space with additional structure that often dictates the type of observed solutions. At the same time, the notion of recurrence becomes relative: asymptotic dynamics visits the neighborhood of any equivalent, translated point, infinitely often. Identification of points related by the symmetry group action, termed symmetry reduction, although conceptually simple as the group action is linear, is hard to implement in practice, yet it leads to dramatic simplification of dynamics. Here we propose a scheme, based on the method of moving frames of Cartan, to efficiently project solutions of high-dimensional truncations of partial differential equations computed in the original space to a reduced state space. The procedure simplifies the visualization of high-dimensional flows and provides new insight into the role the unstable manifolds of equilibria and traveling waves play in organizing Kuramoto-Sivashinsky flow. This in turn elucidates the mechanism that creates unstable modulated traveling waves (periodic orbits in reduced space) that provide a skeleton of the dynamics. The compact description of dynamics thus achieved sets the stage for reduction of the dynamics to mappings between a set of Poincare sections.Ph.D.Committee Chair: Cvitanovic, Predrag; Committee Member: Dieci, Luca; Committee Member: Grigoriev, Roman; Committee Member: Schatz, Michael; Committee Member: Wiesenfeld, Kur

Laser wakefield driven generation of isolated CEP-tunable intense sub-cycle pulses

Sources of intense, ultra-short electromagnetic pulses enable applications such as attosecond pulse generation, control of electron motion in solids and the observation of reaction dynamics at the electronic level. For such applications both high-intensity and carrier envelope phase~(CEP) tunability are beneficial, yet hard to obtain with current methods. In this work we present a new scheme for generation of isolated CEP-tunable intense sub-cycle pulses with central frequencies that range from the midinfrared to the ultraviolet. It utilizes an intense laser pulse which drives a wake in a plasma, co-propagating with a long-wavelength seed pulse. The moving electron density spike of the wake amplifies the seed and forms a sub-cycle pulse. Controlling the CEP of the seed pulse, or the delay between driver and seed leads to CEP-tunability, while frequency tunability can be achieved by adjusting the laser and plasma parameters. Our 2D and 3D Particle-In-Cell simulations predict laser-to-sub-cycle-pulse conversion efficiencies up to 1%, resulting in relativistically intense sub-cycle pulses.Comment: Replaced with updated versio

Parametric study of laser wakefield driven generation of intense sub-cycle pulses

Intense sub-cycle electromagnetic pulses allow one to drive nonlinear processes in matter with unprecedented levels of control. However, it remains challenging to scale such sources in the relativistic regime. Recently, a scheme that utilizes laser-driven wakes in plasmas to amplify and compress seed laser pulses to produce tunable, carrier-envelope-phase stable, relativistic sub-cycle pulses has been proposed. Here, we present parametric studies of this process using particle-in-cell simulations, showing its robustness over a wide range of experimentally accessible laser-plasma interaction parameters, spanning more than two orders of magnitude of background plasma density. The method is shown to work with different gas-jet profiles, including structured density profiles and is robust over a relatively wide range of driver laser intensities. Our study shows that sub-cycle pulses of up to 10mJ of energy can be produced

Electron beam driven generation of frequency-tunable isolated relativistic sub-cycle pulses

We propose a novel scheme for frequency-tunable sub-cycle electromagnetic pulse generation. To this end a pump electron beam is injected into an electromagnetic seed pulse as the latter is reflected by a mirror. The electron beam is shown to be able to amplify the field of the seed pulse while upshifting its central frequency and reducing its number of cycles. We demonstrate the amplification by means of 1D and 2D particle-in-cell simulations. In order to explain and optimize the process, a model based on fluid theory is proposed. We estimate that using currently available electron beams and terahertz pulse sources, our scheme is able to produce mJ-strong mid-infrared sub-cycle pulses.Comment: 8 figure

Origins of plateau formation in ion energy spectra under target normal sheath acceleration

Target normal sheath acceleration (TNSA) is a method employed in laser--matter interaction experiments to accelerate light ions (usually protons). Laser setups with durations of a few 10 fs and relatively low intensity contrasts observe plateau regions in their ion energy spectra when shooting on thin foil targets with thicknesses of order 10 $\mathrm{\mu}$m. In this paper we identify a mechanism which explains this phenomenon using one dimensional particle-in-cell simulations. Fast electrons generated from the laser interaction recirculate back and forth through the target, giving rise to time-oscillating charge and current densities at the target backside. Periodic decreases in the electron density lead to transient disruptions of the TNSA sheath field: peaks in the ion spectra form as a result, which are then spread in energy from a modified potential driven by further electron recirculation. The ratio between the laser pulse duration and the recirculation period (dependent on the target thickness, including the portion of the pre-plasma which is denser than the critical density) determines if a plateau forms in the energy spectra.Comment: 11 pages, 12 figure

Cartography of high-dimensional flows: A visual guide to sections and slices

Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions, qualitatively captured by a `template'. Together these charts provide an atlas of the symmetry-reduced `slice' of state space, charting the regions of the manifold explored by the trajectories of interest. Within the slice, relative equilibria reduce to equilibria and relative periodic orbits reduce to periodic orbits. Visualizations of these solutions and their unstable manifolds reveal their interrelations and the role they play in organizing turbulence/chaos.Comment: 12 Pages, 12 figure

Collisional effects on the electrostatic shock dynamics in thin-foil targets driven by an ultraintense short pulse laser

We numerically investigate the impact of Coulomb collisions on the ion dynamics in high-$Z$, solid density caesium hydride and copper targets, irradiated by high-intensity ($I\approx2{-}5\times10^{20}{\rm\,Wcm^{-2}}$), ultrashort (${\sim}10{\rm\,fs}$), circularly polarized laser pulses, using particle-in-cell simulations. Collisions significantly enhance electron heating, thereby strongly increasing the speed of a shock wave launched in the laser-plasma interaction. In the caesium hydride target, collisions between the two ion species heat the protons to ${\sim}100{-}1000{\rm\,eV}$ temperatures. However, in contrast to previous work (A.E. Turrell etal., 2015 Nat. Commun. 6, 8905), this process happens in the upstream only, due to nearly total proton reflection. This difference is ascribed to distinct models used to treat collisions in dense/cold plasmas. In the case of a copper target, ion reflection can start as a self-amplifying process, bootstrapping itself. Afterwards, collisions between the reflected and upstream ions heat these two populations significantly. When increasing the pulse duration to $60{\rm\,fs}$, the shock front more clearly decouples from the laser piston, and so can be studied without direct interference from the laser. The shock wave formed at early times exhibits properties typical of both hydrodynamic and electrostatic shocks, including ion reflection. At late times, the shock is seen to evolve into a hydrodynamic blast wave

On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain

The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaotic dynamics. The continuous spatial translation symmetry leads to relative equilibrium (traveling wave) and relative periodic orbit (modulated traveling wave) solutions. The discrete symmetries lead to existence of equilibrium and periodic orbit solutions, induce decomposition of state space into invariant subspaces, and enforce certain structurally stable heteroclinic connections between equilibria. We show, on the example of a particular small-cell Kuramoto-Sivashinsky system, how the geometry of its dynamical state space is organized by a rigid `cage' built by heteroclinic connections between equilibria, and demonstrate the preponderance of unstable relative periodic orbits and their likely role as the skeleton underpinning spatiotemporal turbulence in systems with continuous symmetries. We also offer novel visualizations of the high-dimensional Kuramoto-Sivashinsky state space flow through projections onto low-dimensional, PDE representation independent, dynamically invariant intrinsic coordinate frames, as well as in terms of the physical, symmetry invariant energy transfer rates.Comment: 31 pages, 17 figures; added references, corrected typos. Due to file size restrictions some figures in this preprint are of low quality. A high quality copy may be obtained from http://www.cns.gatech.edu/~predrag/papers/preprints.html#rp

Effects of oblique incidence and colliding pulses on laser-driven proton acceleration from relativistically transparent ultrathin targets

The use of ultrathin solid foils offers optimal conditions for accelerating protons from laser-matter interactions. When the target is thin enough that relativistic self-induced transparency (RSIT) sets in, all of the target electrons get heated to high energies by the laser, which maximizes the accelerating electric field and therefore the final ion energy. In this work, we first investigate how ion acceleration by ultraintense femtosecond laser pulses in transparent CH$_2$ solid foils is modified when turning from normal to oblique ($45^\circ$) incidence. Due to stronger electron heating, we find that higher proton energies can be obtained at oblique incidence but in thinner optimum targets. We then show that proton acceleration can be further improved by splitting the laser pulse into two half-pulses focused at opposite incidence angles. An increase by $\sim 30\,\%$ in the maximum proton energy and by a factor of $\sim 4$ in the high-energy proton charge is reported compared to the reference case of a single normally incident pulse.Comment: 11 pages, 7 figure

Fast collisional electron heating and relaxation in thin foils driven by a circularly polarized ultraintense short-pulse laser

The creation of well-thermalized, hot and dense plasmas is attractive for warm dense matter studies. We investigate collisionally induced energy absorption of an ultraintense and ultrashort laser pulse in a solid copper target using particle-in-cell simulations. We find that, upon irradiation by a $2\times10^{20}{\rm\,W\,cm^{-2}}$ intensity, $60{\rm\,fs}$ duration, circularly polarized laser pulse, the electrons in the collisional simulation rapidly reach a well-thermalized distribution with ${\sim}3.5{\rm\,keV}$ temperature, while in the collisionless simulation the absorption is several orders of magnitude weaker. Circular polarization inhibits the generation of suprathermal electrons, while ensuring efficient bulk heating through inverse bremsstrahlung, a mechanism usually overlooked at relativistic laser intensity. An additional simulation, taking account of both collisional and field ionization, yields similar results: the bulk electrons are heated to ${\sim}2.5{\rm\,keV}$, but with a somewhat lower degree of thermalization than in the pre-set, fixed-ionization case. The collisional absorption mechanism is found to be robust against variations in the laser parameters. At fixed laser pulse energy, increasing the pulse duration rather than the intensity leads to a higher electron temperature.Comment: Published in Journal of Plasma Physic