Laser-field synchrotron radiation

An electron with an appropriate initial velocity injected into an oncoming, ultraintense circularly polarized laser pulse can execute a circular relativistic motion at the peak of the laser pulse. The circulating electron then radiates in the same manner as that in the storage ring of a conventional synchrotron source. Owing to the extremely small orbit radius, the laser-field synchrotron radiation thus generated can be a compact source of radiation pulses at short wavelength and short duration.

Photoelectron angular distributions from above threshold ionization of hydrogen atoms in strong laser fields

We apply a scattering theory of nonperturbative quantum electrodynamics to study the photoelectron angular distributions (PADs) of a hydrogen atom irradiated by linearly polarized laser light. The calculated PADs show main lobes and jetlike structure. Previous experimental studies reveal that in a set of above-threshold-ionization peaks when the absorbed-photon number increases by one, the jet number also increases by one. Our study confirms this experimental observation. Our calculations further predict that in some cases three more jets may appear with just one-more-photon absorption. With consideration of laser-frequency change, one less jet may also appear with one-more-photon absorption. The jetlike structure of PADs is due to the maxima of generalized phased Bessel functions, not an indication of the quantum number of photoelectron angular momentum states.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

Attosecond X-ray pulse obtained from linear Thomson scattering

Linear Thomson scattering by a relativistic electron of a short pulse laser has been investigated by computer simulation. Under a laser field with a pulse of 33.3-fs full-width at half-maximum, and the initial energy of an electron of gamma(0) = 10, the motion of the electron is relativistic and generates an ultrashort radiation of 76-as with a photon wave length of 2.5-nm in the backward scattering. The radiation under a high relativistic energy electron has better characteristic than under a low relativistic energy electron in terms of the pulse width and the angular distribution. (c) 2005 Elsevier GrnbH. All rights reserved.

Intense laser beam guiding in self-induced electron cavitation channel in underdense plasmas

In underdense plasmas, the transverse ponderomotive force of an intense laser beam with Gaussian transverse profile expels electrons radially, and it can lead to an electron cavitation. An improved cavitation model with charge conservation constraint is applied to the determination of the width of the electron cavity. The envelope equation for laser spot size derived by using source-dependent expansion method is extended to including the electron cavity. The condition for self-guiding is given and illuminated by an effective potential for the laser spot size. The effects of the laser power, plasma density and energy dissipation on the self-guiding condition are discussed.

Fast growing mode of stimulated Raman scattering in a pure three-wave process

Stimulated Raman scattering (SRS) of a relativistic laser in plasmas is studied in the framework of the standard equation set of a three-wave process. As far as every wave involved in the process is concerned, its evolution has two aspects: time-dependent amplitude and time-dependent frequency. These two aspects affect each other. Strict analysis and numerical experiment on the full three-wave equation set reveal that a fast growing mode of the instability, which could reach a balance or saturation point during a period far shorter than an estimation based on conventional analysis, could take place in a standard three-wave process without coupling with a fourth wave. This fast growing mode is found to stem from the constraint set by the background density on the amplitude of the driven Langmuir wave. The effect of various parameters on the development of the SRS instability is studied by numerical calculation of the history of the instability in different cases. (c) 2007 American Institute of Physics.

Efficient GeV ion generation by ultraintense circularly polarized laser pulse

The interaction of an ultraintense circularly polarized laser pulse and a solid target is studied by one-dimensional particle-in-cell simulations. Ions at the front of the target are reflected by a moving quasisteady electrostatic field and obtain a relativistic velocity. At a laser intensity of 10(22) W/cm(2), almost half of the laser energy is transferred to ions and GeV ions are obtained. Effects of laser polarization state and target thickness on the laser energy conversion are investigated. It is found that a circularly polarized laser pulse can accelerate ions more efficiently than a linearly polarized laser pulse at the same laser and target parameters. A monoenergetic ion bunch is obtained for the ultrathin target, which is accelerated as a single entity. (c) 2007 American Institute of Physics.

Acceleration of ultra-thin electron layer.Analytical treatment compared with 1D-PIC simulation

In this paper, we apply an analytical model [V.V. Kulagin et al., Phys. Plasmas 14, 113101 (2007)] to describe the acceleration of an ultra-thin electron layer by a schematic single-cycle laser pulse and compare with one-dimensional particle-in-cell (1D-PIC) simulations. This is in the context of creating a relativistic mirror for coherent backscattering and supplements two related papers in this EPJD volume. The model is shown to reproduce the 1D-PIC results almost quantitatively for the short time of a few laser periods sufficient for the backscattering of ultra-short probe pulses.

Observations of hydrogen and helium isotopes in solar cosmic rays

The isotopic composition of hydrogen and helium in solar cosmic rays provides a means of studying solar flare particle acceleration mechanisms since the enhanced relative abundance of rare isotopes, such as ²H, ³H and ³He, is due to their production by inelastic nuclear collisions in the solar atmosphere during the flare. In this work the Caltech Electron/Isotope Spectrometer on the IMP-7 spacecraft has been used to measure this isotopic composition. The response of the dE/dx-E particle telescope is discussed and alpha particle channeling in thin detectors is identified as an important background source affecting measurement of low values of (³He/⁴He).

The following flare-averaged results are obtained for the period, October, 1972 - November, 1973: (²H/¹H) = 7⁺¹⁰_-6 X 10^-6 (1.6 - 8.6 MeV/nuc), (³H/¹H) less than 3.4 x 10^-6 (1.2 - 6.8 MeV/nuc), (³He/⁴He) = (9 ± 4) x 10^-3, (³He/¹H) = (1.7 ± 0.7) x 10^-4 (3.1 - 15.0 MeV/nuc). The deuterium and tritium ratios are significantly lower than the same ratios at higher energies, suggesting that the deuterium and tritium spectra are harder than that of the protons. They are, however, consistent with the same thin target model relativistic path length of ~ 1 g/cm² (or equivalently ~ 0.3 g/cm² at 30 MeV/nuc) which is implied by the higher energy results. The ³He results, consistent with previous observations, would imply a path length at least 3 times as long, but the observations may be contaminated by small ³He rich solar events.

During 1973 three "³He rich events," containing much more ³He than ²H or ³H were observed on 14 February, 29 June and 5 September. Although the total production cross sections for ²H,³H and ³He are comparable, an upper limit to (²H/³He) and (³H/³He) was 0.053 (2.9-6.8 MeV/nuc), summing over the three events. This upper limit is marginally consistent with Ramaty and Kozlovsky's thick target model which accounts for such events by the nuclear reaction kinematics and directional properties of the flare acceleration process. The 5 September event was particularly significant in that much more ³He was observed than ⁴He and the fluxes of ³He and ¹H were about equal. The range of (³He/⁴He) for such events reported to date is 0.2 to ~ 6 while (³He/¹H) extends from 10^-3 to ~ 1. The role of backscattered and mirroring protons and alphas in accounting for such variations is discussed.

The needle in the hundred square degree haystack: The hunt for binary neutron star mergers with LIGO and Palomar Transient Factory

The Advanced LIGO and Virgo experiments are poised to detect gravitational waves (GWs) directly for the first time this decade. The ultimate prize will be joint observation of a compact binary merger in both gravitational and electromagnetic channels. However, GW sky locations that are uncertain by hundreds of square degrees will pose a challenge. I describe a real-time detection pipeline and a rapid Bayesian parameter estimation code that will make it possible to search promptly for optical counterparts in Advanced LIGO. Having analyzed a comprehensive population of simulated GW sources, we describe the sky localization accuracy that the GW detector network will achieve as each detector comes online and progresses toward design sensitivity. Next, in preparation for the optical search with the intermediate Palomar Transient Factory (iPTF), we have developed a unique capability to detect optical afterglows of gamma-ray bursts (GRBs) detected by the Fermi Gamma-ray Burst Monitor (GBM). Its comparable error regions offer a close parallel to the Advanced LIGO problem, but Fermi's unique access to MeV-GeV photons and its near all-sky coverage may allow us to look at optical afterglows in a relatively unexplored part of the GRB parameter space. We present the discovery and broadband follow-up observations (X-ray, UV, optical, millimeter, and radio) of eight GBM-IPTF afterglows. Two of the bursts (GRB 130702A / iPTF13bxl and GRB 140606B / iPTF14bfu) are at low redshift (z=0.145 and z = 0.384, respectively), are sub-luminous with respect to "standard" cosmological bursts, and have spectroscopically confirmed broad-line type Ic supernovae. These two bursts are possibly consistent with mildly relativistic shocks breaking out from the progenitor envelopes rather than the standard mechanism of internal shocks within an ultra-relativistic jet. On a technical level, the GBM--IPTF effort is a prototype for locating and observing optical counterparts of GW events in Advanced LIGO with the Zwicky Transient Facility.

Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.

Battery-Powered RF Pre-Ionization System for the Caltech Magnetohydrodynamically-Driven Jet Experiment: RF Discharge Properties and MHD-Driven Jet Dynamics

This thesis describes investigations of two classes of laboratory plasmas with rather different properties: partially ionized low pressure radiofrequency (RF) discharges, and fully ionized high density magnetohydrodynamically (MHD)-driven jets. An RF pre-ionization system was developed to enable neutral gas breakdown at lower pressures and create hotter, faster jets in the Caltech MHD-Driven Jet Experiment. The RF plasma source used a custom pulsed 3 kW 13.56 MHz RF power amplifier that was powered by AA batteries, allowing it to safely float at 4-6 kV with the cathode of the jet experiment. The argon RF discharge equilibrium and transport properties were analyzed, and novel jet dynamics were observed.

Although the RF plasma source was conceived as a wave-heated helicon source, scaling measurements and numerical modeling showed that inductive coupling was the dominant energy input mechanism. A one-dimensional time-dependent fluid model was developed to quantitatively explain the expansion of the pre-ionized plasma into the jet experiment chamber. The plasma transitioned from an ionizing phase with depressed neutral emission to a recombining phase with enhanced emission during the course of the experiment, causing fast camera images to be a poor indicator of the density distribution. Under certain conditions, the total visible and infrared brightness and the downstream ion density both increased after the RF power was turned off. The time-dependent emission patterns were used for an indirect measurement of the neutral gas pressure.

The low-mass jets formed with the aid of the pre-ionization system were extremely narrow and collimated near the electrodes, with peak density exceeding that of jets created without pre-ionization. The initial neutral gas distribution prior to plasma breakdown was found to be critical in determining the ultimate jet structure. The visible radius of the dense central jet column was several times narrower than the axial current channel radius, suggesting that the outer portion of the jet must have been force free, with the current parallel to the magnetic field. The studies of non-equilibrium flows and plasma self-organization being carried out at Caltech are relevant to astrophysical jets and fusion energy research.

Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation

In Part I, we construct a symmetric stress-energy-momentum pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum Pⁱ and angular momentum J^ik. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that Pⁱ and J^ik have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in Pⁱ and J^ik of their source.

In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.

Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.