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Photon emission from a uniformly accelerated charge is among the most mysterious physical phenomena. Theories based on the Lorentz-Abraham-Dirac equation mostly conclude that a uniformly accelerated point charge cannot feel radiation reaction. Such a conclusion suggests that the origin of the photon energy is unclear. In this paper, we determine the self-force of a uniformly accelerated charged sphere using the Lorentz force equation, with an assumption that the sphere is Lorentz-contracted during the acceleration. For large acceleration, the calculated self-force converges to the radiation reaction (given by the Larmor formula) via a new factor $\gamma_{a}$, which describes an acceleration-dependent increase in the effective mass. This increased mass makes it harder to accelerate the particle (compared to a point-charge), which means more energy should be provided to the particle in order to get the expected acceleration. This extra energy can be interpreted as the origin of the photon energy., Comment: 9 pages, 1 figure

The next few years will see next-generation high-power laser facilities (such as the Extreme Light Infrastructure) become operational, for which it is important to understand how interaction with intense laser pulses affects the bulk properties of a relativistic electron beam. At such high field intensities, we expect both radiation reaction and quantum effects to play a significant role in the beam dynamics. The resulting reduction in relative energy spread (beam cooling) at the expense of mean beam energy predicted by classical theories of radiation reaction depends only on the energy of the laser pulse. Quantum effects suppress this cooling, with the dynamics additionally sensitive to the distribution of energy within the pulse. Since chirps occur in both the production of high-intensity pulses (CPA) and the propagation of pulses in media, the effect of using chirps to modify the pulse shape has been investigated using a semi-classical extension to the Landau--Lifshitz theory. Results indicate that even large chirps introduce a significantly smaller change to final state predictions than going from a classical to quantum model for radiation reaction, the nature of which can be intuitively understood., Comment: 8 pages, 3 figures. Invited paper: SPIE Optics + Optoelectronics: Relativistic Plasma Waves and Particle Beams as Coherent and Incoherent Radiation Sources. Prague, CZ (April 2015)

With the emergence in the next few years of a new breed of high power laser facilities, it is becoming increasingly important to understand how interacting with intense laser pulses affects the bulk properties of a relativistic electron beam. A detailed analysis of the radiative cooling of electrons indicates that, classically, equal contributions to the phase space contraction occur in the transverse and longitudinal directions. In the weakly quantum regime, in addition to an overall reduction in beam cooling, this symmetry is broken, leading to significantly less cooling in the longitudinal than the transverse directions. By introducing an efficient new technique for studying the evolution of a particle distribution, we demonstrate the quantum reduction in beam cooling, and find that it depends on the distribution of energy in the laser pulse, rather than just the total energy as in the classical case., Comment: 19 pages, 5 figures. arXiv admin note: text overlap with arXiv:1410.1759

We present a novel technique for studying the evolution of a particle distribution using single particle dynamics such that the distribution can be accurately reconstructed using fewer particles than existing approaches. To demonstrate this, the Landau-Lifshiftz description of radiation reaction is adapted into a semi-classical model, for which the Vlasov equation is intractable. Collision between an energetic electron bunch and high-intensity laser pulses are then compared using the two theories. Reduction in beam cooling is observed for the semi-classical case., Comment: 5 pages, 2 figures, supplemental material

In order to analyse results for structure functions, $S_n(r)$, we propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$. This method differs from the extended self-similarity (ESS) technique, which plots $S_n(r)$ against $S_3(r)$, where $S_3(r) \sim r$. Using this method in conjunction with pseudospectral evaluation of structure functions, for the particular case of $S_2(r)$ we obtain the new result that the exponent $\zeta_2$ decreases as the Taylor-Reynolds number increases, with $\zeta_2 \to 0.67 \pm 0.02$ as $R_\lambda \to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, and is the opposite of the result obtained by ESS.

From the energy balance in wavenumber space expressed by the Lin equation, we derive a new form for the local Karman-Howarth equation for forced isotropic turbulence in real space. This equation is then cast into a dimensionless form, from which a combined analytical and numerical study leads us to deduce a new model for the scale-independent nondimensional dissipation rate $\Ceps$, which takes the form $\Ceps = \Cinf + C_L/R_L$, where the asymptotic value $\Cinf$ can be evaluated from the third-order structure function. This is found to fit the numerical data with $\Cinf = 0.47 \pm 0.01$ and $C_L= 18.5 \pm 1.3$. By considering $\Ceps - \Cinf$ on logarithmic scales, we show that $R_L^{-1}$ is indeed the correct Reynolds number behaviour. The model is compared to previous attempts in the literature, with encouraging agreement. The effects of the scale-dependence of the inertial and viscous terms due to finite forcing are then considered and shown to compensate one another, such that the model equation is applicable for systems subject to finite forcing. In addition, we also show that, contrary to the case of freely decaying turbulence, the characteristic decline in $\Ceps$ with increasing Reynolds number is due to the \emph{increase} in the surrogate expression $U^3/L$; the dissipation rate being maintained constant as a consequence of the fixed rate of forcing. A long-time non-turbulent stable state is found to exist for low Reynolds number numerical simulations which use negative damping as a means of energy injection.

A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a series of runs for freely-decaying turbulence. We explore the use of power-law decay of the total energy to determine an evolved time and compare with the use of dynamic quantities such as the peak dissipation rate, maximum transport power and velocity derivative skewness. Stationary turbulence has also been investigated, where we ensure that the energy input rate remains constant for all runs. We present results for Reynolds numbers up to R{\lambda} = 335 on a 1024^3 lattice. An exploitation of the pseudospectral technique is used to calculate second and third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The K\'arm\'an-Howarth equation (KHE) is studied and a derivation of a new work term presented. The balance of energy represented by the KHE is then investigated. Based on the KHE, we develop a model for the behaviour of the dimensionless dissipation coefficient that predicts C{\epsilon} = C{\epsilon}(\infty) + C_L/R_L, with C{\epsilon}(\infty) = 0.47 and C_L = 19.1 obtained from DNS data. Theoretical methods based on RG and statistical closures are still being developed to study turbulence. The dynamic RG procedure used by Forster, Nelson and Stephen (FNS) is considered in some detail and a disagreement in the literature is resolved here. The application of statistical closure and renormalized perturbation theory is discussed and a new two-time model probability density functional presented., Comment: 292 pages; Ph.D thesis, University of Edinburgh, UK