Laser ion acceleration using a solid target coupled with a low density layer

We investigate by particle-in-cell simulations in two and three dimensions the laser-plasma interaction and the proton acceleration in multilayer targets where a low density "near-critical" layer of a few micron thickness is added on the illuminated side of a thin, high density layer. This target design can be obtained by depositing a "foam" layer on a thin metallic foil. The presence of the near-critical plasma strongly increases both the conversion efficiency and the energy of electrons and leads to enhanced acceleration of proton from a rear side layer via the Target Normal Sheath Acceleration mechanism. The electrons of the foam are strongly accelerated in the forward direction and propagate on the rear side of the target building up a high electric field with a relatively flat longitudinal profile. In these conditions the maximum proton energy is up to three times higher than in the case of the bare solid target.Comment: 9 pages, 11 figures. Submitted to Physical Review

Conditional regularity of solutions of the three dimensional Navier-Stokes equations and implications for intermittency

Two unusual time-integral conditional regularity results are presented for the three-dimensional Navier-Stokes equations. The ideas are based on $L^{2m}$-norms of the vorticity, denoted by $\Omega_{m}(t)$, and particularly on $D_{m} = \Omega_{m}^{\alpha_{m}}$, where $\alpha_{m} = 2m/(4m-3)$ for $m\geq 1$. The first result, more appropriate for the unforced case, can be stated simply : if there exists an $1\leq m < \infty$ for which the integral condition is satisfied ($Z_{m}=D_{m+1}/D_{m}$) $$\int_{0}^{t}\ln (\frac{1 + Z_{m}}{c_{4,m}}) d\tau \geq 0$$ then no singularity can occur on $[0, t]$. The constant $c_{4,m} \searrow 2$ for large $m$. Secondly, for the forced case, by imposing a critical \textit{lower} bound on $\int_{0}^{t}D_{m} d\tau$, no singularity can occur in $D_{m}(t)$ for \textit{large} initial data. Movement across this critical lower bound shows how solutions can behave intermittently, in analogy with a relaxation oscillator. Potential singularities that drive $\int_{0}^{t}D_{m} d\tau$ over this critical value can be ruled out whereas other types cannot.Comment: A frequency was missing in the definition of D_{m} in (I5) v3. 11 pages, 1 figur

Tunable Circularly Polarized Terahertz Radiation from Magnetized Gas Plasma

It is shown, by simulation and theory, that circularly or elliptically polarized terahertz radiation can be generated when a static magnetic (B) field is imposed on a gas target along the propagation direction of a two-color laser driver. The radiation frequency is determined by $\sqrt{\omega_p^2+{\omega_c^2}/{4}} + {\omega_c}/{2}$, where $\omega_p$ is the plasma frequency and $\omega_c$ is the electron cyclotron frequency. With the increase of the B field, the radiation changes from a single-cycle broadband waveform to a continuous narrow-band emission. In high-B-field cases, the radiation strength is proportional to $\omega_p^2/\omega_c$. The B field provides a tunability in the radiation frequency, spectrum width, and field strength.Comment: 6 pages, 5 figure

Laser opacity in underdense preplasma of solid targets due to quantum electrodynamics effects

We investigate how next-generation laser pulses at 10 PW $-$ 200 PW interact with a solid target in the presence of a relativistically underdense preplasma produced by amplified spontaneous emission (ASE). Laser hole boring and relativistic transparency are strongly restrained due to the generation of electron-positron pairs and $\gamma$-ray photons via quantum electrodynamics (QED) processes. A pair plasma with a density above the initial preplasma density is formed, counteracting the electron-free channel produced by the hole boring. This pair-dominated plasma can block the laser transport and trigger an avalanche-like QED cascade, efficiently transfering the laser energy to photons. This renders a 1-$\rm\mu m$-scalelength, underdense preplasma completely opaque to laser pulses at this power level. The QED-induced opacity therefore sets much higher contrast requirements for such pulse in solid-target experiments than expected by classical plasma physics. Our simulations show for example, that proton acceleration from the rear of a solid with a preplasma would be strongly impaired.Comment: 5 figure

A comparison of A-level performance in economics and business studies: how much more difficult is economics?

This paper uses ALIS data to compare academic performance in two subjects often viewed as relatively close substitutes for one another at A-level. The important role of GCSE achievement is confirmed for both subjects. There is evidence of strong gender effects and variation in outcomes across Examination Boards. A counterfactual exercise suggests that if the sample of Business Studies candidates had studied Economics nearly 40% of those who obtained a grade C or better in the former subject would not have done so in the latter. The opposite exercise uggests that 12% more Economics candidates would have achieved a grade C or better if they had taken Business Studies. In order to render a Business Studies A-level grade comparable to an Economics one in terms of relative difficulty, we estimate that a downward adjustment of 1.5 UCAS points should be applied to the former subject. This adjustment is lower than that suggested by correction factors based on conventional subject pair analysis for these two subjects

Dominance of Radiation Pressure in Ion Acceleration with Linearly Polarized Pulses at Intensities of 1021Wcm−210^{21}\textrm{W}\textrm{cm}^{-2}

A novel regime is proposed where, employing linearly polarized laser pulses at intensities $10^{21}\textrm{Wcm}^{-2}$ as two order of magnitude lower than earlier predicted [T. Esirkepov et al., Phys. Rev. Lett. 92, 175003 (2004)], ions are dominantly accelerated from ultrathin foils by the radiation pressure, and have monoenergetic spectra. In the regime, ions accelerated from the hole-boring process quickly catch up with the ions accelerated by target normal sheath acceleration (TNSA), and they then join in a single bunch, undergoing a hybrid Light-Sail/TNSA acceleration. Under an appropriate coupling condition between foil thickness, laser intensity and pulse duration, laser radiation pressure can be dominant in this hybrid acceleration. Two-dimensional PIC simulations show that $1.26\textrm{GeV}$ quasimonoenergetic $\textrm{C}^{6+}$ beams are obtained by linearly polarized laser pulses at intensities of $10^{21}\textrm{Wcm}^{-2}$.Comment: 6 pages, 4 figure

Nonlinear effects in buoyancy-driven variable-density turbulence

We consider the time dependence of a hierarchy of scaled L²ᵐ-norms D_m,ω and D_m,θ of the vorticity ω =∇ x u and the density gradient ∇θ, where θ = log.(ρ*/ ρ*₀), in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli (J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, ρ* (x,t) is the composition density of a mixture of two incompressible miscible fluids with fluid densities ρ*₂ > ρ*₁, and ρ*₀ is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the L²-spatial average of the density gradient can reach extremely large values at intermediate times, even in flows with low Atwood number At = (ρ*₂ - ρ*₁)/(ρ*₂ + ρ*₁) = 0.05, implying that very strong mixing of the density field at small scales can arise in buoyancy-driven turbulence. This large growth raises the possibility that the density gradient ∇θ might blow up in a finite time.We acknowledge, with thanks, the staff of IPAM UCLA where this collaboration began in the Autumn of 2014 on the programme ‘Mathematics of Turbulence’. We would also like to thank C. Doering and D. Livescu for useful discussions. All of the numerical data used are from the JHTDB (Livescu et al. 2014), a publicly available DNS database. For more information, please see http://turbulence.pha.jhu.edu/. We also thank the referees for suggesting substantial improvements

Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics

After a review of the isentropic compressible magnetohydrodynamics (ICMHD) equations, a quaternionic framework for studying the alignment dynamics of a general fluid flow is explained and applied to the ICMHD equations.Comment: 12 pages, 2 figures, submitted to a Focus Issue of New Journal of Physics on "Magnetohydrodynamics and the Dynamo Problem" J-F Pinton, A Pouquet, E Dormy and S Cowley, editor

Estimates for the two-dimensional Navier-Stokes equations in terms of the Reynolds number

The tradition in Navier-Stokes analysis of finding estimates in terms of the Grashof number \bG, whose character depends on the ratio of the forcing to the viscosity $\nu$, means that it is difficult to make comparisons with other results expressed in terms of Reynolds number \Rey, whose character depends on the fluid response to the forcing. The first task of this paper is to apply the approach of Doering and Foias \cite{DF} to the two-dimensional Navier-Stokes equations on a periodic domain $[0,L]^{2}$ by estimating quantities of physical relevance, particularly long-time averages \left, in terms of the Reynolds number \Rey = U\ell/\nu, where U^{2}= L^{-2}\left and $\ell$ is the forcing scale. In particular, the Constantin-Foias-Temam upper bound \cite{CFT} on the attractor dimension converts to a_{\ell}^{2}\Rey(1 + \ln\Rey)^{1/3}, while the estimate for the inverse Kraichnan length is (a_{\ell}^{2}\Rey)^{1/2}, where $a_{\ell}$ is the aspect ratio of the forcing. Other inverse length scales, based on time averages, and associated with higher derivatives, are estimated in a similar manner. The second task is to address the issue of intermittency : it is shown how the time axis is broken up into very short intervals on which various quantities have lower bounds, larger than long time-averages, which are themselves interspersed by longer, more quiescent, intervals of time.Comment: 21 pages, 1 figure, accepted for publication from J. Math. Phys. for the special issue on mathematical fluid mechanic

Relativistic Doppler effect: universal spectra and zeptosecond pulses

We report on a numerical observation of the train of zeptosecond pulses produced by reflection of a relativistically intense femtosecond laser pulse from the oscillating boundary of an overdense plasma because of the Doppler effect. These pulses promise to become a unique experimental and technological tool since their length is of the order of the Bohr radius and the intensity is extremely high $\propto 10^{19}$ W/cm$^2$. We present the physical mechanism, analytical theory, and direct particle-in-cell simulations. We show that the harmonic spectrum is universal: the intensity of $n$th harmonic scales as $1/n^{p}$ for $n < 4\gamma^2$, where $\gamma$ is the largest $\gamma$--factor of the electron fluid boundary, $p=3$ and $p=5/2$ for the broadband and quasimonochromatic laser pulses respectively.Comment: 4 figure