Review: R. Bellamy, D. Castiglione and J. Shaw (eds.), Making European Citizens (Palgrave Macmillan, 2006)

Review of edited collection.

Generation of a quasi-monoergetic proton beam from laser-irradiated sub-micron droplets

Proton bursts with a narrow spectrum at an energy of (2.8 +/- 0.3 MeV) are accelerated from sub-micron water spray droplets irradiated by high-intensity (similar to 5 x 10(19)W/cm(2)), high-contrast (similar to 10(10)), ultra-short (40 fs) laser pulses. The acceleration is preferentially in the laser propagation direction. The explosion dynamics is governed by a residual ps-scale laser pulse pedestal which "mildly" preheats the droplet and changes its density profile before the arrival of the high intensity laser pulse peak. As a result, the energetic electrons extracted from the modified target by the high-intensity part of the laser pulse establish an anisotropic electrostatic field which results in anisotropic Coulomb explosion and proton acceleration predominantly in the forward direction. Hydrodynamic simulations of the target pre-expansion and 3D particle-in-cell simulations of the measured energy and anisotropy of the proton emission have confirmed the proposed acceleration scenario. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4731712]

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. Inr/>particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Atomic harmonic generation in time-dependent R-matrix theory

We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity, or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390-nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code, finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.