SynopsisThe addition reaction between melamine and formaldehyde has been kinetically separated from the subsequent condensation stage by suitable choice of concentration and temperature conditions. The reaction, which is reversible, has been monitored by estimation of the free formaldehyde content of the system. It has been investigated over the range of mean degree of methylolation 1 < R' < 3.7 of the melamine nuclei, the temperature range 25-55'C., and the pH range 5.7-10.2. The rate data thus obtained have been treated according to the random reversible addition scheme for which reasonable, first approximation, agreement was obtained. Average kinetic and thermodynamic constants have been calculated and are discussed in terms of the present model. The factors which are likely to cause deviations from randomness are described. The addition of formaldehyde to melamine proceeds by superposition of an OH --catalyzed step with a minor solvent-catalyzed or uncatalyzed one.

We examine the interaction between intense laser pulses and strongly magnetised plasmas in the weakly relativistic regime. An expression for the electron Lorentz factor coupling both relativistic and cyclotron motion nonlinearities is derived for static magnetic fields along the laser propagation axis. This is applied to predict modifications to the refractive index, critical density, group velocity dispersion and power threshold for relativistic self-focusing. It is found that electron quiver response is enhanced under right circularly-polarised light, decreasing the power threshold for various instabilities, while a dampening effect occurs under left circularly-polarised light, increasing the power thresholds. Derived theoretical predictions are tested by one and three-dimensional particle-in-cell simulations.

The dynamics of three-dimensional (3D) compression of ultrashort intense laser pulses in plasma is investigated theoretically and numerically. Starting from the slowly-varying envelope model, we derive equations describing the spatiotemporal evolution of a short laser pulse towards the singularity, or collapse, based on the variational method. In particular, the laser and plasma conditions leading to spherical compression are obtained. 3D particle-in-cell simulations are carried out to verify these conditions, which also enable one to examine the physical processes both towards and beyond the pulse collapse. Simulations suggest that the laser pulse can be spherically compressed down to a minimum size of the order of the laser wavelength, the so called lambda-cubic regime. The compression process develops over twice as fast in simulation than is predicted by the envelope model, due to the simplified nature of the latter. The final result of this process is pulse collapse, which is accompanied with strong plasma density modulation and spectrum broadening. The collapse can occur multiple times during the laser pulse propagation, until a significant part of the pulse energy is dissipated to electron acceleration by the laser ponderomitve force. It is also shown that a strong external DC magnetic field applied along the laser propagation direction can enhance the rate of compression for circularly-polarised laser pulses, when compared to an unmagnetised plasma, allowing access to strong compression and focusing in the low-density and low-amplitude regime.

The process by which an existing magnetic field of ∼10 2 -10 3 T may be amplified by an order of magnitude along the axis of laser propagation in underdense plasma by an intense laser pulse is investigated. The mechanism underlying the effect is understood to be ponderomotive in nature, initiated by the E × B drift motion of electrons displaced by the laser pulse as they relax towards the axis, and sustained by a combination of quasistatic magnetic field structures and electron Hall and diamagnetic currents. We employ two-and threedimensional particle-in-cell simulations to numerically investigate the process and find qualitative agreement with the scaling relations found in our theory model. The lifetime of the process is considered, and we find the major factor limiting its growth and lifetime is ion motion, which disrupts the electron currents neccessary to sustain the induced magnetic field. This field is found to be of sufficient strength, and is long-lived enough to be relevant for study in relation to applications in radiation production and laboratory astrophysics.