On the critical equilibrium of the spiral spring pendulum

Physical systems such as an inverted pendulum driven by a spiral spring, an unbalanced Euler elastica with a travelling mass, a heavy body with a parabolic section and an Ising ferromagnet are very different. However, they all behave in the same manner close to the critical regime for which nonlinearities are prominent. We demonstrate experimentally, for the first time, an old prediction by Joseph Larmor, which states that a nonlinear oscillator close to its supercritical bifurcation oscillates with a period inversely proportional to its angular amplitude. We perform our experiments with a Holweck–Lejay-like pendulum which was used to measure the gravity field during the twentieth century.

High Power THz Generation from Sub-ps Bunches of Relativistic Electrons

ABSTRACTWe describe a > 100 Watt broadband THz source that takes advantage of the relativistic enhancement of the radiation from accelerating electrons according to the formula assigned the name of Sir Joseph Larmor[1, 2]. This is in contrast to the typical 1 milliwatt sources available in a laboratory. Specifically, for relativistic electrons the emission is enhanced by the fourth power of the increase in mass. Thus for 100 MeV electrons, for which the mass increases by a factor of ∼ 200, the enhancement is > 109. The experiments use a new generation of light source called an energy recovery linac (ERL) [3], in which bunches of electrons circulate once, but in which their energy is recovered. In such a machine the electron bunches can be very much shorter than those, say, in storage rings or synchrotrons.The Jefferson Lab facility operates in new limits of emission from relativistic particles involving both multiparticle coherence and near-field emission in which the velocity (Coulomb) term in the classical electrodynamical theory becomes as important as the acceleration term (synchrotron radiation).The sub-picosecond pulses of light offer unique capabilities in 2 specific areas, namely time-resolved dynamics, and imaging. High resolution THz spectroscopy has recently revealed sharp vibrational modes for many materials including malignant tissue, proteins, DNA, pharmaceuticals and explosive materials. Energetically the THz range embraces superconducting bandgaps, and regions of intense interest in the understanding of systems in which correlated motions of electrons are important, such as colossal magneto-resistive and high-Tc materials. The very high power levels of the new source will allow non-linear effects to be observed as well as the creation of novel states of materials, including electric-field driven localization[4]. We will give examples of existing work in these areas and present opportunities afforded by the new source.