Physical Dissipation and the Method of Controlled Lagrangians

We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a class of underactuated mechanical systems including “balance” systems such as the pendulum on a cart. Since the method involves modifying a system’s kinetic energy metric through feedback, the effect of dissipation is obscured. In particular, it is not generally true that damping makes a feedback-stabilized equilibrium asymptotically stable. Damping in the unactuated directions does tend to enhance stability, however damping in the controlled directions must be “reversed” through feedback. In this paper, we suggest a choice of feedback dissipation to locally exponentially stabilize a class of controlled Lagrangian systems

Dissipation and Controlled Euler-Poincaré Systems

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor

Time dependence in perpendicular media with a soft underlayer

In this paper we describe measurements of magnetic viscosity or time dependence in magnetic thin films suitable for use as perpendicular recording media. Generally, such effects cannot be measured using conventional magnetometry techniques due to the presence of a thin (0.1 mum) soft underlayer (SUL) in the media necessary to focus the head field. To achieve our results we have developed an ultrastable MOKE magnetometer, the construction of which is described. This has enabled us to measure nominally identical films with and without the presence of the SUL. We find that the presence of the SUL narrows the energy barrier distribution in the perpendicular film increasing the nucleation field (H-n), reducing the coercivity (H-c) and results in an increase in the squareness of the loop. This in turn results in an increase in the magnitude of the viscosity in the region of the H-c but that the range of fields over which the viscosity occurs is reduced

Proton radiography in background magnetic fields

Proton radiography has proved increasingly successful as a diagnostic for electric and magnetic fields in high-energy-density physics experiments. Most experiments use target-normal sheath acceleration sources with a wide energy range in the proton beam, since the velocity spread can help differentiate between electric and magnetic fields and provide time histories in a single shot. However, in magnetized plasma experiments with strong background fields, the broadband proton spectrum leads to velocity-spread-dependent displacement of the beam and significant blurring of the radiograph. We describe the origins of this blurring and show how it can be removed from experimental measurements, and we outline the conditions under which such deconvolutions are successful. As an example, we apply this method to a magnetized plasma experiment that used a background magnetic field of 3 T and in which the strong displacement and energy spread of the proton beam reduced the spatial resolution from tens of micrometers to a few millimeters. Application of the deconvolution procedure accurately recovers radiographs with resolutions better than 100 µm, enabling the recovery of more accurate estimates of the path-integrated magnetic field. This work extends accurate proton radiography to a class of experiments with significant background magnetic fields, particularly those experiments with an applied external magnetic field

The effect of grading the atomic number at resistive guide element interface on magnetic collimation

Using 3 dimensional numerical simulations, this paper shows that grading the atomic number and thus the resistivity at the interface between an embedded high atomic number guide element and a lower atomic number substrate enhances the growth of a resistive magnetic field. This can lead to a large integrated magnetic flux density, which is fundamental to confining higher energy fast electrons. This results in significant improvements in both magnetic collimation and fast-electron-temperature uniformity across the guiding. The graded interface target provides a method for resistive guiding that is tolerant to laser pointing

Characterization of electrostatic shock in laser-produced optically-thin plasma flows using optical diagnostics

We present a method for evaluating the properties of electrostatic shock in laser-produced plasmas by using optical diagnostics. A shock is formed by a collimated jet in counter-streaming plasmas in nearly collisionless condition, showing the steepening of the transition width in time. In the present experiment, a streaked optical pyrometry was applied to evaluate the electron density and temperatures in the upstream and downstream regions of the shock so that the shock conditions are satisfied, by assuming thermal bremsstrahlung emission in optically thin plasmas. The derived electron densities are nearly consistent with those estimated from interferometry