A Refractive INdex Gradient (RING) diagnostic for transientdischarges or expansions of vapor or plasmas

The refractive index gradient (RING) diagnostic described uses a fast, silicon, photodiode quadrant detector with a differential amplifier to temporally detect the refraction of a CW laser by transient discharges or expansions of vapor, gas, or plasma. The method is a local one-dimensional time-resolved, quantitative, species-discriminating (i.e., atoms or electrons) Schlieren technique. The diagnostic is easy to field, sensitive (the minimum deflection angles detectable are ≈0.3 μrad), and fast (risetime=11±1 ns). Circuit design, performance, and diagnostic theory are discussed. To illustrate the utility of this technique, examples of measurements on LEVIS (laser evaporation ion source), a laser-produced, active, lithium ion source, are given. Measured properties include vapor/plasma production thresholds, expansion velocities, and time-resolved gradient and density spatial profiles. Comparisons of the RING results with measurements using a Faraday cup and a double-floating Langmuir probe are presented     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.