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Notes: We report on quantitative, spatially resolved density, temperature, and velocity measurements on ground-state atomic hydrogen in an expanding thermal Ar–H plasma using two-photon excitation laser-induced fluorescence (LIF). The method's diagnostic value for application in this plasma is assessed by identifying and evaluating the possibly disturbing factors on the interpretation of the LIF signal in terms of density, temperature, and velocity. In order to obtain quantitative density numbers, the LIF setup is calibrated for H measurements using two different methods. A commonly applied calibration method, in which the LIF signal from a, by titration, known amount of H generated by a flow-tube reactor is used as a reference, is compared to a rather new calibration method, in which the H density in the plasma jet is derived from a measurement of the two-photon LIF signal generated from krypton at a well-known pressure, using a known Kr to H detection sensitivity ratio. The two methods yield nearly the same result, which validates the new H density calibration. Gauging the new "rare gas method" by the "flow-tube reactor method," we find a krypton to hydrogen two-photon excitation cross section ratio σKr(2)/σH(2) of 0.56, close to the reported value of 0.62. Since the H density calibration via two-photon LIF of krypton is experimentally far more easy than the one using a flow-tube reactor, it is foreseen that the "rare gas method" will become the method of choice in two-photon LIF experiments. The current two-photon LIF detection limit for H in the Ar–H plasma jet is 1015 m−3. The accuracy of the density measurements depends on the accuracy of the calibration, which is currently limited to 33%. The reproducibility depends on the signal-to-noise (S/N) ratio in the LIF measurements and is orders of magnitude better. The accuracy in the temperature determination also depends on the S/N ratio of the LIF signal and on the ratio between the Doppler-width of the transition and the linewidth of the excitation laser. Due to the small H mass, the current linewidth of the UV laser radiation is never the accuracy limiting factor in the H temperature determination, even not at room temperature. Quantitative velocity numbers are obtained by measuring the Doppler shift in the H two-photon excitation spectrum. Both the radial and axial velocity components are obtained by applying a perpendicular and an antiparallel excitation configuration, respectively. The required laser frequency calibration is accomplished by simultaneously recording the I2 absorption spectrum with the fundamental frequency component of the laser system. This method, which is well-established in spectroscopic applications, enables us to achieve a relative accuracy in the transition frequency measurement below 10−6, corresponding to an accuracy in the velocity of approximately 200 m/s. This accuracy is nearly laser linewidth limited. © 2002 American Institute of Physics.

Notes: Abstract Consider a Toda chain with uniform friction. Starting with an initial condition that represents a soliton, we investigate its decay. The main result is that the solitary character is almost completely preserved. During the decay the wave activates other nonlinear modes. The corresponding actions appear to be bounded uniformly in time, proportional to the square of the friction coefficient. We focus upon the interaction with the same soliton but opposite direction of propagation. Comparing the numerical observations with an analytical model we conclude that the activated wave is well described by a linear equation, inhomogeneously driven by the main wave. The main wave itself decays as a nonlinear damped oscillator with one degree of freedom.