Observation of period multiplication and instability in a dc glow discharge

Abstract

The temporal dynamics in the fluctuations of the plasma floating potentials from an undriven dc glow discharge argon plasma at an intermediate gas pressure of 250mTorr and at the range of discharge currents I=6-50mA are investigated. In this study, the discharge current I is used as the plasma system's bifurcation parameter in analogy with the parameter space of a numerical dynamical system. Over several regions of the discharge current, the floating potential fluctuation time series data has been indicative of random noise, periodic oscillations, and irregular fluctuations. As the bifurcation parameter (discharge current) is increased, the Fourier spectrum of the data shows increased signs of period multiplication, quasiperiodicity, and instabilities. In addition, the computations of the correlation dimension provide some insight into the complex nature of the instabilities in the glow discharge plasma.

A Configurationally-Resolved-Super-Transition-Arrays method for calculation of the spectral absorption coefficient in hot plasmas

“…(30), on the degeneracies, shell occupation numbers and X is the same as of the standard partition function. Therefore, it obeys the same recursion relations and is accessible to the efficient evaluation methods [14][15], [19], [20], [21]. Unlike references [14][15], [19], [20], [21] where the partition function is used for the evaluation of the energy-moments of the spectrum, Eqs.…”

“…By the second approximation, the relative probabilities of configurations are the same as of those in a system of independent particles in a potential well [18]. This enables the derivation of analytical formulae for the moments (and cumulants) in terms of Slater integrals and partition functions [14], [16] which may be evaluated by recursion relations [14], [20], [21].…”

Chaotic behavior and fractals discovered in the time evolution of discharge current at atmospheric pressure

“…For several decades, nonlinear phenomena such as chaos and fractals have attracted significant attention globally in all fields of science, and their concepts are considered common and beneficial according to the investigation of the structures caused by discharge phenomena. Many different varieties of experimental studies on nonlinear behaviors have been accomplished in plasmas produced by discharges, [1][2][3][4][5][6] observations of chaos, [7][8][9][10][11][12][13][14][15][16][17][18][19] control of chaos, [20][21][22] synchronization of coupled oscillators, [23][24][25][26][27][28] and calculations of fractal dimensions. [29][30][31][32][33][34][35] The properties concerning chaos and fractals can be characterized quantitatively, for example, from experimental data using the calculation of the Lyapunov exponent 36 and the correlation dimension, 37 respectively.…”

Generating functions for canonical systems of fermions

“…However, the interactions could be included, in an approximate way, either in a perturbative manner as suggested by Pratt [2], or following the variational Jensen-Feynman approach [14], which consists in optimizing the one-particle energies ǫ i in order to obtain the best agreement with the exact free energy. Such an approach is driven by the ability to obtain robust recursion relations [15,16] for the calculation of partition functions and introduces no further difficulties in the averaging process.…”