Formation of an ultraviolet radiation pulse in a surface-discharge plasma by the front of an electromagnetic shock wave

Abstract

We prove a conjecture of Il'yashenko, that for a C 1 map in R n which locally contracts k-dimensional volumes, the box dimension of any compact invariant set is less than k. This result was proved independently by Douady and Oesterlé and by Il'yashenko for Hausdorff dimension. An upper bound on the box dimension of an attractor is valuable because, unlike a bound on the Hausdorff dimension, it implies an upper bound on the dimension needed to embed the attractor. We also get the same bound for the fractional part of the box dimension as is obtained by Douady and Oesterlé for Hausdorff dimension. This upper bound can be characterized in terms of a local version of the Lyapunov dimension defined by Kaplan and Yorke.

Transverse-discharge flashlamp operation: a surface model of gas breakdown as a first step towards representing discharge initiation

“…The electrical breakdown is also accompanied by the inter-electrode voltage drop which is delayed with respect to the moment of application of the electrical field. Such a model has also been investigated in numerous works including those related to research concerning the use of extended, multi-channel and homogeneous surface discharges as powerful sources of UV and VUV radiation, as well as of low-inductance-operated multi-channel spark gaps in surface discharges [10][11][12][13][14][15][16][17][18][19][20]. Let us henceforth refer to this model as the 'surface breakdown model'.…”

“…A surface voltage (ionization) wave spreading between the electrodes is a characteristic feature of surface electrical breakdown under the action of a pulsed electrical field [12,17]. The velocity V w of the wave movement may be evaluated from the relation [17] E N…”

Pulsed submicrosecond multichannel sliding discharges of opposite polarities: Filling of the discharge gap with spark channels

“…Earlier, there were numerous reports on experi mental studies of the characteristics of pulsed com pleted multichannel/quasi homogeneous sliding dis charges of submicrosecond duration in He, Ne, Ar, and Xe, their mixtures with Cl 2 , F 2 , and in air and nitrogen [3][4][5][6][7][8][9]. Having answered a number of partic ular questions, each of the works undoubtedly have contributed to understanding of the mechanisms of initiation and progression of discharge, but the analy sis and comparison of the results of different works are hampered partly because these results have been obtained in different experimental conditions, signifi cantly differing in a whole number of parameters such as the durations of the pulse discharge and its front, the voltage/current amplitude, the materials and dimen sions of the dielectric plate, the parameters of the elec tric circuit of the discharge, methods and ranges of measurements of the channels and the entire dis charge, etc.…”

“…The efficiency of practical application of a high current pulsed multichannel quasi homogeneous dis charges in gases on a dielectric surface, e.g., as a cur rent switch or as an electron or radiation source which, in particular, is used for optical pumping of active media of lasers, significantly depends on the degree of homogeneity of the filling of the entire dielectric sur face in the electrode gap with discharge plasma (see [1][2][3][4][5][6][7][8][9] and references therein). It is known that, in the high current regime of completed discharge, when the voltage across the discharge gap exceeds the threshold value for electric breakdown of gas, the structure of the discharge is formed by a series of parallel spark chan nels.…”

Spark cross size in a sliding submicrosecond discharge of opposite polarities in rare gases: experiment and application of ionization wave front propagation theory to analysis

“…Despite numerous studies of the first group of discharges, many of the basic physical processes, in particular, those governing individual channel development, are not well understood. Fewer studies of channel development in the multichannel discharges of the second group are known ( [9,[13][14][15]] and references therein), which also do not offer clear understanding of the mechanisms of their transverse structure development. Comparison and analysis of their data are rather complicated due to the use of different power sources, pulse duration, electrode geometries, gas types and mixtures, their pressures resulting in vastly varied discharge modes and quantitative results.…”