Features of interferometry of small-sized plasma channels obtained during nanosecond discharge

Abstract

The applicability of the method of smooth perturbations for processing interferograms of small (5–100 μm) objects by taking into account the diffraction is investigated. The test problems showed the consistency of the method to the range of parameters that are interesting for us. The requirements for preliminary processing of experimental data are determined, adhering to which it is possible to improve the accuracy of the final results. The analysis of experimental interferograms by assuming the cylindrical symmetry of the plasma object is carried out: the two-dimensional map of the electron density for the plasma object formed at the initial stage of nanosecond discharge was obtained from the phase map.

Filamentary nanosecond surface dielectric barrier discharge. Plasma properties in the filaments

“…It should be noted that in a number of works [33,34], it is assumed that the discharge constriction is the result of magnetic compression of plasma channel. The magnetic pressure P m is a function of the discharge current I and of the filament radius R f :…”

Filamentary nanosecond surface dielectric barrier discharge. Plasma properties in the filaments

“…It should be noted that in a number of works [33,34], it is assumed that the discharge constriction is the result of magnetic compression of plasma channel. The magnetic pressure P m is a function of the discharge current I and of the filament radius R f :…”

Fast fine-scale spark filamentation and its effect on the spark resistance

“…The gap between the wire and the plane copper anode was 3 mm. Notably, it was essential to reduce the deviation of the evolving spark channel from the focal depth (∼200 μm) of the optical system since this deviation results in diffraction of the probing radiation ('defocusing' effect), thus complicating the procedure for interferogram processing [33]. Owing to the gap geometry, the studied spark channel originated at a particular region of the point cathode and propagated almost along the gap axis.…”

“…This allowed us to clarify the directions of the filament development in space and also to monitor the evolution of the characteristic filament number. The techniques of tracing the interferograms and obtaining the 2D phase maps were described in [33,36]. The filaments were traced with a step of ≈10 μm starting from the region, where they were widely spaced, and proceeding to the region of their formation, see, e.g.…”

“…In our study, both schlieren images and shadowgrams were used only qualitatively to additionally clarify the results obtained by interferometry, which is the main method providing quantitative data on the filaments. The corresponding electron density (n e ) distributions were reconstructed from the approximating phase shifts (curves C-R) using the technique based on the solution of the Helmholtz wave equation in the parabolic approximation by the method of smooth perturbations, see more in [33,36,38]. The total accuracy of the employed interferogram processing technique is governed by the errors introduced by the method of smooth perturbations, see more in [38], and the accuracy of obtaining the approximating phase shifts; the latter accuracy, in turn, is governed by smoothing errors (the method operates with smooth curves) as well as by the background noise in the traced interferograms.…”

Extremely fast formation of anode spots in an atmospheric discharge points to a fundamental ultrafast breakdown mechanism

“…With the interferometers adjusted in the way described above, we traced the interferograms and recovered the 2D phase maps, see, e.g. those given in figure 7 in units k=Δf/2π of the relative fringe shift, using the techniques presented in [42,43]; here Δf is the phase shift introduced by the plasma at the passage of the probing radiation. The analyzed phase shifts (curves A) were approximated by smooth curves B which were then used to reconstruct the electron density distributions (n e ).…”

Filamentary nanosecond surface dielectric barrier discharge. Plasma properties in the filaments

“…It should be noted that in a number of works [33,34], it is assumed that the discharge constriction is the result of magnetic compression of plasma channel. The magnetic pressure P m is a function of the discharge current I and of the filament radius R f :…”

Fast fine-scale spark filamentation and its effect on the spark resistance

“…The gap between the wire and the plane copper anode was 3 mm. Notably, it was essential to reduce the deviation of the evolving spark channel from the focal depth (∼200 μm) of the optical system since this deviation results in diffraction of the probing radiation ('defocusing' effect), thus complicating the procedure for interferogram processing [33]. Owing to the gap geometry, the studied spark channel originated at a particular region of the point cathode and propagated almost along the gap axis.…”

“…This allowed us to clarify the directions of the filament development in space and also to monitor the evolution of the characteristic filament number. The techniques of tracing the interferograms and obtaining the 2D phase maps were described in [33,36]. The filaments were traced with a step of ≈10 μm starting from the region, where they were widely spaced, and proceeding to the region of their formation, see, e.g.…”

“…In our study, both schlieren images and shadowgrams were used only qualitatively to additionally clarify the results obtained by interferometry, which is the main method providing quantitative data on the filaments. The corresponding electron density (n e ) distributions were reconstructed from the approximating phase shifts (curves C-R) using the technique based on the solution of the Helmholtz wave equation in the parabolic approximation by the method of smooth perturbations, see more in [33,36,38]. The total accuracy of the employed interferogram processing technique is governed by the errors introduced by the method of smooth perturbations, see more in [38], and the accuracy of obtaining the approximating phase shifts; the latter accuracy, in turn, is governed by smoothing errors (the method operates with smooth curves) as well as by the background noise in the traced interferograms.…”

Extremely fast formation of anode spots in an atmospheric discharge points to a fundamental ultrafast breakdown mechanism

“…With the interferometers adjusted in the way described above, we traced the interferograms and recovered the 2D phase maps, see, e.g. those given in figure 7 in units k=Δf/2π of the relative fringe shift, using the techniques presented in [42,43]; here Δf is the phase shift introduced by the plasma at the passage of the probing radiation. The analyzed phase shifts (curves A) were approximated by smooth curves B which were then used to reconstruct the electron density distributions (n e ).…”

Filamentary nanosecond surface dielectric barrier discharge. Plasma properties in the filaments

“…It should be noted that in a number of works [33,34], it is assumed that the discharge constriction is the result of magnetic compression of plasma channel. The magnetic pressure P m is a function of the discharge current I and of the filament radius R f :…”

Fast fine-scale spark filamentation and its effect on the spark resistance

“…The gap between the wire and the plane copper anode was 3 mm. Notably, it was essential to reduce the deviation of the evolving spark channel from the focal depth (∼200 μm) of the optical system since this deviation results in diffraction of the probing radiation ('defocusing' effect), thus complicating the procedure for interferogram processing [33]. Owing to the gap geometry, the studied spark channel originated at a particular region of the point cathode and propagated almost along the gap axis.…”

“…This allowed us to clarify the directions of the filament development in space and also to monitor the evolution of the characteristic filament number. The techniques of tracing the interferograms and obtaining the 2D phase maps were described in [33,36]. The filaments were traced with a step of ≈10 μm starting from the region, where they were widely spaced, and proceeding to the region of their formation, see, e.g.…”

“…In our study, both schlieren images and shadowgrams were used only qualitatively to additionally clarify the results obtained by interferometry, which is the main method providing quantitative data on the filaments. The corresponding electron density (n e ) distributions were reconstructed from the approximating phase shifts (curves C-R) using the technique based on the solution of the Helmholtz wave equation in the parabolic approximation by the method of smooth perturbations, see more in [33,36,38]. The total accuracy of the employed interferogram processing technique is governed by the errors introduced by the method of smooth perturbations, see more in [38], and the accuracy of obtaining the approximating phase shifts; the latter accuracy, in turn, is governed by smoothing errors (the method operates with smooth curves) as well as by the background noise in the traced interferograms.…”

Extremely fast formation of anode spots in an atmospheric discharge points to a fundamental ultrafast breakdown mechanism

“…With the interferometers adjusted in the way described above, we traced the interferograms and recovered the 2D phase maps, see, e.g. those given in figure 7 in units k=Δf/2π of the relative fringe shift, using the techniques presented in [42,43]; here Δf is the phase shift introduced by the plasma at the passage of the probing radiation. The analyzed phase shifts (curves A) were approximated by smooth curves B which were then used to reconstruct the electron density distributions (n e ).…”