Linearity of charge measurement in laser filaments

TL;DR

This study assesses the linearity of three electric measurement techniques for initial electron density in laser filaments, demonstrating their accuracy and limitations through experiments and simulations.

Contribution

It provides a comparative analysis of measurement methods, highlighting their linearity and reliability in quantifying charge in laser filaments.

Findings

Conductivity measurement is linear within 2% below 100 kV/m.

Ionic current measurement is linear within 2% with ion amount.

Polarization signal deviates up to 80%, serving as a semi-qualitative indicator.

Abstract

We evaluate the linearity of three electric measurement techniques of the initial electron density in laser filaments by comparing their results for a pair of filaments and for the sum of each individual filament. The conductivity measured between two plane electrodes in a longitudinal configuration is linear within 2% provided the electric field is kept below 100 kV/m. Furthermore, simulations show that the signal behaves like the amount of generated free electrons. The slow ionic current measured with plane electrodes in a parallel configuration is representative of the ionic charge available in the filament, after several $\mu$s, when the free electrons have recombined. It is linear within 2% with the amount of ions and is insensitive to misalignment. Finally, the fast polarization signal in the same configuration deviates from linearity by up to 80% and can only be considered as a semi-qualitative indication of the presence of charges, e.g., to characterize the filament length.