Investigating of plasma diagnostics by utilizing spectroscopic measurements of Balmer emission

Plasma technology offers revolutionary potential for particle accelerators by enabling the acceleration of electron beams to ultra-relativistic velocities in a small-scale dimension. The compact nature of plasma-based accelerators permits the creation of accelerating gradients on the GV scale. Plasma acceleration structures are created by utilizing either ultra-short laser pulses (Laser Wakefield Acceleration, LWFA) or energetic particle beams (Particle Wakefield Acceleration, PWFA), which need to be tailored to the plasma parameters. However, both methods face the challenge of limited acceleration length, which is currently only a few centimeters. To overcome this challenge, one approach is to generate plasma within a capillary tube, which can extend the acceleration length up to approximately forty centimeters or more. Consequently, it is crucial to characterize the produced plasma in terms of density and geometric structure. Optical emission spectroscopy (EOS) methods can be employed to measure and characterize the plasma electron density by analyzing the emitted plasma light. This paper presents measurements of the plasma electron density distribution for a hydrogen-filled capillary tube using both Balmer alpha (H_α) and Balmer beta (H_β) lines. Comparing the intensities of H_α and H_β emissions enables more precise measurements of the plasma electron density and provides additional information about other plasma properties.