**2. Plasma diagnostic setup**

#### **2.1 Plasma creation and probing laser setup**

Some of the common approaches to create a laboratory plasma include laser ablation, the spark gap, and exploded wires as illustrated in **Figure 1a**. Each drawing shows a

#### **Figure 1.**

*Illustration of common setup to create plasma and image with a single camera. (a) Driving laser ablates material. (b) Electrical breakdown of air produces electron stream. (c) High driving current vaporizes wire.*

#### *2D Relative Phase Reconstruction in Plasma Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.104748*

probing laser that traverses the plasma medium. Although not shown, the probing laser passes through an interferometer before the charge-coupled-device (CCD) camera captures the interference pattern. **Figure 1a** shows how a driving laser irradiates a sample of very high purity (99.99% or better). The driving laser's power density can range from 109 to 1012 <sup>W</sup> cm<sup>2</sup> for short bursts (≈100 ps) to create a plasma plume or jet [16, 17]. The driving laser's pulse duration and pulse power, and the geometric shape of the sample control the plasma jet's direction and size. The spark gap of [18] as represented in **Figure 1b** uses a pulsed high-voltage to cause the air between the electrodes to break down and form a spark plasma. The low-collisional spark plasma produces a current in air of ≈2*:*7 kA and lasts for ≈4*:*2 ms. An alternative approach uses electrically-exploded wires shown in **Figure 1c**. The thin wire samples also of very high purity have very small diameters of a few microns and are driven from the electrodes with a high-current pulse (≈2*:*5 kA). The pulse has a short rise time of a few nano-seconds and the sudden burst of energy causes the wire to vaporize as a cylindrically expanding plasma [4].

Several recent works use exploding wires to study how the plasma forms and behaves under varying conditions [4, 8, 19]. In particular, the setup of [8] uses two interferograms at 1064 and 532 nm to measure electron and atom densities (illustrated in **Figure 2a**). Also, the addition of a second wire as shown in **Figure 1** allows study of colliding plasma flows [20]. In **Figure 2**, beam splitters and mirrors are understood to change the optical path of probe laser 2.

#### **2.2 Plasma diagnostic methods**

Plasma presents electrical, optical and mechanical behaviors that are observable from the electromagnetic (EM) wave emissions in the visible through x-ray regimes and the EM wave propagation through the plasma. Schlieren, shadowgraph and interferometric images reveal temporal and spatial variation of the plasma's index of refraction. Of interest are the interferometer methods such as [8] that measured electron and atom densities using the classical Mach-Zehnder and also the shearing air wedge interferometer [21].

The basic optical setup of [8] as developed from the experiences of [4, 5] is shown in **Figure 3a**. The 1064-nm probing laser is passed through a harmonic doubler to produce a co-linear probing laser at 532 nm. Both beams are adjusted to illuminate and traverse the windowed vacuum chamber. The interferometer is adjusted to provide a regular fringe pattern before wire explosion. **Figure 3b** shows the resulting interference patterns collected at each wavelength (left: 1064 nm, right: 532 nm) at different time intervals before and after wire explosion. The shadowed regions centered near the top and bottom of each image are the electrodes, and the wire's shadow appears in

#### **Figure 2.**

*Illustration of recent methods with electrically exploded wires [8, 20]. (a) Single and (b) double wire setups.*

**Figure 3.**

*(a) Optical path for dual-wavelength interferometry, and (b) time-sequenced interferograms.* © *2020 IEEE. Reprinted, with permission, from [8].*

the *t* ¼ 0 ns imagery. The CCDs' reference frames are defined with *x* along the optical path and *y* � *z* in the CCD focal planes. Lastly, the setup excludes static electric and magnetic fields, and the laser frequencies are well above the plasma cutoff frequency.
