The best sensitive single-coordinate interference jet-drop measurement of electric field strength

The article discusses the features of the implementation of highly sensitive single-coordinate measurements of electric field strength (EFS) by using of jet-drop optical measuring systems (JDOMS). The use of moving monodisperse charged droplets of a jet-drop coherent flow, which acquire a displacement depending on the directions of movement, the level of the EFS and of the droplet charge, is discussed. The issues of implementation of stroboscopic interference measurements of droplet displacements under impulsed illumination of their surfaces, used as curved reflectors, are considered in JDOMS. It is shown that measuring the displacements of the reflected oh drop of the laser beam makes it possible to determine the displacements of the reflecting drop and the value of the EFS at the selected coordinate, respectively. The features of the use of liquids with pigments and additives in the form of nanopowders of highly reflective metals, liquid metals (or their alloys) with a low melting point are considered in the JDOMS.


Introduction
Measurement and control of electric field strength (EFS) E and/or static charge q are relevant for nuclear, rocket and space, electrical and radio engineering, instrumentation and other industries. And the tasks of preventing electrostatic breakdown and/or ensuring electromagnetic compatibility a re especially important for many electrical devices at all stages of creation and operation. For this purpose, methods and means of measuring EFS E are being actively developed on the basis of different principles of action [1][2][3][4][5]. To solve various applied problems, jet-drop technologies are also being improved, allowing to obtain unique properties for applications, in particular, in reffigerators-emitters of spacecraft [6,7], in electroplating technologies for inkjet printing [6,8], marking, dyeing and washing of fibers and threads [6,9], impulsed radiation sources in the ultraviolet range [10], increasing the efficiency of fuel combustion in aircraft engines [11], technologies for the formation of mono-dispersed spherical granules [12] and other tasks. In this regard, the natural aspiration is to search for original technical solutions for measuring systems of a new type -jet-drop optical measuring systems (JDOMS) [13][14][15] in relation to measurements of EFS, in particular, acousto-optical (AO) interference methods of information processing. The issues of creating such methods of measuring EFS are not reflected in the open press and this article is aimed at filling this shortcoming. The article discusses the features of the implementation of highly sensitive single-coordinate measurements of EFS.

Formulation of the problem
The main objective of this work is to study the developed method of measuring EFS and JDOMS based on jet-drop technologies and acousto-optical interference methods for measuring laser beam displacements. To solve this problem, the dependence of the deviation of moving charged droplets from the EFS is investigated, 2 the dependences of the deviation of the reflected optical flow from the displacement of moving charged droplets are determined, and the sensitivity threshold is estimated when measuring the EFS.

Theory
To measure the EFS along one coordinate on the basis of an electric jet generator and a impulsed interference meter of droplet displacements (in future -an interference meter), an interference JDOMS has been developed, the composition, principle of operation and features of which are discussed below.

Structure and principle of operation of JDOMS for measuring EFS.
The developed JDOMS for monitoring the EFS is shown in figure 1, which indicates a droplet generator 1, a jet consisting ofa non-formed part of the jet 2 and a drip stream 3, a charger (a device for communicating a unipolar charge to drops) 4, the interference meter 5. Under the action of constant pressure and additional perturbation created by the monoharmonic (with high spectral purity) signal U g (t), a liquid jet flows out of the droplet generator 1 through the nozzle in the forced capillary decay mode. This liquid jet consists of a non-formed part of the jet 2 and a stream of moving droplets 3 with a diameter of at least more than 1-1.5 mm with high monodispersity (small size spread) and coherence (small spread of intervals between drops). In the process of separation from the jet, each drop is charged from the charger 4 to the q drop value. A charged moving drop, flying through the measuring section l meas , deviates by a value corresponding to the action of the EFS. In accordance with the results of calculations of displacements of a moving drop Δl drop carried out in [8,9] and by analogy with the electric field created by two plane-parallel deflecting plates with a length l o [9] forming a measuring section l o =l meas , provided that the influence of the charge field of this drop is neglected, we have E=U 0 /l o and we can write:

Structure and principle of operation of the interference meter.
To measure the deviations of droplet motion, a highly sensitive interference meter 5 is used, which is a laser impulse interferometer of Mach-Zender displacements with two arms, designed for high-precision measurements of transverse displacements of the laser flux in the task of controlling deviations from straightness [16]. Its scheme is shown in figure 2, which shows a impulsed laser 6, a beam splitter 7, a drop 8, an optical circuit 9, an AO modulator 10, microlenses 11 and 12 of the input 13 and 14 light guides of a Yshaped fiber splitter 15, a photodetector 16, a running AO impulse 17. The principle of operation is based on the impulse measurement of the phase shift of light waves arising from displacements of the center of AO interaction due to transverse displacements of the reflected laser beam Δ1 ref from the displacements of the droplet Δl drop . It uses the diffraction of light in the Bragg mode on a short zug ultrasound waves (USW), a "diffraction window" running through the AO modulator 10. The physical aspects of such modes of laser measuring systems (LMS) operation are considered in [16]. During the action of the light impulse , the streams pass through the following routes: in the reference arm: A→B→ photodetector 16, in the measuring arm: A→D (drop surface) → E→ F→G → photodetector 16. Spatial alignment of the reference and measuring flows during the light impulse leads to their interference and the formation of a impulsed signal at the output of the photodetector 16. Offset drops Δl drop alter the angle of reflection and the transverse displacements of the laser beam with the passage of the optical flow in the measuring shoulder along the following route: D (the surface of the drop) → E → F → G → photodetector 16. As shown in [16], the phase shift Δφ(Δl lb ) caused by transverse displacements of the laser beam Δl lb can be written using the expression: where k b is the "angular" coefficient. And then the expression for calculating the displacement of the optical flow Δl ref from the measured phase shift Δφ(Δl lb ) can be written as: The limit resolution (threshold offset) Δl lim currently achieved in practice for similar LMS can be Δl lim ≈λ/1350.005 μm =5•10 -9 m at λ=0.63 μm [16].

Features of the use of liquids in the JDOMS EFS.
At large angles of incidence of light on the surface of the drop (>60º), the reflection from it approaches the mirror. An increase in the reflection coefficient is possible due to the use of special inks based on a solution with an opaque dye (with high radiation absorption) and/or a metallic pigment based on metal nanopowders (aluminum, bronze, copper, incl. with additives "similar gold") with particle sizes <50-100 nm with a high reflection coefficient. Molten metals or their alloys can also be used as a liquid. Thus, melts of metals of the alkaline group of lithium (Li), potassium (K), sodium (Na) have a density less than that of water: 539, 862, 986 (kg/m 3 figure 3. In this scheme, the angle of incidence of light α is equivalent to the angle of the OCA, and then from the aspect ratios of the right triangle OCA, we can get a formula for calculating the angle of reflection the laser beam is relative to the normal to the surface of the drop: From where it is possible to obtain an expression for α gen , taking into account that the angle between the incident and reflected streams is equal to the double angle of reflection relative to the normal to the surface of the drop α gen =2α ref : where Δl dis is the displacement of the center of the illumination spot from the boundary of the drop, r d r o p is the radius of the drop.

Features of the use of the optical system.
The structure, characteristics, features of the optical system 9 and the parameters of light diffraction in the AO modulator 10 strongly influence the process of converting measurement information to an interference meter 5 ( figure 2) and, accordingly, on the methods for calculating the displacement of the optical flow reflected from the drop. Their two possible variants can be based, first of all, on taking into account mainly angular or linear displacements of the reflected beam, discussed below.

The method of сalculation of the displacement of the droplet based on the angular displacement of the reflected beam.
This approach is based on the formation of a collimated or close to it flow after the optical system 9, the displacements of which Δl ref are due to the angular displacement α dis of the reflected light from the movement of the droplet, i.e., the displacement of the center of the illumination spot on the surface of the Δl dis droplet. Therefore two segments: [EEꞌ] which is the displacement of the reflected beam with a length of Δl ref and [DE] which is the distance to the optical system 9 with a length of l opt are the cathets of the right triangle DEE' (figure 3). The ratio of the first to the second is the tangent of the desired angular displacement of the α dis or at small its values correspond to the angular displacement of the α dis itself. So we can write: Taking into account this formula and the angular displacement of the reflected beam from the movements of the droplet, determined by equation (5), we can obtain expression: where α in and l in are the initial angle of reflection and the position of the center of the illumination spot on the surface of the drop, provided the following condition: For expression (7), the second term is constant, and the desired parameter is Δl dis . So equation (7) after small transformations can be rewritten to the next form: And then from this expression you can derive the desired formula (10)

The method of сalculation of the droplet's displacement based on the linear displacement of the reflected beam.
This approach is based on focusing the optical flow after the optical system 9 so that the emerging focus is located in the middle of the AO modulator 10 in the position of the center of the AO interaction. The displacement of the droplet Δl dis leads to focus shifts. And for certain ratios of the optical parameters of the optical system 9 and the AO mode of light diffraction this displacement of the droplet Δl dis can be associate with the limit small displacement Δl lim recorded by the interference meter 5. So we can write next expression: Δl dis =k dis •Δl lim (11) where k dis is the linear displacement coefficient. This approach, linking the movements of the Δl dis droplet, is simpler and will be used in the future to assess the sensitivity threshold of the JDOMS EFS.

Calculation of the sensitivity threshold of the JDOMS EFS.
When using the calculation of the displacement of the droplet based on the linear displacement of the reflected beam according to formula (11), provided k dis =1, it is possible to write Δl dis =Δl lim . Substituting this condition into the transformed expression (1), we obtain the desired equation for calculating the sensitivity threshold of the JDOMS The obtained value can be refined with further studies and all the parameters of the interference meter 5, but this result show us the potential level of the developed JDOMS EFS for comparison it with similar parameters of other measuring systems.

Experimental result
In figure 4 shows experimentally certain schedules deviations of the trajectory of droplets with a diameter of 0.1825 mm 5% strength aqueous emulsion of the oiling agent M11, moving with velocity v drop =10 m/s when the length plots measuring l 0 =40 mm (curves 1-3) and l 0 =20 mm (curves 4,5) formed parallel deflecting plates with a gap of 5 mm from the edges to the EFS: Е 1 =Е 2 ≈1.33•10 6 V/m, Е 2 =E 5 =1.0•10 6 V/m, Е 3 ≈0.67•10 6 V/m. The droplets received a charge when the voltage U ch was applied to the charging electrode, varying in the range from 0 to 200 V. The M11 emulsion is similar to the synthox-20M oiler used in the textile industry for oiling fabrics and consists mainly of dioctylsebacinate oil -44%, genanol-08-080-R -34 %, genanol-08-080 -15% and other ingredients [9]. In figure 5 the interference signal of impulsed phase measurements generated by the photodetector 16 of the interference meter 5 is shown. It is formed by at optical flow diffraction on a running modulated USW zug (inpulse) in the AO modulator 10 (accordint to scheme of interference measurements of the EFS on figure 2).  5. The discussion of the results 1. A highly sensitive single-coordinate interference jet-drop method for measuring EFS has been developed, implemented in the JDOMS EFS, based on an electric jet generator and a impulse interference meter of droplet displacements. 2. The most sensitive method of measuring the displacement of a drop can be based on measuring the displacement of the optical flow reflected from it.
3. An increase in the light reflection coefflcient from a liquid drop is possible due to the use of liquids with a dye or/and pigment.