Study on propagation of pulse current discharges in plant tissue

This article provides a theoretical description of the propagation of current pulses in plant tissue and the processes of destruction of cellular structures of harmful pathogens in the plant organism. Plants, from the point of view of electricity, are regarded as a well-conductive cable. The peel of the plant is the sheath of the cable, the fire (core) is the electrically conductive conductor. When infected with diseases, the growth of the cellular structure occurs and, as a result, the resistance of the plant tissue decreases. When current is applied, it passes through the circuit with the least resistance and thus provides the lethal effect of harmful microorganisms.


Introduction
Electrical effects on plants can be used to encourage their growth, development, and productivity, as well as to cause deadly harm for ripening, drying, increasing juice output, eliminating weeds, and so forth [1][2][3][4]. This action can be carried out by a variety of electric and magnetic fields, different types and stages of electrical discharges, and various electric currents, such as DC pulsed, alternating sinusoidal, non-sinusoidal AC with and without an electric spark discharge, and so on [5,6]. It is crucial to determine the most valuable of these currents from an energy and technology standpoint. Depending on the type and method of growing and fruiting, cultivated plants are very diverse in structure. Therefore, the impact on plant organisms requires a thorough study of their cellular structures [7][8][9]. As a rule, perennial plants and trees have a tighter and stronger cellular structure [10]. This feature allows them to resist certain viruses and diseases. Plants of vegetable and melon crops, in comparison with them, have, on the contrary, a less dense cellular structure [11][12][13]. Their peel and shives consist mainly of moisture, through which nutrients are transferred to all parts of the plant organism. When evaluated in terms of electricity, these plants can be regarded as a well-electrically conductive cable. The peel is the sheath of the cable, the shives (core) is the electrically conductive conductor. If the plant organism is infected with the larvae of worms of pathogenic nematodes, then, according to the known features of the nematodes, liquid-filled swellings are formed in the infected areas of plant material [14]. In these areas of a diseased plant, as is known, the cell membranes are upset [2]. For this reason, for theoretical study and creation of diseased and healthy plants as a material for processing, they can be considered as a vessel filled with a variety of liquid. Our goal was to theoretically study the propagation of high-voltage pulsed current over the infected plant areas and the mechanism of propagation of high-voltage pulses.

Theory and Methods
As a rule, instantaneous forces are called forces acting during a negligible time interval "", to which high-voltage pulses of voltage and current can be attributed, which have a finite value and which can be described by the following general formula [4]: Usually, such pulses arise, for example, when molecules collide in a liquid medium.
To study the vibrations caused by these pulses, we use the general solution of the differential equation of forced vibrations under the initial conditions by the following formula [3]: where: Пenergy pulse Spulse number where: * k -damped-vibration frequency.
Let us first of all find the equation of vibrations caused by a constant generalized force Q F , suddenly applied to the system at a time t 1 = 0 and valid for a certain period of time  t . By equating formula (2), we get: where, Q F -forces acting by voltage pulses. Vibrations determined by equation (4) exist as long as the force acts Q F i.e. if t   , i.e. current pulse occurs.
Find the maximum value of the coordinate q = q (t). From equation (4) we have: By equating the generalized speed of the pulse current to zero, we get e -nt sin k * t = 0, which for a finite value of t leads to the condition sin k * t = 0:, t =  / к  since at t = 0, q o = 0 consequently, the maximum value of q reaches at t T   2 i.е. in that case, when time interval t is equal to half the period of damped-vibrations. (T * ) Maximum value of "q" equals: Since under the force static action Q F q Q c c F  then the dynamic factor for the considered case is ( This factor is always greater than one. For the case n = 0 (resistance not considered) equation (4) takes the following form: The dynamic effect of a suddenly applied constant force (shock wave of a pulsed current) in this case, according to formula (6), is twice the static  = 2.
The equation of vibrations of the system after the termination of the action of the force (the passage of the impulse current is stopped) (t) can be obtained as follows: generalized force equal to -Q F , applied to the system at a point in time t = , causes vibrations determined by an equation similar to equation (4), namely: By summing up these vibrations with the vibrations caused by the force + QF applied to the system at the moment of time t = 0, we get the following vibration equation for the case t, where  -force action duration +Q F: then the generalized coordinate q, determined by equation (7) If value « n » much less than « k », then the resistance can be neglected. All formulas in that case (n = 0) simplify and take this form:

Results
Depending on the duration of the action of a constant force suddenly applied to the system (the strength of the shock of the impulse current) Q F , factor , defined by formulas (9) and (10), can be more and less than unity [1].
To study vibrations caused by a current pulse of instantaneous strength 0 lim( ) we represent the previous equation in the following form: Value S k can be viewed as an equivalent generalized force Q eqv. , the static action of which determines the maximum deviation of the system from its equilibrium position, caused by S. Consider vibrations caused by instantaneous current impulses. If impulses arise after a period of time then: 1,2,......,s ) (t 1 =0) where, Spulse number, then the equation of forced vibrations at t  t 1 has a form as follows: For the next intervals, the cycle is repeated, i.e. the motion of the system is determined by the same equation. The vibration graph is shown in Fig. 1. The graph of the growth of these fluctuations is shown in Fig. 2.  Fig. 3 shows a graph of the growth of these vibrations with an increase in the number of shock current pulses, «s». This is due to the fact that with an increase in the number of pulses in liquid-filled vessels (such as the infected areas of plants), a resonant increase in the amplitude of subsequent pulses can occur. Through a measured increase in the amplitude of the impulses, they can have insignificant effectiveness in the destruction of microscopic membranes, such as the egg cell structure of nematode helminth Therefore, we believe that the best efficiency of the understanding of cells can be achieved with the parameters of pulsed discharges having, according to the formula 25 and the harmonic amplitude shown in Fig. 2.