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On the cause of like charges beam squeeze

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On the cause of like charges beam squeeze

D.P. Borycenko-Karavashkina

Published in SELF Transactions, 1 (1994), p. 52- 56

“Whether the like charges repel always?” - asks Andrey Borzykh in his notice in the magazine “Technika - Molodezhi” (“Engineering for Youth”), 1988, No 7. He answers negatively, basing on his own observations of squeeze in a dielectric of a beam of like charges. A. Borzykh gives to this real fact his physical explanation on the grounds of Vavilov - Cherenkov effect: an electron arriving into a dielectric material becomes a ‘hyper-relativistic’, so the electromagnetic field produced by it delays from it and is as if ejected backwards, sucking into it the electrons flying behind. But does this explanation really account all necessary points? I doubt. There is known one more effect squeezing the current - the pinch.

A flow of high-speed like charged particles is factually the current. The ringed EM field is produced around it. The interaction of this field with the current causes the pinch - squeeze of both the current and wire where it runs.

The pinch was multiply observed and experimentally studied, though a full theoretical development of it is practically absent. It yet was not explained why pinch squeezes also a wire or plasma current. So I think, we have to consider the squeeze of flow of like charged particles also from the view of pinch.

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This will surely not only help to grasp the cause of squeeze but will broaden our idea of this effect.

I also came to the pinch of flow of like charged particles through my study of the nature of electric spark and lightning, the subject of supposed discovery claimed in 1976. This study showed that a separated from electrons and, thus, positively charged plasma ejected from the discharge gap and flying in the medium with the speed of only one or two orders slower than the speed of light can be considered as such flow. Such plasma produces the ionised tracks called leaders and streamers, and also scorching sparks.

The results of this study were discussed on 25.04.1988 at the ball lightning section of the laboratory “Inversor” attached to the “Technika - Molodezhi” editorial board. This session in fact accepted the possibility, the positively charged plasma to be produced within the electric spark. They questioned only, whether it is able to fly without an explosive expansion and expressed a doubt to my explanation that the plasma is squeezed by pinch. Now, when A. Borzykh’s studies corroborate the fact of like-charge beam squeeze in the dielectric, which is applicable also to the gas medium, I would like to return to the pinch and to consider it for this case from some other point of view.

The cause of pinch squeezing the current is known to be the Lorentz force affecting the charges running in the magnetic field.

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The formula of this force is

where q₀  is the charge of running particle, V₀ is its speed, and B is the magnetic field induction.

This formula is true also for the field produced around the wire with current I. If we substitute to (1) the expression for the induction B related to this case, it will take the following form:

where R  is the distance from the particle to the axis of flow. In this case the Lorentz force is always directed towards the axis of current, so it squeezes the whole flow of such particles. This is just the pinch.

It seems quite natural to extend this formula also to the flow of like charged particles. But here the question arises: what have we to take as the speed V₀ of the particle? If we use the speed conventionally averaged across the flow and take as V₀ the average speed of the particles in the flow, all particles will naturally move synchronously, as was given, and only outer magnetic field will control the interaction. While we know, the particles in the flow have at least Maxwellian distribution,

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and if moving in continua, the difference in maximal and minimal possible speeds will grow in proportion with the degree of interaction with the substance. With it, there arises the mutual difference of speeds of particles and, hence, their interaction under the Lorentz force affection. This factor was not reflected in (2). So it seems to be more correct to take in (2) the differential speed:

where V_f  is the average speed of particles in the flow.

This differential speed is calculated in its absolute value, because, the Lorentz force to arise in same direction, it does not matter, whether the charge crosses the field  (V₀ > V_f)   either the field moves against the charge (V₀ < V_f) . Then (2) will take the following form:

Now let us analyse this formula. In the vacuum, brakeage of peripheral particles is small, and with small energy of beam (in limits of keV) V₀ = V_f   and F_L = 0 . Though in the flow of high-energetical particles, when their speeds tend to c and the intensity of beam squeeze provides enough interaction between the particles,

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we already may not neglect the part of this force. At definite value of product of pressure in the beam into the energy, this force affection will turn the beam inside out even in the outer homogeneous and symmetrical magnetic fields. Just this occurs in tokamaks. In continuum either in low vacuum, when we may not neglect the interaction of flow particles with surrounding medium, the dispersion of particle speeds in the flow V_f abruptly grows and causes the growth of F_L  . Thus, the more and stronger particles are braked in relation to general flow the more current is squeezed by the Lorentz force affection.

Let us now return to the problem of tokamaks or of pinch squeezing the wires and plasma, e.g., in the discharge gaps. The slow positively charged ions produced due to ionisation will move against the flow of electrons either will be fixed in the lattice nodes (in a wire) and cause the dispersion of speed of particles and automatic squeeze of the wire and turning the plasma beam inside out, which is called a pinch.

Thus, we have proven the existence of forces of inner interaction between the like charged particles that determines the known but not explained experiments. Hopefully, this will help to get over some today difficulties in achieving the positive results in high-energy physics, in that number in solving the problem of controlled thermonuclear synthesis.

30.08.88