The name "Oscillatory Chamber" is given to a completely new principle of magnetic field production which employs the effects of the oscillation of electric sparks. These sparks circulate around the inner perimeter of a cubical chamber made of an electric insulator and filled with a dielectric gas. The four packets of electrodes, joined to the inner surfaces of four side walls of this chamber, perform alone the function of two oscillatory circuits with a spark gap. Each one of these two circuits is created by two packets of electrodes attached to two opposite walls. The appropriate formation of the oscillatory discharges occurring in both these circuits allows for the production of a dipolar magnetic field. The principles applied for this production not only eliminate from the chamber the drawbacks of today's electromagnets, but also provide the Oscillatory Chamber with a variety of unique operational advantages.
The complete elimination of drawbacks inherent in the electromagnets is ensured by the following attributes of the chamber:
1.The elimination of electromagnetic forces acting on the structure of the chamber.
2. Leaving to the user's choice the time and amount of energy supply (i.e. each portion of energy, whatever its amount and whenever it is delivered, is collected, stored, converted into a magnetic field and released when necessary).
3. The recovery and conversion back into electricity of all the energy dissipated by sparks.
4. The channeling of the destructive consequences of the accumulation of huge electric charges into the direction which reinforces the chamber's proper operation.
5. The independence of the power of control devices from the power involved in field production (i.e. a weak control signal will cause a change in the enormously powerful field produced by the chamber).
The Oscillatory Chamber displays also the following unique advantages unknown in any other appliance built by man to date:
A. The ability to absorb and store theoretically unlimited amounts of energy.
B.Full controllability over all properties and parameters of the field produced, achieved without any change in the level of energy contained in it.
C. Producing the kind of magnetic field which does not attract, nor repel, ferromagnetic objects (i.e. which behaves like a kind of "antigravity field", not a magnetic one).
D. Three dimensional transformation of energy (electricity/ magnetic field/heat) which allow the Oscillatory Chamber to take over the function of almost every other conventional energy-converting device (e.g. electromagnets, transformers, generators, accumulators, cells, combustion engines, heaters, air conditioners, etc.).
As the final result of such a formation of the Oscillatory Chamber, this device, when completed, will be able to raise the value of a produced magnetic flux to a level unlimited by theoretical premises. Practically it also means that this source of field will be the first one able to lift itself as the effect of a repulsive interaction with the Earth's magnetic field.
F1. Why there is a necessity to replace the electromagnet by the Oscillatory Chamber
The recent achievements in the development of propulsion systems prompt one to ask the question: What is this remarkable principle of controlled magnetic field production of which today's technology can be so proud? The answer is (at the beginning of the space exploration era): exactly the same principle as the one which was used over 170 years ago, i.e. the principle discovered by the Danish professor, Hans Oersted, in 1820, depending on the application of the magnetic effects created by an electric current flowing through the coils of a conductor. The device utilizing this principle, called an electromagnet, is now one of the most archaic appliances still in common use. We can realize how outdated its operation is from the following example: if the progress in propulsion systems were equal to that of magnetic field production devices, our only mechanical vehicle would still be a steam engine.
Electromagnets possess a whole range of drawbacks, which make it impossible to raise their output above a particular - and not very high - level. These disadvantages can in no way be eliminated, because they result from the principle of operation of these devices alone. Below are listed the most significant drawbacks of electromagnets:
(1) Electromagnets create deflecting forces which tense their coils in the radial direction trying to tear coils apart. These forces are produced as the result of mutual interaction between the magnetic field produced by an electromagnet, and the same coils of the conductor which created this field. The field tries to push these coils out from its own range (see the "left-hand rule" often called the "motor effect"). The deflecting forces so formed in coils are of a type identical to the ones utilized in the operation of electric motors. In order to prevent the electromagnet from being torn apart, these electromagnetic containment forces must ultimately be resisted by some form of physical structure. This increases the weight of any really powerful steady-field magnet, whose output must be balanced by the mechanical strength of its structure. When the current's flow in electromagnets exceeds a certain level, the deflecting forces grow to such an extent that they cause the coils to explode. Therefore, too high an increase in the output of electromagnets results in their self-destruction (explosion).
(2) Electromagnets must be continuously supplied with electric current if they are to produce a magnetic field whose all parameters are controllable (i.e. a field whose parameters can be changed in accordance with the application requirements). If such continuous energy supply is cut off, the controllability over the electromagnet's field finishes. This requirement of controllability causes that during the production of powerful magnetic fields, a single electromagnet consumes the output from a whole electricity plant.
(3) Electromagnets cause significant energy losses. The electric current flowing through coils of a conventional electromagnet releases a vast amount of heat (see Joule's law of electric heating). This heat not only decreases the energetic efficiency of the magnetic field production, but also, when the energies involved are high, it leads to a melting of the coils.
The superconductive electromagnet removes the heating from a current flowing through resistance. However, it introduces another loss of energy resulting from the necessity to maintain a very low temperature of the coils. This also causes a permanent consumption of energy which decreases the efficiency of such a magnet. Moreover, it should be noted here that the high density of magnetic fields cancels the effect of superconductivity and thereby restores a resistance to the coils.
(4) Electromagnets are prone to electric wear-out. The geometrical configuration of electromagnets is formed in such a way that the direction of the greatest electric field strength does not coincide with the path of the conductor through the coil. This directs the destructive action of electric energy into the insulation, causing its eventual damage (short-circuit followed by the electric breakdown) which initiates the destruction of the entire device.
(5) Electromagnets can not be controlled by weak signals. The parameters of their magnetic field can be controlled only through the changes in the power of the electrical energy supply. Therefore controlling the electromagnets requires the same powers as those powers involved in the production of a magnetic field.
The only way to eliminate the five disadvantages listed above is to apply a completely different principle of magnetic field production. Such a principle, invented by the author, will be presented in later sections of this chapter. Because this new principle utilizes the mechanism of oscillatory discharges occurring inside a cubical chamber, it is called an "Oscillatory Chamber".
The principle of the Oscillatory Chamber avoids the limitations which prevent an increase of output in electromagnets. Also, it promises a more effective and convenient preparation and exploitation, long life without the necessity of maintenance, a very high field-to-weight ratio, and a wide range of applications (e.g. energy storage, propulsion devices, sources of magnetic fields, etc.). The explanations that follow (especially the one from subsection F5) will describe the mechanisms for achieving this. Therefore, it appears highly desirable to promote the fast development of this device in the not-too-distant future so that it may replace electromagnets presently in use.
F2. The principle of operation of the Oscillatory Chamber
The electric current flowing through a wire is not the only source of a controlled magnetic field. The other well-known source is the phenomenon manifesting the flow of electric energy in its purest form, i.e. an electric spark. There are many different methods for the creation of electric sparks, but the purpose considered here is best served by the so-called "oscillatory circuit with a spark gap". The unique property of such a circuit is its ability to absorb, total and utilize the energy supplied to it. This energy then appears in the form of a gradually diminishing sequence of oscillatory sparks created by the circuit.
The discovery of the oscillatory circuit with a spark gap was achieved in 1845 by the American physicist, Joseph Henry, who noticed that when a Layden jar was discharged through coils of wire, the discharge and a spark were oscillatory. A few years later Lord Kelvin, the great English physicist and engineer, proved mathematically that the discharge in a circuit so constituted must manifest itself in the oscillatory form.
F2.1. The electrical inertia of an inductor as the motive force for oscillations in a conventional oscillatory circuit with a spark gap
Figure F1 "a" shows a conventional configuration of the oscillatory circuit with a spark gap. The most distinctive characteristic of this configuration is that it is constituted by connecting together into one closed circuit the configuration of three vital elements, i.e. L, C1 and E, which have the form of separate devices. These elements are: (1) inductor L, containing a long wire wound into many coils, which provides the circuit with the property called an "inductance"; (2) capacitor C1, whose property, called a "capacitance", allows the circuit to accumulate electric charges; (3) electrodes E, whose two parallel plates ER and EL, separated by a layer of gas, introduce a "spark gap" to the circuit.
When the electric charges "+q" and "-q" are supplied to the plates PF and PB of the capacitor C1, this forces the flow of an electric current "i" through the spark gap E and the inductor L. The current "i" must appear in the form of a spark "S" and must also produce the magnetic flux "F". The mechanisms of consecutive energy transformations occurring within the inductor L and described in many books on electronics, cause the spark "S", since once created between electrodes E, to continue oscillating until the energy involved is dissipated.
The oscillatory circuit with a spark gap represents an electric version of the device which produces one of the most common phenomena of nature, an oscillatory motion. The mechanical analogy of this device, well-known to everyone, is a swing. In all devices of that type, the occurrence of oscillations is caused by the action of the Conservation Energy Principle. This principle compels the initial energy provided to such an oscillating system to be bound in a continuous process of repetitive transformations into two forms: potential and kinetic. The "potential energy" within the oscillatory circuit is represented by the opposite electric charges "+q" and "-q" carried within both plates of a capacitor - see Figure F1 "a". The electric potential difference introduced by the presence of these charges causes the flow of an electric current "i" through the circuit. In a swing, the same potential energy is introduced by slanting the arm of it away from the vertical position. As a result, a load (e.g. a swinging child) is raised to a particular height, later forcing its own acceleration down into the equilibrium position. The second from of energy, the "kinetic energy", within the oscillatory circuit manifests itself in the from of a magnetic flux "F" produced by the inductor L. In a swing this kinetic energy appears as the speed of a load's motion.
The mutual transformation of the potential form of energy into a kinetic one, and vice versa, requires the involvement of an agent which activates the mechanisms of energy conversion. This agent is introduced by the element possessing the property called "inertia". Inertia is a motive force maintaining the oscillations within any oscillating system. It works as a kind of "pump" which forces the transformations of energy from a potential form, through a kinetic one, back into a reversed potential form. This "pump" always restores the initial amount of potential energy existing at the beginning of the oscillation's cycle, decreased only by its dissipation occurring during the transformations. Therefore the inertial element is the most vital component of every oscillating system. In the oscillatory circuit its function is performed by the inductor L, whose inductance (expressed in henrys) represents electrical inertia. In the swing, mechanical inertia is provided by the mass of a load (expressed in kilograms). This is the reason why the inductance in the electric oscillations is considered to be the equivalent of the mass from the mechanical oscillations.
To increase mechanical inertia it is necessary to join additional mass to that which is already involved in the energy transformations. The increase of electrical inertia requires the extending of the length of an electric current flow, exposed to the action of its own magnetic field. Practically this is obtained by building an inductor containing many coils of the same wire, closely wound, so that each of them is within the range of the magnetic field produced by the other coils.
Let us review the mechanism of oscillations within the oscillatory circuit shown in Figure F1 "a". We assume that initially the plates PB and PF of the capacitor C1 carry the opposite electric charges "-q" and "+q" and that the current "i" within the inductor L is zero. At this instant the whole energy of the circuit is stored in the potential form in the capacitor C1. The opposite charges accumulated on the plates of the capacitor C1 create an electromotive force which activates the current flow "i". To facilitate the interpretation of the sparks' behavior, in this publication the electric current is defined as a movement of electrons from negative to positive. The current "i" appears on the electrodes E in the form of a spark "S", whereas in the inductor L it produces a magnetic flux "F". As the difference of charges "q" on the plates of the capacitor C1 decreases, the potential energy stored in the electric field also decreases. This energy is transferred to the magnetic field that appears around the inductor because of the current "i" that is building up there. Thus the electric field decreases, the magnetic field builds up and energy is transformed from the potential to the kinetic form. When all the charge on the capacitor C1 disappears, the electric field in the capacitor will be zero, and the potential energy stored there will be transferred entirely to the magnetic field of the inductor L. The electromotive force which before caused the current "i" to flow is now eliminated. But the current in the inductor continues to transport the negative charge from the PB plate of the capacitor C1 to the PF plate, because of the electrical inertia. This preserves the current "i" (therefore also the spark "S") from extinction and maintains its flow at the cost of the kinetic energy contained in the magnetic field. Energy now flows from the inductor L back to the capacitor C1 as the electric field builds up again. Eventually, the energy will have been transferred back completely to the capacitor C1. The situation now reached is like the initial situation, except that the capacitor is charged in the reverse way. The capacitor will start to discharge again, and the whole process will repeat itself, this time in the opposite direction. Once started, such oscillations continue until the resistance of this process dissipates the energy involved.
F2.2. In the modified oscillatory circuit with a spark gap, the inductance of a stream of sparks replaces the electrical inertia of an inductor
It is known that an electric spark alone introduces a high electric inertia. Therefore a spark is able to replace the inductor in providing the inductance to the circuit. The condition of such a replacement is that the spark must possess the appropriate active length and also that its path must follow a course within the range of its own magnetic field. To achieve this condition, it is impossible to repeat the solution used in the inductor, because an electric spark is reluctant to wind itself into the form of consecutive coils. However, the same can be achieved in another way, through replacing a single spark by a whole stream of sparks jumping simultaneously along parallel paths. Each single spark in such a stream will be the equivalent of one coil of wire within an inductor. All sparks together will provide the necessary inductance to the circuit.
Figure F1 "b" shows the author's modified version of the oscillatory circuit with a spark gap, which makes use of the electrical inertia of the stream of parallel jumping sparks. The most distinctive characteristic of this version is that all three vital components of the Henry's circuit, i.e. inductance L, capacitance C1 and spark gap E, are now provided by a single physical device, which simultaneously performs three different functions. The modified device consists of only a couple of conductive plates PF and PB, attached to the inner surfaces of two opposite walls of a cubical chamber made of an electric insulator and filled with a dielectric gas. Each of the plates is divided into a number of small segments each insulated from the other (in the diagram marked by 1, 2, 3, ..., p). Each pair of facing segments marked by the same number, e.g. "p", forms a single component capacitor, which after receiving a sufficient electric charge transforms itself into a couple of electrodes exchanging the electric spark "Sp". The total number of all electric sparks jumping simultaneously in the form of a single compact stream provides the device with the required inductance.
To summarize the modification described above, one can say that the three separate devices, each of which has provided the conventional circuit with one selected property, are now replaced by the single device (i.e. a pair of plates) simultaneously providing all three vital properties, i.e. L, C and E.
If the principle of operation of this modified oscillatory circuit is considered, it becomes obvious that it is identical to Henry's circuit. After all segments of both plates are uniformly charged, the potential energy of the circuit is built up. When the difference of potentials between plates overcomes the breakdown value "U", the discharge is initiated. This discharge will take the form of a stream of parallel sparks S1, S2, S3, ..., Sp, joining facing segments of the plates. The magnetic field produced by these sparks will gradually absorb the energy stored initially within the electric field. When both plates PF and PB reach the equilibrium of potentials, the electrical inertia of sparks will continue the transmission of the charge between them, transforming the kinetic energy contained within the magnetic field back into the potential energy of the electric field. Therefore at the end of the first stage of the oscillation of sparks, the plates will again contain the initial charge, but of the opposite kind. Then the whole process repeats itself but in the reverse direction. If the slight dissipation of energy occurring in this device is somehow compensated for, the process described above will be repeated endlessly.
Such an operation of the modified oscillatory circuit liberates all the electric phenomena from material ties. In effect the electric current does not need to flow through a wire and its value is not the subject of limitation by the properties of the materials used. Also the electric phenomena are exposed to a controlling action that allows them to be channeled into the desired course. These are very important achievements, and as it will be proved later, they are the source of many of the advantages of this device.
The sequence of sparks that oscillate in the device shown in Figure F1 "b", will produce an alternating magnetic field. Because the stream of sparks follows the same path in both directions, this field will also be a vortex, i.e. have all force lines lying on parallel planes. Such a field will not display clear polarity, because its magnetic poles N and S are not fixed. To create a bipolar magnetic field with the steadily positioned magnetic poles N and S, it is necessary to continue one step further in the development of this modified oscillatory circuit.
F2.3. The combination of two modified circuits forms an "Oscillatory Chamber" producing a bipolar magnetic field
The final form of the circuit considered here is shown in Figure F1 "c". This is the form to which the name "Oscillatory Chamber" has been ascribed. The Oscillatory chamber is constituted by combining together two circuits indicated as C1 and C2, both identical to the one presented in Figure F1 "b". Therefore it consists of four segmented plates (i.e. twice as many as in the modified oscillatory circuit in Figure F1 "b"), indicated as PF, PB, PR and PL (i.e. front, back, right and left). Each of these plates contains the same number of segments "p", and faces the other identical plate, together with this other plate forming one of the two co-operating oscillatory circuits. Both of these circuits produce the four streams of sparks marked as SR-L, SF-B, SL-R, and SB-F, which oscillate between opposite plates. These sparks appear in succession, one after the other, having the mutual phase shift between them equal to one quarter of a period of their entire sequence (%T).
Before the mechanism of the discharges in this final configuration is analyzed, we should remind ourselves of the action of the electromagnetic containment forces which will try to deflect the sparks away from the range of the bipolar magnetic field. They are the same forces which cause the explosion of coils in powerful electromagnets. In the case of the Oscillatory Chamber, these forces will push the stream of sparks against the plate along which the discharge occurs. For example all sparks within the stream SR-L jumping from the plate PR to the plate PL will be pushed to the surface of the plate PF (at this moment the plate PF increases its own negative charge). For this reason the individual sparks forming consecutive streams SR-L, SF-B, SL-R, and SB-F, instead of crossing the paths of the other sparks, will bend themselves at the edges of the chamber and produce a kind of rotating arc. Notice that the plate along which the sparks are jumping is prevented from being entered by them. This prevention mainly depends on the formation of the plate from a large number of small segments (needles), each insulated from the other, and therefore the resistance against conduction along the plate is not less than the resistance of the discharge through the dielectric gas in the chamber.
Let us assume that the initial charging of the Oscillatory Chamber is provided in such a way that first the stream of sparks marked as SR-L will occur, and then after a period of time equal to t=%T - the stream SF-B (compare Figure F1 "c" with Figure F3). Let us also assume that right from this initial time, along the vertical (magnetic) axis "m" of the chamber the magnetic flux "F", produced by this device, prevails. This flux pushes sparks against the side walls. After the initial charging of the C2 capacitor, at the time t=0, the stream of sparks SR-L will appear, which will jump from plate PR to plate PL. These sparks produce the magnetic flux "F" which is totaled to the one already existing in the chamber. The flux bends the paths of all these sparks, pushing them close to the surface of plate PF. At time t=%T the potentials of plates PR and PL reach an equilibrium, but the inertia of sparks SR-L still continues transporting charges from PR to PL, at the cost of the kinetic energy accumulated in the magnetic field. At the same instant (t=%T) the operation of the second circuit begins and the jump of the SF-B stream of sparks is initiated. Similarly this stream produces a magnetic field which pushes it against the surface of plate PL. So in the timespan t=%T to t=^T, there are two streams of sparks present, SR-L and SF-B, the first of which transfers energy from the magnetic to the electric field, whereas the second one transfers energy from the electric to the magnetic field. At time t=^T the plates PL and PR reach a difference of potentials equal to the initial one (at t=0), but with the opposite location of charges. Therefore the stream of sparks SR-L disappears, whereas the stream SL-R jumping in an opposite direction is now initiated. This stream is pushed to the surface of plate PB. At the same instant (t=^T) the plates PF and PB reach the equilibrium of potentials, so that the stream of sparks SF-B passes into its inertial stage. In the timespan t=^T to t=3/4T there are two streams of sparks, i.e. SF-B and SL-R, the first of which consumes the magnetic field, whereas the other produces it. At the instant t=3/4T the sparks SF-B disappear and the sparks SB-F are formed (pushed against plate PR), whereas the sparks SL-R are passing into their inertial stage. At time t=1T the sparks SL-R also disappear and the sparks SR-L are created (pushed against the plate PF), whereas the sparks SB-F pass into their inertial stage. With this the whole cycle of the sparks' rotation is closed, and the situation at time t=1T is identical to the one at the initial moment t=0. The process that follows will be a repetition of the cycle just described.
The above analysis of the sequence and paths of the sparks reveals a very desirable regularity. The streams of sparks turn into a kind of electric arc combined from the four separate segments. This arc rotates around the inner perimeter of the Oscillatory Chamber. Such a process, in accordance with the rules of electro-magnetism, must produce a strong, pulsating, bipolar magnetic field. The obtaining of such a field crowns the long and difficult search for the new method of the magnetic field production presented here.
The principle of operation of the Oscillatory Chamber does not require a strictly cubical shape for this device, and can also be executed in any chamber consisting of four rectangular side walls of identical dimensions. The only condition is that its cross-section in a plane perpendicular to the magnetic axis "m" must be a square. In this publication, however, for simplicity in deduction, only the cubical shape is considered.
We should also consider the characteristics of the magnetic field produced by the Oscillatory Chamber. If we analyze the field produced by only a single stream of sparks, it would be a discrete pulsating field of approximately half-sinusoidal course, which, at the points where the sparks reverse, would drop to zero. Because in the chamber two streams of sparks always appear simultaneously, the resultant field will follow the course described approximately by totaling together the series of positive halves of sinusoids. It will still pulsate, but will contain a constant component and a varying component. The relation between both components, as well as the course of the varying component, will be determined by the amount of energy involved in the pulsations.
F3. The future appearance of the Oscillatory Chamber
It is not difficult to satisfy the requirements of the Oscillatory Chamber for construction materials. This device can be made of practically anything, provided that its housing is a good electric insulator and its electrodes made of good electric conductors. Moreover, all parts should be magnetically neutral. So even ancient material available thousands of years ago, such as wood and gold, can be used. If made out of these, the Oscillatory Chamber would look like an ordinary wooden box or cube. Its appearance would not indicate its hidden power.
At our present level of technological development there are available transparent nonconductors, which are also excellent robust construction materials. If the housing of the chamber were made of them, it would reveal to the observer the contents of this device. Contemporary electronics has also created a high demand for transparent conductors, which can already be found in some watches and calculators. The quality of these conductors will gradually improve and we may soon expect their properties to be comparable to those of metals. Let us assume that the Oscillatory Chamber will be made wholly of such transparent materials. Therefore the casual observer of the chamber in operation will notice it has the form of a very simple transparent cube - see figure F2. Along the inner surfaces of the plain side walls of this cube, bright gold shimmering sparks will flash. Although these sparks will flicker, they will appear to be frozen in the same positions. Their paths will closely follow the inner surface of the plates, because of the electromagnetic containment forces pushing the sparks against the walls of the chamber. The inside of the cube will be filled with a dielectric gas and an extremely concentrated magnetic field. This field, when observed from the direction perpendicular to its force lines, will be impenetrable to light, looking like dense black smoke.
It is very noticeable in any scientific exhibition or "open day" in a laboratory, that when a demonstrator starts up an apparatus producing sparks, for example a Tesla coil, an Induction coil or a Van de Graaff machine, spectators irresistibly gravitate towards the display. Claps of thunder and lightning flashes have always possessed a kind of mysterious, hypnotic power which acts on everyone and which provides memorable experiences. The power emanating from inside the Oscillatory Chamber will similarly capture the attention and imagination of people witnessing it. Future observers of the operation of this device will have the impression that they are facing an unknown living creature, absorbed in the fulfillment of its own fascinating and mysterious physiological functions, rather than seeing a piece of machinery engaged in its ordinary process of operation. The wealth of energy, trapped, curbed and waiting within the walls of the chamber, will fascinate witnesses, leaving them with a multitude of vivid impressions, indelibly etched on their memories.
Observing this transparent cube, one will find it difficult to imagine that to reach the point of its creation, this device, so simple in structure, required the accumulation of almost 200 years of human knowledge and experience.
F4. The condition under which the sparks will oscillate within the Oscillatory Chamber
Our present knowledge of magnetic and electric phenomena enables us to deduce the equations expressing the values of the resistance, inductance and capacitance of the Oscillatory Chamber. Further combination of these equations will lead to the prediction of the behavior of this device.
F4.1. Resistance of the Oscillatory Chamber
The general form of the equation for the resistance of any resistor of cross section "A" and length "l" is as follows:
In this equation the "6" represents the resistivity of a material from which the resistor is made. In our case it will be the maximal resistivity of the dielectric gas that fills the Oscillatory Chamber, determined for the conditions of the initial moment of electric breakdown.
If in the above general equation, we replace the variables by the specific parameters determined for the Oscillatory Chamber, i.e. l=a and A=a2 (compare with Figure F1 "b"), this gives:
The equation received represents the resistance of the Oscillatory Chamber, which is a function of the chamber's side wall dimension "a".
The determination of the chamber's inductance is an extremely difficult and complex task. It is beyond the author's knowledge of the subject. Also a number of experts consulted in this matter were unable to help. (Perhaps some of the readers know how to resolve this problem -all advice will be warmly welcomed.) Being unable to find the exact solution, the author decided to apply temporarily a simplified one. To justify this simplification it should be stated that the deducted equation for inductance (F2) will be used only once in the entire monograph, when the meaning of factor "s" (see (F5)) is interpreted. Therefore all the vital equations in this work remain unaffected.
In the simplified deductions of the chamber's inductance an assumption is made that a unitary inductance of a stream of sparks (i.e. the inductance related to the unit of a spark's length) will be equal to the inductance of the equivalent strand of wires. This assumption allows for the application of a well-known equation for the inductance of a solenoid (see "Fundamentals of Physics" by David Halliday et al, John Willey & Sons, 1966):
When in this equation we substitute: n=p/a, l=a, and A=a2 (where "p" is the number of segments in each of the chamber's plates, whereas "a" is the dimension of the chamber's walls), the simplified equation for the inductance of the Oscillatory Chamber is derived:
It can be theoretically asserted that the unitary electrical inertia of a stream of sparks should be greater than such an inertia in the equivalent strand of wires. The justification for this assertion can be obtained from the analysis of the inertia mechanism. The inertia reveals itself only when the motion involves the reversible phenomena or media which absorb energy in the initial stage of the motion's development, and which release this energy when the motion declines. The greater the number of such phenomena and media involved, and the higher their energy absorption, the larger is the resultant inertia. The stream of sparks jumping through gas in every aspect manifests better potentials for causing an inertia higher than the one of a current flowing through wires. The first reason for this lies in the more efficient energy absorption and releasing by sparks, occurring because:
a) The speed of electrons in a spark can be higher than in a wire, b) The contiguous sparks can pass closer to each other because they do not require thick insulation layers in between them (as is the case for wires).
The second reason for the higher inertia of sparks in gas results from their involving a variety of reversible phenomena - not appearing at all during flows of currents through wires. These are:
c) The ionization of surrounding gases. This, due to the returning of the absorbed energy, supports the inertia of the process at the moment of the sparks' decline.
d) The causing of the motion of heavy ions, whose mass absorbs and then releases the kinetic energy.
e) The initiation of hydrodynamic phenomena (e.g. dynamic pressure, rotation of the gas) which also will be the cause of the charges' dislocation and energy return at the moment of the sparks' decline.
The above theoretical premises should not be difficult to verify by experiments.
F4.3. Capacitance of the Oscillatory Chamber
When we use the well-known equation for the capacitance of a parallel-plate capacitor, of the form:
and when we apply the substitutions: A=a2, l=a, this yields the final equation for the capacitance of the Oscillatory Chamber:
F4.4. The "sparks' motivity factor" and its interpretation
Each of the relations (F1), (F2) and (F3) describes only one selected parameter of the Oscillatory Chamber. On the other hand, it would be very useful to obtain a single complex factor which would express simultaneously all electromagnetic and design characteristics of this device. Such a factor is now introduced, and will be called a "sparks' motivity factor". Its defining equation is the following:
Notice that, according to the definition, this "s" factor is dimensionless.
Independently from the above defining equation, the "s" factor has also an interpretative description. This is obtained when in (F4) the variables R, L and C are substituted by the values expressed by equations (F1), (F2) and (F3). When this is done, the following interpretative equation for "s" is received:
Equation (F5) reveals that the "s" factor perfectly represents the current state of all environmental conditions in which the sparks occur, and which determine their course and effectiveness. It describes the type and consistency of the gas used as a dielectric, and the actual conditions under which this gas is stored. It also describes the size of the chamber. Therefore the "s" factor constitutes a perfect parameter which is able to inform exactly about the working situation existing within the chamber at any particular instant in time.
The value of the "s" factor can be controlled at the design stage and at the exploitation stage. At the design stage it is achieved by changing the size "a" of a cubical chamber. At the exploitation stage it requires the change of the pressure of a gas within the chamber or altering its composition. In both cases this influences the constants 6, m and e, describing the properties of this gas.
From the electric point of view the Oscillatory Chamber represents a typical RLC circuit. The research on Electric Networks has determined for such circuits the condition under which, once they are charged, they will maintain the oscillatory response. This condition, presented in the book by Hugh H. Skilling, "Electric Network" (John Willey & Sons, 1974), takes the form:
If the above relation is transformed and then its variables are substituted by the equation (F4), it takes the final form:
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