The ecology and power engineering are the main problems of modernity. There is no sense to determine, what it is the first and what it is the second one. The different points of view may arrange the importance of these problems as they like. On principle, the business consists in answer on questions, where can the energy be taken and how can the environment be kept for next generations? The solving of these problems determines the humanity future.

In this connection the so named progressive technologies acquire great importance. Such technologies must satisfy to requirements of ecological purity, high productivity and low energy consumption. Two last facts are closely connected, because the productivity level defines the level of energy consumption and vice versa. The justice of this statement is obvious. In fact, if the productivity increases at the expense of the articles quantity growth at each production operation, but not its velocity, then, ultimately, the energy expenditures for production of one article can be the corresponding times less.

The practice employment of the pulse electromagnetic fields energy opens the exclusive perspectives for the development of the new progressive technologies on the any raw materials working (to be more exact, of the any physical nature!). Here are some possibilities for the complex combination of all attributes defining the progressiveness of the technical solutions in the different production problems.

The basic characteristic feature of the field working is absence of the direct contact with the worked materials. It is not necessary any contact. The energy transformation takes place immediately in the workpiece. The practic sense of this feature is being developed, for instance, in comparison of the mechanical and electromagnetic stamping. The last one need no puansons on the modern level of the pulse technical development. More that, in the nearest future the field technology will permit any material working solely by the forces of the field with odered configuration. It means the matrix will disappear in the electromagnetic stamping. Speech goes about the element of the technology equipment for giving of the assigned form to a workpiece.

The book, which is being offered to attention of the readers, contains an effort to generalize existing elaboration and throw light upon pulse electromagnetic fields possibilities for the materials of any physical nature working: conductors and dielectrics. And if the electromagnetic stamping of the dielectric workpieces has been staying until by the subject of the science discussions, the pulse magnetic metal forming has been findling its wide industrial application.

The intensive development of the different field technologies had been lasting till the beginning of 80^th. The falling down is being marked now. This fact can be explained by the many circumstances. Here are many technical and social reasons. Among the technical reasons (it is our view point!) the main negative moment is the aspiration to the universality of the installations and tools (inductor systems) for solving of the different production problems. The more of that, there is not any published scientific work what would be devoted the investigation and elaboration of the inductor system as the tool for the only concrete technological operation. It has leaded, ultimately, to the deterioration of the working quality. Besides, the ecology and resources saving problems (the main advantages of the magnetic pulse metal working!) have not acquired the paramount importance.

For the being time the world public is disturbed by the nature resources exhaustion, the our planet pollution and poisoning even. The humanity already has the high productivity technologies in the different areas of activity. The productivity growth is becoming non paramount problem of the science technical progress.

The ecology, resources saving and economy of energy is going out to the first places.

In this connection it is worth to pay attention to the magnetic pulse methods in the working manufactures and come up to their practic realization from the new position what differ from the times of 60-70^th years.

Undoubtedly, this electromagnetic fields application does not solve an energy sources problem directly but it permits practically to realize the idea of ecological pure and high productive modern manufacture of different metal articles.

The magnetic pulse working of metals information has been appearing in science periodical literature beginning from 60th years. There are enough numerous separate publications devoted to this theme, however, any science works with all-round complex analysis of the problem are absent. The book "Spravochnik po magnitnoimpulsnoy obrabotke metallov" is exception. It was published in 1977. Till last time this monograph has been staying the only guidance on calculating and designing of magnetic pulse equipment for metal working. Nevertheless, the books like that have been exciting the interest. So, in spite of numerous demerits, which are the usual things for the first and unique works like that, the present textbook had been translated into English by USA specialists at different times. There are the manuscript versions of these translations in US Army Foreign Science and Technology Center (1978) and in Materials Science and Engineering Department of the Ohio State University (1996).

The present monograph "The pulse magnetic fields for progressive technologies" may be examined as a next step to all-round generalizing of magnetic metal forming questions for modern manufactures. The previous textbook published in 1977 was devoted to approximate methods of calculations on the whole. Unlike it, the given monograph contains a deep physical analysis of electromagnetic processes in inductor systems - the tools for magnetic pulse forming. Physical analysis is confirmed by exact solutions of field problems and experiments.

The traditional constructions are considered. Such systems have been acting when skin depth of the field is enough little .

For thin-walled metal forming when the skin depth is too big the new solutions are suggested. During the course of analysis, inductor systems are not being devided into components (a coil as field source, worked detail, matrix). It is being considered as united object on the whole. An approach like that acquires the particular importance when the field penetration effect is too essential and the metal thickness is more less of the skin depth.

The materials of the book "The pulse magnetic fields for progressive technologies" are based in the main on original authors's works as well as on results obtained by coworkers of the Engineering Electrophysical Department of the Kharkov State Polytechnical University.

The present monograph consists of introduction, five chapters and conclusion with bibliography.

In the first chapter the common physical principles of the power interaction between pulse magnetic fields and conductors are considered. Here is the analysis of the pondermotor forces excitement when the skin depth is more less their the workpiece thickness (massive metal billets!) as well when the field penetration effects is too considerable (the thin-walled conductors forming!).

The main problems of the theoretical and experimental investigations are formulated. Their solutions define the practical possibilities of magnetic pulse methods for different technology operations carrying out.

A discussion is presented of the rapidly changing magnetic fields application for solid plastic dielectric forming.

The second chapter is devoted to the processes analysis into inductor systems with the magnetic field concentrators. These constructions are traditional tools for the magnetic metal forming and being applied for working of the massive metal billets when the field penetration effect is too negligible. In the strong skin-effect assumption the electromagnetic fields distributions and the main parameters of systems with short and long billets are calculated. The different approaches to solution of the corresponding problems are shown.One part of them is based on the exact integration of the Maxwell equations, another part - on some preliminary assumption about the processes nature with the following experimental check.

The ways of the inductor systems strengthening are considered. There is given the physical interpretation of a mechanism of the stresses lowering in bimetal constructions. This fact is defined by choice of the inside layer thickness. It is shown, the diffusion phenomenon action is similar to putting on with a stress in the assembled cylindrical constructions (the gun barrels , for instance). The heat processes were analyzed. The some practic recommendations on the heat lowering of the inductor systems at the expense of the determined constructive solutions are given here.

This chapter is being completed by the sample of the optimum magnetic field concentrator construction.

The material of third chapter - the electrodynamic electrodynamic description of the inductor systems for the metal forming when the field penetration through workpiece is higly essential.

The traditional constructions turn out absolutly unfit because the diffusion effect brings down the magnetic pressure on a metal when its thickness is more less of the skin depth. The demanded frequency increasing is the technical unpracticable problem. It is known the solution which proposes the application of so named "Sputnik" made from the massive good conductors. The magnetic forces is acting on "Sputnik". This pressure is being transmitted to the workpiece through an intermediate elastic environment. At the scheme like that traditional inductor systems are enough hard-working. However, the intermediate transmitting environment brings down the process deformation efficiency very much and reduces essentially the list of the field method advantages proposing the mechanical action without an immediate contact.

But some constructions , where the magnetic pressure increasing is possible without the "Sputnik" application , may be offered. Among them the flat inductor systems with a dielectric matrix for the thin metal sheets working is being distinguished by its simplicity. In the construction like that the phenomenon of the flat electromagnetic waves penetration through the thin conductor screen into the free space is being modeled. The essence of this phenomenon consists in the neglectible field diffusion through the screen. Thus, in the real flat inductor systems the magnetic pressure on a thin metal sheet is not being slacken practically. The effective uncontact force action on the workpiece is being realized.

The inductor systems constructions like that are not traditional for the known magnetic pulse working of metals. Their realization has demanded the new theoretical analysis, the new experimental investigations, the consideration of the different alternatives and so on. Finally , the model inductor systems were created. They demonstrated the capacity for work on practice. The some optimum constructions is presented in the conclusive part of the chapter.

Speaking about the magnetic pulse fields application for the progressive working technologies it can not avoid of the elucidation of the technical provision problems.

The fourth chapter of present monograph contains the brief description of the magnetic pulse installations intended for the pulse currents generating in the inductor systems windings. On principle , any installation cinsists of the capacitor bank, the charging device, the commutators, the automation modules, the measuring schemes of the different intending and the connecting conductors (so named , busbar).

The inductor systems are the tools for the different technology operations carrying out. They are being connected with the electrical output of the installation. Thus, the magnetic pulse installation plus the according inductor system are the technical equipment for the practicable realization of the magnetic pulse metals working.

Finally , the last fifth chapter contains the technology operation list which are realized by the magnetic pulse methods. It is shown the accomplishment of production processes with the traditional technical solutions application ensuring the great pressure on the conductor workpieces surfaces by the strong skin effect.

The magnetic pulse methods advantages are described in the production operations such as the metals stamping, the mechanical constructions assembly, the joining of metal parts to non-metallic materials, the pressing of the cable tips, the connecting of elements in the electrical engineering systems, the welding of the turbular workpieces and another.

The printed curcuit boards production is distinguished especially. The physical essence of this operation consists in the demanded picture stamping by the magnetic field forces in the copper foil. In present case the worked metal thickness is more less of the field penetration depth. The magnetic pulse method realization is possible with the non-traditional inductor systems help only. This chapter contains the concrete technical solutions and the results of their experimental tests.

The discussion is presented of the possible direction on the technology processes organization.

The main advantages of the magnetic pulse printed curcuit boards production are formulated in comparison with the known chemical methods. The ecological purity of process, the economy (no expenditures for the clearance structures!), the saving of the valuable non-ferrous metal-copper and the high productivity are marked.

Completing the introduction it is necessary to indicate for whom the monograph "The pulse magnetic fields for progressive technologies" is written.

The present book is written with the electrophysical bias. This fact defines the materials choice , the account style , the terminology and the arrangement of accents. Therefore , despite of succession the given monograph is being distinguished from "Spravochnik po magnitnoimpulsnoy obrabotke metallov" written by the collective of electrical engineers with their according vision of the problem.

The monograph "The pulse magnetic fields for progressive technologies" is designed in the first turn for specialists engaged by elaboration of the magnetic pulse apparatus for different purposes where in a little volume the strong fields and power pressures on metals are being created. The suggested monograph will be interesting for specialists carrying out the new technology processes and also for businessmen-organizers of the manufactures satisfying of the modern requirements.

The book contains not only mathematical formulas and physical commentaries. The enough numerous pictures and photographies visually illustrating the processes of the magnetic pulse metal working are given here.
 

Beginning the consideration of the physical processes in the inductor systems for working of the materials of any physical nature it is necessary to give the inductor system definition.

What is it ?

The inductor system is the electrotechnical apparatus representing by itself the determined technological operation tool and consisting from the electromagnetic field source (so named, inductor), the specimen to be worked and a matrix, the form of which makes sure the demanded article manufacture.

In the common case, the inductor system of such kind realizes the technology operation named as the electromagnetic stamping. Unlike its analogue in the forge-press production, here is absent the puanson (we marked it before!), coming in the immediate contact with a workpiece and deforming it in accordance with the matrix form. Under the electromagnetic stamping the force influence on a billet is being realized without a mechanical contact with the workpiece. The pressure forces appear in consequence of the field interaction with a substance. It is necessary to mark the termin "electromagnetic stamping" till last time corresponded to the production operation for the article making from the metal workpieces. We will use this termin in more common sense. The inductor system (determined as before!) is the apparatus for working of metals and dielectric.

At the same time the different mechanism of the electromagnetic fields interaction with conducting and non-conducting substances defines the inductor systems differences for the metal working from the analogy systems for the dielectrics deforming.

As it is known, the appearing forces mechanism is conditioned, in the first turn, by a physical nature of a substance. Speech goes about its belonging to conductors or dielectrics. For conductors this mechanism is defined by the Lorentz forces excitement, for dielectrics - by the polarization effects. It means, force influence on conductors is possible with the help of the variable magnetic fields only. For exciting of the pressure forces on dielectrics it is necessary, ultimately, the high intensive electric fields of the short duration. This way, the principle difference of the inductor systems for the various purposes consists in the usage of the different energy sources.

Briefly, we will try to throw light on the modern high voltage technique possibilities in the creation area of the electromagnetic fields sources for the production purposes.

The coils of different geometry is being used in the magnetic fields creating practic. As the field sources they have found application in the inductor systems for the magnetic pulse metal forming.

The problem of the power electric fields generator creation is staying as a theme for science discussions.

As it seems an idea is perspective of the, so named,"the resonance blow excitement". It is possible to get a high electric energy intensity in such electrodynamic systems. The well known electromagnetic induction effect is the basis of this suggestion. The abrupt magnetic field change in time is a reason of the power electric pulse appearance. The usage of the resonance structure like that can permit creating of the inductor systems for the dielectric materials working.

At the end of chapter the numerical evaluations are given of the fast changing magnetic fields possibilities for the transistory electric pulses excitement. The pressure forces on dielectric samples were calculated there.

As it were mentioned before, the physical processes in the inductor systems for the magnetic pulse metal working is being characterized by the Lorentz forces excitement. They are named as the pondermotor forces in the technical terminology. Their appearance is conditioned by the interaction of the magnetic field with the whirlwind currents induced in the workpiece metal.

The pondermotor forces define the magnetic pressure on conductor. This remark is very important. The magnetic pressure will take place in the case only, when the currents induced in the workpiece metal flow on the closed circuit. In another case, when the ways where the induced currents must flow are not closed, the pondermotor forces will not be excited. The magnetic field does no act on conductor.

Let the excitement of pondermotor forces conditions are executed. The magnetic pressure acts on the workpiece. Now the pressure value will be defined by correlation between the effective field penetration depth and the workpiece thickness. The force influence will be the highest in the abrupt skin-effect case, when a field diffusion is negligible (really, it is the massive well conducting metals!). Such conductor is named as "opaque" (non-transparent). In the "transparent" conductor case (thin-walled or bad conducting metal!), when the field penetration through workpiece is essential enough, the magnetic pressure falls down abruptly. These facts determine the necessarily of the different approaches to the electrodynamics processes analysis under the magnetic fields interaction with the "non-transparent" and "transparent" conductors. The final intention of these consideration is the getting of the most effective force influence over metals to be woked conditions.

The physical processes in the traditional inductor systems for the well conductors working are being analyzed in this chapter primarily. Then the particularities of the force influence over thin-walled conductors are considered.

Finally, the recommendation to the inductor system constructions, where the negative field diffusion action are slaeken essentially, are given here.
 
 

The electromagnetic processes in the inductor systems for the metal working is being described by the fundamental Maxwell equations:

where  and  are the electric and magnetic fields intensities, respectively;  and  are the vectors of the electric and magnetic inductions, respectively; and  is the current density.

The equations (1.1) are being added, the so named material correlations. They define the connection between currents, inductions and the field intensities in substances with the different electrophysical parameters. Each of them is the integral quantity characteristic of the some substance property. One defines the substance ability to be polarized (it is the electric permeability of substance), the second parameter characterizes the magnetic properties (it is the magnetic permeability of substance), the third parameter speaks about the ability to conduct or not to conduct an electrical current (it is the material electrical conductivity). Thus, we may write

The pondermotor forces excitement is the result of the inductor field interaction with the conducting workpiece. And if their value is the space-time function of the field distribution through a thickness, the total pressure does not depend on the distribution nuances. It is being defined by the difference between the squares of the magnetic fields intensities on the workpiece boundary surfaces, that is

The formula (1.3) is the consequence of the fundamental law defining the electromagnetic field energy per unit volume into non-magnetic substance.

The justice and universality of the formula for the magnetic pressure (1.3) can be based with help of the Maxwell equations (1.1) and the material correlations (1.2). For a better understanding we will consider the magnetic fields influence on workpieces in the inductor systems with the different geometry: the cylindrical construction (the solenoid and the tube workpiece, fig. 1.1) and the plane system (the flat multiturn coil with the metal sheet, fig. 1.2).

In the cylindrical system long enough the tangent component of the magnetic intensity is being excited only. In consequence of the asimutal uniformity it will be function of radius only, this is . The whirlwind currents are being induced in the workpiece metal under magnetic field influence. The circuits of their flowing are the circles on the tube surface.

The pondermotor forces appear between the external magnetic field and the whirlwind currents. Per anit volume their value is being defined by the vectorís multiplication:

Integrating the formula (1.5) on  we can find the magnetic pressure on the conductor with thickness :

where  H₁ and H₂ are the magnetic intensities on the boundary surfaces , accordingly.

The same way permits to get the formula for magnetic pressure in the case of the plane inductor system. The "element" of such system is shown at Fig. 1.2.

When the diametrical sizes in the directions OZ and OY are great enough, the coil magnetic field is uniform and has the only component. This field induces into the flat conducting workpiece the whirlwind currents flowing in the closed circuits which are the mirror reflections of the coil turns.

The appearing pondermotor forces is being defined by formula (1.5).

After substitution the (1.5) in (1.7) and integration of the found result we will get the magnetic pressure on the conducting sheet in the plane inductor system.

where

H₁ and H₂ are the magnetic fields intensities on the boundary surfaces  and , accordingly.

The formulas (1.6) and (1.8) are identical to the correlation (1.3). Thus, the pressure value on the conductor in the field is being defined by the difference between the squares of the tangent components of the magnetic intensities on the workpieces boundary surfaces really.

The pressure forces direction is being determined by the sign of difference in the formula (1.8): if H₁ > H₂, vector  is directed from the inductor to matrix (in the decreasing side of the field value).

It is necessary to mark the importance of this result. Quantitatitely it describes the second factor defining the force influence intensity on the conductor in the magnetic field. Should remember, the first factor is the compulsory existence of the closed circuits for the induced whirlwind currents flowing.

Formulas (1.3), (1.6) and (1.8) fix the bound of the magnetic pulse method natural possibilities.

And it can be explained by the following.

The traditional inductor system consists of the field source, the workpiece and the metal matrix. The intensity value  is being established by the field diffusion through conductor into the cavity bounded by the matrix surface. If the thickness and conductivity of the workpiece metal are small enough, the field penetration becomes essential highly. The H₂ value is growing, but the magnetic pressure is falling down accordingly. When the penetration depth becomes the more the conductor thickness, this conductor will be transparent for the field and will experience no forceís influence. If the penetration depth is the much less the workpiece characteristic sizes (it means the abrupt skin-effect takes place), the field diffusion becomes negligible, but the pressure forces will have the maximum values. This is  , because H_2»0.

In accordance with this fact the magnetic pulse method found the most practical application in the manufactureís processes where the massive well conducting metal billets working had taken place (for instance, copper, aluminum, brass, bronze and others).

At the same time the field diffusion through conductor to be worked can play the positive role.

In the numerous works the problem has been discussed of the tube cylindrical work-piece expansion by the inside pressure without the inductor innerlocation. For this aim it is necessary to realize the abrupt trailing edge of the external inductor field - H₁(t) till zero value with the special apparatus help. Then the intensity of the magnetic field what had penetrated through the tube workpiece walls became more than H₁(t). The magnetic pressure forces direction will be turned to opposite side. The worked cylinder will be expanding. Its walls will be moving to the inductor.

The such process mathematical illustration may be the influence on the metal tube of the trangular magnetic field pulse with the gently sloping front:

where  is the intensity amplitude value;

is the assigned duration of the external magnetic field; and

is the time.

The quality picture, illustrating the electrodynamics forces change, is shown at the Fig. 1.3. Really, after the abrupt trailing edge of the inductor magnetic field the force is changing its direction to the opposite side.
 
 

The relative pressure on the tube workpiece walls under the trangular

magnetic field pulse action ().

The calculations show this phenomena is being developed abruptly highly when the current is growing slowly enough in the inductor winding: T_u>>t , t is the time of the magnetic field diffusion in a metal sheet with conductivity g and thickness d,  In this case the primary force compressing the cylinder will be small enough. It grows abruptly and changes the sign after the field trailing edge.

Summing up the conducted consideration of the equations and correlations describing the electrodynamics processes in the inductor systems for the metal working it is necessary to mark the main conclusion what is the most interesting thing for practice: the pulse force magnetic pressure on the conductor is effective only under the abrupt skin-phenomena condition when the inductor field has not time to penetrate through the workpiece metal during the pulse action.

This conclusion defines the pulse magnetic fields possibilities for the according technology operations execution. Later on we will name the inductor systems for work under the abrupt skin-effect condition by the traditional inductor systems.
 
 

In the time of the pulse electromagnetic fields interaction with thin-walled conductors the diffusion phenomena exerts a great influence on the pondermotor forces value. As it follows from formula (1.3), if , the magnetic pressure on the conductor vanishes practically.

We will conduct the analysis of the pulse magneyic fields penetration through the workpiece metal with attraction of the inductor system model shown at Fig.1.4.

The calculation model of the inductor system with massive matrix from the

ideal conducting metal:

We will consider a metal workpiece as thin-walled one if the condition is being fulfilled for it:

where

- is the angular frequency, of the magnetic field spectrum;

- is the characteristic diffusion time into the conducting layer with conductivity g and thickness .

For understanding of the physical sense of the thin-walled conductor condition we will transform it to distinguish the relation of the conducting layer thickness  to the field penetration depth d (in accordance with definition ).

In real inductor system the all electromagnetic phenomenas are stationary. After the simple transforming in the formula (1.9) we is coming to the equal inequality;

The correlation (1.10) shows that the metal workpiece is thin-walled from the physical view point, if its thickness is the much less of the field penetration depth into a substance with the identical parameters.

Under conducting of analysis it is necessary to add the electromagnetic field stationarity condition to the thin-walled conductor condition (1.9). In the real inductor systems the electromagnetic processes are stationary.

And so, this stationary condition has view:

where - is the greatest characteristic size of the system;

- the velocity of light in vacuum,  .

Our calculation model is the single dimension model. Here is a dependence from the only space coordinate , so that  If the inductor magnetic field intensity has the only Y-component, then the electromagnetic field with the non-zero components  and  will be excited in the considered system.

If to take in account the remarks to the adopted calculation model, the Maxwell equations (1.2) can be written in the form:
 

1) into the workpiece metal, the area 1:

(1.12)

2) into the cavity between the workpiece and the matrix, the area 2:

(1.13)

where  are the non-zero components of the electromagnetic fields intensities into the distinguished areas 1 and 2, accordingly.

The solutions of equations (1.12) and (1.13) must satisfy to the initial zero conditions and the following boundary conditions;

The boundary conditions reflect the continuation of the electromagnetic fields tangent components under transition from one substance to another. The last correlation for the electric field tangent component on the matrix surface accords to the field absolute screening by the ideal conductor physically.

Under the differential equations systems (1.12) and (1.13) integration we make use the Laplace transform on the variable . After transition into the L-imagition space we will get:
 

a) the area 1,  :

(1.15)

b) the area 2, 

(1.16)

where  is the parameter of the integral Laplace transform.

From the equations of the systems (1.15),(1.16) and the boundary conditions (1.4) we can find the electromagnetic fields vectors L-imagitions in the distinguished areas

where

- is the magnetic field intensity on the workpiece surface from the side of matrix;
is the wave factor into the substance with conductivity g ;

(1.18)

where  is the vacuum wave factor, ;  is the vacuum wave resistance, 

We are interested in the magnetic field penetration through the workpiece metal. Equating the electric field intensities on the distinguished areas boundaries, where , we may get, that

where  is the screening factor under the magnetic field penetration into the cavity bounded by an ideal conductor,

The formula for screening factor G₁(p) can be simplified, if to use the thin-walled conductor and stationary conditions.

As it follows from the inequality (1.9),  From the correlation (1.11) -  In this case, after the limit calculations in the formula for G₁(p) we will get:

where 

Further, it is necessary to substitute the correlation (1.20) in the (1.19). In the received result we will execute the reverse Laplace back transform. Ultimately, we may find the intensity of the magnetic field penetrated through the thin-walled metal workpiece in the cavity bounded by the ideal conducting matrix:

Now we will product the quantity value of the penetration process parameters for the inductor magnetic field changing in time, as , where H_m is the amplitude.

Integrating the (1.21) with the time function for  we may find the intensity amplitude of the magnetic field penetrated through workpiece :

For the concrete evaluations we will adopt: the workpiece is the copper sheet with thickness  and conductivity ; the distance between workpiece and matrix -; the magnetic frequency .

After substitution the initial dates in formula (1.22) we may find, that H_2m=0.94H_1m. This result we will use for the magnetic pressure amplitude calculation. With help of the formula (1.3) we get .

The calculations result should be analyzed.

In the considered instance the thin-walled sheet workpiece is transparent one for the inductor magnetic field (the intensity lowering is negligible, about 6%). In this connection the field diffusion brings down the magnetic pressure forces more 10 times as much.

The general conclusion: the traditional inductor systems can not be used for the thin-walled metal billets working.

What is necessary to do? How can we remove the negative action of the magnetic field diffusion through the transparent workpieces?

The first suggestion consists in a creation of the inductor systems with the several magnetic field sources. The identical technical solution was used in the plasma experiments: the opposing connection of the two low-inductive solenoids has been permitting to synthesize the special form of the magnetic field for the plasma confinement and compression.

In the magnetic pulse thin-walled metals working this field synthesis idea can be realized too. In this case the demanded space-time geometry of the field must be such: on the workpiece surface from the side of inductor the intensity amplitude must have the maximum value, but on the workpiece surface from the side of matrix it has to be zero. To get such magnetic field distribution the additional magnetic field source should be used. It is being disposed behind the matrix which must be made metal with from the low conductivity.

The such inductor system is shown on Fig. 1. 5.

The scheme of inductor system with the additional magnetic field source for the

thin-walled metal working:

(1) is the main inductor; (2) is the workpiece; (3) is the matrix; (4) is the additional inductor.

The capacity for work of suggested construction is being made sure by the following conditions;

In the time evolution tests the demanded space-time distribution of the magnetic fields intensities has been received. The so named "artifical" boundary conditions for the intensities tangent components have been created. Into the space between the workpiece and matrix the field was equal to zero practically. On the opposite workpiece surface the magnetic intensity was equal to the inductor field intensity nearly.

This technical solution has its advantages and demerits too. It is not so important. The important thing is the idea about the great future of the inductor systems with the several magnetic fields sources. Their application will permit to assign the necessary space-time distribution of the resulting field into a billet to be worked and realize the electromagnetic metal stamping without any matrix.

The following suggestion is directed on the removal of the diffusion negative action too. It consists in modeling of the plane electromagnetic wave penetration process through thin-walled conducting screen into free space.

This suggestion can be realized in the cylindrical or plane inductor systems with dielectric matrix (Fig.1.6).

To be convinced of the suggested construction efficiency for the transparent metal billets working it is enough to conduct an analysis of the electromagnetic phenomenas in any one of them.

For instance, the solution is simple and clear for the plane system case. The obtained results can be generalized for the cylindrical geometry.
 
 

The processes in the system at issue are being described by the Maxwell equations (1.12) and (1.13). The boundary conditions for the field vectors are the correlations (1.14) excepting the last one. Instead the equality to zero of the electric field tangent component on the ideal conductor surface we should take the limitation condition on the space variable  in the infinity, that is 

In the sheet metal workpiece the Laplace-imagitions of the electromagnetic field intensities will be described by formulas (1.17). In a free space (dielectric matrix does not change the substance character behind a workpiece!) the equations (1.16) solutions satisfying the limitation condition under  have the form:

Further, we use the correlations (1.17), (1.23) and the transition condition for the electric field tangent components. After the mathematical transforming we will get the correlation describing the penetration process of the magnetic intensity tangent component through thin-walled conductor into free space:

where  - is the screening factor under the magnetic field penetration into free space, 

The connection between the screening factors  (into the bounded cavity) and  (into the free apace) exist :

Physically, such limit transforming accords to the transference of the ideal conducting boundary in infinity.

In the formula (1.24) we will execute the reverse Laplace transform and transit into the originals space. But before we will simplify the factor screening  correlation with help of the thin-walled conductor condition (1.9).

Calculating a limit under  we find, that

Taking into account (1.25) the formula (1.24) receives the form:

As it follows from correlation (1.26), the time shapes of the external and penetrated into free space magnetic fields are the same quite. Their amplitudes are connected by the directly proportional dependence with the factor .

This result shows the high efficiency of screening. As the calculations show, the intensivities relation consists , when the cooper sheet workpiece with thickness  takes place.

Thus, in the suggested construction with dielectric matrix the magnetic field does not penetrate through the thin-walled conducting workpiece practically. The magnetic pressure forces are the same to forces in the traditional metal working systems acting under the abrupt skin-effect condition.

There is a physical explanaition of the screening efficiency in the different inductor systems. It is necessary to compare the diffusion processes into free space and the bounded cavity.

Really, if a metal matrix takes place, the penetrated through workpiece magnetic field will be reflected from the matrix surface with a reverse sign. This phenomena leads to lowering of the whirlwind currents proper field in the workpiece metal. This field has the less compensating effect on external one relatively. If a free space is behind the workpiece, there are no reasons of the whirlwind currents lowering. Their magnetic field is not being lowed at all. And its action compensates the external inductor field (what means, it creates obstacles for the penetration effect).

Speaking of the physical essence of the field screening by the thin-walled conductor under the plane waves penetration into free space, it is necessary to mark the essential difference of this process from the absolute field screening by the ideal conductor.

In the thin-walled conductor case the magnetic field tangent component is being screened efficiently only. The electric field diffuses undistorted. Physically, it can be explained by the homogeneous distribution of the induced currents through conductor thickness.

Ultimately, the transparent metal screens the magnetic field effectively and does not screen the electric field at all.

If the ideal conductor takes place, whirlwind currents are concentrated in the thin surface layer. Their field compensates the external magnetic field of the inductor. The skin-layer infinitesimal means that electric intensity will equal to zero through the conductor thickness practically.

Thus, the ideal conductor screens both the magnetic and electric fields always.

Now we will transit to the cylindrical system consideration (Fig.1.6 a), where the dielectric matrix usage permits increasing of the force influence on the thin-walled workpiece from the inductor magnetic field side.

The received for the plane geometry result remains a justice, if the cylindrical construction radius will be the much more others characteristic sizes of the inductor system. In the opposite case (radius is small) it is necessary to apply the more strict calculations for the efficiency evaluations of the force influence. But as it follows from the physical consideration, the magnetic pressure on the transparent workpiece in inductor system with dielectric matrix will be much higher than in system where the metal matrix is used.

Finishing the analysis of the considered technical solutions directed to increasing of the magnetic pressure on thin-walled conductors the main advantage of the last suggestion should be marked. In the first turn it is the practical realization simplicity.

This fact was decisive under the choice of the inductor system concrete construction for the magnetic stamping of the circuit boards picture in the electrical engineering. This operation was suggested and based for the first time. In the scientific literature the analogues are absent in the scientific literature.
 
 

Sometimes the field calculations simplification becomes possible at the expense of different physical models using. These models must be faithful to the real electromagnetic processes and make available the simple connection for the field vectors on the different substances boundaries. So, for instance, the known approximate condition of Leontovich-Rytov has been formulated. It establishes the proportional dependence between the tangent components  and  on the boundary surface with the specified impendance.

The physical processes in the inductor system modeling of the electromagnetic field penetration phenomena into a free space have some determined peculiarities. They permits to base the connection between the tangent components of the electromagnetic field vectors on the thin-walled sheet workpiece to be deformed.

Let the thin-walled sheet with conductivity and thickness  separates the magnetic field source from the free space. There is an infinite extent in two dimensions X and Y.

The model for calculaton is presented on Fig. 1.7.

The intensity on the sheet surface from the inductor side is specified by the only non-trivial tangent component  not depending from the cross coordinates. The Umov-Pointing vector defining the electromagnetic energy flux is directed with the coordinate axis - OZ. Accordingly, the electric field intensity has the only non-trivial component on the surface, where 

The Laplace transforms were found before of the electric and magnetic fields intensities in the conducting substance (the thin metal sheet - the condition (1.9)). These are the formulas (1.17).

We will copy them for the further convinience.

Thus, for  we have

From the correlations (1.27) we will get the connection between the electric and magnetic fields intensities on the sheet surface from the side of the electromagentic field source (z=0).

The Umov-Pointing vector and the normal to surface , faced to the field source, have the opposite directions.

Using this fact we can find,

In the (1.28) we will execute the limit transforming for 

We will remind: the possibility of such mathematical operation is being established by the thin-walled conductor condition (1.9) and the Laplace transform properties.

We will get,

Executing the inverse Laplace transforming in the correlation (1.29) we will find

where - the function was named as the screening factor conventionally,

It is necessary to mark the received result is justifiable for , whre  is the field diffusion time in the considered conductiviting layer, 

The screening factor can be calculated if to consider the magnetic field penetration into a free space.

We will use the results of the calculations conducted before and find following,

After the substitution (1.31) in (1.30) we will get the approximate condition fixing the directly proportional connection between the tangent components of the pulse electromagnetic field vectors on the thin-walled metal sheet surface in the time of the plane-parallel field penetration into the free space:

Now we will analyse this result.
 

1. If  (the metal sheet is absent), we are getting the known correlation between the electric and magnetic fields intensities into vacuum:

2. If  the formula (1.32) is being transformed to the view:

(1.33)

At the first, this result is in agreement with the Leontovish-Rytov boundary condition, where the surface impedance 

At the second, the correlation (1.33) can be interpreted physically easy, if the thin-walled metal is being considered as the conducting film with the uniform distribution of the induced current through a thickness (this is the electric intensty from (1.27) if ).

Really, under  we is getting from the formula (1.31) that  This fact and the current uniform distribution through the thickness permits to come to conclusion that  where  the current intensity. If we substitute the dependence for  (it follows from one of the material correlations (1.22)) in this formula, we will come to the (1.33).

Thus, the truth of the found boundary condition was based both mathematically and physically.

The further calculations of the electromagnetic processes in the inductor system with the thin-walled metal billets will be based on the received correlation for the tangent components of the electromagnetic field vectors (1.32).
 
 

The plastic deformation and failure of the dielectric specimens under the power electric fields influence have been marked in the experiments on the investigation of the insulation puncture in the high-voltage installations at the beginning of the 1960's.

Supposing that the energy value is the same for the dielectric specimen and the metal workpiece deformation we can get some approximate imagition about the acting fields amplitudes.

The connection between the fields intensities can be find from the equality:  where  and - are the relative magnetic and electric permeabilities.

where  the vacuum wave resistance,  Ohm.

The typical intensity value for the magnetic pulse metal working constitutes about  A/m. Supposing  with the help of the correlation (1.34) we may get the upper value of the electric field intensity which is necessary for the dielectric specimen deformation  V/m.

Besides the external influence estimation, the formula (1.34) permits to trace the dependence of the mechanical processes in dielectrics from their inner properties.

As it is known, the polarization phenomenas lie in the base of the electrical influence forces, to be more exact - the electrical pressure. The property to be polarized is being characterized by the relative electric permeability . The more e the higher inner fields amplitude and the external electric field pressure becomes more intensive.

Really, as it follows from the quality dependence (1.34), the deformation of the dielectric specimens with high value of the relative electric permeability occurs under the lower intensities of the external electric field.

The force influence efficiency on dielectric is being defined by the electric pulse duration too. The time parameters of acting fields must provide the specimens deformation before the electrical puncture occurance.

The main conclusion from the conducted quality consideration is the statement: on principle, the methods of the dielectric deformation with the electromagnetic pressure forces help have to be based on the power fields application with the small duration enough. The influence time does not have to exceed the discharge and puncture evolution time of the dielectric specimen.

The more concrete remarks consist in the following:

Now we will transit from the qualitative analysis to the quantitative one. We will calculate the main parameters of the high-speed force influence processes on dielectric workpieces in the of concrete construction inductor system with the according electromagnetic fields sources.

At the beginning we will determine the pressure on a dielectric in the non-homogeneous electric field. We want to get the common formula analogous to the dependence (1.3) for the magnetic pulse metal working.

Let a dielectric plate (infinitely long and wide) with the thickness L and the relative electric permeability  is situated in the electric field , which changes through the dielectric thickness only (the according coordinate is X). The intensity vector direction is arbitrarily.

In the non-homogeneous electric field each elementary volume of the liniar-polarized dielectric experiences the action of the force which equals to the sum of all forces applying to each its molecule. The separate dielectric molecule can be considered as the electric dipole polarized by the external field . The acting on an elementary volume force may be described by the known correlation:

where  - is the polarization vector.

The field pressure on the dielectric is directed with the inner normal vector to its surface (in the OX-axis). The pressure value will equal:

In the linear approach we may suppose that  If to take onto account it the formula (1.36) is being transformed to the view:

where  and  are the electric field intensities on the boundary surfaces of the dielectric plate.

As it is seen from formula (1.37), the acting on the liniar dielectric in the non-homogeneous electric field force is directed to the side of the intensity magnitude increase. Quantitatively, the pressure on the specimen is being defined by the difference between the electric intensities squares on its boundary surfaces.

It is obvious, this difference has maximum, if the field equals to zero on some one surface of the plate. Besides, the else one conclusion follows from formula (1.37): the influence force on the dielectric does not equal to zero, if  only. Speaking by another words the electric field acts on the susbstances which can be polarized.

We have said the pressure would be maximum if the electric field intensity equaled to zero on the one of the specimen surfaces. In this connection the natural suggestion appears after the constructive execution of one of the main elements of the inductor system for the electromagnetic dielectric articles stamping: it is necessary to place the worked billet on the metal surface where the tangent component of the electric field intensity vector will equal to zero.

The processes analysis in the suggested construction can be conducted with the simplified model help. In this case we may consider the fast-changing magnetic field action on the plane dielectric layer situated on the ideal conducting metal surface.

The problem of the field excitment will not be considered. It will be the separate investigation subject.

We will conduct calculations in the Decart rectangular coordinates system. We will combine the plane ZOY with the ideal conducting metal surface. The dielectric thickness (in the OX-axis) equal to . The model for calculation is being supposed as the infinite long in the dimensions X and Y (Fig.1.8). The relative electric permeability of the layer equals to e .

In the area where  the homogeneous external magnetic field exists with the only intensity tangent component .

For the problem solving we will use the integral Fourier transform. We will look for the non-zero field components into the dielectric in the following form:

where w is the angular frequency.

where  is the wave factor, 

c is the velocity of the light into vacuum.

The functions satisfying to the system of the differential equations are the following:

where  and  are the unknown constants of integration;

Z₀ - is the wave resistance of vacuum.

The unknown constants in the formula (1.40) can be defined with the boundary conditions help:  where  is the Fourier transform of the external magnetic field intensity.

Without the intermediate transformations we are writing:

where 

Now we will find the electromagnetic fields intensities taking in account the formulas (1.41) and the function 

Further it is necessary to find the integrals in the correlations (1.42).

These integrals

can be calculated with the residues theory methods.

From the analysis of the functions in the integrals (1.43) we see they have the infinite number of the simple poles on the real axis (naturally ) :

where and 

As it is known, the integrals of such view can be calculated if to suppose the small field attention existence in the real physical system. It means the appearance of the positive imaginary part in the resolved spectrum frequencies (1.44). The presence of the positive imaginary parts permits to regard that the functions poles will be situated not on the real axis, they will lie in the upper half-plane of the complex variables, where .

In accordance with the Jordan lemma from the complex variable functions theory the integration circuit can be closed in the lower half-plane for (t-t )<0 where the poles are absent. If , the integration circuit is being closed in the upper half-plane where the infinite number of the simple poles is situated.

If to take in account the integrals (1.43), we can get:

where d (t-t ) - is the Dirac function.

Now we will find the space-time dependences for the field vectors excited in the dielectric layer for the zero initial conditions.

Using the formulas (1.45),(1.46) we are writing:

For the further analysis we will define the electric field intensity on the dielectric boundary surface.

Substituting  in the formula (1.48) we may get

If the frequency spectrum has the top limit

then with the formula (1.41) help after the reverse Fourier transform and the substitution  we will find

The received results should be analysed.

As if follows from the formulas (1.47), (1.48) and (1.49), if the spectrum limits are absent, the electromagnetic field is being excited in the dielectric. The intensities will be presented by the infinite sums of the harmonics with the frequencies which are the inversely proportional to the wave trip time through the dielectric layer with the relative electric prmeability e and thickness .

In the case of the low frequency excitement the electric field intensity on the dielectric boundary surface (formula (1.51)) is proportional to the velocity of the external magnetic field change in the time, to the layer thickness and does not depend on the relative electric permeability (the polarization phenomenas).

Let us execute some numerical evalutions.

We will begin from the case, when the external field represents by the only harmonic:

This harmonic excites on the dielectric surface the electric field. Its intensity can be found after substitution (1.52) in the formula (1.49):

As it follows from the (1.53), if the resonance phenomena for the electric field  will take place.

For  we have

In the real conditions the electric field intensity resonance value is limited by the energy dissipation processes in the dielectric substance. It is attributed by the small conductivity presence and being defined quantitatively by the attenuation factor d . From the physical reasons its value will have to equal 

Now we will consider the concrete dielectric, for instance, the plastic material with the relative electric permeability  and thickness m (from any chemical handbook).

For A/m and the resonance frequency  Hz with the formula (1.54) help we is finding for w t=0.5p , that  V/m.

For the low frequency fields, for instance, when Hz, after substitution these dates in (1.51) we will get, that V/m.

Having used by the formula (1.37) we can calculate the according pressure forces. We will take in account, that the tangent component of the electric field intensity will equal to zero on the ideal conducting metal surface.

In the resonance case we will have,  N/m².

For the low frequency fields the forces amplitudes are less essentially,  N/m².

The conducted evalutions are being agreed with the preliminary consideration. They show that the essential dynamic forces appear under of the short-time electric fields influence with the dielectrics. These forces can reach the strengh limit of the specimens to be worked. In this case it is possible their mechanical deforming and failure even.

The analysis of the basic possibilities of the fast-changing magnetic fields for the dielectrics working can be finished by the suggestion of the according inductor system construction.

The scheme of the inductor system for the flat electromagnetic stamping of the dielectric specimens is presented on the Fig. 1.9.

The scheme of the inductor system for the flat electromagnetic stamping of the dielectric specimens.

(1) is the commutator; (2) is the "sharpening" pulse apparatus; (3) is the voltage source; (4) is the busbar; (5) is the matrix; (6) is the flat dielectric workpiece; (7) is the conductor for making available of the pressure maximum.

Neglecting by the details we will describe the action of the suggested construction.

After the commutator (1) closure the apparatus (2) transforms the power current from the high voltage source (3) in the blow pulse with the abrupt leading or trailing edge.

The current in the conductor (4) excites the magnetic field. Its intensity vector is directed to the plane of the figure perpendicularly. In fact, this conductor shows up by the magnetic enrgy source in the suggested construction of the inductor system.

The matrix is situated on the inner side of this conductor. The matrix profile makes sure the demanded form of the article, which has to be produced from the dielectric workpiece (6). The magnetic field excites in the billet (6) the longitudinal electric field. Its direction coincides with the current direction in the conductor (4).

As we have said, the one of the dielectric workpiece surfaces is situated on the conductor plane (7). It was the ideal conducting metal surface in the analytical model before.

The electric field tangent component will equal to zero on this plane. That is why the difference between the squares of the electric field intensities on the dielectric boundary surfaces will be maximum in comparison with the case when the conductor (7) is absent.

As it was shown before, the pressure force acts on dielectric in the electric field. Its value is proportional to the difference of the intensities squares. This force is directed in the side of the field increase. Under this field influence the worlpiece will get the momentum pulse directed to the matrix (5). In the result of the collision the dielectric specimen will be defomed in accordance with the matrix profile.