SELF-ORGANIZING NUCLEOSYNTHESIS IN SUPERDENSE PLASMA
Main Hypotheses to the Conception of Optimal Conditions for Nuclear Synthesis
Based on the results of researches from a viewpoint of the control theory on the qualitative features of multilinked dynamical systems using methods of the control theory, as well algorithms of optimization for their phase trajectories(seeRefs.16,17),welateranalyzedthemostcharacteristictraits of self-organization in multilinked, stable dynamical structures (systems) of any physical nature, including atomic nuclei as stable assemblies of nucleons. Thisanalysisresultedinunderstandingofthekeyroleofthefollowing factors in processes of such nature:
• intense external disturbances of a certain kind, called dominating
• general universal law, which can be called the principle of regularization of dominating disturbances and dynamic harmonization of systems The dynamic harmonization principle is implemented when a set of links between source units is formed in a self-consistent way in the structure that is created or reorganized. The set of links formed under this principle minimizes or maximizes its inertness of the structure in the direction of the dominating disturbance vector in the system’s phase space. Note that, in physical terms, the problem of inertness evolution can be reduced (taking into account the equivalence between energy and mass) to the problem of evolution of the system’s energy. That is, the energy of a system of particles will include, of course, the energy of their interaction, which will define the binding energy. Thus, the conclusions made using the control theory could, in principle, be applied to the problems of energy consumption and release. This idea compels us to analyze the problem of fusion from the nontraditional perspective of self-organization theory and control theory. As a starting point for such an analysis, we take a set of basic hypotheses on the possible universal mechanisms of self-organization and reorganization in complex dynamical electron, nucleon, and nuclear structures considered from the most general perspective of the system analysis and stability theory.
The first basic hypothesis is as follows: A set of interacting nuclei (as well as that of interacting atoms) is a dynamical system with links, which is subjected to the general laws of self-organization in multilinked, stable dynamical systems, in particular, the dynamic harmonization of systems. The assumption about the universal nature of the dynamic harmonization principle results in the statement that any set2 of interacting elements in which old links are destroyed and/or new ones are established betweenelements,whenexternalforcesareappliedtoit,willself-consistently “determine” the optimal direction for changing its structure. The forceful coercive creation of the subjectively “needed” structure by applying an external impact directly to the system elements or links between them (controlled synthesis) may produce the required result in the only case where the structure being forcefully created is identical to the one that corresponds to the dynamic harmonization principle. Looking at the problem of the initiation of self-sustaining exoergic reactions of nucleosynthesis, we can single out what is probably the most important factor in this process: a decrease in the average and/or total mass of participating nucleons (i.e., the creation of the mass defect). As we know, the mass of any material object (nucleon, nucleus, atom, etc.) is a measure of inertness of that object. Following the above logic of the principle of dynamic harmonization, a solution to the problem of obtaining a negative mass defect and corresponding energy release should be found in the area of choosing an initiating mechanism (a driver) whose action would stimulate the system being reformed, which is in general an electron-nucleus or electron-nucleon megasystem—the local volume of the target source matter, precisely to decrease the average and/or total inertness (i.e., mass) of the particles affected by the dominating impact. It is obvious that if there is no acceleration, then the motion (behavior) of the system will not depend on the inertness or masses of the particles that make up the system. Hence, a conclusion can be made that, in terms of the dynamic harmonization principle, spending the energy of an external impact (driver) for the source particles to only reach a high final velocity or energy would mean a failure to use the evolutionary potential of the system for its nuclear transmutation, i.e., the inefficient way of action. The physical sense of the dynamic harmonization principle can be reduced to the following. The evolutionary synthesis using an optimal external dominating disturbance (optimal driver) is all about initiating the proper
2Strictly speaking, not “any” set but that whose elements have a finite inertness (which is small for the dominating disturbance) and can interact through establishing the links of some physical nature and changing the intensity of those links.
motion of the ensemble of interacting source elements (particles) into a new state in terms of both energy and topology, and, accordingly, to a new required structure, whose motion will be along the steepest descent path, with minimization of energy or another more general functional spent during the transition from the initial to the final state. In the general case, we are talking about a new approach towards the synthesis of multiparticle multilinked stable systems or structures of any physical nature. The distinctive feature of this new approach is the thesis that, in the Nature, the synthesis of a system or the self-organization of its structure is always a self-consistent collective response of elements in the source ensemble to the common dominating force which disturbs their state of rest or a nonaccelerated motion in the system’s eigenfunction space. The common dominating disturbance coherently transfers the momentum pD of the unidirectional motion in the phase space to all elements of the ensemble, the momentum being satisfied the condition
|pD| | pTmax|,
where |pTmax| is the maximum absolute value of the momentum for the proper (uncoordinated) thermal motion of any element of the ensemble in thesamephasespaceoverthewholeperiodoftransitionfromtheinitialstate (before the common dominating disturbance appeared) into the steady final state. A fundamental distinctive feature of the proposed new approach toward the synthesis is the search for and the selection of such a mechanism of initiating the self-sustaining and self-consistent process using the criterion of optimality of the process of transition of the dynamic system (ensemble of interacting particles) from the initial state/configuration into a new state/configuration being “energy-efficient” not only at the final point, but also integrally over the whole duration of the transient process. The second basic hypothesis is as follows: With increasing the number of the elements being excited in the synthesized system, there is a fast growth in the influence of cross-links of small intensity, the establishment of such links resulting in decreasing the inertness of the system in the designated direction, i.e., that of the impact direction. It is possible to increase the number of interacting particles of the matter to any value by transforming the matter into a critical state, where the particles’ behavior is as if each of them “feels” the current state of all other particles (see Ref. 6), i.e., the characteristic correlation length under the phase transition in the system tends to infinity. The physical nature of this generally recognized “feeling” has not been studied completely as yet; this fact, however, does not prevent us in any way from taking this effect
into account when arranging the initiation of a self-organizing process of nucleosynthesis. We have assumed that the effective range of interaction for nuclear forces is determined by the degree of coherence of dominating disturbances that initiate the interaction between particles. Particles in the matter are able to interact, including the exchange interaction and, respectively, the collective behavior in any of the possible critical states of the matter. Thefundamentalimportancewillbeattachedtotherightdefinitionofwhich critical state of the matter is optimal (or at least favorable) for the initiating and the intense running of self-sustaining collective nuclear reactions. States on the liquid–gas or gas–plasma interface are indeed critical; however, in those states, “criticality” is applied to electrons only, as nuclei, while they still keep electron shells, are not in a critical state, because each of those nuclei stays in its own “rest niche”. The nearest critical state where those nichesarecommonisthe electron-nucleusplasma,i.e.,the state,where the ionization number for atoms is equal to their nuclear charge. In this case, because of the dynamic harmonization principle, nuclei involved in the collective are “faced with the problem” of choosing the “way towards a new stability”, the options here being (1) back to the formation of nonionized atoms or (2) forward to the creation of new nucleon ensembles or new nuclei. It is important to note that, in the state of electron-nuclei plasma, electrons are, like nuclei, elements within the ensemble that has to “make its choice”. Therefore, if their participation in the collective nuclear process may contribute to its efficiency, i.e., the creation of the maximum mass defect within the minimum period of time, then they will participate in the process of collective interaction between particles in the system, even without external impact, under the self-organization, or evolutionary synthesis, scenario. The third basic hypothesis is as follows: The required synergetic process of collective transmutation of nuclei is nothing but the natural nuclear combustion of a collapsing matter. Its essential features are identical to those of the natural nucleosynthesis (where the whole range of the stable isotopes of chemical elements is created). This is a fundamentally multiparticle self-organizing process which cannot be implemented through pair collisions between particles, and thus it is fundamentally impossible to reproduce it in any conditions other than the collapse (the compression to extreme densities) of macroscopic quantities of matter. When applied to explosive astrophysical processes, such as the collapse in a burned massive star resulting in a supernova burst, the hypothesis
has allowed us to assume that the stable isotopes of chemical elements found in the Nature are not created through a long decay of their radioactive predecessors, which, in turn, have been created in the Big Bang. Instead, those stable isotopes themselves are immediate products of the natural nucleosynthesis which develops in the following ways: • either as a collective, exoergic process of nuclear combustion of matter in a collapsing supernova • or, as a process of decay of superheavy nuclei (superdense matter) created as a result of the collapse in massive stars via the cluster radioactivity mechanism Thereisnoneedtospendmuchtimelookingforcandidatestobecome a natural driver for nuclear combustion, since such a driver is obvious. It is the universal gravitation which mutually attracts huge amounts of matter and results in the development of a gravitational collapse. It does not seem possible to use this kind of a driver under the earth conditions, but there is no fundamental reason to expect that the same final outcome cannot be achieved using a different tool, i.e., a different driver. It is clear that in order to do that, we need to find some key distinctive feature of the natural collapse mechanism we are trying to substitute, and then this distinctive feature has to be reproduced, without reproducing the whole mechanism. Asaresultofanalyzingthosepeculiaritiesofgravitationalforcesinitiatingacollapseinmassivespaceobjects,whicharesignificantintermsofthe efficiency of the required process, the fourth basic hypothesis has emerged. It consists of the following two interrelated statements:
1. The most important property of the gravitational collapse is its being initiated by a self-generated common dominating disturbance which has character of a mass force and emerges due to the coherent amplification of gravitation effects for a macroscopic ensemble of particles of matter located at the same distance from the center of mass of the collapsing object, i.e., those located in the volume of a thin spherical layer (see Ref. 19); 2. Collective self-consistent coherently accelerated motion of a set of particles of matter, where the centripetal component of the momentum of each particle is much higher than its thermal (chaotic) component, brings a portion of matter made of those particles into a special “collectivized” critical state.
In Part IV, we will show that it can be formally drawn from solutions to the kinetic equations for the particle system under a dominating
impact. Solutions to a number of approximate forms of kinetic equations (Boltzmann, Landau, Lennard–Balescu, and nonlinear Fokker–Planck equation) under the condition of a constant flux in the phase space (the existence of a dominating impact in the system!) have power asymptotics, i.e., states characterized by strong large-scale correlations. In such a state with strong correlations, the optimal conditions may emerge for the avalanche-like spontaneous creation of highly organized multiparticle multilinked dynamical network structures. In thin macroscopic structured spherical shells with a common center of mass, the dynamical structures may emerge on the basis of all kinds of physical interactions (including the strong and Coulomb ones), for which the necessary conditions exist (within the respective shell where the matter is in the critical state). Those processes should probably depend on the reaching of the threshold densities by the matter within the shell in the state of electron-nucleonnucleus plasma. In this case, because the energy of the collective interaction grows with the number N of interacting particles, the energy of the “global” interaction of particles in a self-structurizing shell at sufficiently great N can significantly exceed the energy of their “local” interaction and can define the topology of a spontaneously self-organizing branched macroscopic nuclear structure which minimizes or maximizes the own total inertia relative to the action of a centripetal mass force (i.e., which minimizes or maximizes the own inertial mass) and, respectively, maximizes or minimizes the arising mass defect and the energy of a global coupling of all particles of the shell. Based on this hypothesis, we have finally come to an assumption that in the process of gravitational collapse in a massive burned star, the decisive role for the self-sustaining process of exoergic nuclear combustion may be played in some cases by a solitary spherical wave of the matter (energy) density collapsing to the center, such a wave being formed on the surface of the collapsing body through one physical mechanism or another. As a result of the nonlinear increase in the steepness of the leading edge of this collapsing wave and the increase in the matter density in the wave to the critical point, there is a possibility for the spontaneous start of the collective processes of formation of a macroscopic electron-nucleus structure. In that structure, there are coherent states of interacting particles along the radial coordinate r(t), their states being at the same time strongly correlated (see Ref. 20) in the 2D subspace of angular coordinates ψ, ϕ (the shell surface subspace).
ANAΔΗΜΟΣΙΕΥΣΗ ΑΠΟ ΤΟ ΒΙΒΛΊΟ :
"Controlled Nucleosynthesis Breakthroughs in Experiment and Theory"
Electrodynamics Laboratory “Proton-21” Kiev, Ukraine
Franco Selleri Universit`a di Bari Bari, Italy
Alwyn van der Merwe University of Denver Denver, Colorado, U.S.A.
Stanislav Adamenko
5/5/2016
Main Hypotheses to the Conception of Optimal Conditions for Nuclear Synthesis
Based on the results of researches from a viewpoint of the control theory on the qualitative features of multilinked dynamical systems using methods of the control theory, as well algorithms of optimization for their phase trajectories(seeRefs.16,17),welateranalyzedthemostcharacteristictraits of self-organization in multilinked, stable dynamical structures (systems) of any physical nature, including atomic nuclei as stable assemblies of nucleons. Thisanalysisresultedinunderstandingofthekeyroleofthefollowing factors in processes of such nature:
• intense external disturbances of a certain kind, called dominating
• general universal law, which can be called the principle of regularization of dominating disturbances and dynamic harmonization of systems The dynamic harmonization principle is implemented when a set of links between source units is formed in a self-consistent way in the structure that is created or reorganized. The set of links formed under this principle minimizes or maximizes its inertness of the structure in the direction of the dominating disturbance vector in the system’s phase space. Note that, in physical terms, the problem of inertness evolution can be reduced (taking into account the equivalence between energy and mass) to the problem of evolution of the system’s energy. That is, the energy of a system of particles will include, of course, the energy of their interaction, which will define the binding energy. Thus, the conclusions made using the control theory could, in principle, be applied to the problems of energy consumption and release. This idea compels us to analyze the problem of fusion from the nontraditional perspective of self-organization theory and control theory. As a starting point for such an analysis, we take a set of basic hypotheses on the possible universal mechanisms of self-organization and reorganization in complex dynamical electron, nucleon, and nuclear structures considered from the most general perspective of the system analysis and stability theory.
The first basic hypothesis is as follows: A set of interacting nuclei (as well as that of interacting atoms) is a dynamical system with links, which is subjected to the general laws of self-organization in multilinked, stable dynamical systems, in particular, the dynamic harmonization of systems. The assumption about the universal nature of the dynamic harmonization principle results in the statement that any set2 of interacting elements in which old links are destroyed and/or new ones are established betweenelements,whenexternalforcesareappliedtoit,willself-consistently “determine” the optimal direction for changing its structure. The forceful coercive creation of the subjectively “needed” structure by applying an external impact directly to the system elements or links between them (controlled synthesis) may produce the required result in the only case where the structure being forcefully created is identical to the one that corresponds to the dynamic harmonization principle. Looking at the problem of the initiation of self-sustaining exoergic reactions of nucleosynthesis, we can single out what is probably the most important factor in this process: a decrease in the average and/or total mass of participating nucleons (i.e., the creation of the mass defect). As we know, the mass of any material object (nucleon, nucleus, atom, etc.) is a measure of inertness of that object. Following the above logic of the principle of dynamic harmonization, a solution to the problem of obtaining a negative mass defect and corresponding energy release should be found in the area of choosing an initiating mechanism (a driver) whose action would stimulate the system being reformed, which is in general an electron-nucleus or electron-nucleon megasystem—the local volume of the target source matter, precisely to decrease the average and/or total inertness (i.e., mass) of the particles affected by the dominating impact. It is obvious that if there is no acceleration, then the motion (behavior) of the system will not depend on the inertness or masses of the particles that make up the system. Hence, a conclusion can be made that, in terms of the dynamic harmonization principle, spending the energy of an external impact (driver) for the source particles to only reach a high final velocity or energy would mean a failure to use the evolutionary potential of the system for its nuclear transmutation, i.e., the inefficient way of action. The physical sense of the dynamic harmonization principle can be reduced to the following. The evolutionary synthesis using an optimal external dominating disturbance (optimal driver) is all about initiating the proper
2Strictly speaking, not “any” set but that whose elements have a finite inertness (which is small for the dominating disturbance) and can interact through establishing the links of some physical nature and changing the intensity of those links.
motion of the ensemble of interacting source elements (particles) into a new state in terms of both energy and topology, and, accordingly, to a new required structure, whose motion will be along the steepest descent path, with minimization of energy or another more general functional spent during the transition from the initial to the final state. In the general case, we are talking about a new approach towards the synthesis of multiparticle multilinked stable systems or structures of any physical nature. The distinctive feature of this new approach is the thesis that, in the Nature, the synthesis of a system or the self-organization of its structure is always a self-consistent collective response of elements in the source ensemble to the common dominating force which disturbs their state of rest or a nonaccelerated motion in the system’s eigenfunction space. The common dominating disturbance coherently transfers the momentum pD of the unidirectional motion in the phase space to all elements of the ensemble, the momentum being satisfied the condition
|pD| | pTmax|,
where |pTmax| is the maximum absolute value of the momentum for the proper (uncoordinated) thermal motion of any element of the ensemble in thesamephasespaceoverthewholeperiodoftransitionfromtheinitialstate (before the common dominating disturbance appeared) into the steady final state. A fundamental distinctive feature of the proposed new approach toward the synthesis is the search for and the selection of such a mechanism of initiating the self-sustaining and self-consistent process using the criterion of optimality of the process of transition of the dynamic system (ensemble of interacting particles) from the initial state/configuration into a new state/configuration being “energy-efficient” not only at the final point, but also integrally over the whole duration of the transient process. The second basic hypothesis is as follows: With increasing the number of the elements being excited in the synthesized system, there is a fast growth in the influence of cross-links of small intensity, the establishment of such links resulting in decreasing the inertness of the system in the designated direction, i.e., that of the impact direction. It is possible to increase the number of interacting particles of the matter to any value by transforming the matter into a critical state, where the particles’ behavior is as if each of them “feels” the current state of all other particles (see Ref. 6), i.e., the characteristic correlation length under the phase transition in the system tends to infinity. The physical nature of this generally recognized “feeling” has not been studied completely as yet; this fact, however, does not prevent us in any way from taking this effect
into account when arranging the initiation of a self-organizing process of nucleosynthesis. We have assumed that the effective range of interaction for nuclear forces is determined by the degree of coherence of dominating disturbances that initiate the interaction between particles. Particles in the matter are able to interact, including the exchange interaction and, respectively, the collective behavior in any of the possible critical states of the matter. Thefundamentalimportancewillbeattachedtotherightdefinitionofwhich critical state of the matter is optimal (or at least favorable) for the initiating and the intense running of self-sustaining collective nuclear reactions. States on the liquid–gas or gas–plasma interface are indeed critical; however, in those states, “criticality” is applied to electrons only, as nuclei, while they still keep electron shells, are not in a critical state, because each of those nuclei stays in its own “rest niche”. The nearest critical state where those nichesarecommonisthe electron-nucleusplasma,i.e.,the state,where the ionization number for atoms is equal to their nuclear charge. In this case, because of the dynamic harmonization principle, nuclei involved in the collective are “faced with the problem” of choosing the “way towards a new stability”, the options here being (1) back to the formation of nonionized atoms or (2) forward to the creation of new nucleon ensembles or new nuclei. It is important to note that, in the state of electron-nuclei plasma, electrons are, like nuclei, elements within the ensemble that has to “make its choice”. Therefore, if their participation in the collective nuclear process may contribute to its efficiency, i.e., the creation of the maximum mass defect within the minimum period of time, then they will participate in the process of collective interaction between particles in the system, even without external impact, under the self-organization, or evolutionary synthesis, scenario. The third basic hypothesis is as follows: The required synergetic process of collective transmutation of nuclei is nothing but the natural nuclear combustion of a collapsing matter. Its essential features are identical to those of the natural nucleosynthesis (where the whole range of the stable isotopes of chemical elements is created). This is a fundamentally multiparticle self-organizing process which cannot be implemented through pair collisions between particles, and thus it is fundamentally impossible to reproduce it in any conditions other than the collapse (the compression to extreme densities) of macroscopic quantities of matter. When applied to explosive astrophysical processes, such as the collapse in a burned massive star resulting in a supernova burst, the hypothesis
has allowed us to assume that the stable isotopes of chemical elements found in the Nature are not created through a long decay of their radioactive predecessors, which, in turn, have been created in the Big Bang. Instead, those stable isotopes themselves are immediate products of the natural nucleosynthesis which develops in the following ways: • either as a collective, exoergic process of nuclear combustion of matter in a collapsing supernova • or, as a process of decay of superheavy nuclei (superdense matter) created as a result of the collapse in massive stars via the cluster radioactivity mechanism Thereisnoneedtospendmuchtimelookingforcandidatestobecome a natural driver for nuclear combustion, since such a driver is obvious. It is the universal gravitation which mutually attracts huge amounts of matter and results in the development of a gravitational collapse. It does not seem possible to use this kind of a driver under the earth conditions, but there is no fundamental reason to expect that the same final outcome cannot be achieved using a different tool, i.e., a different driver. It is clear that in order to do that, we need to find some key distinctive feature of the natural collapse mechanism we are trying to substitute, and then this distinctive feature has to be reproduced, without reproducing the whole mechanism. Asaresultofanalyzingthosepeculiaritiesofgravitationalforcesinitiatingacollapseinmassivespaceobjects,whicharesignificantintermsofthe efficiency of the required process, the fourth basic hypothesis has emerged. It consists of the following two interrelated statements:
1. The most important property of the gravitational collapse is its being initiated by a self-generated common dominating disturbance which has character of a mass force and emerges due to the coherent amplification of gravitation effects for a macroscopic ensemble of particles of matter located at the same distance from the center of mass of the collapsing object, i.e., those located in the volume of a thin spherical layer (see Ref. 19); 2. Collective self-consistent coherently accelerated motion of a set of particles of matter, where the centripetal component of the momentum of each particle is much higher than its thermal (chaotic) component, brings a portion of matter made of those particles into a special “collectivized” critical state.
In Part IV, we will show that it can be formally drawn from solutions to the kinetic equations for the particle system under a dominating
impact. Solutions to a number of approximate forms of kinetic equations (Boltzmann, Landau, Lennard–Balescu, and nonlinear Fokker–Planck equation) under the condition of a constant flux in the phase space (the existence of a dominating impact in the system!) have power asymptotics, i.e., states characterized by strong large-scale correlations. In such a state with strong correlations, the optimal conditions may emerge for the avalanche-like spontaneous creation of highly organized multiparticle multilinked dynamical network structures. In thin macroscopic structured spherical shells with a common center of mass, the dynamical structures may emerge on the basis of all kinds of physical interactions (including the strong and Coulomb ones), for which the necessary conditions exist (within the respective shell where the matter is in the critical state). Those processes should probably depend on the reaching of the threshold densities by the matter within the shell in the state of electron-nucleonnucleus plasma. In this case, because the energy of the collective interaction grows with the number N of interacting particles, the energy of the “global” interaction of particles in a self-structurizing shell at sufficiently great N can significantly exceed the energy of their “local” interaction and can define the topology of a spontaneously self-organizing branched macroscopic nuclear structure which minimizes or maximizes the own total inertia relative to the action of a centripetal mass force (i.e., which minimizes or maximizes the own inertial mass) and, respectively, maximizes or minimizes the arising mass defect and the energy of a global coupling of all particles of the shell. Based on this hypothesis, we have finally come to an assumption that in the process of gravitational collapse in a massive burned star, the decisive role for the self-sustaining process of exoergic nuclear combustion may be played in some cases by a solitary spherical wave of the matter (energy) density collapsing to the center, such a wave being formed on the surface of the collapsing body through one physical mechanism or another. As a result of the nonlinear increase in the steepness of the leading edge of this collapsing wave and the increase in the matter density in the wave to the critical point, there is a possibility for the spontaneous start of the collective processes of formation of a macroscopic electron-nucleus structure. In that structure, there are coherent states of interacting particles along the radial coordinate r(t), their states being at the same time strongly correlated (see Ref. 20) in the 2D subspace of angular coordinates ψ, ϕ (the shell surface subspace).
ANAΔΗΜΟΣΙΕΥΣΗ ΑΠΟ ΤΟ ΒΙΒΛΊΟ :
"Controlled Nucleosynthesis Breakthroughs in Experiment and Theory"
Electrodynamics Laboratory “Proton-21” Kiev, Ukraine
Franco Selleri Universit`a di Bari Bari, Italy
Alwyn van der Merwe University of Denver Denver, Colorado, U.S.A.
Stanislav Adamenko
5/5/2016
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