Search

EP-4736186-A2 - CONTROL SYSTEM FOR NUCLEAR PROCESSES AND COHERENT NUCLEAR FUSION DURING THE EXPLOSIVE BLOW-UP MODE OF SELF- HARMONIZED ELECTROMAGNETIC CONFINEMENT AND METHOD OF ITS IMPLEMENTATION

EP4736186A2EP 4736186 A2EP4736186 A2EP 4736186A2EP-4736186-A2

Inventors

  • ADAMENKO, Andrii
  • BOGOLYUBOV, Gennadiy
  • DIDENKO, IGOR
  • KOLOMOYSKYY, Igor
  • LEVCHENKO, VOLODYMYR
  • NOVIKOV, Valerii
  • SHAPOVAL, Anatolii

Assignees

  • Tovarystvo z Obmezhenou Vidpovidalnistiu "Proton-21"

Dates

Publication Date
20260506
Application Date
20240808

Claims (20)

  1. CLAIMS 1. A control system for nuclear processes and coherent nuclear fusion during the explosive blow-up mode of the self-harmonized electromagnetic confinement comprising the following components: ^ an industrial electrical network module (1.0); ^ a charging module (1.1) of the primary energy storage device; ^ a primary energy storage device (1.2); ^ main fusion driver No.4 with a module (1.4) for delivering energy to the target, while the module (1.4) comprises a unit (1.4.1) for synchronizing the primary energy storage device (1.2) and generating energy flows of fusion driver No.4; ^ a reaction chamber (1.8); ^ a grounded reverse current conductor (1.13); ^ a target (1.10.1), characterized in that the system further comprises: ^ a module (1.10) for the sequential supply of targets (1.10.1) to the reaction chamber (1.8); ^ a module (1.11) for the preparation of the reaction chamber (1.8); ^ additional fusion driver No. 1 with a module (1.7) for controlling plasma electrodes, while the module (1.7) comprises a unit (1.7.1) for coordinating and synchronizing energy flows of the primary energy storage device (1.2) and energy flows of additional fusion driver No.1 and a unit (1.7.2) for generating energy flows of fusion driver No.1; ^ additional fusion driver No. 2 with a module (1.6) to control the initiation of the explosive blow-up mode, while the module (1.6) comprises: unit (1.6.1) for coordinating and synchronizing energy flows of the primary energy storage device (1.2) and energy flows of additional fusion driver No. 2 and a unit (1.6.2) for generating energy flows of fusion driver No.2; ^ additional fusion driver No. 3 with a module (1.5) to control the initiation of a non- linear wave in the target and modify properties of the target substance, while the module (1.5) comprises: unit (1.5.1) for coordinating and synchronizing energy flows of the primary energy storage device (1.2) and energy flows of additional fusion driver No. 3 and a unit (1.5.2) for generating energy flows of fusion driver No.3; ^ while under the condition of optimal synchronization of units 1.4.1, 1.5.1, 1.6.1, and 1.7.1, additional fusion driver No. 3 also controls the process of initiating a non-linear wave with an edge (11.2), which contains the leading edge structure (11.3) of the non-linear wave, 1 the main "body" (11.4) of the non-linear wave edge, and the trailing edge structure (11.5) of the non-linear wave and moves from the target surface (11.7) to its center of symmetry (11.8), whereas, the wave with the leading edge (11.3) moves in such a way that the target's inner central part (fusion fuel) (11.1) is in front of it, and the region (11.6) of fusion products evaporating from the trailing edge of the non-linear wave is behind it; ^ while the module (1.4) for delivering energy to the target further comprises a unit (1.4.2) for coordinating the energy flows of fusion driver No.4 and the target (1.10.1); ^ output energy storage device No.1 (1.17); ^ output energy storage device No.2 (1.18); ^ a module (1.3) for controlling a primary energy storage device (1.2), a unit (1.4.1) for synchronizing the primary energy storage device (1.2) and generating energy flows of fusion driver No.4; a unit (1.4.2) for coordinating energy flows of fusion driver No.4 and the target (1.10.1); a unit (1.5.1) for coordinating and synchronizing energy of the primary energy storage device (1.2) and energy flows of additional fusion driver No. 3; a unit (1.5.2) for generating energy flows of fusion driver No. 3; a unit (1.6.1) for coordinating and synchronizing energy flows of the primary energy storage device (1.2) and energy flows of additional fusion driver No. 2; a unit (1.6.2) for generating energy flows of the fusion driver No.2; a unit (1. 7.1) for coordinating and synchronizing energy flows of the primary energy storage device (1.2) and energy flows of additional fusion driver No. 1; a unit (1.7.2) for generating energy flows of fusion driver No. 1; a module (1.11) for the preparation of the reaction chamber (1.8) and a module (1.10) for the sequential supply of targets (1.10.1); ^ while the module (1.14) for converting the kinetic energy flow of fusion products from the target explosion area (2.16) comprises a unit (1.14.1) for taking kinetic energy of fusion products and a unit (1.14.2) for coordinating converted energy with the unit of output energy storage devices No.1 (1.17); ^ the module (1.15) for converting the electromagnetic radiation energy flow from the target explosion area (2.16) comprises a unit (1.15.1) for taking electromagnetic radiation energy from the target explosion area and a unit (1.15.2) for coordinating the converted energy with the output energy storage unit No.1 (1.17); ^ the module (1.16) for converting the energy flow in the return current conductor with grounding (1.13) comprises a unit (1.16.1) for taking the energy of currents of the grounded return current line (1.13) and a unit (1.16.2) for coordinating the converted energy with output energy storage unit No.2 (1.18); ^ a module (1.19) for coordinating the unit of output energy storage devices No.2 (1.18) with the primary energy storage device (1.2); 2 wherein the system contains the above-mentioned three additional fusion drivers (No. 1, No. 2, No. 3) controlling the state of the electron beam and the target during the operation of main driver No.4; the choice of parameters of the above drivers is aimed at achieving the condition of initiation of a non-linear implosion wave in the blow-up mode in the general case in a multilayer target, where the upper layer of the target should be made of a material with sufficiently low conductivity and have a fractal structure to increase the values of the absorbed energy of the beam; wherein the driver parameters are subjected to optimization based on the condition of exceeding the acceleration of the absorbed power density in the surface layer of the beam calculated by formula eff over the acceleration of the power density of energy n T a 0 eff T ^ 3 dissipation in the target calculated by formula ^ dis , where ap – evolution impact, Pdis – power density of the driver energy, Vint – absorbed in the near-surface volume, ^ eff – target during the characteristic time, a T – acceleration of the power density of dissipative losses, n 0 – is the density of the medium, T eff is the temperature of the medium, and ^ dis is the characteristic time of dissipation, when this condition is met, a non-linear wave in the blow-up mode is formed and the substance of the target goes into an unstable state, i.e. a positive density feedback at the wave edge occurs and the internal energy of the electron shells of the substance is released, which together with the energy of the external driver moves to the central region of the target and an explosion of the central region of the target is formed, wherein if there is thermonuclear fuel in the central region of the target, additional nuclear fusion reactions which also contribute to the release of internal energy of the substance and increase the efficiency of the explosion may be initiated. 2. The system according to claim 1, characterized in that the reaction chamber (1.8) comprises the following components: ^ the plasma guns (2.1) of fusion driver No.1, preferably arranged with central symmetry around the axis of the reaction chamber and designed to generate plasma (2.6) of the reaction chamber; ^ the electromagnetic field generators (2.2) of fusion driver No. 1, preferably arranged with central symmetry around the axis of the reaction chamber; ^ the plasma guns (2.3) of fusion driver No.2, preferably arranged with central symmetry around the axis of the reaction chamber; 3 ^ the electromagnetic field generators (2.4) of fusion driver No. 2, preferably arranged with central symmetry around the axis of the reaction chamber; ^ the radial current field generators (2.5) of fusion driver No.3, preferably arranged with central symmetry around the axis of the reaction chamber; ^ a multicomponent cathode plasma module (2.7) designed to generate a cathode plasma flow (2.8); ^ anode plasma structures module (2.9) designed to generate anode plasma flow (2.10); ^ a unit (2.11) of coils of a special structure of the module (1.15) for converting the current and electromagnetic fields energy flow (1.23) from the target explosion area (2.16) to excite voltage and current pulses in their elements initiated by the kinetic energy flow of explosion products of the target (1.10.1); ^ a housing (2.12) of the reaction chamber (1.8); ^ a target explosion area (2.16); ^ a module (2.13) for taking the flow of high-level radiation energy from the target explosion area (2.16) with a blanket for absorbing high-level radiation and taking thermal energy; ^ a gap (2.14) between the cathode and anode plasma flows; ^ a module (2.15) for taking the current energy flow that passed the target explosion area (2.16) and the anode plasma structures module (2.9). 3. The system according to claims 1 to 2, characterized in that fusion driver No. 1 comprises the following components: ^ a module for synchronizing the pulse equipment with the signal from the module (1.3); ^ a source (4.2) of pulsed current and voltage; ^ a module (4.3) for setting the signal offset; ^ the plasma guns (4.4) for focusing the electron beam; ^ a module (4.5) for generating pulsed electromagnetic radiation and/or laser radiation to control the initiation of emission processes by the cathode unit of fusion driver's No.1. 4. The system according to claims 1 to 3, characterized in that fusion driver No. 2 comprises the following components: ^ a module (5.1) for synchronizing the pulse equipment with the signal from the module (1.3); ^ a source (5.2) of pulsed current and voltage; ^ a module (5.3) for setting the signal offset; ^ a plasma gun (5.4) for focusing the electron beam of fusion driver No.2; 4 ^ a module (5.5) for generating pulsed electromagnetic radiation and/or laser radiation to control the shape of the beam current and the processes for generating the blow-up mode in the target (1.10.1). 5. The system according to claims 1 to 4, characterized in that fusion driver No. 3 comprises the following components: ^ a module (6.1) for synchronizing the pulse equipment with the signal from the module (1.3); ^ a source (6.
  2. 2) of pulsed current and voltage; ^ a module (6.
  3. 3) for setting the signal offset; ^ a module (6.
  4. 4) for generating radial currents to focus and/or self-focus the electron beam on the target surface (1.10.1); and/or ^ a module (6.
  5. 5) for generating pulsed electromagnetic radiation with longitudinal polarization to control the blow-up mode in the target (1.10.1).
  6. 6. The system according to claims 1 to 5, characterized in that the module (1.14) for converting the kinetic energy flow (1.22) of fusion products from the target explosion area (2.16) further comprises the following components: ^ a module's condensed working medium (7.1) made of the ferroelectric and/or ferromagnetic material and/or a finely dispersed mixture of dielectric and conductive components; ^ a unit (7.2) for taking the energy flow of voltage and current pulses initiated in the condensed working medium (7.1) by the kinetic energy flow (1.22) of fusion products from the target explosion area (2.16); ^ a module (7.3) for coordinating the output energy flow of the unit (7.2) with the unit of output energy storage devices No.1 (1.17); ^ the unit of output energy storage devices No.1 (1.17).
  7. 7. The system according to claims 1 to 6, characterized in that the module (1.15) for converting the current and electromagnetic fields energy flow (1.23) from the target explosion area (2.16) further comprises the following components: ^ a unit (8.1) for taking the current and electromagnetic fields energy flow (1.23) from the target explosion area (2.16); ^ a transmission line (8.2) for transmitting the target explosion energy taken in the unit (8.1) to the module (8.3) for transforming and coordinating the flows of the taken energy with the unit of output energy storage devices No.1 (1.17); ^ a module (8.3) for transforming and coordinating the flows of the taken energy with the 5 unit of output energy storage devices No.1 (1.17); 8. The system according to claims 1 to 7, characterized in that the module (1.9) for taking the kinetic energy flow (1.12) of fusion products and high-level radiation energy from the target explosion area (2.16) further comprises the following components: ^ a unit (9.1) for converting the energy released in the module blanket (2.13) into electrical and/or thermal energy; ^ an electrical energy storage unit (9.2); ^ a thermal energy storage unit (9.3). 9. The system according to claims 1 to 8, characterized in that the reaction chamber (1.
  8. 8) further comprises a multicomponent cathode plasma module (2.7) and an anode plasma structures module (2.
  9. 9).
  10. 10. The system according to claims 1 to 9, characterized in that unsteady plasma electrical and electromagnetic structures are placed additionally in the focusing zone of the electron beam, providing an impact sufficient to change the energy direction of the processes, while electromagnetic sources and high-voltage discharge plasma generated by plasma guns and/or laser sources are used to control their implementation.
  11. 11. The system according to claims 1 to 10, characterized in that in the reaction chamber (1.8), the system further comprises toroidal electromagnetic field generators (2.4) of fusion driver No. 2 and the radial current field generators (2.5) of fusion driver No. 3 to control the value of the Coulomb barrier and the internal structure of the fuel nuclei of reactor target (1.10.1).
  12. 12. The system according to claims 1 to 11, characterized in that the reaction chamber (1.8) further comprises a module (1.14) for converting the kinetic energy flow (1.22) of fusion products from the target explosion area (2.16); a module (1.15) for converting the current and electromagnetic fields energy flow (1.23) from the target explosion area (2.16); a module (1.16) for converting the energy flow (1.20) in the reverse current area in the grounded reverse current conductor (1.13).
  13. 13. The system according to claims 1 to 12, characterized in that the system comprises more than one additional fusion driver No. 1 and/or additional fusion driver No. 2 and/or additional fusion driver No.3. 14. A method for controlling nuclear processes and coherent nuclear fusion during the explosive blow-up mode of the self-harmonized electromagnetic confinement according to the system described in claims 1 to 13, characterized in that it includes the following steps: ^ with the charging module (1.1) of the primary storage unit, the energy supplied from the industrial electrical network module (1.0) is accumulated in the primary energy storage unit 6 (1.2); ^ with the module (1.3), the primary energy storage device (1.2), units (1.4.1, 1.4.2, 1.5.1, 1.5.2, 1.6.1, 1.6.2, 1.7.1, 1.7.2) of fusion drivers, the module (1.11) for the preparation of the reaction chamber (1.8), and the module (1.10) for the supply of targets (1.10.1) are controlled; ^ with the module (1.10), a sequential supply of targets (1.10.1) into the reaction chamber (1.8) with a specified repetition rate is implemented; ^ with the module (1.11), the reaction chamber (1.8) is prepared; ^ with the unit (1.7.1), the energy flows of the primary energy storage device (1.2) and the energy flows of additional fusion driver No.1 are coordinated and synchronized; ^ with additional fusion driver No. 1, the medium around the target (1.10.1) is prepared in the reaction chamber (1.8) to ensure primary ionization of the target surface layer; ^ with the unit (1.4.1), the energy flows of the primary energy storage device (1.2) and the energy flows of main fusion driver No.4 are generated and synchronized; ^ with the unit (1.6.1), the energy flows of the primary energy storage device (1.2) and the energy flows of additional fusion driver No.1 are coordinated and synchronized; ^ with additional fusion driver No.2 and the unit (1.4.2) of fusion driver No.4, the power profile of the energy flow from main fusion driver No.4 is formed depending on the time; ^ with additional fusion driver No. 2 and the unit (1.3), the moment of initiation of the blow-up mode is controlled and energy is accumulated in the surface layer of the target to initiate a non-linear wave; ^ with additional fusion driver No. 2, the blow-up mode is initiated in the reaction chamber's (1.8) medium around the target (1.10.1) and in the target itself to ensure the primary ionization of the surface layers of the condensed matter; ^ with the unit (1.5.1), the energy flows of the primary energy storage device (1.2) and the energy flows of additional fusion driver No.3 are coordinated and synchronized; ^ with additional fusion driver No. 3, the properties of target materials and fusion processes are controlled at the initial stage of the blow-up mode; ^ with additional fusion driver No. 3 and additional fusion driver No. 2, the following processes are controlled: - initiation of the beginning of the edge (11.2) movement of the non-linear wave in the correlated coherent state with the center of symmetry (11.8) and the internal structure of the leading edge structure (11.3) moving from the surface (11.7) to the center of symmetry (11.8) of the target; - the state of the main "body" (11.4) of the non-linear wave edge, the structure of the 7 trailing edge structure (11.5) of the non-linear wave, while the target's inner central part (fusion fuel) (11.1) is located in front of the non-linear wave, while the region (11.6) of fusion products evaporating from the trailing edge of the non- linear wave is located behind it; ^ with the module (1.14), the kinetic energy of fusion products is converted into electrical energy; ^ with the module (1.
  14. 14.2), the converted energy is coordinated with the unit of output energy storage devices No.1 (1.17). ^ with the module (1.15), the flow of kinetic energy of the fusion products from the target explosion area is converted into electrical energy; ^ with the unit (1.15.2), the flow of converted energy is coordinated with the unit of output energy storage devices No. 1 (1.17) and the received energy is accumulated in output energy storage device No.1 (1.17). ^ with the module (1.9), the flow of kinetic energy of the fusion products from the target explosion area (2.16) is converted into electrical energy and/or thermal energy; ^ with the unit (1.16.1), the energy flow (1.20) of currents of the grounded reverse current conductor (1.13) is taken; ^ with the unit (1.16.2), the taken energy is coordinated with output energy storage device No.2 (1.18); ^ with the module (1.19), the unit of output energy storage devices No. 2 (1.18) is coordinated with the primary energy storage device (1.2), and the kinetic energy of the fusion products and the energy of electromagnetic radiation are taken.
  15. 15. The method according to claim 14, characterized in that it further includes the following steps: ^ With the module (4.1), the signals of the pulse equipment of fusion driver No. 1 are synchronized with the module (1.3); ^ With the source (4.2), a pulse current and voltage are generated; ^ With the module (4.3), the offset of the signals of fusion driver No.1 is initiated; ^ With the plasma gun (4.4), the electron beam of fusion driver No.4 is focused; ^ with the module (4.5), pulsed electromagnetic radiation and/or laser radiation are generated to control the initiation of emission processes by the cathode unit of fusion driver No. 4.
  16. 16. The method according to claims 14 to 15, characterized in that it further includes the 8 following steps: ^ with the module (5.1), the signals of the pulse equipment of fusion driver No. 2 are synchronized; ^ with the source (5.2), the pulse current and voltage of fusion driver No.2 are generated; ^ With the module (5.3), the offset of signals of fusion driver No.2 is initiated; ^ with the plasma gun (5.4), the electron beam of fusion driver No.4 is focused; ^ with the module (5.5), pulsed electromagnetic radiation and/or laser radiation of fusion driver no.2 are generated to control the shape of the beam current and the processes for generating the blow-up mode in the target (1.10.1).
  17. 17. The method according to claims 14 to 16, characterized in that it further includes the following steps: ^ with the module (6.1), the signals of the pulse equipment of fusion driver No. 3 are synchronized with the signal of the module (1.3); ^ with the source (6.2), the pulse current and voltage of fusion driver No.3 are generated; ^ with the module (6.3), the offset of the signals of fusion driver No.3 is initiated; ^ with module (6.4), radial currents of the electron beam that self-focuses on the target surface (1.14) are generated, and/or ^ with the module (6.5), pulsed electromagnetic radiation with longitudinal polarisation is generated to control the blow-up mode in the target (1.10.1) and the properties of the target materials in the target explosion area.
  18. 18. The method according to claims 14 to 17, characterized in that the kinetic energy of the target explosion is converted into electrical energy accumulated in the system of output energy storage devices No.1 (1.17), while: ^ with the impact of explosion products flow (1.22) of the target (1.10.1) in the condensed working medium (7.1) made of the ferroelectric and/or ferromagnetic material and/or a finely dispersed mixture of dielectric and conductive components, a polarization wave propagating through the medium is initiated; ^ with the unit (7.2) for taking the energy flow of voltage and current pulses initiated in the condensed working medium (7.1) by the kinetic energy flow (1.22) of fusion products from the target explosion area (2.16), voltage and current pulses initiated by a polarization wave in the working medium (7.1) are excited; ^ with the module (7.3), the output energy flow of the unit (7.2) is coordinated with the unit of output energy storage devices No.1 (1.17); ^ with the unit of output energy storage devices No. 1 (1.17), the received electrical 9 energy is accumulated.
  19. 19. The method according to claims 14 to 18, characterized in that the energy of the current and electromagnetic fields that have passed through the explosion area is converted into electrical energy accumulated in the system of energy storage devices No.1 (1.17), while: ^ with the unit (8.1) for taking the current and electromagnetic fields energy flow (1.23) from the target explosion area (2.16), the energy flow that has passed the target explosion area (2.16) and the transmission lines is coordinated; ^ with the transmission line (8.2), the flow of the taken target explosion energy is transmitted to the module (8.3) for coordinating and transforming the pulse power; ^ in the module (8.3), the pulse power is coordinated and transformed from relatively high values after the explosion of the target (1.10.1) to the power values necessary for efficient energy storage in the unit of output energy storage devices No.1 (1.17).
  20. 20. The method according to claims 14 to 19, characterized in that the energy of the radiation and explosion plasma is converted into electrical and thermal energy, while: ^ with the module (2.13) and the unit (9.1), the energy flows (1.12) of high-level radiation and fusion products resulting from the fusion processes in the target explosion area (2.16) are converted into thermal and/or electrical energy; ^ electrical energy is accumulated in the unit (9.2); ^ thermal energy is accumulated in the unit (9.3).

Description

CONTROL SYSTEM FOR NUCLEAR PROCESSES AND COHERENT NUCLEAR FUSION DURING THE EXPLOSIVE BLOW-UP MODE OF SELF- HARMONIZED ELECTROMAGNETIC CONFINEMENT AND METHOD OF ITS IMPLEMENTATION THE FIELD OF THE INVENTION The invention relates to the technology of controlling nuclear processes and, in particular, nuclear fusion in condensed matter, in which controlled self-consistent pycnonuclear processes, in particular, processes of controlled coherent inertial nuclear fusion, may occur under self- harmonized inertial electromagnetic confinement in the blow-up mode; and to the design of devices for electromagnetic control of nuclear fusion based on relativistic plasma diodes with a system of controlled plasma and virtual electrodes and currents arising during the evolution of the process initiated by a high-voltage potential difference pulse with an appropriate shape applied between the plasma cathode and anode systems after a certain time delay relative to the sequence of moments of the start of the operation of drivers which form plasma components with different energies and the required distribution of electromagnetic fields and currents with different amplitudes in the focusing zone of the electron beam. With electromagnetic control of nuclear fusion processes, this technology is intended mainly for the transmutation of the nuclei of atoms of some chemical elements into the nuclei of other chemical elements to obtain mainly stable isotopes of chemical elements, including the synthesis of stable transuranic elements, and to process radioactive waste containing long-lived isotopes into materials containing short-lived and/or stable isotopes, for the release of nuclear fusion energy in the form of kinetic energy of fusion products with a certain distribution by composition and energy, electromagnetic fields and currents in a wide range of frequencies, and for the conversion of these various components of the target explosion energy into the thermal and/or electrical form of energy at the output. TERMS AND DEFINITIONS target is a single-use dose for impact compaction of at least one arbitrary isotope of at least one chemical element being a raw material for obtaining nuclear transformation products and, optionally, as a primary energy carrier for energy production; diode or plasma diode is a diode which is a system of electrodes (in particular, these may be plasma electrodes) placed in a vacuum volume (with a certain degree of vacuum, that is, with a certain pressure of a neutral gas) or a volume filled with plasma (generally heterogeneous); plasma electrode is a consumable part of the negative or positive electrode of a diode that is capable (for a certain time during the discharge pulse) of generating a plasma shell (of the near-surface layer material and injected by special devices) with a near-zero electron or ion work function; plasma cathode system is a system of one or more (metal, dielectric and/or virtual) electrodes surrounded by plasma layers, from the surface of which electrons are emitted; virtual electrode is a potential barrier or potential "hole" that arises inside the plasma volume between real electrodes due to the distribution of the spatial charge created by the flow of charged particles in the volume. For example, a virtual cathode partially transmits and partially reflects these particle flows; concentrator anode is a single-use part of the diode anode that serves as a target and may be at least a single-layer shell made of a solid durable material, inside which a part of the target made of another material is also fixed axisymmetrically to ensure acoustic contact; focal space is such a volume in the diode vacuum chamber which spatially confines a certain length of the common geometric axis of symmetry of the diode electrodes, and in which (in the absence of obstacles and under pre-set values of the emitting surface area of the plasma cathode, energy of electrons and current density) a pinch of electron beam is possible due to self-focusing of relativistic electrons; fusion driver is a physical object that delivers energy, which is necessary either for fusion or for fusion control, to the area of fusion processes; coupled oscillatory systems are oscillatory systems with more than one degree of freedom, which may be considered as a set of separate systems interacting (coupled) with each other; resonance is the correspondence between the system's spatial and temporal structure and external influence; system impedance is a value characterizing the inertia and dissipation of the system (the ratio of a force to the velocity caused by this force – the rate of change of inertia); parametric instabilities are instabilities of oscillating systems, i.e. the exponential increase of the system energy over time caused by the time variation of impedance; open system is a system that exchanges energy, mass, and information with the environment; closed system is a system that does not exchange energy, mass, and