TW202416297A - Method and apparatus for controlled fusion reactions - Google Patents

Abstract

A method and an apparatus are provided for performing a fusion reaction. The method comprises providing neutral gas within a gas chamber, supplying energy to the gas chamber to initiate heating of a cathode and ionization of the neutral gas into protons and electrons, causing formation of a conducting channel due to the ionized neutral gas, causing formation of an electron layer outside the cathode based on set of thermionically emitted electrons by the heated cathode, causing acceleration of the electrons towards the cathode to cause the heated cathode to emit a set of secondary electrons due to a potential associated with the electron layer. The set of secondary electrons enhance strength of the electron layer. The method comprises causing formation of an electrostatic potential profile with dips and peaks, due to an electron-ion two-stream instability. The protons are accelerated towards the cathode at peaks and bombardment of the protons into the cathode enables fusion reaction.

Description

Method and apparatus for controlled fusion reactions

The present invention relates to nuclear reactions and reactors. In particular, the present invention relates to compact fusion reactors for initiating and maintaining fusion reactions.

With the increase in population, urbanization and expansion of electricity consumption in developing countries, energy demand is expected to increase exponentially. In addition, in recent years, due to the depletion of reserves of conventional energy resources and the serious impact of greenhouse gases released from conventional energy resources on the environment, it is crucial to ensure that greenhouse gas emissions are reduced during energy generation. Therefore, there is a need to explore alternative large-scale, sustainable and carbon-free forms of energy resources.

Fusion energy has been identified as an ideal future energy source due to carbon-free baseload electricity production, no long-lived radioactive waste, sustainable fuels and reduced safety threats. Therefore, fusion energy can make a positive contribution to the energy sector as well as the environment. Nuclear fusion is the process of combining two atoms to form a larger atom, thereby generating energy. However, controlled fusion reactions have been performed for decades, with the goal of making the fusion reactor produce more energy than it absorbs, i.e., high clean gain.

Previous efforts in large-scale fusion research have focused primarily on two methods of creating conditions for fusion ignition: inertial confinement fusion (ICF) and magnetic confinement fusion. ICF attempts to initiate fusion reactions by compressing and heating fusion reactants in the form of small particles, such as a mixture of deuterium ( ^2H ) and tritium ( ^3H ), and stimulating the fuel by delivering a high-energy beam, such as laser light, electrons, or ions, to the fuel. However, the duration of such ICF fusion is very short, and excess heat may have to be removed from the reaction chamber without disturbing the fuel target and drive beam, thereby making ICF a non-sustainable reaction. Magnetic confinement attempts to induce fusion by confining hot fusion fuel in the form of a plasma using a magnetic field. Magnetic fusion devices apply magnetic forces to charged particles in a way that acts as a centripetal force, causing the particles to move in a circular or spiral path within the plasma. Most research on magnetic confinement is based on designs such as the Tokamak, in which a hot plasma is confined within a toroidal magnetic field. However, these Tokamak reactors also fail to achieve high energy net power gains in terms of output energy and input energy in order to use fusion reactions as a sustainable energy source. For this reason, all credible previous approaches face constraints and engineering problems.

In practice, only a portion of the output fusion energy of a fusion reactor can be converted into a useful form. Anecdotal thinking suggests that only strongly ionized plasmas without a large number of neutral particles can be beneficial. Strongly ionized plasmas limit the particle density and energy confinement time that can be achieved in a fusion reactor. Therefore, in certain experimental settings, the Lawson criterion is used as a benchmark for controlled fusion reactions.

The commonly used formula for Lawson's criterion (called the triple product) is as follows:

Specifically, the Lawson criterion states that the product of the particle density (n), temperature (T), and confinement time (τ _E ) must be greater than a value determined by the energy of the charged fusion products (E _ch ), the Boltzmann constant (k _B ), the fusion cross section (σ), the relative velocity (v), and the temperature in order to achieve ignition conditions. For the deuterium-tritium reaction, the triple product has a minimum at k _B T = 14 keV and has a value of about 3 × 10 ²¹ keV s/m ³ . In order to satisfy the Lawson criterion, fusion reactors have been constructed to be large, complex, unmanageable, expensive, and not yet economically feasible. In practice, achieving positive energy balance using DT fusion reactions requires temperatures in excess of 150,000,000 degrees Celsius. For proton-boron based fusion reactions, Lawson's criterion suggests that the required temperature must be substantially higher. Since conventional wisdom holds that sustained fusion reactions require high temperatures and strongly ionized plasmas, cheap physical containment of atoms for fusion reactions is difficult. Therefore, designing fusion reactors based on Lawson's criterion may be infeasible.

Various methods have been proposed to capture the energy produced by nuclear fusion reactions. One such method is to use the aneutronic fusion of protons and boron. Recently, proton-boron (p- ¹¹ B) fusion reactions have become attractive because boron is more abundant in nature and easier to handle. In addition, the fusion power from proton-boron (p- ¹¹ B) fusion reactions is mainly released as charged alpha particles rather than neutrons, so proton-boron fusion reactions are also called aneutronic reactions. The aneutronless proton-boron fusion reaction can be written as: p+ ¹¹ B→3 ⁴ He+8.68 MeV (1)

As shown above, a neutronless proton-boron fusion reaction can produce 3 ⁴ He and release 8.68 MeV of energy without producing neutrons. Due to the neutronless reaction or the substantially neutronless reaction, this energy is clean.

In nuclear fusion reactions, the fusion reaction rate R can be estimated by the following expression: R = n ₁ n ₂ 〈σu〉 (2)

where _n1 and _n2 are the reactant densities, σ is the fusion cross section, and u is the velocity. The average term 〈σu〉 is called the reactivity. In certain known fusion technologies, superheated plasma aims to increase the reaction rate, i.e., by increasing the temperature of the plasma. To this end, it has become a challenge to find ways to maintain the fusion reaction in an economical, safe, reliable and environmentally friendly manner.

Therefore, there is a need to overcome the disadvantages associated with known fusion reactions, particularly known proton-boron based fusion reactions, such as increased reaction rate requirements, higher power gain, and reduced temperature requirements. In particular, there is a need to develop a fusion reactor that produces more fusion power so that fusion energy can become a commercially viable energy source.

A method and apparatus for performing a controlled fusion reaction are provided herein. In one aspect, the method for performing the controlled fusion reaction includes providing a neutral gas in a gas chamber, the gas chamber including an anode and a cathode and the neutral gas dispersed in the gas chamber. According to an embodiment, the method includes supplying energy to the gas chamber. The supply of the energy at least initiates: heating the cathode; and ionizing the neutral gas into protons and electrons. According to an embodiment, the method includes causing a conductive channel to form due to the ionized neutral gas. According to an embodiment, the method includes causing an electron layer to form outside the outer surface of the cathode based on a group of electrons thermally emitted by the heated cathode. According to an embodiment, the method includes: causing the electrons from the ionized neutral gas to accelerate toward the cathode due to the potential associated with the electron layer to cause the heated cathode to emit a group of secondary electrons. The group of secondary electrons enhances the strength of the electron layer. According to an embodiment, the method includes forming an electrostatic potential profile in the conductive channel due to electron-ion double current instability. The electrostatic potential profile includes a plurality of dips and a plurality of peaks. The protons from the ionized neutral gas are accelerated toward the cathode at the plurality of potential peaks, and the accelerated protons impact the cathode to achieve the controlled fusion reaction.

According to some example embodiments, the method further includes: causing an initial discharge current to heat the cathode and ionize the neutral gas; and causing a first potential valley of the plurality of potential valleys to be formed due to electrons emitted by the set of thermal ions emitted by the heated cathode.

According to some example embodiments, the method further includes causing the electrons to be accelerated between a region associated with the first potential valley and the cathode to impact the cathode. The region is located between the anode and the cathode. According to an embodiment, the method further includes causing the group of secondary electrons to be emitted due to the impact of the accelerated electrons at the cathode. According to an embodiment, the method further includes causing the electronic layer to be strengthened at the first potential valley of the plurality of potential valleys due to the group of secondary electrons emitted by the cathode. According to an embodiment, the method further includes forming the electrostatic potential distribution in the conductive channel due to the enhanced electron layer, the conductive channel having the electrostatic potential distribution is associated with the enhanced electron layer and the formation of the enhanced first potential valley.

According to some example embodiments, the method further includes causing the group of thermal ion emission electrons to be emitted due to the heating of the cathode. The group of thermal ion emission electrons are emitted from the surface of the cathode to the region associated with the first potential valley. According to an embodiment, the method further includes causing the electron layer having a negative charge density to be locally formed outside the surface of the cathode.

According to some example embodiments, the method further includes supplying energy to the gas chamber to partially ionize the neutral gas to produce plasma. The plasma includes the protons, the electrons, positive ions and negative ions. According to an embodiment, the method further includes causing the electrons and the negative ions to accelerate toward the cathode to cause the struck cathode to emit the set of secondary electrons.

According to some example embodiments, the method further includes forming a region of the first potential valley outside the cathode of the gas cell due to the enhanced strength of the electronic layer. The region of the first potential valley has a minimum potential value at the center of the electronic layer. A first electric field is directed from the cathode to the center of the electronic layer, and a second electric field is directed from the anode to the center of the electronic layer.

According to some example embodiments, the method further includes causing negative charges and positive charges to accelerate. The negative charges include the electrons and the negative ions, and the positive charges include the protons and the positive ions. The negative charges are accelerated from the cathode toward the anode, and the positive charges are accelerated from the anode toward the cathode. The positive charges and the negative charges are accelerated in opposite directions with a speed difference. According to an embodiment, the method further includes causing the electron-ion dual current instability in the gas chamber due to the speed difference between the positive charges and the negative charges.

According to some example embodiments, the method further includes causing the negative charges to accelerate toward the cathode at each of the plurality of valleys to cause the cathode to emit the set of secondary electrons. According to an embodiment, the method further includes causing the positive charges to accelerate toward the cathode at each of the plurality of peaks to impact into the cathode, wherein the impact of the accelerated protons and the positive ions into the cathode occurs with kinetic energy.

According to some example embodiments, the kinetic energy of each charged particle impacting the cathode is in the range of 1 keV to 100 keV.

According to some example embodiments, the method further comprises applying a heating source across the gas chamber to perform at least: the heating of the cathode; and ionizing the neutral gas into the protons and the electrons. According to an embodiment, the heating source comprises at least one of the following: a superconducting magnet source, a permanent magnet source, an electromagnetic source, a radio frequency (RF) source, a microwave source, an electric field source, an electrode source, a laser source, an ion gun source, or a combination thereof.

According to some exemplary embodiments, the diameter of the conductive channel is in the range of 0.01 mm to 1 mm.

According to some exemplary embodiments, the density of the neutral gas is in the range of 1×10 ²⁰ to 1×10 ²⁵ m ^-3 .

According to some exemplary embodiments, the neutral gas includes at least hydrogen (H ₂ ) gas.

According to some example embodiments, the gas chamber is energized by externally applying a voltage in the range of 10 volts to 1000 volts.

According to some exemplary embodiments, the cathode comprises a boron-rich material. The boron-rich material comprises at least one of the following: lumen hexaboride (LaB ₆ ), cerium hexaboride (CeB ₆ ), lithium boride, pure boron or boron nitride. According to an embodiment, the cathode provides boron for the controlled fusion reaction.

Embodiments disclosed herein may provide a device for performing a controlled fusion reaction. The device includes a gas chamber, the gas chamber including an anode and a cathode enclosed within the gas chamber and a neutral gas distributed within the gas chamber. The device further includes an energy source configured to supply energy to the gas chamber. According to an embodiment, the supply of the energy causes at least the initiation of: heating the cathode; and ionizing the neutral gas into protons and electrons. According to an embodiment, the supply of the energy causes the formation of a conductive channel due to the ionized neutral gas. According to an embodiment, the supply of the energy causes the formation of an electron layer outside the outer surface of the cathode based on a group of electrons thermally emitted by the heated cathode. According to an embodiment, due to the potential associated with the electron layer, the supply of energy causes the electrons from the ionized neutral gas to be accelerated toward the cathode to cause the heated cathode to emit a group of secondary electrons. The group of secondary electrons enhances the strength of the electron layer. According to an embodiment, due to the electron-ion double current instability, the supply of energy causes a static potential distribution to be formed in the conductive channel. The static potential distribution has a plurality of valleys and a plurality of peaks. The protons from the ionized neutral gas are accelerated toward the cathode at the plurality of potential peaks, and the accelerated protons impact into the cathode to achieve the controlled fusion reaction.

The foregoing invention is illustrative only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.

In the following description, for the purpose of explanation, many specific details are set forth to provide a thorough understanding of the present invention. However, those skilled in the art will appreciate that the present invention can be practiced without these specific details. In other examples, systems and devices are shown in block diagram form only to avoid obscuring the present invention.

Some embodiments of the present invention will now be more fully described below with reference to the accompanying drawings, in which some but not all embodiments of the present invention are shown. In fact, various embodiments of the present invention may be embodied in many different forms and should not be construed as limited to the embodiments described herein; rather, such embodiments are provided so that the present invention will satisfy applicable legal requirements. The same element symbols refer to the same elements throughout the text. Moreover, references in this specification to "an embodiment" or "an embodiment" mean that the specific features, structures, or characteristics described in conjunction with the embodiment are included in at least one embodiment of the present invention. The phrase "in an embodiment" appearing in various places in the specification does not necessarily all refer to the same embodiment, nor is it necessarily a separate or alternative embodiment that is mutually exclusive with other embodiments. Furthermore, the terms "a" and "an" herein do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced items. Furthermore, various features are described that may be exhibited by some embodiments but not by other embodiments. Similarly, various requirements are described that may be requirements for some embodiments but not for other embodiments. Therefore, the use of any such terms should not be construed as limiting the spirit and scope of the embodiments of the present invention.

Embodiments are described herein for illustrative purposes and are subject to numerous variations. It is understood that various omissions and substitutions of equivalents are contemplated as circumstances may suggest or be advantageous without departing from the spirit or scope of the invention, but are intended to cover applications or implementations. Furthermore, it is understood that the phraseology and terminology employed herein are for descriptive purposes and should not be construed as limiting. Any headings utilized within this description are for convenience only and have no legal or limiting effect. Definitions

Throughout the present invention, the term "fusion" refers to a nuclear reaction that occurs when the nuclei of two or more atoms combine, whereby the combined nuclei have a mass number less than or equal to ⁶² Ni. By this definition, the combined nuclei are unstable and will therefore release their excess energy by generally decaying into multiple product nuclei, which may include neutrons. Specifically, the total mass of the products is less than the combined mass of the reactants. The mass difference is released as energy according to the Einstein equation E=mc ^2. The energy gained from a fusion reaction is based on the difference in the nuclear binding energies. Since the speed of light "c" in a vacuum is very large, a small amount of lost mass becomes a large amount of energy. According to the present invention, the term "fusion" may be used interchangeably with "fusion reaction" and "nuclear fusion".

Throughout the present invention, the term "aneutronic fusion" refers to a form of fusion reaction in which very little of the energy released from the fusion reaction is carried by neutrons. The energy released in an aneutronic fusion reaction is in the form of high-energy charged particles, usually protons or alpha particles. According to embodiments of the present invention, an aneutronic fusion reaction can be performed by fusing protons and boron nuclei. The proton-boron aneutronic fusion reaction releases its energy in the form of high-energy alpha particles without producing neutrons, thereby making the released energy cleaner and easier to use.

Throughout the present invention, the term "fusion reactor" refers to a device or apparatus or system for generating the energy released in a fusion reaction (or fusion energy). The terms "fusion reactor" and "fusion power plant" may be used interchangeably.

Throughout the present invention, the term "ion", "ionized atom" or "charged particle" refers to an atom or particle that has at least one more electron than the total number of proton(s) or at least one more proton than the total number of electron(s).

Throughout the present invention, the term "neutral species" or "neutral particle" refers to an atom or molecule with a neutral charge. Specifically, a neutral atom may have the same number of electrons and protons, i.e., corresponding to its atomic number.

Throughout the present invention, the term "cathode" refers to an electrode that is negatively charged or grounded. In addition, the term "anode" refers to an electrode that is positively charged. According to the present invention, the cathode is made of a boron-rich material, such as lumen hexaboride (LaB ₆ ).

Throughout the present invention, the term "gas cell" refers to a housing for a gas. According to the present invention, the gas cell is filled with a neutral gas, and the gas cell also encloses a cathode and an anode. In this regard, the gas cell can use electrical energy to promote non-spontaneous ionization of the neutral gas inside the gas cell. For example, the gas cell can enclose a neutral gas, a cathode, and an anode to perform a fusion reaction.

Throughout this disclosure, the term "plasma" refers to the state of matter dispersed in a chamber. In a plasma, some electrons may have been stripped from their atoms. Because the particles (electrons and ions) in a plasma have an electric charge, the motion and behavior of the plasma is affected by electric and magnetic fields. Plasma is created when one or more electrons separate from atoms and/or atoms may capture one or more excess electrons. An ionized atom may lose at least one electron, or an ionized atom may be completely stripped of electrons, leaving behind a nucleus (of one or more protons and usually some neutrons). Atoms that lose electrons are called "positive ions." Positive ions can have a positive charge because they have more positively charged protons than negatively charged electrons. Conversely, atoms with excess electrons are called "negative ions." Negative ions can have a negative charge because they have more negatively charged electrons than positively charged protons. Plasma is usually a mixture of these positively charged ions or protons, negatively charged ions, and electrons. End of definition

Methods and apparatus for initiating and maintaining controlled fusion reactions according to example embodiments are provided herein. The methods and apparatus disclosed herein enable aneutronic fusion reactions to be performed for the generation of clean energy. The methods and apparatus disclosed herein enable the initiation of fusion reactions at substantially lower temperatures. The methods and apparatus disclosed herein enable the commercial viability of fusion reactions such that the fusion energy generated can be used, for example, to obtain heat, generate electricity, etc. The methods and apparatus disclosed herein further enable the design and construction of compact fusion reactors in which fusion reactions can occur. Such compact fusion reactors have reduced size and weight, are easy to handle, and have a less complex design.

The methods and devices disclosed herein may provide a gas chamber for performing a fusion reaction. In an example, the gas chamber may include a grounded cathode, an anode, and a gas dispersed within the gas chamber. In this regard, a voltage (i.e., electrical energy) is applied to the gas chamber to ionize the gas within the gas chamber to form a plasma and heat the grounded cathode within the gas chamber. Due to the ionization of the gas, a conductive path may be formed between the cathode and the anode. In addition, the heated cathode may cause thermal ion emission of a set of thermal ion emission electrons. Therefore, an electron layer may be formed outside the outer surface of the cathode. In addition, due to the negative potential associated with the electron layer outside the cathode, electrons may be accelerated from the plasma toward the cathode. This may cause the heated cathode to further emit a set of secondary electrons. The group of secondary electrons can strengthen the electron layer by increasing the negative charge density of the electron layer. Strengthening the electron layer can cause electron-ion double current instability in the gas chamber, which produces a static potential distribution in the conductive channel. The static potential distribution includes a plurality of valleys and a plurality of peaks. In this regard, protons (or positive charges) from an ionized neutral gas (i.e., plasma) are accelerated toward the cathode at a plurality of potential peaks. Subsequently, the accelerated protons can impact into the cathode to achieve a controlled fusion reaction.

FIG1 shows a diagram of a device 100 for initiating and maintaining a fusion reaction according to an embodiment of the present invention. According to an embodiment of the present invention, a fusion reaction is initiated by supplying an electric potential, and a fusion reaction is maintained by establishing a conductive channel with a static potential distribution between a cathode and an anode. The conductive channel accelerates protons and electrons to bombard the cathode to perform a nuclear fusion reaction.

The device includes an air chamber 102. The air chamber 102 includes one or more chamber walls to form an enclosed air chamber 102. In one embodiment, the air chamber 102 is filled with a neutral gas 104. In this regard, the neutral gas 104 can be introduced from an inlet to achieve a desired pressure. For example, the pressure in the air chamber 102 can be in the range of 1 mTorr to about 100 Torr. According to an embodiment, the device 100 further includes an input power supply 106 for supplying electrical energy to the air chamber 102. For example, the power supply 106 can be a constant voltage source, a constant current source, or a constant power source.

The air chamber 102 further includes one or more anodes 108 at one end of the air chamber 102 and a cathode 110 at the other end of the air chamber 102. In an example, the distance between the anode 108 and the cathode 110 can be adjustable. In an example, the anode 108 is a filament. For example, the anode 108 can be made of stainless steel, tungsten, copper, tantalum, hexaboride, carbon and the like. In one embodiment, the cathode 110 is made of a boron-rich material. In an example, the cathode 110 has a length in the range of 1 cm to 20 cm. In another example, the cathode 110 has a length in the range of 3 cm to 10 cm. For example, cathode 110 may be coated with an electron emitting material. For this purpose, the reactant of the cathode is boron or ( ^11B ). Examples of such boron-rich materials may include but are not limited to lumen hexaboride ( _LaB6 ), cerium hexaboride ( _CeB6 ), lithium boride ( _LiB2 ), pure boron (B) and boron nitride (BN). According to an embodiment of the present invention, cathode 110 may be made of lumen hexaboride or _LaB6 sheets and may emit electrons when heated.

In one embodiment, the input power supply 106 applies a potential across the anode 108 and the cathode 110. According to an embodiment of the present invention, a voltage is applied to the gas cell 102 across the anode 108 and the cathode 110. In an embodiment, the gas cell 102 is energized by externally applying a voltage in the range of 10 volts to 1000 volts.

In an example, an insulating material is used to insulate the gas chamber 102. For example, the insulating material is made of boron nitride (BN) or any other suitable non-conductive material.

The gas chamber 102 is filled with a neutral gas 104. For example, the neutral gas 104 may include at least molecular hydrogen (H ₂ ) gas. In other examples, the neutral gas 104 may be a mixture of H ₂ gas and other gases. In an example, the neutral gas 104 may include H ₂ gas and argon (Ar) gas. For example, the density of the neutral gas 104 (hereinafter also referred to as H ₂ gas 104) may be in the range of 1×10 ²⁰ to 1×10 ²⁵ m ^-3 .

According to the present invention, the cathode 110 can be a LaB ₆ plate. In an example, the cathode 110 is grounded and therefore has a potential of 0 V. In addition, the anode 108 is at a given potential, for example, φ _{a is} in the range of 1 V to 1000 V. The LaB ₆ cathode 110 is placed in a gas chamber 102 filled with hydrogen. In an example, the gas pressure of the hydrogen is maintained at about 1 to 100 torr using a pressure gauge, for example. To this end, the current inside the gas chamber 102 flows from the anode 108 to the LaB ₆ cathode 110.

In addition, the applied voltage can heat the _LaB6 cathode 110 and ionize the neutral gas 104. The heated _LaB6 cathode 110 can emit electrons. Subsequently, a conductive channel 112 with a small diameter can be established between the charged cathode or _LaB6 cathode 110 and the anode 108. In an example, the diameter of the conductive channel 112 can be in the range of 0.01 mm to 1 mm.

According to an embodiment, a conductive channel 112 is established between the cathode 110 and the anode 108 for individual protons and electrons, which are configured to overcome collisions with the hydrogen gas 104 and are accelerated by the electric potential to cause a p- ^11B fusion reaction.

In one embodiment, the input power supply 106 applies a potential across the anode 108 and the cathode 110, for example, in the range of 1 V to 1000 V.

Continuing further, an externally applied potential across the cathode 110 and the anode 108 of the gas chamber 102 causes ionization of the neutral gas 104. In other words, the applied potential causes the formation of fully or partially ionized hydrogen 104. In an example, the partially or fully ionized hydrogen may include electrons and ions. For example, the ions may include at least one of positively charged ions (such as H ⁺ ions) or negatively charged ions (such as ^H- ions). According to the present invention, the positively charged H ⁺ ions correspond to protons of the plasma. For example, the terms "H ⁺ ions" and protons may be used interchangeably. In certain cases, when the neutral gas 104 is composed of hydrogen and argon, the fully or partially ionized plasma may also contain other types of positively charged ions, such as Ar ⁺ ions. Specifically, during the ionization of the neutral gas 104, a plurality of protons and other positive ions (Ar ⁺ ions) (collectively referred to as positive charges) as well as electrons and negative ions (H ^- ions) (collectively referred to as negative charges) are generated in the gas chamber 102.

The potential heats the cathode 110 and causes a set of thermal ion emission electrons to be emitted from the cathode 110. The set of thermal ion emission electrons forms an electron layer 114 having a negative charge density. For example, the electron layer 114 may be formed near the outer surface of the cathode 110 (i.e., outside at a certain distance from the cathode 110). In an example, the set of thermal ion emission electrons locally forms an electron layer 114 of negative charge density near the cathode 110 in the gas chamber 102.

In one embodiment, the electron layer 114, together with the potential applied across the gas chamber 102, results in a large electrostatic potential with valley values. For example, the electrostatic potential at the peak and valley values may be in the range of 1 kV to 100 kV. In this regard, the initial potential valley (hereinafter referred to as the first potential valley) is formed by the presence of the electron layer 114, wherein the electron layer 114 is formed due to the group of electrons thermally emitted by the heated cathode 110.

To this end, due to the first potential valley, positive charges and negative charges may be accelerated at different speeds, thereby causing electron-ion double current instabilities. Specifically, negative charges are accelerated away from the electron layer 114 at a first speed, and positive charges are accelerated toward the electron layer 114 at a second speed. In the region between the electron layer 114 and the anode 108, electron-ion double current instabilities occur. In addition, according to the present invention, a specific amount of positive and negative charges from the ionized neutral gas 104 is accelerated by an electric field formed due to the electron layer 114. For example, an electric field may be formed between the region associated with the first potential valley and the cathode 110. In an example, a certain amount of negative charges or electrons from the ionized neutral gas 104 can be accelerated by the electric field between the region associated with the first potential valley and the cathode 110, so that the negative charges are accelerated toward the cathode 110. It can be noted that the region associated with the first potential valley or the region of the electronic layer 114 is located between the anode 108 and the cathode 110. This acceleration of positive and negative charges in different directions and at different speeds can lead to electron-ion double current instabilities and a static potential distribution with multiple valleys and multiple peaks.

In this way, the ionized neutral gas 104 (specifically, the negative charge of the ionized neutral gas 104) can be accelerated by the first potential valley and the potential of the electron layer 114 to hit the cathode 110 to emit another plurality of electrons (hereinafter referred to as a group of secondary electrons). The group of secondary electrons can further enhance the strength of the electron layer 114. For example, the group of secondary electrons can increase the negative charge density of the electron layer 114. In an embodiment, the group of secondary emission electrons causes the formation of an enhanced electron layer 114 near the cathode 110, and the enhanced electron layer 114 causes the formation of a static potential distribution in the conductive channel 112.

Therefore, due to the instability of the electron-ion double current, a static potential distribution having a plurality of valley values and a plurality of peak values is formed in the conductive channel 112.

In an example, individual electrons and positive and negative ions (hereinafter collectively referred to as ions) from the ionized neutral gas 104 can overcome collisions between the electrons and ions from the ionized neutral gas 104 and molecules of the dense non-ionized hydrogen gas 104. The electrons and ions from the ionized neutral gas 104 can be accelerated to high speeds by the potential within the conductive channel 112. In an example, due to the electron layer 114, protons and electrons are accelerated by the potential in the gas chamber 102 to perform p- ^11B fusion, where there is a relatively dense hydrogen gas density in the gas chamber 104. For example, protons of the ionized neutral gas 104 can hit the cathode 110. Accelerating protons to impact the cathode 110 enables controlled fusion reactions to be performed and energy to be generated. Specifically, protons may impact the LaB ₆ cathode 110, where the cathode 110 provides boron as fuel for the fusion reaction. In this way, a p- ¹¹ B fusion reaction is performed. In an example, the kinetic energy of each charged particle (such as a proton or H ⁺ ion) impacting the cathode 110 is in the range of 1 keV to 100 keV.

FIG. 2 shows a flow chart 200 depicting steps of a method for performing a controlled fusion reaction according to some embodiments of the present invention. A controlled fusion reaction is performed between protons and boron in a gas chamber, such as gas chamber 102. As described above, gas chamber 102 includes an anode 108, a cathode or LaB ₆ cathode 110, and a neutral gas 104 dispersed within gas chamber 102. In an example, neutral gas 104 includes at least molecular hydrogen (H ₂ ) gas. In addition, gas chamber 102 is connected to an input power supply 106. For example, the input power supply can apply a potential to gas chamber 102. Cathode 110 is grounded.

At 202, a potential is applied across the gas chamber 102 filled with neutral hydrogen 104. To this end, an initial discharge current due to the potential externally applied to the gas chamber 102 causes ionization of the neutral hydrogen 104 and heats the _LaB6 cathode 110.

In step 204, the neutral hydrogen gas 104 is partially ionized due to the potential to generate electrons and ions. In an example, the partially ionized neutral gas 104 generates a plasma having positively charged or positive H ⁺ ions, negatively charged or negative H ^- ions, and electrons. According to other examples, the ionization of the neutral hydrogen gas 104 can form a plasma including H ⁺ ions, H ^- ions, and electrons (e ^- ).

At 206, a conductive path 112 is formed due to the ionization of the neutral gas 104. The conductive path 112 is formed between the anode 108 and the cathode 110.

At 208, a set of thermal ion emission electrons are emitted from the _LaB6 cathode 110 due to the heating of the _LaB6 cathode 110. Specifically, the set of thermal ion emission electrons may be emitted from the surface of the _LaB6 cathode 110 to a region outside the cathode 110 and at a certain distance from the cathode 110. In the region outside the cathode 110 in which the set of thermal ion emission electrons are accumulated, the formation of an electron layer 114 may occur. The electron layer 114 may have a negative charge density locally outside the surface of the cathode 110. The set of thermal ion emission electrons emitted from the surface of the cathode 110 into the region may form a first potential valley in the region. Subsequently, the region of the electronic layer 114 may also indicate the region associated with the first potential valley.

At 210, the electron layer 114, along with the potential applied across the gas chamber 102, causes electrons and negative ions (or negative charges) from the plasma (ionized neutral gas 104) to accelerate toward the cathode 110. The negative charges impact into the cathode 110.

At 212, a first electric field ( _E1 ) between the region of the first potential valley and the cathode 110 causes negative charges to accelerate to hit the _LaB6 cathode 110 to emit a group of secondary electrons. The first electric field can be directed from the cathode 110 to the center of the electron layer 114 corresponding to the first potential valley. In addition, the emitted group of secondary electrons moves to the region of the electron layer 114 to enhance the strength of the electron layer 114.

At 214, a second electric field ( _E2 ) is formed between the anode 108 and the electron layer 114. The second electric field causes negative charges to accelerate toward the anode 108 and positive charges to accelerate toward the electron layer 114. This acceleration of positive and negative charges due to the second electric field causes electron-ion dual current instabilities.

Due to the electron-ion double current instability, a static potential distribution having a plurality of potential peaks and a plurality of potential valleys is formed in the conductive channel 112 in the gas chamber 102. For this reason, the negative charge is accelerated toward the cathode 110 at each of the plurality of valleys to cause the cathode 110 to emit the group of secondary electrons and enhance the intensity of the negative charge density of the electron layer 114.

At 216, positive and negative charges are accelerated to cause a fusion reaction. Specifically, at multiple valleys of the electrostatic potential distribution, negative charges (such as electrons and/or H ^- ions) are accelerated toward the _LaB6 cathode 110. This acceleration of the negative charges causes electrons to be emitted from the _LaB6 cathode 110, thereby causing potential valleys, which further cause electron-ion dual current instabilities within the gas cell 102, as described in detail above. In addition, at multiple peaks of the electrostatic potential distribution, positive charges (specifically, protons) are accelerated toward the _LaB6 cathode 110. This acceleration of the protons toward the LaB ₆ cathode 110 may cause the protons to strike the LaB ₆ cathode 110 with high velocity and kinetic energy, thereby causing a fusion reaction between the protons and the boron of the LaB ₆ cathode 110 .

At 218, power is generated from the fusion reaction. In an example, energies in the range of 1 keV to 100 keV can be obtained from the acceleration of protons. In addition, an average energy of about 3 MeV can be generated for each ⁴ He ion formed by the fusion of protons and boron atoms. In addition, the impact of the protons on the LaB ₆ cathode 110 can generate more sets of secondary electrons to enhance the electron layer 114 and the associated potential valley.

FIG. 3 shows a graph 300 depicting electron flow at a first potential valley according to some embodiments. Graph 300 represents _x0 on a horizontal axis 302, where _x0 represents the length between cathode 110 and anode 108 within gas cell 102. In addition, graph 300 represents φ on a vertical axis 304, where φ represents the potential across gas cell 102. As shown, at valley 306, the potential is substantially low, indicated by φ _dip . In addition, valley 306 is formed toward the left hand side of gas cell 102, where cathode 110 is positioned at the left hand side of gas cell 102. To this end, valley 306 is formed near cathode 110, for example, due to the formation of electron layer 114 due to thermal ion emission of electrons.

As described above, the externally applied potential φ _a causes the formation of partially ionized hydrogen. When the LaB ₆ cathode 110 is heated, the set of thermal ion emission electrons are emitted from the surface of the LaB ₆ cathode 110 to form an electron layer 114 having a negative charge density. Due to the potential valley 306, such as the first potential valley φ _dip , the net negative charge density causes a large static potential well near the surface of the LaB ₆ cathode 110.

In addition, a first electric field ( _E1 ) 308 is formed near the cathode 110. For example, _E1 308 is directed from the cathode 110 toward the center of the electron layer 114. _E1 308 can accelerate electrons and/or negatively charged ions (i.e., negative charges from the ionized neutral gas 104 or plasma) to strike the _LaB6 cathode 110. This can cause the _LaB6 cathode 110 to emit a set of secondary electrons. The set of secondary electrons can enhance the strength of the electron layer 114, thereby forming a positive feedback loop. For example, the set of secondary electrons can enhance the strength of the potential valley 306 φ _dip . As shown in FIG. 3 , the first electric field E ₁ 308 causes negative charges to accelerate toward a region associated with a first potential valley (φ _dip ) to strike the cathode 110 .

Additionally, a second electric field ( _E2 ) 310 is also formed within the plenum 102. The second electric field _E2 310 causes negative charges to accelerate away from the region associated with the first potential valley (i.e., toward the anode 108) and positive charges to accelerate toward the region associated with the first potential valley and toward the cathode 110.

In a region slightly away from the _LaB6 cathode 110 and the electron layer 114, the potential φ increases toward the anode 108 (right hand side). Due to the acceleration of positive and negative charges with different flow rates ( _Vp and _Ve , respectively) and in opposite directions, electron-ion double current instability may occur in the gas chamber 102. This electron-ion double current instability excites strong waves, resulting in the formation of a static potential distribution with multiple potential valleys and multiple potential peaks.

As shown, the potential is substantially low, indicated by φ _dip , at valley 306. Furthermore, valley 306 is formed toward the left hand side of gas cell 102, where cathode 110 is positioned at the left hand side of gas cell 102. To this end, valley 306 is formed near cathode 110, for example, due to the formation of electron layer 114 due to thermal ion emission of the set of thermal ion emission electrons.

4 shows a graph 400 depicting a distribution of electrostatic potential according to some embodiments. Graph 400 represents x ₀ on a horizontal axis 402, where x ₀ represents the distance between cathode 110 and anode 108 within gas cell 102. In addition, graph 400 represents φ on a vertical axis 404, where φ represents the potential across gas cell 102.

The electrostatic potential distribution includes a plurality of valleys, depicted as valleys 406A, 406B, and 406C. The electrostatic potential distribution also includes a plurality of peaks, depicted as peaks 408A and 408B. Specifically, the electrostatic potential distribution is initialized with a valley, such as a first potential valley. From the peak, positive charges can impact on the LaB ₆ cathode 110 to perform a proton-boron (p- ¹¹ B) fusion reaction.

Specifically, at some of the plurality of valleys 406A, 406B, and 406C, negative charges from the ionized neutral gas 104 are accelerated toward the cathode 110. The valleys upon which the negative charges are accelerated toward the cathode 110 may cause the cathode 110 to emit the set of secondary electrons. For example, the valleys are formed near the cathode 110 due to the electron layer 114 formed outside the cathode 110.

Additionally, at some of the plurality of peaks 408A and 408B, positive charges from the ionized neutral gas 104 are accelerated toward the cathode 110. The peaks 408 upon which the positive charges are accelerated toward the cathode 110 cause the positive charges to impact into the cathode 110. For example, the accelerated protons and positive ions (such as Ar ⁺ ions) (i.e., positive charges) impacting into the cathode 110 cause a controlled fusion reaction and generate power from the fusion reaction.

To determine the output of the proton-boron fusion reaction, certain results of the fusion reaction performed in the gas chamber 102 can be determined. Such results can include, for example, estimates of the proton-boron fusion cross section, the transport of protons and electrons in relatively dense neutral hydrogen, and power gain. It is understood that accelerating protons can lead to proton-boron fusion. To this end, calculations of the output of p- ^11B fusion can be performed based on simulations of p- ^11B fusion reactions.

In practice, the fusion cross section varies depending on the center-of-mass energy (E _cm ) of the proton-boron (p-11B) fusion reaction. Specifically, the effect of the center-of-mass energy is particularly significant in the low-energy region. For example, when the center-of-mass energy changes from about 1 keV to about 40 keV, the fusion cross section increases by about 50 orders of magnitude.

The formation of the electron layer 114 results in a strong electric field, which accelerates the protons. During the acceleration, proton-neutral particle collisions occur, that is, the protons collide with atoms of neutral hydrogen 104. For this reason, when the protons reach the LaB ₆ cathode 110 target, a small portion of the protons cannot be accelerated to the peak energy. In addition, solid boron compounds are also used as reactants in the p- ¹¹ B fusion process. In this regard, based on the proton-neutral particle collision effect, the acceleration and collision process used to obtain the energy distribution of the protons reaching the LaB ₆ cathode target 110 is identified.

A series of calculations are performed. In the calculations, the potential difference is assumed to be 50 kV, and the length of the acceleration path is assumed to be 1 mm or 10 mm. High-density neutral gas (molecular hydrogen) is uniformly filled in the space. The transport of protons through high-density molecular hydrogen under a strong electric field is simulated by Geant4 (geometry and tracking software), which is a Monte Carlo toolkit for simulating particle transport through matter. It can be understood that a proton with an initial energy ϵ _in is injected into the hydrogen gas and undergoes acceleration and collision, and when it reaches the other side, its final energy ϵ _f is recorded. The following Figure 7 describes in detail the simulation results of proton transport through high-density molecular hydrogen. The manner of simulating proton transport in FIG7 is merely exemplary and should not be construed as limiting. In other embodiments of the present invention, proton transport may be simulated under different conditions, for example, with different values of potential difference, length of acceleration path, etc.

5A to 5F show example graphical representations of energy distributions of protons that collide with the cathode 110 target after traveling through the acceleration path in calculations according to some embodiments of the present invention. Graphs 500A, 500B, 500C, 500D, 500E, and 500F of FIG. 5A, FIG. 5B, FIG. 5C, FIG. 5D, FIG. 5E, and FIG. 5F represent the corresponding final energy ϵ _f on the horizontal axis, respectively, where ϵ _f represents the final energy of the accelerated proton in the calculation when it is equal to the final energy of the proton that collided with the cathode 110 target after traveling through the acceleration path. Additionally, graphs 500A, 500B, 500C, 500D, 500E, and 500F represent counts on the vertical axis, where the counts represent the number of protons that collided with the target after traveling through the acceleration path in the calculation.

To this end, the energy distribution of the outgoing protons for different incident energies ϵ _in = 0.01 keV, 0.1 keV and 1 keV and acceleration path lengths of 1 mm and 10 mm is shown in Figures 5A to 5F. In the calculations, the density of the neutral hydrogen gas was assumed to be 3.3×10 ²³ m ^-3 and the temperature was assumed to be in the range of 1000 K to 5000 K. The final energy 〈ϵ _f 〉 and the standard deviation S〈ϵ _f 〉 of the accelerated protons were determined. From Figures 5A to 5F, it can be concluded that the energy loss from collisions along the acceleration path is negligible.

Multi-fluid simulation is studied along the x-axis to study the formation of electrostatic potential distribution in the conductive channel 112 in the gas chamber 102. The electrostatic potential distribution has a plurality of potential peaks and a plurality of potential valleys. Therefore, protons or H ⁺ ions from plasma are accelerated through the conductive channel 112 at the plurality of peaks to cause p- ¹¹ B fusion reaction.

In an example, the system length _x0 or the length of the conductive channel 112 corresponding to the gas chamber 102 can be in the range of 1 mm to 10 mm. According to this example, the system length _x0 is given by _x0 = 2 mm. The initial plasma temperature (T) is assumed to be about 4000 K. Since the ionization ratio in the gas chamber 102 is very small, the neutral gas density n _n is assumed to be constant in the simulation.

Since neutral fluids are mainly affected by collision effects, the proton-neutral particle collision frequency v _pn is about 10 ⁹ Hz. In addition, the proton-neutral particle mass density ratio is 4×10 ^-4 . In an example, when plasma collides with a neutral fluid, the plasma can ionize the neutral fluid.

The relationship m _p n _p v _pn = m _n n _n v _np gives the neutral-proton collision frequency as v _np = m _p n _p v _pn / m _n n _n . For example, the neutral-proton collision frequency is about 10 ⁵ Hz to 10 ⁶ Hz. Therefore, on the nanosecond time scale, the neutral fluid can be assumed to be motionless.

The incident electron collides into the boundary of the LaB ₆ cathode 110 and is bounced back due to the bounded boundary. Thermal ion emission electrons and secondary electrons are considered in the simulation system. Due to the increase in the boundary electron density or due to the increased strength of the electron layer 114 of the group of secondary electrons, an increase in the potential and electric field at the electron layer 114 is observed. The electric field causes further heating and ionization. Therefore, the ion density and the ionization ratio in the neutral gas 104 increase. In the simulation, the plasma temperature is assumed to increase from, for example, 4000 K to about 5000 K. The plasma density also increases with the plasma temperature from, for example, 10 ^-6 n ₀ to about 10 ^-4 n ₀ . In the gas chamber 102, electron-ion double current instability may occur. Therefore, a static potential distribution having a plurality of peaks and a plurality of valleys is formed in the conductive channel 112. In this way, a plurality of potential peaks may be achieved, wherein protons of the ionized neutral gas 104 or plasma are accelerated to bombard the LaB ₆ cathode 110 to cause a fusion reaction.

6A to 6C show simulation results corresponding to potential peaks and potential valleys according to some embodiments of the present invention. In FIG. 600A, FIG. 600B and FIG. 600C, simulation results are shown at t=40.0 nanoseconds (ns), t=41.0 ns and t=42.3 ns.

During operation in the simulation, the boundary electron density or negative charge density outside the LaB ₆ cathode 110 increases to about 10 ²³ m ^-3 due to the enhanced electron layer. The increase in boundary electron density over time is due to continuous electron emission from the LaB ₆ cathode 110, for example, due to the emission of thermal ion emission electrons and the group of secondary electrons. It can be noted that although the present invention only describes the emission of the group of thermal ion emission electrons and the group of secondary electrons from the LaB ₆ cathode 110, this should not be interpreted as a limitation. To this end, the LaB ₆ cathode 110 can continuously emit electrons. In addition, the electrons forming the group of thermal ion emission electrons and the electrons forming the group of secondary electrons or other groups of electrons emitted from the _LaB6 cathode 110 do not exclude each other. In an example, a specific electron emitted from the _LaB6 cathode 110 may be incident back to the _LaB6 cathode 110 at a plurality of valley values, and the _LaB6 cathode 110 may further re-emit electrons.

Around the electron layer 114, a potential valley is formed due to the high density electron layer 114. For example, due to the enhanced strength of the electron layer 114, the negative charge density is, for example, in the range of 10 to 100 kilovolts (kV), which can be indicated by the electrostatic potential distribution.

In an example, the set of thermal ion emission electrons and the set of secondary electrons from thermal ion emission of the _LaB6 cathode 110 result in the formation of an electron layer 114 near the cathode 110 (e.g., at x≈0). Due to the electron layer 114, the potential φ drops sharply from φ(x=0) to φ _dip <0. Then, the potential φ increases slowly toward the anode 108, for example, at the anode 108, φ(x=x ₀ )=φ _a V. The electric field in the region from the anode 108 toward the electron layer 114 may be negative (E _x <0). The negative electric field in the gas chamber 102 can accelerate the electrons at a high speed _Ue≈2.4 × ¹⁰⁷ m/s toward the anode 108, while due to the large mass of the positive charges, the positive charges are accelerated at a low speed toward the cathode 110. The positive and negative charges are accelerated in opposite directions at different speeds, which leads to electron-ion dual current instability.

In the electrostatic potential distribution, due to this instability, waves with large amplitudes are formed. For example, the amplitude of these waves can be tens of kilovolts. The number density and velocity distribution of positive and negative charges also show this large amplitude pattern of electrostatic waves.

6A, 6B, and 6C show plots 602A, 602B, and 602C, respectively. Plots 602A, 602B, and 602C show changes in electron density ( _ne ) and/or ion density ( _ni ) over a system length _x0 at different times, for example, at 40.0 ns, 41.0 ns, and 42.3 ns, respectively. In addition, FIG. 6A, 6B, and 6C show plots 604A, 604B, and 604C, respectively, which show changes in electron flow rate ( _Ve ) over a system length ( _x0 ) at times, for example, 40.0 ns, 41.0 ns, and 42.3 ns, respectively. 6A, 6B and 6C also show plots 606A, 606B and 606C, respectively, which show the change of proton flux (V _i ) over the system length (x ₀ ) at times such as 40.0 ns, 41.0 ns and 42.3 ns, respectively. FIG10A, 10B and 10C also show plots 608A, 608B and 608C, respectively, which show the change of potential (ϕ) over the system length (x ₀ ) at different times such as 40.0 ns, 41.0 ns and 42.3 ns, respectively.

From plots 608A, 608B, and 608C, it is observed that the potential at the peak reaches about 30 kV, and the potential at the valley reaches about -10 kV.

The formation of a negative potential valley can accelerate electrons toward the LaB ₆ cathode 110, and the formation of a positive potential peak can accelerate protons toward the LaB ₆ cathode 110. The bombardment of the LaB ₆ cathode 110 by protons leads to p- ¹¹ B fusion. The fusion emits about 3 MeV helium (He) on average, which can further produce protons through collisions. These protons bombard the LaB ₆ cathode 110 and produce more helium, thereby ensuring the continuity of the fusion reaction, thereby forming a positive feedback loop.

FIG. 7 shows an example flow chart depicting steps of a method for performing a controlled fusion reaction in gas chamber 102 according to some example embodiments.

At 702, a neutral gas 104 is distributed in the gas chamber 102. The gas chamber 102 includes an anode 108, a cathode 110, and the neutral gas 104 dispersed in the gas chamber 102. In an example, the cathode 110 includes a boron-rich material, such as lumen hexaboride (LaB ₆ ), caesium hexaboride (CeB ₆ ), lithium boride, pure boron, boron nitride (BN), or a combination thereof. The cathode 110 provides boron for a controlled fusion reaction. In an example, the neutral gas 104 includes at least molecular hydrogen (H ₂ ) gas. For example, the density of the neutral gas 104 is in the range of 1×10 ²⁰ m ^-3 to 1×10 ²⁵ m ^-3 .

At 704, energy is supplied to the gas cell 102. Specifically, an external potential is applied to the anode 108 and cathode 110 in the gas cell 102. The external potential initially heats the cathode 110 and ionizes the neutral gas 104 into protons and electrons. In an example, the initial discharge current due to the external potential may heat the cathode 110 and ionize the neutral gas 104. In some cases, the neutral gas 104 may be weakly ionized. In this case, the neutral gas 104 may be ionized into protons or positive ions (H ⁺ ions), electrons, and negative ions ( ^H- ions). In an example, the gas cell 102 is energized by externally applying a voltage in the range of 10 V to 1000 V.

In certain cases, a heating source may be applied to the gas chamber 102 to perform heating of the cathode 110 and ionize the neutral gas 104 into protons and electrons. For example, the heating source may be a superconducting magnet source, a permanent magnet source, an electromagnetic source, a radio frequency (RF) source, a microwave source, an electric field source, an electrode source, a laser source, an ion gun source, or a combination thereof.

At 706, a conductive channel 112 is formed between the anode 108 and the cathode 110. The conductive channel 112 is formed due to the ionization of the neutral gas 104. In an example, the diameter of the conductive channel 112 is in the range of 0.01 mm to 1 mm.

At 708, an electron layer 114 is formed outside the outer surface of the cathode 110. The electron layer 114 is formed due to a set of thermal ion emission electrons emitted by the heated cathode 110. In an example, the electron layer 114 causes a first potential valley to be formed due to the set of thermal ion emission electrons emitted by the heated cathode 110. For example, the set of thermal ion emission electrons can be emitted from the surface of the cathode 110 to a region associated with the first potential valley. Subsequently, an electron layer 114 having a negative charge density is locally formed outside the surface of the cathode 110.

At 710, electrons from the ionized neutral gas 104 are accelerated toward the cathode 110 due to the potential associated with the electron layer 114. The electrons accelerated toward the cathode 110 may strike the cathode 110 to cause the heated cathode 110 to emit a set of secondary electrons. The set of secondary electrons may also be deposited outside the cathode 110, within the electron layer 114. Thus, the set of secondary electrons enhances the strength of the electron layer 114.

Specifically, electrons are accelerated between the region associated with the first potential valley and the cathode 110 to impact the cathode 110. The region is located between the anode 108 and the cathode 110. The impact of the accelerated electrons at the cathode 110 results in the emission of the group of secondary electrons. In addition, due to the group of secondary electrons emitted by the cathode 110, the electron layer 114 is enhanced at the first potential valley.

In an example, a region of a first potential valley outside the cathode 110 of the gas cell 102 is formed due to the enhanced strength of the electronic layer 114. The region of the first potential valley has a minimum potential value at the center of the electronic layer 114. In addition, a first electric field is directed from the cathode 110 to the center of the electronic layer 114, and a second electric field is directed from the anode 108 to the center of the electronic layer 114.

At 712, due to the electron-ion double current instability, an electrostatic potential distribution is formed in the conductive channel 112. The electrostatic potential distribution may include a plurality of valleys and a plurality of peaks. In an example, the formation of the electrostatic potential distribution in the conductive channel 112 is associated with the formation of the enhanced electron layer 114 and the strengthening of the first potential valley.

For example, due to the enhanced strength of the electron layer 114, negative charges or electrons and positive charges or protons are accelerated. In an example, the negative charges may include electrons and negative ions (e.g., H ^- ions), and the positive charges may include protons (e.g., H ⁺ ions) and positive ions (e.g., Ar ⁺ ions). Due to the enhanced first potential valley, the negative charges may be accelerated from the cathode 110 toward the anode 108, and the positive charges may be accelerated from the anode 108 toward the cathode 110. To this end, the positive and negative charges are accelerated in opposite directions and have a speed difference. The speed difference between the positive and negative charges and the opposite flow directions of the positive and negative charges may cause electron-ion dual-current instabilities within the gas chamber 102.

In this regard, negative charges or electrons are accelerated toward the cathode 110 at each of a plurality of valleys to cause the cathode 110 to emit the set of secondary electrons. In addition, positive charges or protons are accelerated toward the cathode 110 at each of a plurality of peaks to impact into the cathode 110. Accelerating protons and positive ions (H ⁺ ions) to impact into the cathode 110 achieves a controlled fusion reaction and results in power generation. In an example, the protons and positive ions are accelerated to impact the cathode 110 with high kinetic energy. For example, the kinetic energy of each charged particle (proton or positive ion) impacting into the cathode 110 is in the range of 1 keV to 100 keV.

Those skilled in the art to which the present invention belongs who benefit from the teachings presented in the foregoing description and the associated drawings will think of many modifications and other embodiments of the present invention as described herein. Therefore, it should be understood that the present invention is not limited to the specific embodiments disclosed and modifications and other embodiments are intended to be included within the scope of the accompanying invention application. In addition, although the foregoing description and the associated drawings describe example embodiments in the context of a specific example combination of elements and/or functions, it should be understood that different combinations of elements and/or functions may be provided by alternative embodiments without departing from the scope of the accompanying invention application. In this regard, for example, combinations of elements and/or functions that are different from the above explicit descriptions may also be considered, as may be described in some of the accompanying invention application. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

100: device 102: gas chamber 104: neutral gas 106: input power supply 108: anode 110: cathode 112: conductive channel 114: electronic layer 200: flow chart 202: step 204: step 206: step 208: step 210: step 212: step 214: step 216: step 218: step 300: graph 302: horizontal axis 304: vertical axis 306: valley value 308: first electric field (E ₁ ) 310: second electric field (E ₂ ) 400: graph 402: horizontal axis 404: vertical axis 406A: valley 406B: valley 406C: valley 408A: peak 408B: peak 500A to 500F: graphs 600A to 600C: graphs 602A to 602C: plots 604A to 604C: plots 606A to 606C: plots 608A to 608C: plots 702: step 704: step 706: step 708: step 710: step 712: step

Having therefore generally described example embodiments of the present invention, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and in which:

FIG. 1 is a diagram showing a gas chamber for promoting fusion reactions according to an example embodiment;

FIG. 2 shows a flow chart depicting the steps of a method for performing a controlled fusion reaction according to an example embodiment;

FIG. 3 shows a graph depicting electron current at a first potential valley according to an example embodiment;

FIG. 4 shows a graph depicting electrostatic potential distribution according to an example embodiment;

5A-5F illustrate example graphical representations of energy distribution of accelerated protons according to example embodiments;

6A to 6C show simulation results corresponding to potential peaks and potential valleys according to an example embodiment; and

7 shows an example flow chart depicting steps of a method for performing a controlled fusion reaction in a gas cell according to an example embodiment.

100:Device

102: Air chamber

104: Neutral gas

106: Input power supply

108: Yang pole

110: cathode

112: Conductive channel

114: Electronic layer

Claims (20)

A method for performing a controlled fusion reaction, the method comprising: Providing a neutral gas in a gas chamber, the gas chamber comprising an anode and a cathode and the neutral gas dispersed in the gas chamber; Supplying energy to the gas chamber, wherein the supply of the energy at least initiates: heating the cathode, and ionizing the neutral gas into protons and electrons; Forming a conductive channel due to the ionized neutral gas; Forming an electron layer outside the outer surface of the cathode based on a group of electrons thermally emitted by the heated cathode; Due to the potential associated with the electron layer, the electrons from the ionized neutral gas are accelerated toward the cathode to cause the heated cathode to emit a group of secondary electrons, wherein the emitted group of secondary electrons enhance the strength of the electron layer; and Due to the electron-ion double current instability, a static potential distribution is formed in the conductive channel, the static potential distribution includes a plurality of valleys and a plurality of peaks, wherein the protons from the ionized neutral gas are accelerated toward the cathode under the plurality of potential peaks, and the accelerated protons impact the cathode to achieve the controlled fusion reaction. The method of claim 1, wherein the method comprises: causing an initial discharge current to heat the cathode and ionize the neutral gas; and causing a first potential valley of the plurality of potential valleys to be formed due to the group of electrons thermally emitted from the heated cathode. The method of claim 2, wherein the method includes: causing the electrons to be accelerated between a region associated with the first potential valley and the cathode to impact the cathode, wherein the region is located between the anode and the cathode; causing the group of secondary electrons to be emitted due to the impact of the accelerated electrons at the cathode; causing the electron layer to be enhanced at the first potential valley of the plurality of potential valleys due to the group of secondary electrons emitted by the cathode; and causing the electrostatic potential distribution to be formed in the conductive channel due to the enhanced electron layer, the conductive channel having the electrostatic potential distribution being associated with the enhanced electron layer and the formation of the enhanced first potential valley. The method of claim 3, wherein the method further comprises: causing the group of thermal ion emission electrons to be emitted due to the heating of the cathode, the group of thermal ion emission electrons being emitted from the surface of the cathode to the region associated with the first potential valley; and causing the electron layer having a negative charge density to be locally formed outside the surface of the cathode. The method of claim 1, wherein the method comprises: supplying energy to the gas chamber to partially ionize the neutral gas to produce plasma, the plasma comprising the protons, the electrons, positive ions and negative ions, and causing the electrons and the negative ions to accelerate toward the cathode to cause the struck cathode to emit the set of secondary electrons. The method of claim 5, wherein the method further comprises: Due to the enhanced strength of the electronic layer, a region of the first potential valley is formed outside the cathode of the gas chamber, the region of the first potential valley has a minimum potential value at the center of the electronic layer, wherein a first electric field is directed from the cathode to the center of the electronic layer, and a second electric field is directed from the anode to the center of the electronic layer. The method of claim 5, wherein the method further comprises: causing negative charges and positive charges to accelerate, the negative charges including the electrons and the negative ions, and the positive charges including the protons and the positive ions, wherein the negative charges are accelerated from the cathode toward the anode, and the positive charges are accelerated from the anode toward the cathode, wherein the positive charges and the negative charges are accelerated in opposite directions with a speed difference; and causing the electron-ion dual current instability in the gas chamber due to the speed difference between the positive charges and the negative charges. The method of claim 7, wherein the method further comprises: causing the negative charges to accelerate toward the cathode at each of the plurality of valley values to cause the cathode to emit the group of secondary electrons, and causing the positive charges to accelerate toward the cathode at each of the plurality of peak values to impact into the cathode, wherein the impact of the accelerated protons and the positive ions into the cathode occurs with kinetic energy. The method of claim 8, wherein the kinetic energy of each charged particle impacting the cathode is in the range of 1 keV to 100 keV. The method of claim 1, wherein the method further comprises: Applying a heating source across the gas chamber to perform at least: the heating of the cathode; and ionizing the neutral gas into the protons and the electrons, wherein The heating source comprises at least one of the following: a superconducting magnet source, a permanent magnet source, an electromagnetic source, a radio frequency (RF) source, a microwave source, an electric field source, an electrode source, a laser source, an ion gun source, or a combination thereof. The method of claim 1, wherein the diameter of the conductive channel is in the range of 0.01 mm to 1 mm. The method of claim 1, wherein the density of the neutral gas is in the range of 1×10 ²⁰ to 1×10 ²⁵ m ^-3 . The method of claim 1, wherein the neutral gas comprises at least hydrogen (H ₂ ) gas. A method as claimed in claim 1, wherein the gas chamber is energized by externally applying a voltage in the range of 10 volts to 1000 volts. The method of claim 1, wherein the cathode comprises a boron-rich material, the boron-rich material comprising at least one of: lumen hexaboride (LaB ₆ ), cerium hexaboride (CeB ₆ ), lithium boride, pure boron, or boron nitride, and wherein the cathode provides boron for the controlled fusion reaction. A device for performing a controlled fusion reaction, the device comprising: a gas chamber comprising an anode and a cathode enclosed within the gas chamber and a neutral gas distributed within the gas chamber; and an energy source configured to supply energy to the gas chamber, wherein the supply of the energy results in: at least initially: heating the cathode; and ionizing the neutral gas into protons and electrons; forming a conductive channel due to the ionized neutral gas; forming an electron layer outside the outer surface of the cathode based on a group of electrons thermally emitted by the heated cathode; The electrons from the ionized neutral gas are accelerated toward the cathode due to the potential associated with the electron layer to cause the heated cathode to emit a group of secondary electrons, wherein the group of secondary electrons enhance the strength of the electron layer; and Due to the electron-ion double current instability, a static potential distribution is formed in the conductive channel, the static potential distribution includes a plurality of valleys and a plurality of peaks, wherein the protons from the ionized neutral gas are accelerated toward the cathode under the plurality of potential peaks, and the accelerated protons impact the cathode to achieve the controlled fusion reaction. The device of claim 16, wherein the supply of the energy further causes: heating the cathode and ionizing the neutral gas due to the initial discharge current; and forming a first potential valley of the plurality of potential valleys due to the group of electrons thermally emitted from the heated cathode. The device of claim 17, wherein the supply of the energy further results in: Accelerating the electrons between the region associated with the first potential valley and the cathode to impact the cathode, wherein the region is located between the anode and the cathode; Emitting the group of secondary electrons from the cathode due to the impact of the accelerated electrons at the cathode; Strengthening the electron layer at the first potential valley of the plurality of potential valleys due to the group of secondary electrons emitted by the cathode; and Forming the electrostatic potential distribution in the conductive channel due to the strengthened electron layer, the conductive channel having the electrostatic potential distribution being associated with the strengthened electron layer and the formation of the strengthened first potential valley. The device of claim 16, wherein the supply of energy further results in: Partially ionizing the neutral gas to generate plasma, the plasma comprising the protons, the electrons, positive ions and negative ions; Accelerating the electrons and the negative ions toward the cathode to cause the struck cathode to emit the group of secondary electrons to enhance the strength of the electron layer; Forming a region of the first potential valley outside the cathode of the gas chamber due to the enhanced strength of the electron layer, the region of the first potential valley having a minimum potential value at the center of the electron layer, wherein a first electric field is directed from the cathode to the center of the electron layer, and a second electric field is directed from the anode to the center of the electron layer; Accelerating negative charges and positive charges, the negative charges including the electrons and the negative ions, and the positive charges including the protons and the positive ions, wherein the negative charges are accelerated from the cathode toward the anode, and the positive charges are accelerated from the anode toward the cathode, wherein the positive charges and the negative charges are accelerated in opposite directions with a speed difference; and forming the electron-ion dual current instability in the gas chamber due to the speed difference between the positive charges and the negative charges. The device of claim 19, wherein the supply of the energy further results in: accelerating the negative charges toward the cathode at each of the plurality of valleys to cause the cathode to emit the set of secondary electrons; and accelerating the positive charges toward the cathode at each of the plurality of peaks to impact into the cathode, wherein the impact of the accelerated protons and the positive ions into the cathode results in the generation of kinetic energy.