Patent Publication Number: US-2023154631-A1

Title: Method and apparatus for controlled fusion reactions

Description:
TECHNOLOGICAL FIELD 
     The present disclosure relates to nuclear reactions and reactors. In particular, the present disclosure relates to compact fusion reactors for initiating and maintaining fusion reactions. 
     BACKGROUND 
     With increased population, increased urbanization and expanding access to electricity in developing countries, demand of energy is expected to grow manifolds. Moreover, in recent years, due to depleting reserves of conventional energy resources and severe impact on the environment due to green-house gasses released form conventional energy resources, it is crucially important to ensure reduced green-house gas emissions during energy generation. Therefore, there is a need for exploring alternate large-scale, sustainable, and carbon-free form of energy resources. 
     Fusion energy has been identified as an ideal future energy owing to carbon-free base-load electricity production, no long-lived radioactive waste, sustainable fuels, and reduced safety threats. As a result, fusion energy may make positive contribution to the energy sector as well as the environment. Nuclear fusion is a process that occurs when two atoms combine to make a larger atom, creating energy. Controlled fusion reactions have been performed for decades, however, the goal is to make a fusion reactor that produces more energy than it takes in, i.e., high net gain. 
     Prior efforts in large-scale fusion research have primarily focused on two methods of creating conditions for fusion ignition: inertial confinement fusion (ICF) and magnetic confinement fusion. ICF attempts to initiate a fusion reaction by compressing and heating fusion reactants, such as a mixture of deuterium ( 2 H) and tritium ( 3 H), in the form of a small pellet and energizing the fuel by delivering high-energy beams of, for example, laser light, electrons, or ions to the fuel. However, time duration of such ICF fusion is very short, and excess heat may have to be removed from a reaction chamber without interfering with the fuel targets and driver beams, thereby making ICF an unsustainable reaction. The magnetic confinement attempts to induce fusion by using magnetic fields to confine hot fusion fuel in the form of plasma. Magnetic fusion devices apply a magnetic force on charged particles in a manner that serves as a centripetal force, causing the particles to move in circular or helical path within the plasma. Most of the research in magnetic confinement is based on, for example, Tokamak design in which hot plasma is confined within a toroidal magnetic field. However, such tokamak reactors also failed to achieve a high net power gain of energy in terms of output energy and input energy in order to use fusion reaction as a sustainable energy source. To this end, all the credible prior approaches have faced confinement and engineering issues. 
     In practice, only a portion of output fusion energy of a fusion reactor can be converted to a useful form. Conventional thinking holds that only strongly ionized plasmas that do not have significant quantities of neutrals may be advantageous. The strongly ionized plasmas limit particle densities and energy confinement times that can be achieved in the fusion reactor. Thus, in certain experimental set-ups Lawson criterion is used as a benchmark for controlled fusion reactions. 
     A common formulation of the Lawson criterion, known as the triple product, is as follows: 
     
       
         
           
             
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                 τ 
                 E 
               
             
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                   12 
                   ⁢ 
                   
                     k 
                     B 
                   
                 
                 
                   E 
                   ch 
                 
               
               ⁢ 
               
                 
                   T 
                   2 
                 
                 
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                     σ 
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     In particular, the Lawson criterion states that a product of a particle density (n), temperature (T), and confinement time (τ E ) must be greater than a number dependent on the energy of the charged fusion products (E ch ), the Boltzmann constant (k B ), the fusion cross section (σ), the relative velocity (v), and temperature in order for ignition conditions to be reached. For the deuterium-tritium reaction, a minimum of a triple product occurs at k B T=14 keV and the number for the triple product is about 3×10 21  keV s/m 3 . In order to satisfy Lawson criterion, fusion reactors are constructed that are large, complex, difficult to manage, expensive, and, as yet, economically unviable. In practice, temperatures in excess of 150,000,000 degrees Celsius are required to achieve positive energy balance using a D-T fusion reaction. For a proton-boron based fusion reaction, the Lawson criterion suggests that a required temperature must be yet substantially higher. As the conventional thinking holds that high temperatures and strongly ionized plasma are required for sustainable fusion reaction, inexpensive physical containment of atoms for fusion reaction is difficult. Therefore, designing of the fusion reactor based on Lawson criterion may not be feasible. 
     Multiple approaches have been proposed to capture the energy produced by the nuclear fusion reaction. One such approach is aneutronic fusion using proton and boron. Recently, proton-boron (p- 11 B) nuclear fusion reaction has become attractive because boron is more abundant in nature and easy to handle. Moreover, fusion power from proton-boron (p- 11 B) nuclear fusion reaction is released mainly in charged α particles rather than neutrons, hence, the proton-boron nuclear fusion reaction is also known as aneutronic reaction. The aneutronic proton-boron nuclear fusion reaction can be written as: 
         p+   11 B→3 4 He+8.68 MeV  (1)
 
     As shown above, the aneutronic proton-boron nuclear fusion reaction may produce three  4 He and release energy of 8.68 MeV, and no neutrons are produced. Owing to aneutronic reaction or substantially aneutronic reaction, such energy is clean. 
     In a nuclear fusion reaction, a fusion reaction rate R may be estimated by the expression: 
         R=n   1   n   2     σu         (2)
 
     Where n 1  and n 2  are reactant densities, σ is a fusion cross section, and u is velocity. The average term  σu  is called reactivity. In certain conventional fusion techniques, super thermal plasma aims to increase the reaction rate, i.e., reaction rate is increased by increasing temperature of the plasma. To this end, it has been a challenge to find a way to sustain a fusion reaction in a way that is economical, safe, reliable, and environmentally sound. 
     Therefore, there is a need to overcome drawbacks, for example, requirement of increased reaction rate, higher power gain and lower temperature requirement, associated with the conventional fusion reactions, especially conventional proton-boron based fusion reaction. In particular, there is a need to develop a fusion reactor that generates more fusion power such that fusion energy can become a commercially viable source of energy. 
     SUMMARY 
     A method and an apparatus are provided herein for performing a controlled fusion reaction. In one aspect, the method for performing the controlled fusion reaction comprises providing a neutral gas within a gas chamber, the gas chamber comprising an anode and a cathode and neutral gas dispersed within the gas chamber. In accordance with an embodiment, the method comprises supplying energy to the gas chamber. The supplying of the energy initiates at least: heating of the cathode, and ionization of the neutral gas into protons and electrons. In accordance with an embodiment, the method comprises causing formation of a conducting channel, due to the ionized neutral gas. In accordance with an embodiment, the method comprises causing formation of an electron layer outside an outer surface of the cathode, based on a set of thermionically emitted electrons by the heated cathode. In accordance with an embodiment, the method comprises causing acceleration of the electrons from the ionized neutral gas towards the cathode, due to a potential associated with the electron layer, to cause the heated cathode to emit a set of secondary electrons. The set of secondary electrons enhance a strength of the electron layer. In accordance with an embodiment, the method comprises causing formation of an electrostatic potential profile within the conducting channel due to an electron-ion two-stream instability. The electrostatic potential profile comprises a plurality of dips and a plurality of peaks. The protons from the ionized neutral gas are accelerated towards the cathode at the plurality of potential peaks and bombardment of the accelerated protons into the cathode enables the controlled fusion reaction. 
     According to some example embodiments, the method further comprises causing an initial discharge current to heat the cathode and ionize the neutral gas and causing formation of a first potential dip of the plurality of potential dips due to the set of thermionically emitted electrons emitted by the heated cathode. 
     According to some example embodiments, the method further comprises causing acceleration of the electrons between a region associated with the first potential dip and the cathode to bombard the cathode. The region lies between the anode and the cathode. In accordance with an embodiment, the method further comprises causing emission of the set of secondary electrons, due to the bombardment of the accelerated electrons at the cathode. In accordance with an embodiment, the method further comprises causing strengthening of the electron layer, at the first potential dip of the plurality of potential dips, due to the set of secondary electrons emitted by the cathode. In accordance with an embodiment, the method further comprises causing formation of the electrostatic potential profile within the conducting channel, due to the strengthened electron layer, the conducting channel with the electrostatic potential profile being associated with the formation of the enhanced electron layer and the strengthened first potential dip. 
     According to some example embodiments, the method further comprises causing emission of the set of thermionically emitted electrons, due to the heating of the cathode. The set of thermionically emitted electrons are emitted from the surface of the cathode into the region associated with the first potential dip. In accordance with an embodiment, the method further comprises causing formation of the electron layer having a negative charge density locally outside the surface of the cathode. 
     According to some example embodiments, the method further comprises supplying energy to the gas chamber to partially ionize the neutral gas to generate plasma. The plasma comprises the protons, the electrons, positive ions, and negative ions. In accordance with an embodiment, the method further comprises causing the electrons and the negative ions to accelerate towards the cathode to cause the bombarded cathode to emit the set of secondary electrons. 
     According to some example embodiments, the method further comprises causing formation of a region of the first potential dip outside the cathode of the gas chamber, due to the enhanced strength of the electron layer. The region of the first potential dip has a minimum potential value at a center of the electron layer. A first electric field is directed from the cathode towards the center of the electron layer, and a second electric field is directed from the anode towards the center of the electron layer. 
     According to some example embodiments, the method further comprises causing acceleration of negative charges and positive charges. The negative charges comprise the electrons and the negative ions, and the positive charges comprise the protons and the positive ions. The negative charges are accelerated from the cathode towards the anode and the positive charges are accelerated from the anode towards the cathode. The positive charges and the negative charges are accelerated in opposite directions and have a velocity difference. In accordance with an embodiment, the method further comprises causing the electron-ion two-stream instability within the gas chamber, due to the velocity difference between the positive charges and the negative charges. 
     According to some example embodiments, the method further comprises causing acceleration of the negative charges towards the cathode, at each of the plurality of dips, to cause the cathode to emit the set of secondary electrons. In accordance with an embodiment, the method further comprises causing acceleration of the positive charges towards the cathode, at each of the plurality of peaks, to bombard into the cathode, wherein the bombardment of the accelerated protons and the positive ions into the cathode occurs with a kinetic energy. 
     According to some example embodiments, the kinetic energy of each charged particle bombarding into the cathode is in a 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 ionization of the neutral gas into the protons and the electrons. In accordance with an embodiment, the heating source comprises at least one of: superconducting magnet source, permanent magnet source, electromagnet source, radiofrequency (RF) source, microwave source, electric field source, electrode source, laser source, ion gun source, or a combination thereof. 
     According to some example embodiments, a diameter of the conducting channel is in a range of 0.01 millimeters to 1 millimeter. 
     According to some example embodiments, a density of the neutral gas is in a range of 1×10 20  to 1×10 25  m −3 . 
     According to some example embodiments, the neutral gas comprises at least hydrogen (H 2 ) gas. 
     According to some example embodiments, the gas chamber is energized by externally applying a voltage in a range of 10 Volts to 1000 Volts. 
     According to some example embodiments, the cathode comprises a boron rich material. The boron-rich material comprises at least one of: lanthanum hexaboride (LaB 6 ), cerium hexaboride (CeB 6 ), lithium boride, pure boron, or boron nitride. In accordance with an embodiment, the cathode provides boron for the controlled fusion reaction. 
     Embodiments disclosed herein may provide an apparatus for performing a controlled fusion reaction. The apparatus comprises a gas chamber comprising an anode and a cathode enclosed within the gas chamber, and a neutral gas distributed within the gas chamber. The apparatus further comprises an energy source configured to supply energy to the gas chamber. In accordance with an embodiment, the supply of the energy causes to initiate at least: heating of the cathode, and ionization of the neutral gas into protons and electrons. In accordance with an embodiment, the supply of the energy causes to form a conducting channel, due to the ionized neutral gas. In accordance with an embodiment, the supply of the energy causes to form an electron layer outside an outer surface of the cathode, based on a set of thermionically emitted electrons by the heated cathode. In accordance with an embodiment, the supply of the energy causes to accelerate the electrons from the ionized neutral gas towards the cathode, due to a potential associated with the electron layer, to cause the heated cathode to emit a set of secondary electrons. The set of secondary electrons enhance a strength of the electron layer. In accordance with an embodiment, the supply of the energy causes to form an electrostatic potential profile in the conducting channel due to an electron-ion two-stream instability. The electrostatic potential profile has a plurality of dips and a plurality of peaks. The protons from the ionized neutral gas are accelerated towards the cathode at the plurality of potential peaks and bombardment of the accelerated protons into the cathode enables the controlled fusion reaction. 
     The foregoing summary is illustrative only and is not intended to be in any way limiting. 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. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Having thus described example embodiments of the disclosure in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein: 
         FIG.  1    illustrates a diagram of a gas chamber for facilitating a fusion reaction, in accordance with an example embodiment; 
         FIG.  2    shows a flowchart depicting steps of a method for performing a controlled fusion reaction, in accordance with an example embodiment; 
         FIG.  3    illustrates a graph depicting flow of electron at a first potential dip, in accordance with an example embodiment; 
         FIG.  4    illustrates a graph depicting an electrostatic potential profile, in accordance with an example embodiment; 
         FIGS.  5 A- 5 F  illustrates example graphical representation of an energy distribution of accelerated protons, in accordance with an example embodiment; 
         FIGS.  6 A- 6 C  illustrate simulation results corresponding to potential peaks and potential dips, in accordance with an example embodiment; and 
         FIG.  7    illustrates an example flowchart depicting steps of a method for performing a controlled fusion reaction in a gas chamber, in accordance with an example embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. It will be apparent, however, to one skilled in the art that the present disclosure may be practiced without these specific details. In other instances, systems and methods are shown in block diagram form only in order to avoid obscuring the present disclosure. 
     Some embodiments of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all, embodiments of the disclosure are shown. Indeed, various embodiments of the disclosure may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like reference numerals refer to like elements throughout. Also, reference in this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. The appearance of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Further, 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. Moreover, various features are described which may be exhibited by some embodiments and not by others. Similarly, various requirements are described which may be requirements for some embodiments but not for other embodiments. Thus, use of any such terms should not be taken to limit the spirit and scope of embodiments of the present disclosure. 
     The embodiments are described herein for illustrative purposes and are subject to many variations. It is understood that various omissions and substitutions of equivalents are contemplated as circumstances may suggest or render expedient but are intended to cover the application or implementation without departing from the spirit or the scope of the present disclosure. Further, it is to be understood that the phraseology and terminology employed herein are for the purpose of the description and should not be regarded as limiting. Any heading utilized within this description is for convenience only and has no legal or limiting effect. 
     Definitions 
     Throughout the present disclosure, the term “fusion” refers to a nuclear reaction that occurs when the nuclei of two or more atoms combine, whereby the combined nucleus has a mass number less than or equal to that of  62 Ni. By this definition, the combined nucleus is unstable, and will thus release its excess energy by decaying, typically into multiple product nuclei, with the possible inclusion of neutrons. Particularly, the total mass of the products is smaller than the combined mass of the reactants. The difference in the mass is released as energy in accordance with Einstein&#39;s equation E=mc 2 . The energy obtained from fusion reaction is based on differences in nuclear binding energy. As the speed of light in vacuum, ‘c’, is very large, a small amount of missing mass turns into a large amount of energy. Pursuant to present disclosure, the term “fusion” is used interchangeably with “fusion reaction” and “nuclear fusion”. 
     Throughout the present disclosure, the term “aneutronic fusion” refers to a form of fusion reaction in which very little of the released energy from fusion reaction is carried by neutrons. The energy released in the aneutronic fusion reaction is in the form of energetic charged particles, typically protons or alpha particles. Pursuant to embodiments of the present disclosure, the aneutronic fusion reaction may be performed by fusing nuclei of a proton and boron. The proton-boron aneutronic fusion reaction releases its energy in the form of energetic alpha particles without producing neutrons, thereby making the released energy cleaner and easier to use. 
     Throughout the present disclosure, the term “fusion reactor” refers to a device or an apparatus or a system for producing energy (or fusion energy) released in a fusion reaction. The term “fusion reactor” is used interchangeably with “fusion power plant”. 
     Throughout the present disclosure, the terms “ion”, “ionized atom” or “charged particle” refer to an atom or a particle having at least one more electron than a total number of proton(s) or having at least one more proton than a total number of electron(s). 
     Throughout the present disclosure, the terms “neutral species” or “neutrals” refer to atoms or molecules with a neutral charge. In particular, a neutral atom may have a same number of electrons and protons, i.e., corresponding to its atomic number. 
     Throughout the present disclosure, the term “cathode” refers to a negatively charged or grounded electrode. Moreover, the term “anode” refers to a positively charged electrode. Pursuant to present disclosure, the cathode is made of a boron-rich material, for example, Lanthanum hexaboride (LaB 6 ). 
     Throughout the present disclosure, the term “gas chamber” refers to an enclosing for a gas. Pursuant to present disclosure, the gas chamber is filled with a neutral gas and the gas chamber also encloses a cathode and an anode. In this regard, the gas chamber may use electrical energy to facilitate a non-spontaneous ionization of the neutral gas inside the gas chamber. For example, the gas chamber may enclose the neutral gas, the cathode, and the anode for performing a fusion reaction. 
     Throughout the present disclosure, the term “plasma” refers to states of matter dispersed in a chamber. In the plasma, some electrons may have been stripped away from their atoms. As the particles (electrons and ions) in plasma have an electrical charge, the motions and behaviors of plasmas are affected by electrical and magnetic fields. The plasma is created when one or more electrons are torn free from an atom and/or an atom may capture one or more excess electrons. An ionized atom may be missing at least one electron, or the ionized atom may be stripped of electrons entirely leaving behind an atomic nucleus (of one or more protons and usually some neutrons). Atoms that are missing electrons are called “positive ions”. Positive ions may have a positive electrical charge because they have more positively charged protons than negatively charged electrons. Conversely, atoms that have excess of electrons are called “negative ions”. Negative ions may have a negative electrical charge because they have more negatively charged electrons than positively charged protons. The plasma is generally a mix of these positively charged ions or protons, negatively charged ions and electrons. 
     End of Definitions 
     A method and an apparatus are provided herein in accordance with an example embodiment for initiating and maintaining a controlled fusion reaction. The method and the apparatus disclosed herein enables performing aneutronic fusion reaction for generating clean energy. The method and the apparatus disclosed herein enables initiation of the fusion reaction at a substantially lower temperature. The method and the apparatus disclosed herein enables commercial viability of fusion reaction such that produced fusion energy can be used for, for example, obtaining heat, generating electricity, and so forth. The method and the apparatus disclosed herein further enables design and construction of compact fusion reactors within which fusion reaction may occur. Such compact fusion reactors have reduced size and weight, are easy to handle, and have less complex design. 
     The method and the apparatus disclosed herein may provide a gas chamber for performing a fusion reaction. In an example, the gas chamber may include a cathode that may be grounded, an anode and gas dispersed within the gas chamber. In this regard, a voltage, i.e., electric energy is applied to the gas chamber for ionization of the gas within the gas chamber to form plasma and heat the grounded cathode within the gas chamber. Due to the ionization of the gas, a conducting channel may be formed between the cathode and the anode. Further, the heated cathode may cause thermionic emission of a set of thermionically emitted electrons. As a result, an electron layer may be formed outside an outer surface of the cathode. Further, due to a negative potential associated with the electron layer outside the cathode, electrons may be accelerated towards the cathode from the plasma. This may cause the heated cathode to further emit a set of secondary electrons. The set of secondary electrons may strengthen the electron layer by increasing a negative charge density thereof. The strengthened electron layer may cause electron-ion two-stream instability within the gas chamber that creates an electrostatic potential profile within the conducting channel. The electrostatic potential profile comprises a plurality of dips and a plurality of peaks. In this regard, protons (or positive charges) from the ionized neutral gas, i.e., the plasma, are accelerated towards the cathode at the plurality of potential peaks. Subsequently, the accelerated protons may bombard into the cathode to enable the controlled fusion reaction. 
       FIG.  1    illustrates a diagram of the apparatus  100  for initiating and maintaining a fusion reaction, according to embodiments of the present disclosure. According to embodiments of the present disclosure, the fusion reaction is initiated by supplying an electric potential and the fusion reaction is maintained by establishing a conducting channel having an electrostatic potential profile between a cathode and an anode. The conducting channel accelerates protons and electrons to bombard onto the cathode to perform nuclear fusion reactions. 
     The apparatus comprises a gas chamber  102 . The gas chamber  102  comprises one or more chamber walls to form the enclosed gas chamber  102 . In one embodiment, the gas chamber  102  is filled with a neutral gas  104 . In this regard, the neutral gas  104  may be introduced by an inlet to achieve a required pressure. For example, the pressure within the gas chamber  102  may be in a range of 1 Millitorr (mTorr) to about 100 Torr. In accordance with an embodiment, the apparatus  100  further comprises an input power supply  106  for supplying electric energy to the gas chamber  102 . For example, the power supply  106  may be a constant voltage source, a constant current source, or a constant power source. 
     The gas chamber  102  further comprises one or more anodes  108  at one end of the gas chamber  102  and a cathode  110  at another end of the gas chamber  102 . In an example, a distance between the anode  108  and the cathode  110  may be adjustable. In an example, the anode  108  is a filament. For example, the anode  108  may be made of stainless steel, tungsten, copper, tantalum, lanthanum 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 a range of 1 cm to 20 cm. In another example, the cathode  110  has a length in a range of 3 cm to 10 cm. For example, the cathode  110  may be coated with an electron-emitting material. To this end, a reactant of the cathode is boron or ( 11 B). Examples of such boron-rich material may include, but are not limited to, lanthanum hexaboride (LaB 6 ), cerium hexaboride (CeB 6 ), lithium boride (LiB 2 ), pure boron (B), and boron nitride (BN). Pursuant to embodiments of the present disclosure, the cathode  110  may be made of lanthanum hexaboride or LaB 6  slab and may emit electrons when heated. 
     In one embodiment, the input power supply  106  imposes an electric potential across the anode  108  and the cathode  110 . Pursuant to examples of the present disclosure, the gas chamber  102  is imposed with a voltage across the anode  108  and the cathode  110 . In an example, the gas chamber  102  is energized by externally applying the voltage in a range of 10 Volts to 1000 Volts. 
     In an example, the gas chamber  102  is insulated using an insulation material. For example, the insulation material is made of boron nitride (BN) or any other suitable materials which is electrically non-conductive. 
     The gas chamber  102  is filled with the neutral gas  104 . For example, the neutral gas  104  may comprise at least molecular hydrogen (H 2 ) gas. In other example, the neutral gas  104  may be a mixture of H 2  gas along with other gasses. In an example, the neutral gas  104  may comprise the H 2  gas and Argon (Ar) gas. For example, a density of the neutral gas  104  (also referred to as, H 2  gas  104 , hereinafter) may be in a range of 1×10 20  to 1×10 25  m −3 . 
     Pursuant to present disclosure, the cathode  110  may be a LaB 6  slab. In an example, the cathode  110  is grounded and thus has a potential of 0 V. Moreover, the anode  108  is at a given potential, for example, ϕ a  is in a range of 1 V to 1000 V. The LaB 6  cathode  110  is placed in the gas chamber  102  filled with hydrogen gas. In an example, a gas pressure of the hydrogen gas is maintained at about 1-100 Torr, for example using a pressure gauge. To this end, current inside the gas chamber  102  flows from the anode  108  to the LaB 6  cathode  110 . 
     Further, the applied voltage may heat the LaB 6  cathode  110  and ionize the neutral gas  104 . The heated LaB 6  cathode  110  may emit electrons. Subsequently, a conducting channel  112  with a small diameter may be built up between the charged cathode or the LaB 6  cathode  110  and the anode  108 . In an example, a diameter of the conducting channel  112  may be in a range of 0.01 millimeters to 1 millimeter (mm). 
     In accordance with an embodiment, the conducting channel  112  is established between the cathode  110  and the anode  108  for individual protons and electrons configured to overcome the collisions with the hydrogen gas  104  and accelerated by an electric potential to result in a p- 11 B fusion reaction. 
     In one embodiment, the input power supply  106  imposes an electric potential, for example, in a range of 1 V to 1000 V, across the anode  108  and the cathode  110 . 
     Continuing further, the externally imposed electric 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 imposed electric potential leads to the formation of a fully or partially ionized hydrogen gas  104 . In an example, the partially or fully ionized hydrogen gas 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. Pursuant to present disclosure, the positively charged H +  ions correspond to protons of the plasma. For example, the term “H +  ions” and protons may be used interchangeably. In certain cases, the fully or partially ionized plasma may also include other type of positively charged ions, such as Ar +  ions, when the neutral gas  104  is composed of hydrogen gas and Argon gas. In particular, 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 produced in the gas chamber  102  during the ionization of the neutral gas  104 . 
     The electric potential heats the cathode  110  and causes emission of a set of thermionically emitted electrons by the cathode  110 . The set of thermionically emitted electrons forms an electron layer  114  having a negative charge density. For example, the electron layer  114  may be formed near an outer surface of the cathode  110 , i.e., outside at a distance from the cathode  110 . In an example, the set of thermionically emitted electrons forms the electron layer  114  of negative charge density locally within the gas chamber  102  near the cathode  110 . 
     In one embodiment, the electron layer  114  together with the imposed electric potential across the gas chamber  102  leads to the formation of a large electrostatic potential with a dip. For example, the electrostatic potential at the peak and the dip may be in a range of 1 kV to 100 kV. In this regard, the initial potential dip (referred to as a first potential dip, hereinafter) is formed by the presence of the electron layer  114 , wherein the electron layer  114  is formed due to the set of thermionically emitted electrons by the heated cathode  110 . 
     To this end, the positive charges and the negative charges may be accelerated with different velocities leading to an electron-ion two-stream instability, due to the first potential dip. In particular, the negative charges are accelerated away from the electron layer  114  with a first velocity, and the positive charges are accelerated towards the electron layer  114  with a second velocity. In the region between the electron layer  114  and the anode  108 , electron-ion two-stream instability takes place. Further, pursuant to present disclosure, certain amount of the positive charges and the negative charges from the ionized neutral gas  104  are accelerated by electric fields formed due to the electron layer  114 . For example, an electric field may be formed between a region associated with the first potential dip and the cathode  110 . In an example, some amount of the negative charges or electrons from the ionized neutral gas  104  may be accelerated by the electric field between the region associated with the first potential dip and the cathode  110 , such that the negative charges are accelerated towards the cathode  110 . It may be noted that the region associated with the first potential dip, or the region of the electron layer  114 , lies between the anode  108  and the cathode  110 . Such acceleration of the positive charges and the negative charges in different directions and with different velocities may lead to the electron-ion two-stream instability and an electrostatic potential profile with a plurality of dips and a plurality of peaks. 
     In this manner, the ionized neutral gas  104 , specifically negative charges of the ionized neutral gas  104 , may be accelerated by the first potential dip and the electric potential of the electron layer  114  to bombard the cathode  110  to emit another plurality of electrons (referred to as a set of secondary electrons, hereinafter). The set of secondary electrons may further enhance the strength of the electron layer  114 . For example, the set of secondary electrons may increase negative charge density of the electron layer  114 . In an embodiment, the set of secondary emitted electrons lead to the formation of the enhanced electron layer  114  near the cathode  110  that causes formation of the electrostatic potential profile within the conducting channel  112 . 
     To this end, due to the electron-ion two-stream instability, an electrostatic potential profile with a plurality of dips and a plurality of peaks is formed within the conducting channel  112 . 
     In an example, individual electrons and positive and negative ions (collectively referred to as ions, hereinafter) from the ionized neutral gas  104  may overcome the collisions between the electrons and ions from the ionized neutral gas  104  and the molecules of dense non-ionized hydrogen gas  104 . The electrons and ions from the ionized neutral gas  104  may be accelerated to high velocity by an electric potential, within the conducting channel  112 . In an example, the protons and electrons are accelerated for the p- 11 B fusion by the electric potential in the gas chamber  102  due to the electron layer  114 , with relatively dense hydrogen gas density in the gas chamber  104 . For example, the protons of the ionized neutral gas  104  may bombard into the cathode  110 . The bombardment of the accelerated protons into the cathode  110  enables to perform a controlled fusion reaction and produce energy. In particular, the protons may bombard in to the LaB 6  cathode  110 , wherein the cathode  110  provides boron as the fuel for the fusion reaction. In this manner, p- 11 B fusion reaction is performed. In an example, the kinetic energy of each charged particle, such as the proton or H +  ion, bombarding onto the cathode  110  is in a range of 1 keV to 100 keV. 
       FIG.  2    shows a flowchart  200  depicting steps of a method for performing a controlled fusion reaction, according to some embodiments of the present disclosure. The controlled fusion reaction is performed between proton and boron in a gas chamber, such as the gas chamber  102 . As described above, the gas chamber  102  includes the anode  108 , the cathode or LaB 6  cathode  110  and the neutral gas  104  dispersed within the gas chamber  102 . In an example, the neutral gas  104  comprises at least molecular hydrogen (H 2 ) gas. Further, the gas chamber  102  is connected to the input power supply  106 . For example, the input power supply may impose electric potential on the gas chamber  102 . The cathode  110  is grounded. 
     At  202 , an electric potential is imposed across the gas chamber  102  filled with the neutral hydrogen gas  104 . To this end, an initial discharge current due to the electric potential imposed externally on the gas chamber  102  causes ionization of the neutral hydrogen gas  104  and heats the LaB 6  cathode  110 . 
     At step  204  the neutral hydrogen gas  104  is partially ionized due to the electric potential to produce electrons, and ions. In an example, the partially ionized neutral gas  104  generates plasma with positively charged or positive H +  ions, negatively charged or negative H −  ions and electrons. In accordance with other examples, ionization of the neutral hydrogen gas  104  may form the plasma comprising of H +  ions, H −  ions, and electrons (e − ). 
     At  206 , a conducting channel  112  is formed, due to the ionization of the neutral gas  104 . The conducting channel  112  is formed between the anode  108  and the cathode  110 . 
     At  208 , a set of thermionically emitted electrons are emitted by the LaB 6  cathode  110 , due to the heating of the LaB 6  cathode  110 . In particular, the set of thermionically emitted electrons may be emitted from a surface of the LaB 6  cathode  110  into a region outside the cathode  110  and at a distance from the cathode  110 . Within the region outside the cathode  110 , where the set of thermionically emitted electrons accumulate, formation of the 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 thermionically emitted electrons emitted from the surface of the cathode  110  into the region may form a first potential dip within the region. Subsequently, the region of the electron layer  114  may also indicate the region associated with the first potential dip. 
     At  210 , the electron layer  114  together with the imposed electric potential across the gas chamber  102  causes the electrons and the negative ions (or negative charges) from the plasma (ionized neutral gas  104 ) to accelerate towards the cathode  110 . The negative charges bombard into the cathode  110 . 
     At  212 , a first electric field (E 1 ) between the region of the first potential dip and the cathode  110  causes acceleration of negative charges to bombard the LaB 6  cathode  110  to emit a set of secondary electrons. The first electric field may be directed from the cathode  110  towards a center of the electron layer  114  corresponding to the first potential dip. Further, the emitted set of secondary electrons move into the electron layer  114  region to enhance the strength of the electron layer  114 . 
     At  214 , a second electric field (E 2 ) between the anode  108  and the electron layer  114  is formed. The second electric field causes acceleration of the negative charges towards the anode  108  and acceleration of the positive charges towards the electron layer  114 . Such acceleration of the positive charges and the negative charges due to the second electric field leads to electron-ion two-stream instability. 
     Due to the electron-ion two-stream instability, an electrostatic potential profile having a plurality of potential peaks and a plurality of potential dips is formed within the conducting channel  112  in the gas chamber  102 . To this end, the negative charges are accelerated towards the cathode  110 , at each of the plurality of dips, to cause the cathode  110  to emit the set of secondary electrons and enhance the strength of the negative charge density of the electron layer  114 . 
     At  216 , the positive charges and the negative charges are accelerated to cause fusion reaction. In particular, at the plurality of dips of the electrostatic potential profile, the negative charges, such as the electrons and/or H −  ions are accelerated towards the LaB 6  cathode  110 . Such acceleration of the negative charges cause emission of electrons from the LaB 6  cathode  110  causing a potential dip that further causes the electron-ion two stream instability within the gas chamber  102 , as described in detail above. Further, at the plurality of peaks of the electrostatic potential profile, the positive charges, specifically, the protons are accelerated towards the LaB 6  cathode  110 . Such acceleration of the protons towards the LaB 6  cathode  110  may cause the protons to bombard the LaB 6  cathode  110  with high velocity and kinetic energy, thereby causing a fusion reaction between the proton and boron of the LaB 6  cathode  110 . 
     At  218 , a power is generated from the fusion reaction. In an example, an energy in a range of 1 keV-100 keV may be achieved from the acceleration of the proton. Further, an average energy of about 3 MeV may be generated for each  4 He ion formed from the fusion of a proton and a boron atom. Further, the bombardment of the protons on the LaB 6  cathode  110  may produce more sets of secondary electrons to enhance the electron layer  114  and the associated potential dip. 
       FIG.  3    illustrates a graph  300  depicting the flow of electron at a first potential dip, in accordance with some embodiments. The graph  300  represents x 0  at a horizontal axis  302 , wherein the x 0  represents length between the cathode  110  and the anode  108  within the gas chamber  102 . Further, the graph  300  represents φ at a vertical axis  304 , wherein the φ represents electric potential across the gas chamber  102 . As shown, at the dip  306 , the electric potential is substantially low, indicated by φ dip . Further the dip  306  is formed towards left-hand side of the gas chamber  102 , wherein the cathode  110  is positioned at the left-hand side of the gas chamber  102 . To this end, the dip  306  is formed near the cathode  110 , for example, due to the formation of the electron layer  114  due to the thermionically emission of electrons. 
     As described above, an externally imposed electric potential ϕ a  leads to the formation of partially ionized hydrogen gas. As the LaB 6  cathode  110  is heated, the set of thermionically emitted electrons are emitted from a surface of the LaB 6  cathode  110  to form the electron layer  114  having negative charge density. The net negative charge density leads to a large electrostatic potential well near the surface of the LaB 6  cathode  110  due to the potential dip  306 , such as the first potential dip, φ dip . 
     Further, a first electric field (E 1 )  308  is formed near the cathode  110 . For example, the E 1    308  is directed from the cathode  110  towards a center of the electron layer  114 . The E 1    308  may accelerate electrons and/or negatively charged ions, i.e., negative charges from the ionized neutral gas  104  or plasma to bombard the LaB 6  cathode  110 . This may cause the LaB 6  cathode  110  to emit a set of secondary electrons. The set of secondary electrons may enhance the strength of the electron layer  114 , forming a positive feedback loop. For example, the set of secondary electrons may enhance the strength of the potential dip  306 , φ dip . As shown in  FIG.  3   , the first electric field E 1    308  causes acceleration of the negative charges towards a region associated with the first potential dip (φ dip ) to bombard the cathode  110 . 
     Moreover, a second electric field (E 2 )  310  is also formed within the gas chamber  102 . The second electric field E 2    310  causes acceleration of the negative charges away from the region associated with the first potential dip, i.e., towards the anode  108  and acceleration of the positive charges towards the region associated with the first potential dip and towards the cathode  110 . 
     In a region slightly away from the LaB 6  cathode  110  and the electron layer  114 , an electric potential φ increases toward the anode  108  (right-hand side). Due to acceleration of positive charges and negative charges with different flow velocities (V p  and V e , respectively) and in opposite direction, electron-ion two-stream instability may occur in the gas chamber  102 . This electron-ion two-stream instability excites strong waves, leading to forming of an electrostatic potential profile having the plurality of potential dips and the plurality of potential peaks. 
     As shown, at the dip  306 , the electric potential is substantially low, indicated by φ dip . Further the dip  306  is formed towards left-hand side of the gas chamber  102 , wherein the cathode  110  is positioned at the left-hand side of the gas chamber  102 . To this end, the dip  306  is formed near the cathode  110 , for example, due to the formation of the electron layer  114  due to thermionic emission of the set of thermionically emitted electrons. 
       FIG.  4    illustrates a graph  400  depicting an electrostatic potential profile, in accordance with some embodiments. The graph  400  represents x 0  at a horizontal axis  402 , wherein the x 0  represents distance between the cathode  110  and the anode  108  within the gas chamber  102 . Further, the graph  400  represents φ at a vertical axis  404 , wherein the φ represents electric potential across the gas chamber  102 . 
     The electrostatic potential profile includes a plurality of dips, depicted as dips  406 A,  406 B and  406 C. The electrostatic potential profile also includes a plurality of peaks, depicted as peaks  408 A and  408 B. In particular, the electrostatic potential profile is initialized with a dip, such as the first potential dip. From the peak, positive charges may bombard on the LaB 6  cathode  110  to carry out the proton-Boron (p- 11 B) fusion reaction. 
     In particular, the negative charges from the ionized neutral gas  104  are accelerated towards the cathode  110 , at some of the plurality of dips  406 A,  406 B and  406 C. The dips, at which the negative charges are accelerated towards the cathode  110 , may cause the cathode  110  to emit the set of secondary electrons. For example, the dips are formed near the cathode  110  due to the electron layer  114  formed outside the cathode  110 . 
     Further, the positive charges from the ionized neutral gas  104  are accelerated towards the cathode  110 , at some of the plurality of peaks  408 A and  408 B. The peaks  408 , at which the positive charges are accelerated towards the cathode  110 , cause positive charges to bombard into the cathode  110 . For example, the bombardment of the accelerated protons and the positive ions (such as Ar +  ions) (i.e., the positive charges) into the cathode  110  causes a controlled fusion reaction and generation of a power from the fusion reaction. 
     To ascertain the output of the proton-boron fusion reaction, certain outcomes of the fusion reaction performed in the gas chamber  102  may be determined. Such outcomes may include, for example, a proton-boron fusion cross section, a transportation of protons and electrons in the relatively dense neutral hydrogen gas, and an estimation of a power gain. As may be understood, the accelerated protons may cause the proton-Boron fusion. To this end, calculation of output for the p- 11 B fusion may be performed based on a simulation of the p- 11 B fusion reaction. 
     In an example, the fusion cross section is a function of a center-of-mass energy (E cm ) for the proton-boron (p-11B) fusion reaction. In particular, the effect of the center-of-mass energy is particularly significant in low-energy region. For example, when the center-of-mass energy is varied from about 1 keV to about 40 keV, the fusion cross section is increased by about 50 orders of magnitude. 
     The formation of the electron layer  114  leads to a strong electric field, which accelerates protons. During the acceleration, proton-neutral collisions occur, i.e., collision of proton with atoms of the neutral hydrogen gas  104 . To this end, a fraction of the protons cannot be accelerated to the peak energy as they reach the LaB 6  cathode  110  target. Further, the solid boron compound is also used as a reactant for the p- 11 B fusion process. In this regard, based on the proton-neutral collision effect, an acceleration and collision process to obtain the energy distributions of protons reaching the LaB 6  cathode target  110  is identified. 
     A series of calculations is conducted. The electric potential difference is assumed to be 50 kV, and a length of an acceleration path is assumed to be 1 mm or 10 mm in the calculations. High-density neutrals gas (molecular hydrogen) is uniformly filled in a space. The proton transportation through the high-density molecular hydrogen with a strong electric field is simulated by Geant4 (Geometry and Tracking software), which is a Monte Carlo toolkit used for the simulation of the transportation of particles through matter. As may be understood, a proton with an initial energy ∈ in  is injected into the hydrogen gas and undergoes acceleration and collisions, and its final energy ∈ f  is recorded as it reaches the other side. The simulation result of the proton transportation through the high-density molecular hydrogen is described in detail with the following  FIG.  7   . The manner in which the proton transportation is simulated in  FIG.  7    is only exemplary and should not be construed as a limitation. In other embodiments of the present disclosure, the proton transportation may be simulated under different conditions, for example, with different values for the electric potential difference, the length for the acceleration path, and so forth. 
       FIGS.  5 A- 5 F  illustrates example graphical representation of an energy distribution of protons colliding onto the cathode  110  target after travelling through the acceleration path in the calculations, according to some embodiments of the present disclosure. The graphs  500 A,  500 B,  500 C,  500 D,  500 E, and  500 F of the  FIGS.  5 A,  5 B,  5 C,  5 D,  5 E, and  5 F , respectively, represent a corresponding final energy ∈ f  at a horizontal axis, wherein the ∈ f  represents final energy of the accelerated protons as they collide onto the cathode  110  target after travelling through the acceleration path in the calculations. Further, the graphs  500 A,  500 B,  500 C,  500 D,  500 E, and  500 F represents counts at a vertical axis, wherein the counts represents a number of protons colliding onto the target after travelling through the acceleration path in the calculations. 
     To this end, in  FIGS.  5 A- 5 F  show an energy distribution of outgoing protons for different incident energies ∈ in =0.01, 0.1, and 1 keV with acceleration path lengths of 1 mm and 10 mm. The density of neutral hydrogen gas is assumed to be 3.3×10 23  m −3  and the temperature is assumed to be in a range of 1000 K to 5000 K in the calculations. A final energy  ∈ f    and standard deviation S ∈ f    of the accelerated protons are determined. From  FIG.  5 A- 5 F , it may be concluded that the energy loss from collisions along the acceleration path is insignificant. 
     The multi-fluid simulation is studied along an x-axis to study the formation of the electrostatic potential profile in the conducting channel  112  in the gas chamber  102 . The electrostatic potential profile has a plurality of potential peaks and a plurality of potential dips. To this end, the protons or the H +  ions from the plasma are accelerated through the conducting channel  112  at the plurality of peaks to cause the p- 11 B fusion reaction. 
     In an example, the system length x 0  or the length corresponding to the conducting channel  112  within the gas chamber  102  may be in a range of 1 mm to 10 mm. Pursuant to the present example, the system length x 0  is given by x 0 =2 mm. The initial plasma temperature (T) is assumed to be about 4000 K. Since the ionization ratio within the gas chamber  102  is very small, the neutral gas density n n  is assumed to be constant in the simulation. 
     Since the neutral fluid is affected mainly through the collisional effect, the proton-neutral collision frequency v pn  is the order of 10 9  Hertz (Hz). Further, the proton to neutral mass density ratio is 4×10 −4 . In an example, when the plasma collides with the neutral fluid, the plasma may ionize the neutral fluid. 
     A relation m p n p v pn =m n n n v np  gives that the neutral to proton collision frequency is v np =m p n p v pn /m n n n . For example, the neutral-proton collision frequency is in the order of 10 5 -10 6  Hz. As a result, in a time scale of nanoseconds, the neutral fluid can be assumed to be immobile. 
     The incident electrons collide into the LaB 6  cathode  110  boundary and are bounced back due to the bounded boundary. Thermionically emitted electrons and secondary electrons are considered in the simulation system. Due to the increase of boundary electron density or the increased strength of the electron layer  114  due to the set of secondary electrons, an increase of electric potential at the electron layer  114  and electric field is observed. The electric field leads to further heating and ionization. As a result, the ion density as well as ionization ratio in the neutral gas  104  increases. 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 two-stream instability may occur. As a result, an electrostatic potential profile of plurality of peaks and plurality of dips is formed within the conducting channel  112 . In this manner, the plurality of potential peaks may be achieved where the protons of the ionized neutral gas  104  or plasma are accelerated to bombard onto the LaB 6  cathode  110  to cause fusion reactions. 
       FIGS.  6 A- 6 C  illustrate simulation results corresponding to potential peaks and potential dips, according to some embodiments of the present disclosure. In  FIGS.  600 A,  600 B and  600 C , the simulation results are shown at t=40.0 nanoseconds (ns), t=41.0 ns and t=42.3 ns. 
     During the operation in the simulation, the boundary electron density or negative charge density outside the LaB 6  cathode  110  due to the enhanced electron layer increases approximately to 10 23  m −3 . The increase in the boundary electron density with time is due to continuous electron emission from LaB 6  cathode  110 , for example, due to emission of the thermionically emitted electrons and the set of secondary electrons. It may be noted that although the present disclosure only describes emission of the set of thermionically emitted electrons and the set of secondary electrons from the LaB 6  cathode  110 , however, this should not be construed as a limitation. To this end, the LaB 6  cathode  110  may emit electrons continuously. Moreover, electrons forming the set of thermionically emitted electrons and electrons forming the set of secondary electrons, or other set of electrons emitted from the LaB 6  cathode  110 , are not mutually exclusive. In an example, certain electrons emitted from the LaB 6  cathode  110  may be incident back to the LaB 6  cathode  110  at the plurality of dips and the LaB 6  cathode  110  may further re-emit electrons. 
     Around the electron layer  114 , an electric potential dip is formed due to the high-density electron layer  114 . For example, due to enhanced strength of the electron layer  114 , the negative charge density is, for example, in a range of 10 to 100 kilovolts (kV), that may be indicated by the electrostatic potential profile. 
     In an example, the set of thermionically emitted electrons from thermionic emission from the LaB 6  cathode  110  and the set of secondary electrons lead to the formation of the electron layer  114  near the cathode  110 , for example, at x≈0. Due to the electron layer  114 , an electric potential ϕ has a sharp decrease from ϕ(x=0) to ϕ dip &lt;0. The electric potential ϕ then increases slowly towards the anode  108 , for example, ϕ(x=x 0 )=ϕ a  V at the anode  108 . The electric field in a region from the anode  108  towards the electron layer  114  and may be negative (E x &lt;0). The negative electric field in the gas chamber  102  may accelerate electrons at high speed U e ≈2.4×10 7  m/s towards the anode  108 , while positive charges are accelerated towards the cathode  110  with small velocity due to large mass of the positive charges. The positive charges and the negative charges are accelerated in opposite directions with different velocities, which leads to the electron-ion two-stream instability. 
     In the electrostatic potential profile, large amplitude of waves is formed due to this instability. For example, the amplitude of the waves may be in tens of kilovolts. The number density and velocity profiles of the positive charges and the negative charges also show such pattern of large amplitude of electrostatic waves. 
     The  FIGS.  6 A,  6 B and  6 C  illustrate plot  602 A,  602 B and  602 C, respectively. The plots  602 A,  602 B and  602 C show change in electron density (n e ) and/or ion density (n i ) over system length x 0 , at different times, for example, at 40.0 ns, 41.0 ns and 42.3 ns, respectively. Further,  FIGS.  6 A,  6 B and  6 C  illustrate plot  604 A,  604 B and  604 C, respectively, illustrating change in flow velocity of electrons (V e ) over the system length (x 0 ), at time, for example, at 40.0 ns, 41.0 ns and 42.3 ns, respectively.  FIGS.  6 A,  6 B and  6 C  also illustrate plot  606 A,  606 B and  606 C, respectively, illustrating change in flow velocity of protons (V i ) over the system length (x 0 ), at time, for example, at 40.0 ns, 41.0 ns and 42.3 ns, respectively.  FIGS.  10 A,  10 B and  10 C  also illustrate a plot  608 A,  608 B and  608 C, respectively, illustrating change in electric potential (ϕ) over the system length (x 0 ), at different times, for example, at 40.0 ns, 41.0 ns and 42.3 ns, respectively. 
     From the plots  608 A,  608 B and  608 C, an electric potential at a peak is observed to reach about 30 kV, whereas electric potential at a dip is observed to reach about −10 kV. 
     The formation of negative electric potential dips may accelerate electrons towards the LaB 6  cathode  110 , and formation of positive electric potential peaks may accelerate protons towards the LaB 6  cathode  110 . Bombardment of the LaB 6  cathode  110  by the protons leads to p- 11 B fusion. The fusion emits ˜3 MeV helium (He) in average, which may further generate protons through collisions. These protons bombard the LaB 6  cathode  110  and generate more helium whereby ensure the continuity of fusion reactions, thereby forming a positive feedback loop. 
       FIG.  7    illustrates an example flowchart depicting steps of a method for performing a controlled fusion reaction in the gas chamber  102 , according to some example embodiments. 
     At  702 , a neutral gas  104  is distributed within the gas chamber  102 . The gas chamber  102  comprises the anode  108 , the cathode  110  and the neutral gas  104  dispersed within the gas chamber  102 . In an example, the cathode  110  comprises a boron rich material, such as lanthanum hexaboride (LaB 6 ), cerium hexaboride (CeB 6 ), lithium boride, pure boron, boron nitride (BN), or a combination thereof. The cathode  110  provides boron for the controlled fusion reaction. In an example, the neutral gas  104  comprises at least molecular hydrogen (H 2 ) gas. For example, a density of the neutral gas  104  is in a range of 1×10 20  m −3  to 1×10 25  m −3 . 
     At  704 , energy is supplied to the gas chamber  102 . In particular, an external electric potential is applied to the anode  108  and the cathode  110  in the gas chamber  102 . The external electric potential initiates heating of the cathode  110 , and ionization of the neutral gas  104  into protons and electrons. In an example, an initial discharge current due to the external electric potential may heat the cathode  110  and ionize the neutral gas  104 . In some cases, the neutral gas  104  may be weakly ionized. In such a case, the neutral gas  104  may be ionized into the protons or the positive ions (H +  ions), the electrons, and the negative ions (H −  ions). In an example, the gas chamber  102  is energized by externally applying a voltage in a range of 10 V to 1000 V. 
     In certain cases, a heating source may be applied to the gas chamber  102  to perform the heating of the cathode  110  and the ionization of the neutral gas  104  into the protons and the electrons. For example, the heating source may be a superconducting magnet source, a permanent magnet source, an electromagnet source, a radiofrequency (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 , the conducting channel  112  is formed between the anode  108  and the cathode  110 . The conducting channel  112  is formed due to the ionization of the neutral gas  104 . In an example, a diameter of the conducting channel  112  is in a range of 0.01 mm to 1 mm. 
     At  708 , the electron layer  114  is formed outside an outer surface of the cathode  110 . The electron layer  114  is formed due to emission of a set of thermionically emitted electrons by the heated cathode  110 . In an example, the electron layer  114  causes formation of a first potential dip, due to the set of thermionically emitted electrons emitted by the heated cathode  110 . For example, the set of thermionically emitted electrons may be emitted from the surface of the cathode  110  into a region associated with the first potential dip. Subsequently, the electron layer  114  having a negative charge density is formed locally outside the surface of the cathode  110 . 
     At  710 , the electrons from the ionized neutral gas  104  are accelerated towards the cathode  110 , due to a potential associated with the electron layer  114 . The electrons accelerated towards the cathode  110  may bombard 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 . As a result, the set of secondary electrons enhances strength of the electron layer  114 . 
     In particular, the electrons are accelerated between a region associated with the first potential dip and the cathode  110  to bombard the cathode  110 . The region lies between the anode  108  and the cathode  110 . The bombardment of the accelerated electrons at the cathode  110  causes emission of the set of secondary electrons. Further, the electron layer  114  is strengthened at the first potential dip, due to the set of secondary electrons emitted by the cathode  110 . 
     In an example, the region of the first potential dip outside the cathode  110  of the gas chamber  102  is formed due to the enhanced strength of the electron layer  114 . The region of the first potential dip has a minimum potential value at a center of the electron layer  114 . Moreover, a first electric field is directed from the cathode  110  towards the center of the electron layer  114 , and a second electric field is directed from the anode  108  towards the center of the electron layer  114 . 
     At  712 , an electrostatic potential profile is formed within the conducting channel  112 , due to an electron-ion two-stream instability. The electrostatic potential profile may comprise a plurality of dips and a plurality of peaks, In an example, the formation of the electrostatic potential profile within the conducting channel  112  is associated with the formation of the enhanced electron layer  114  and the strengthened first potential dip. 
     For example, negative charges or electrons and positive charges or protons are accelerated due to the enhanced strength of the electron layer  114 . In an example, the negative charges may include the electrons and the negative ions (for example, H −  ions), and the positive charges may include the protons (for example, H +  ions) and the positive ions (for example, Ar +  ions). Due to the strengthened first potential dip, the negative charges may be accelerated from the cathode  110  towards the anode  108  and the positive charges are accelerated from the anode  108  towards the cathode  110 . To this end, the positive charges and the negative charges are accelerated in opposite directions and have a velocity difference. The velocity difference between the positive charges and the negative charges and opposite direction of flow of the positive charges and the negative charges may cause the electron-ion two-stream instability within the gas chamber  102 . 
     In this regard, the negative charges or electrons are accelerated towards the cathode  110 , at each of the plurality of dips, to cause the cathode  110  to emit the set of secondary electrons. Further, the positive charges or protons are accelerated towards the cathode  110  at each of the plurality of peaks, to bombard into the cathode  110 . The bombardment of the accelerated protons and the positive ions (H +  ions) into the cathode  110  enables the controlled fusion reaction and causes generation of power. In an example, the protons and the positive ions are accelerated to bombard the cathode  110  with a high kinetic energy. For example, the kinetic energy of each charged particle (proton or positive ion) bombarding into the cathode  110  is in a range of 1 keV to 100 keV. 
     Many modifications and other embodiments of the disclosures set forth herein will come to mind to one skilled in the art to which these disclosures pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the disclosures are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Moreover, although the foregoing descriptions and the associated drawings describe example embodiments in the context of certain example combinations of elements and/or functions, it should be appreciated that different combinations of elements and/or functions may be provided by alternative embodiments without departing from the scope of the appended claims. In this regard, for example, different combinations of elements and/or functions than those explicitly described above are also contemplated as may be set forth in some of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.