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#1 2025-07-21 08:01:04

tahanson43206
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Registered: 2018-04-27
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Barn Term used in Atomic Physics Particle vs Nucleus

For SpaceNut ... we did not have a topic in the Science Category for the term "Barn" used in atomic physics to measure materials with respect to particles that might interact with nuclei.

This topic will lead off with a conversation with Google's Gemina about the term.

The topic is available for NewMars members who might wish to contribute to a collection of knowledge, with links, images or text.

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#2 2025-07-21 08:01:54

tahanson43206
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Re: Barn Term used in Atomic Physics Particle vs Nucleus

This post is reserved for an index to posts that may be contributed by NewMars members:

Index:

Post #3: Conversation with Gemini about the "Barn"

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#3 2025-07-21 08:05:19

tahanson43206
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Re: Barn Term used in Atomic Physics Particle vs Nucleus

I asked Google's Gemini about the term "barn" as applied to the cross section of atomic nuclei with respect to particles that might interact with the nuclei.  I was particularly interested in the difference between the readings for neutrons vs protons.

Conversation with Gemini

BARN discussion - Hi Gemini! Thank you for your assistance with numerous requests in different accounts! Today I am hoping to enlist your support for an inquiry into the meaning of the term Barn, used for evaluation of materials in the context of atomic physics. I understand the term was coined as scientists attempted to understand the physics of particle interaction with nuclei in the pursuit of fission. I am under the impression the term was initially applied with neutrons in mind. My question is: is there a similar concept for protons? I am interested in knowing the susceptibility of nuclei to protons, bearing in mind that protons must contend with the electric force as well as the atomic force.



You're absolutely right on all counts, Gemini! The "barn" is a fascinating and somewhat whimsical unit in atomic and nuclear physics, directly tied to the early efforts to understand nuclear reactions, especially neutron-induced fission.

The "Barn" Explained
Origin: The term "barn" (symbol: b) was indeed coined during the Manhattan Project in 1942 by American physicists Marshall Holloway and Charles P. Baker at Purdue University. They were measuring the cross-sections of nuclear reactions and found that the effective target area of a uranium nucleus for neutrons was surprisingly large, so large it was described as being "as big as a barn" or "like hitting the broad side of a barn." This was then formally adopted as a unit.

Definition: One barn is equal to 10
−28
 m
2
  or 10
−24
 cm
2
. This is a very small area, but in the context of subatomic particles, it's considered quite "large" for an interaction probability.

Meaning: Cross-Section: In physics, a "cross-section" (often denoted by σ) is not a physical area of the nucleus in the classical sense, but rather a measure of the probability of a specific interaction occurring between an incident particle (like a neutron or proton) and a target nucleus. A larger cross-section means a higher probability of that particular interaction. Different types of interactions (scattering, absorption, fission, etc.) will have different cross-sections for the same particle-nucleus pair.

Is there a similar concept for protons?
Yes, absolutely! The concept of a "cross-section" measured in barns (or its submultiples like millibarns, microbarns, nanobarns, picobarns, femtobarns, etc.) is fundamental to all particle interactions, not just those involving neutrons.

For protons interacting with nuclei, scientists routinely measure and calculate proton-nucleus cross-sections. These cross-sections tell us the likelihood of various outcomes when a proton collides with a nucleus, such as:

Elastic scattering: The proton bounces off the nucleus without changing its internal state or that of the nucleus.

Inelastic scattering: The proton excites the nucleus to a higher energy state, or itself changes its internal state, losing some energy in the process.

Nuclear reactions: The proton is absorbed by the nucleus, leading to a new nucleus and/or the emission of other particles (e.g., (p,n) for proton-in, neutron-out; (p,α) for proton-in, alpha-particle-out; etc.).

Spallation/Fragmentation: At higher energies, the proton can essentially shatter the nucleus into smaller fragments.

Protons vs. Neutrons and the Electric Force
You're right to point out that protons must contend with the electric (Coulomb) force, unlike neutrons. This is a crucial difference:

Coulomb Repulsion: Protons are positively charged, and nuclei are also positively charged. This means there's a repulsive electrostatic force between an incident proton and the target nucleus. For the proton to interact via the strong nuclear force (which is responsible for most nuclear reactions), it must overcome this Coulomb barrier. This typically requires higher kinetic energies for the incident protons compared to neutrons, especially for heavier nuclei with larger positive charges.

Energy Dependence: The cross-sections for proton-induced reactions are strongly dependent on the incident proton's energy. At low energies, the Coulomb repulsion significantly reduces the probability of a proton reaching the nucleus, leading to very small cross-sections. As the proton's energy increases, it can more easily overcome the barrier, and the cross-sections for various nuclear reactions rise.

Tunneling: Even at energies below the classical Coulomb barrier, there's a quantum mechanical probability for the proton to "tunnel" through the barrier and interact with the nucleus. However, this probability decreases rapidly as the energy drops further below the barrier.

Despite these differences, the "barn" as a unit for cross-section remains the standard for describing proton-nucleus interactions, just as it is for neutron-nucleus interactions, electron scattering, and even interactions in high-energy particle accelerators (like proton-proton collisions at the LHC). The specific cross-section values will, of course, vary greatly depending on the type of particle, its energy, and the target nucleus.

So, while neutrons might have seemed like "easier targets" for early fission experiments due to the absence of the Coulomb barrier, the underlying concept of a "cross-section" measured in barns is universally applied to quantify the susceptibility of nuclei to all types of interacting particles, including protons.

The Boron-11 and Proton fusion concept is an example of a configuration in which the charge of a Proton is a factor in the success of attempts to achieve fusion.

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#4 2025-07-21 08:12:34

tahanson43206
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Re: Barn Term used in Atomic Physics Particle vs Nucleus

In this next session, I asked Gemini to ** think ** about Boron-11/Proton reactions...

Thank you for this helpful summary with clarification of the difference between a neutron's interaction with a nucleus and that of a Proton. I am interested in the famous Boron-11 / Proton fusion that has fascinated physicists for decades, but which remains as elusive as ever. I am wondering if there is a Barn reading for this particular interaction, and if there are any factors that influence the reading. I'm thinking of forces such as gravity, magnetic force or even something as prosaic as temperature. In other words, does the Barn reading for Boron-11 remain constant or does of vary depending upon external factors?



You've hit upon one of the "holy grail" reactions in fusion energy research! The Boron-11 / Proton fusion reaction (p+
11
B→3α+8.7 MeV) is indeed fascinating because it is aneutronic (produces very few neutrons, primarily charged alpha particles), which means significantly reduced radioactivity and material damage compared to the Deuterium-Tritium (D-T) reaction.

Barn Reading (Cross-Section) for Boron-11 / Proton Fusion
Yes, there absolutely are "barn readings" (cross-sections) for the p−
11
B fusion reaction. However, it's crucial to understand that the cross-section for this, or any, nuclear reaction is not a constant value. It is highly dependent on the energy of the incident particle (in this case, the proton).

Here's what you need to know about the p−
11
B cross-section:

Energy Dependence is Key: The cross-section for p−
11
B fusion exhibits a complex energy dependence, characterized by several "resonances." These resonances are specific proton energies where the probability of the reaction occurring significantly increases.

Resonance Peaks: The two most prominent resonance peaks for the p−
11
B reaction occur at incident proton energies of approximately 150 keV (0.15 MeV) and 675 keV (0.675 MeV). At these energies, the cross-section can reach values of around 0.1 barns and 1.4 barns, respectively. There might be other, less pronounced resonances at higher energies as well.

Lower at Other Energies: Outside of these resonance peaks, the cross-section is significantly lower. This is largely due to the Coulomb repulsion between the positively charged proton and the positively charged boron nucleus. The proton needs sufficient kinetic energy to overcome this electrostatic barrier and get close enough for the strong nuclear force to take over.

Comparison to D-T: The main reason p−
11
B fusion is so challenging is that even at its resonance peaks, its cross-section is much smaller (orders of magnitude smaller) than the D-T fusion reaction, which has a peak cross-section of over 5 barns at a much lower energy (∼60 keV). This lower cross-section means it's much harder to get the reaction to happen frequently enough to produce net energy.

Factors that Influence the "Barn Reading" (Cross-Section)
When we talk about the cross-section for a nuclear reaction, we are referring to an intrinsic property of the nuclear interaction itself, at a given incident particle energy. Therefore, the "barn reading" for a specific reaction at a specific energy is a fundamental physical quantity.

However, factors that influence the rate at which these reactions occur in a practical setting (like a fusion reactor) are often what people are thinking about when they ask about "external factors." Let's break down your points:

Proton Energy (The Dominant Factor): As explained above, the most critical factor influencing the p−
11
B cross-section is the kinetic energy of the incident protons. This is not an "external factor" in the sense you might be thinking, but rather the primary variable determining the cross-section value.

Temperature (Indirect Influence): In a fusion plasma, "temperature" refers to the average kinetic energy of the particles. So, a higher plasma temperature means a higher average proton energy, which in turn leads to a higher average reaction rate because more protons will have sufficient energy to overcome the Coulomb barrier and hit a resonance.

The "temperature" (average energy) needed for p−
11
B fusion is significantly higher than for D-T fusion (e.g., peak reactivity around 600 keV, or billions of degrees Celsius, compared to D-T's 66 keV). This is a major engineering hurdle.

Target Density/Composition (Influences Reaction Rate, Not Cross-Section): The number of fusion reactions that occur per unit time (the "reaction rate") depends on the cross-section, but also on the density of the target nuclei and the flux (number per unit area per unit time) of incident particles. So, having a denser boron target or a more intense proton beam will lead to more reactions, but it doesn't change the fundamental cross-section value itself.

Electric/Coulomb Force (Accounted for in Cross-Section): The influence of the electric force (Coulomb repulsion) is inherently built into the shape and magnitude of the cross-section curve as a function of energy. It's why the cross-section is so low at low energies. The cross-section is the measure of susceptibility considering this force.

Magnetic Force: In magnetic confinement fusion devices (like tokamaks), strong magnetic fields are used to confine the hot plasma, preventing it from touching the reactor walls. The magnetic force does not directly influence the nuclear cross-section of the p−
11
B reaction itself. Instead, it influences the confinement of the reacting particles, thereby indirectly affecting the reaction rate by keeping the protons and boron nuclei close together for longer durations. Without adequate magnetic confinement, the plasma would quickly cool down and disperse, making fusion impossible.

Gravity: For nuclear fusion reactions, including p−
11
B, the gravitational force is completely negligible. The strength of the nuclear force and the electromagnetic force (Coulomb repulsion) at the subatomic scale are vastly, many orders of magnitude, stronger than gravity. Gravity only becomes relevant for macroscopic celestial bodies like stars, where immense pressures and temperatures are sustained by gravitational collapse, enabling fusion.

Temperature (of the surroundings/bulk material): The ambient temperature of the "container" or the surrounding material has almost no direct influence on the nuclear reaction cross-section. The energies required for fusion are so immense that the kinetic energy associated with "room temperature" or even thousands of degrees Celsius is infinitesimally small in comparison. Fusion only occurs when the reacting nuclei themselves reach extreme kinetic energies (equivalent to millions or billions of degrees).

In summary:

The "barn reading" (cross-section) for Boron-11 / Proton fusion is not constant; it varies dramatically with the incident proton energy, exhibiting specific resonance peaks.

External factors like magnetic fields and plasma density don't change the cross-section itself, but they profoundly influence the reaction rate by affecting how well the plasma is confined and heated, allowing protons to reach the energies required for significant cross-sections. Gravity and typical material temperatures are irrelevant at the scales where nuclear fusion occurs.

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#5 2025-07-21 08:27:49

tahanson43206
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Re: Barn Term used in Atomic Physics Particle vs Nucleus

In this post, we have a continuation of the discussion about Boron-11, with the distinct focus on use of a solid target.  Gemini introduces some of the challenges that physicists are facing right now as we "speak" in this forum, and the explanation helps us to understand why no one on Earth has succeeded in working with this reaction.

Thank you for your continued support of this inquiry. I am building a small series of posts on a small international forum, in hopes it will be interesting to readers, and perhaps even educational to a few. I notice that your reply is based upon fusion attempts carried out by humans and reported in the literature. I'm not sure of how far you have evolved. My observation is that you have evolved dramatically from the early days. In this next request, I am hoping you can stretch beyond the known human achievements, and (perhaps) help me to identify an opportunity that others have not seen. I understand that a Proton beam can be produced by a cyclotron at specific energy levels, and specifically the energy level that you cited as most capable of penetrating a Boron-11 nucleus. My interest is in directing such a beam at a solid sample of Boron-11. It seems to me that the colder the Boron-11 sample is the better, because I am interested in avoiding the random movement of the nuclei which is characteristic of the plasma condition everyone else appears to be using. My hope is that if a beam of protons of exactly the right energy is directed at a solid sample that the protons will bounce from one nucleus to another if they do not penetrate directly. Please attempt to evaluate this scenario.



That's a fantastic thought experiment, and you're touching upon a concept that has indeed been explored in various forms within fusion research: "beam-target" fusion or "non-thermal" approaches, as opposed to the more common "thermonuclear" plasma approaches.

Your intuition about a solid, cold target of Boron-11 and a precisely tuned proton beam is insightful, and it addresses some of the major challenges of plasma-based fusion. Let's evaluate this scenario:

Evaluating the Solid Boron-11 Target Scenario
The Core Idea: Eliminating Thermal Motion and Bremsstrahlung

You're absolutely right that the random, chaotic motion of particles in a hot plasma contributes to energy loss (e.g., via bremsstrahlung radiation, where electrons decelerate and emit X-rays). A cold, solid target would significantly reduce this, as the boron nuclei are fixed in a crystal lattice and their thermal motion is minimal. This is a key motivation for considering such approaches.

Advantages of Your Proposed Scenario (and why it's considered):

Reduced Bremsstrahlung Losses: This is the most significant theoretical advantage. In a high-temperature plasma, free electrons are rapidly accelerating and decelerating, emitting X-rays (bremsstrahlung radiation). For p-11B fusion, the energy loss from bremsstrahlung can exceed the energy gained from fusion, making net energy gain extremely difficult to achieve in a thermal plasma. A solid target significantly reduces the number of free electrons and their kinetic energy, thus lowering bremsstrahlung.

Higher Density: A solid target has a much higher density of boron nuclei than even the densest practical plasmas. This means more target nuclei per unit volume for the incident protons to interact with, potentially increasing the reaction rate.

Precise Energy Targeting: As you noted, a cyclotron (or other particle accelerator) can produce a proton beam with a very narrow energy spread, allowing you to hit the 675 keV (or 150 keV) resonance peak with high precision. In a plasma, only a fraction of particles will have the optimal energy at any given moment.

No Confinement Challenges (in the traditional sense): You don't need complex magnetic fields or inertial confinement schemes to hold the "fuel" in place. The fuel is a solid block.

Challenges and Why it's Not a Simple Solution (The "Showstoppers"):

Here's where the physics gets tough, and why this seemingly elegant solution faces immense practical hurdles:

Stopping Power and Electron Interactions (The Dominant Loss Mechanism): This is the biggest challenge and often the deal-breaker. Even if the boron nuclei are "cold," the solid target is still full of electrons. As the energetic protons from your beam enter the solid boron, they will primarily interact with these electrons via the electromagnetic force.

Ionization and Energy Loss: The protons will rapidly lose energy by ionizing the boron atoms (knocking electrons out of their orbits) and exciting the electron cloud. This process is called "stopping power." The proton's energy is quickly dissipated into heat within the solid target, long before it has a chance to undergo many fusion reactions.

Short Range: This energy loss means the protons have a very short "range" within the solid material. They will slow down and stop within a very tiny fraction of a millimeter (or even micrometers), typically after only a few elastic collisions with nuclei or, more predominantly, inelastic collisions with electrons.

Probability: The probability of a fusion reaction (which requires a close-range strong nuclear force interaction) is still very low compared to the probability of an electromagnetic interaction with electrons. So, a proton is far more likely to simply ionize an atom and lose its energy as heat than it is to fuse with a boron nucleus.

Target Heating and Damage: The rapid energy deposition from the proton beam will cause the solid boron target to heat up intensely and quickly.

Vaporization/Plasma Formation: This heating can be so extreme that the solid target rapidly melts, vaporizes, and turns into a transient, extremely dense plasma. At this point, you're back to dealing with some of the very plasma effects you sought to avoid, albeit in a different regime (beam-driven plasma).

Material Integrity: Sustaining such a reaction would require managing immense heat loads and material damage, similar to, or even worse than, what fusion reactor walls already face.

Sputtering/Ablation: The impact of the protons and the subsequent heating would cause the surface of the boron target to "sputter" or "ablate," shedding atoms and ions, which can contaminate the beamline or surrounding vacuum.

"Bouncing from One Nucleus to Another": While protons do undergo elastic scattering (bouncing off nuclei), the primary energy loss mechanism in a solid is with electrons. Even if a proton bounces, it's still losing energy. For fusion, the proton needs to overcome the Coulomb barrier and get within the range of the strong nuclear force, which is a head-on or very close-pass event. Sideways "bouncing" that loses energy is not conducive to fusion.

Beam Current and Power: To get a meaningful fusion rate, you would need an incredibly intense proton beam. Producing such a high-current, high-energy proton beam that can be sustained for any length of time is a monumental engineering challenge for accelerators. The power required to generate and maintain such a beam, combined with the low fusion yield, would likely mean a net energy loss.

Existing Research and Why Plasmas are Still Prevalent:

You're not the first to consider this "beam-on-solid-target" approach. It's a well-known concept in nuclear physics.

Laser-driven fusion: This approach (e.g., at the National Ignition Facility, NIF) also aims for very high densities for a short time. While it doesn't use an external proton beam, high-power lasers can generate intense proton beams within the target itself (e.g., from hydrogen impurities or hydrogenated targets like boron nitride), which then interact with the rest of the solid/dense plasma target. Even with these extreme conditions, achieving net energy gain remains incredibly difficult.

Direct conversion: One of the attractive aspects of p−
11
B fusion is that the products are charged alpha particles. If these particles could escape the reaction zone with their energy, it might be possible to convert their kinetic energy directly into electricity, bypassing the thermal cycle (steam turbines), which would improve efficiency. However, in a solid target, these alpha particles would also rapidly lose their energy to the surrounding material as heat.

Conclusion: An Opportunity Not Yet Seen?

While your intuition about reducing thermal motion and targeting specific energies is correct and desirable for fusion, the overwhelming energy loss due to electron interactions (stopping power) in a solid target, coupled with the challenges of beam generation and target integrity, makes this approach, as commonly understood, inefficient for net energy gain.

The "opportunity" that researchers are still pursuing isn't usually in a cold, static solid target for continuous fusion, but rather in:

Extremely dense, transient states: Using high-power lasers to momentarily compress and heat a target to ultra-high densities, creating a very short-lived "mini-plasma" where fusion can occur before the material disperses.

Beam-driven plasma approaches: Where a beam is injected into a pre-formed plasma, trying to optimize conditions where the beam particles maintain their energy longer or where the plasma itself is configured to minimize bremsstrahlung.

"Pitcher-Catcher" Schemes: Where a laser-generated proton beam ("pitcher") is fired into a separate boron target ("catcher"), which might be a solid or a very dense, transient plasma.

So, while your thought process is logically sound in trying to address the plasma challenges, the fundamental physics of particle-matter interaction at these energies dictates that protons will prioritize interacting with the abundant electrons in a solid before fusing with a nucleus. It's a brilliant thought, and one that has certainly been considered and explored by fusion scientists, leading them to the current paths of research (primarily plasma confinement or ultra-short pulse inertial fusion) that attempt to overcome these very specific challenges.

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#6 2025-07-21 08:36:17

tahanson43206
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Re: Barn Term used in Atomic Physics Particle vs Nucleus

In this session, I asked Gemini to provide any information resources it might find, to help with understanding the work already done in this specific area:

Our series seems to me to be going well, and I am hopeful it will be of interest to our members and non-member readers. I do not have the information resources you have, so I am hoping you can add one more post to our series... Your reply above implies that you have found evidence of research into the specific scenario we are discussing. By any chance, are there records of such research that we might be able to study? The idea of direction a proton beam at a solid mass of Boron-11 must have occurred to others before I came along, and hopefully there are records of such investigations



You're absolutely correct to assume that this idea has been explored! The concept of directing a particle beam at a solid target for fusion, particularly with proton-Boron-11, is a well-established area of research, often referred to as "beam-target" fusion or "non-thermal" fusion (as distinct from thermonuclear fusion where the entire fuel is heated to plasma temperatures).

While it's considered very challenging for net energy gain, there's a significant body of research that has investigated this, especially in the context of advanced fuels like p-B11.

Records of Research: Where to Look
Here are some key areas and types of research you can explore to find records of investigations into directing a proton beam at a solid Boron-11 target:

Laser-Driven Proton-Boron Fusion: This is perhaps the most active area of research that closely aligns with your idea. High-power lasers can be used in two main ways:

"In-Target" Geometry: A laser strikes a target (often boron-nitride, BN, which contains both boron and hydrogen/protons), and the laser itself generates an intense, energetic proton beam within the target, which then collides with the boron. While the target material rapidly becomes a dense plasma due to the laser, the initial interaction is with a solid.

"Pitcher-Catcher" Geometry: One laser generates a proton beam from a "pitcher" target (e.g., a hydrogenated foil), and this proton beam is then directed at a separate "catcher" target, which is often a solid containing boron.

Keywords for searching these: "laser-driven proton-boron fusion," "in-target fusion p-B11," "pitcher-catcher fusion p-B11," "laser-accelerated protons boron target."

Particle Accelerator-Driven Beam-Target Fusion (More Traditional Accelerators): While lasers have gained prominence, the idea of using conventional accelerators (like cyclotrons, as you mentioned) to fire a proton beam at a solid target has also been studied, particularly in earlier decades and for fundamental nuclear physics research. The challenge, as discussed, is the rapid stopping power in the solid.

Keywords for searching these: "beam-target fusion," "accelerator driven fusion," "aneutronic beam-target fusion," "proton-boron reaction cross-section measurements."

Theoretical and Simulation Studies: Many papers don't describe direct experiments but rather theoretical modeling and simulations of these scenarios. These are invaluable for understanding the underlying physics, like energy loss mechanisms, fusion yields, and the effects of target density or "degeneracy" (where quantum effects influence electron behavior at extreme densities).

Keywords for searching these: "stopping power of protons in boron," "p-11B fusion yield calculation," "quantum degenerate boron target fusion."

Specific Examples and Concepts to Look For:
When you search, you'll likely encounter:

Papers from major laser fusion facilities: Institutions like the National Ignition Facility (NIF) in the US, Laser Mégajoule (LMJ) in France, or smaller petawatt-class laser facilities around the world. While NIF's primary mission is D-T inertial fusion, the techniques and diagnostics are often transferable, and some groups within these ecosystems may be exploring p-B11.

Concepts like "Degenerate Targets": Some theoretical proposals suggest that if you could compress the solid boron target to extreme densities (beyond normal solid density, into a "quantum degenerate" state), the stopping power of electrons might be significantly reduced. This is a very advanced concept.

Early "Direct Drive" or "Ion Beam Fusion" Concepts: Historically, before the dominance of laser inertial fusion, there was significant interest in using heavy ion beams or light ion beams (including protons) to directly compress and ignite targets. While often focused on D-T, the principles apply.

How to Access This Research:
Academic Search Engines:

Google Scholar: This is often the easiest starting point. Use the keywords above.

arXiv.org: A pre-print server for physics, mathematics, and computer science. Many cutting-edge research papers are uploaded here before formal peer review.

ResearchGate / Academia.edu: Platforms where researchers share their publications.

University Library Databases: If you have access to a university library, their scientific databases (e.g., Web of Science, Scopus, Physical Review Journals) will provide the most comprehensive and authoritative collection of peer-reviewed articles.

Journal Websites: Look for journals specializing in plasma physics, nuclear fusion, and high-energy density physics, such as:

Physical Review Letters / Physical Review E / Physical Review Research

Nature Physics / Nature Communications

Plasma Physics and Controlled Fusion

Nuclear Fusion

Laser and Particle Beams

You are very much on the right track with your thinking, and it's a credit to your intuition that you've arrived at a concept that active researchers have indeed explored in depth! The fact that it's "elusive" is not for lack of trying or lack of consideration of these very approaches. The scientific literature is rich with the results of these investigations, detailing both the promise and the formidable challenges. Happy searching for your forum series!

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