I Best way to focus charged particles back to their source?

[CMTacoTophat]

TL;DR

What combination of electric and magnetic fields could direct the emitted charged particles, say alphas, back to the point source, while being able to monitor them or increase their energy?

Basically the TL;DR.

I was entertaining the idea of some sort of device as a challenge, but I couldn't think of a surefire way to capture as much of the output of, say, a collection of radionuclides, and direct the output charged particles back into them, while being in a form consistent and convenient enough for measurement, energy boosting (or degradation), etc.

I am sure there are varying solutions for different energy levels, especially with the equipment involved (like electrostatic vs. magnetostatic lenses), but I'm really looking for the simplest solution: low energy, even spread in all directions, etc.

So far my best design would be to have a cylindrical surrounding the source, with a magnetic field running axially, but getting stronger towards the shell radius so the particles would make tighter and tighter turns near the edge. This would hypothetically "reflect" them and contain them within the cylinder until accelerated enough or otherwise deflected to be split into two, even streams. Of course, I have no idea how to form that sort of field, or if it would even work.

Thanks in advance.

 

[anuttarasammyak]

Some alpha particles could be on circle track in constant kinetic energy and come back to the heavy source with a designed homogeneous magnetic field.

 

[CMTacoTophat]

Thanks for the reply. I've considered something along those lines, but the issue I always stagger with is the particles with velocities off-plane (the "plane" being defined as the one with the homogeneous field as its normal). Wouldn't they spiral away from that source? Forgive me if there's something obvious I'm missing.

 

[anuttarasammyak]

Applied magnetic field should be perpendicular to the velocity of the particle so that its track is a circle not a spiral.

 

[CMTacoTophat]

I think I get what you're implying: A magnetic field akin to that produced by a current wire, running circumferentially to an axis, with all emitted particles except those exactly aligned to the axis returning in a loop back to the source. How could you then, say, boost them? Would that require a series of banked rings with differing electric potentials? I apologize if any of my questions appear ill-informed.

 

[anuttarasammyak]

https://www.feynmanlectures.caltech.edu/II_29.html is a good one to know the fundamentals.

 

[CMTacoTophat]

Thanks for the resource - I haven't come across that one yet. However, it seems mostly concerned with point sources in 2D, and only capturing the emitted particles with a very particular range of velocities. I've been trying to figure out how to do so in 3D, and how to capture as many of them as possible. I get that they can loop back on themselves in a strong uniform magnetic field, but it would have to then be perpendicular to all surface normals of a (hypothetical, surrounding the point source) sphere, and the hairy-ball theorem then requires that it necessarily vanish in certain areas, thus preventing complete or near complete capture.

 

[Astronuc]

TL;DR: What combination of electric and magnetic fields could direct the emitted charged particles, say alphas, back to the point source, while being able to monitor them or increase their energy?

I was entertaining the idea of some sort of device as a challenge, but I couldn't think of a surefire way to capture as much of the output of, say, a collection of radionuclides, and direct the output charged particles back into them, while being in a form consistent and convenient enough for measurement, energy boosting (or degradation), etc.

It is not clear why one would do that. Every radionuclide has a characteristic spectrum of alpha particles, which depend on internal nuclear states. In addition, for mass of a radionuclide, say in a spherical form, alphas will emit out of the sphere or into the sphere. Internally, the alphas will collide with atoms within the sphere losing energy before they emerge, if they emerge.

An electrostatic field could be achieved by a spherical shell, one would need a potential difference between the mass of radionuclide and the outer shell, with the outer shell positively charged with respect to the centrally located mass.

One does not usually monitor individual alpha particles, but rather, one may monitor a current, or population of alpha particles. When alpha particle leaves the surface of a solid mass, it may leave behind two electrons, which could leave the surface by virtue of the Coulomb force. The alpha will eventually find two electrons to become a helium atom.

Magnetic confinement is use to confine plasmas, e.g., fusion plasmas, in which ions (nuclei) and electrons are separated by virtue of high temperature, which maintains ionization by collision; one has to consider the ion pressure as well as the electron pressure. At the same time, electrons and ions my recombine, and neutral atoms will leak out of a plasma.

Magnetic confinment systems may be toroidal (tokamak) or linear, as in a tandem mirror reactor, in which the magnetic field is increased at both ends in order to deflect ionz back to the central volume. There are other exotic designs like the spheromak.

Evolution of the Tandem-Mirror Approach to Magnetic Fusion
https://www.llnl.gov/sites/www/files/2020-06/mftf_etr_nov_86.pdf
Tandem Mirror Approach to Magnetic Fusion
https://www.europhysicsnews.org/articles/epn/pdf/1981/08/epn19811208p4.pdf

https://www.europhysicsnews.org/articles/epn/pdf/1986/06/epn19861706p73.pdf
https://iopscience.iop.org/article/10.1088/0741-3335/39/5/003

Besides magnetically confining the plasma, another objective is to use the kinetic energy of the alpha particles to heat the plasma before they neutralize and leave the plasma. One concept of 'direct conversion' is the use the positive charge of the alphas and the negative charge of the electron to establish a potential difference, such that the electrons are collected and flow through a conductor and eventually combine with the alphas, which are neutralized at a cathode. The positive ions (with kinetic energy) provide a current, and the postive charge produces a positive potential
https://en.wikipedia.org/wiki/Direct_energy_conversion

 

[CMTacoTophat]

Wow, thanks for the detailed reply! To answer your question, it was supposed to be for a concept I was considering - chaining together (a, n) and (n, a) reactions, along with a constant input source as a method of high alpha flux generation without requiring much power, or being able to power itself in some way.

The best way I figure this could be to have a small target for the (a, n) reaction, surrounded by a moderator for the neutrons, and then a spherical shell of a material partial to (n, a) reactions. Thus, I was wondering how one could deflect alphas back towards their source, while accelerating them (to reach reasonable cross sections for (a, n) reactions).

I'm sorry for not including this initially - I wanted the focus to be on the redirection part, as I was having the most trouble with that. Plus, the entire notion is probably ill - conceived, but I figured it was worth at least theorizing about.

Do you have any insight you would mind sharing?

 

[Astronuc]

it was supposed to be for a concept I was considering - chaining together (a, n) and (n, a) reactions,

Ah, that's an important detail, and it's not so simple. For example, an (n,p) reaction might be preferred; one has to compare the threshold (neutron) energy and cross-section for the (n,p) and (n,α) reactions.

along with a constant input source as a method of high alpha flux generation without requiring much power, or being able to power itself in some way.

So, what is the functional output of the system? Neutrons? Thermal energy?

The best way I figure this could be to have a small target for the (a, n) reaction, surrounded by a moderator for the neutrons, and then a spherical shell of a material partial to (n, a) reactions.

Well, that would not work.

Firstly, (α, n) reaction requires an α-source (usually from decay of a radionuclide heavier than ²⁰⁹Bi. Some sites claim alpha emission (from decay) has been observed in lighter nuclides.

In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitter being the lightest isotopes (mass numbers 106–110) of tellurium (element 52).

Ref: http://srv2.fis.puc.cl/mediawiki/images/f/fd/Alpha_decay.pdf

Production and Supply of α-Particle–Emitting Radionuclides for Targeted α-Therapy​

https://pmc.ncbi.nlm.nih.gov/articles/PMC8612335/

Normally, for a neutron source involving alpha decay, one creates an intimate mixture of an alpha-emitting nuclide, e.g., an isotope of Po, Ra, Pu, or Am mixed with ⁹Be, or nowadays, ²⁵²Cf, which produces neutrons from spontaneous fission in 3.1% of decays; the californium source precludes the need for Be. Some secondary sources of neutrons (in nuclear reactors) use ¹²³Sb, which absorbs a neutron to become ^124*Sb, which beta-decays to ^124mTe, which emits a 1.667 MeV gamma, which interacts with ⁹Be in an (γ,n) reaction with a co-production of 2α in a so-called SbBe-neutron source..

The best way I figure this could be to have a small target for the (a, n) reaction, surrounded by a moderator for the neutrons, and then a spherical shell of a material partial to (n, a) reactions. Thus, I was wondering how one could deflect alphas back towards their source, while accelerating them (to reach reasonable cross sections for (a, n) reactions).

Well, that configuration will not work for at least two reasons: 1) the moderator (a solid material in which fast neutrons lose energy by colliding with nuclei) will interact with alpha particles, and 2) the (n,α) reaction requires fast neutron energy above a certain threshold, unless one is planning to use n-capture to produce an alpha-emitting nuclide, in which case one must consider the cross-section of the (n,γ) reaction, the half-life of the alpha-emitting nuclide, and the energy spectrum of the alpha emission. In either case, placing a moderator between the alpha-emitting point (central spherical) source and surrounding source of (n,α) reactions is self-defeating.

Furthermore, alpha-particles don't travel very far in solid materials. For example, skin can stop most alpha particles, or a thin foil of a heavy (period 6) element, e.g., gold. Refer to Ernest Rutherford's alpha scattering experiments.

Regarding an electrostatic configuration with a small spherical alpha source surrounded by a metal appropriate for an (n,α) reaction, there will be a practical limit on the potential difference between the two conductors. if alpha particles have a kinetic energy up to 5 MeV (+/-), then one must consider a potential difference of 5 MV, if one wants to arrest all alpha particles and deflect them back to the central source. One must consider that not all alphas or neutrons move in the desirable radial direction, which would further degrade the efficiency of the scheme. Any solid material (layer) will necessarily interact with the alphas (by atomic collision) and thus reduce the energy of the alpha particles.

If one wants a thermal (heat) source, then ²³⁸Pu, usualy in the form of PuO₂, is often the choice. However, a decay source cannot be turned off - it's constantly decaying. it would be interesting though to consider a PuN or PuC matrix.

 

[CMTacoTophat]

You certainly have good merit behind your considerations. I also figured that the moderator would interfere with the alpha particles, which is why I wanted to focus them into a beam first, such that they could be redirected and focused back to the core through a narrow hole instead of simple electrostatic spherical shell.

As for the purpose, I figured it could be used to create a burst (moderately) high alpha flux, without requiring significant radioactive materials, as a sufficiently high "efficiency" (proportion of alpha particles that go on to cause another reaction) could lead to a large multiple of an initial flux. I've modelled that simplified scenario here, in this desmos graph.

Boron-10 seems like an ideal (n, a) candidate, as it only needs thermal neutron energies for a decently high cross section (several kilo to megabarns), with a seemingly low tendency in the same energy range for radiative capture.

However, I would also like to focus the alpha particles into a beam in order to accelerate them, as it appears that the outgoing alpha particle energy range is only 1 - 2 MeV, while an (a, n) reaction source typically requires more (like 4 - 5 MeV at the low end for Be-9).

Obviously, this pivoted quite a lot from my original question, so if you think it best to make this into a new thread, please tell me - I'm quite new here. Also, I got my figures from (my best interpretation of) ENDF queries.

 

[Astronuc]

I figured it could be used to create a burst (moderately) high alpha flux, without requiring significant radioactive materials

Alpha particles can be created by ionizing and accelerating helium atoms, but requires significant energy. Otherwise, one needs a radionuclide source that decays by alpha emission, or a nuclide that undergoes an (n,α), which requires a neutron source.

Boron-10

One refers to ¹⁰B(n,α)⁷Li, so as the ¹⁰B is consumed, sup]7[/sup]Li accumulates, which makes the systems less efficient as the Li competes with B for neutrons.

What is the ultimate goal of the system, e.g., an alpha source, a neutron source, or a thermal energy source, which could provide heat or electricity?

 

[CMTacoTophat]

The ultimate goal for a machine like this would be to provide an alpha particle source without requiring nearly as many radionuclides, and without needed as much energy (as they already start off at several MeV from the reaction). Any source needed could be smaller, as each next "step" in flux (the alpha particles going back to trigger another set of (a, n) and (n, a) reactions) can grow very large, if the proportion of alphas that make it back and trigger more reactions is sufficiently close to 100% (F_(n+1) = p*F_n + i, where F is the flux, p is the proportion, and i is the constant input flux).

Also, the Lithium wouldn't be a problem, as it is awful at absorbing neutrons. Plus, even if it absorbs them, it would help overall, as Lithium-8 decays into Beryllium-8, which decays into two alpha particles.

That's why I was originally asking how the particles could be most efficiently captured and returned to the source in a beam-like configuration: so they could be accelerated, and so as many of them can be captured as possible (to get p as close to 1 as reasonably achieveable)

 

[CMTacoTophat]

if one wants to arrest all alpha particles and deflect them back to the central source. One must consider that not all alphas or neutrons move in the desirable radial direction,

I had another idea for this: an electrostatic paraboloid surface, to make the trajectories of (most of) the alpha particles parallel. I know it wouldn't be useful directly as a classic z = x^2 + y^2 shape, but I'm still trying to figure out exact what form in would take. At the edge, even though they can't all be perfectly aligned, they can be aligned enough for further refinement with Einzel lenses, after which it can be redirected around to, and through the back to hit the target again, through a small hole in the base of the paraboloid