Electrostatic focusing on the atomic scale

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    • Electrostatic focusing on the atomic scale

      About 12 years ago or so I thought I'd write an article for the proverbial average interested layman that would explore the ways, if any, that nanotechnology could be applied to nuclear fusion. Problem was, I actually didn't know the answer and there was almost nothing formally done other than hand-waving speculation. Besides, there are enormous differences in energy scales between chemical bindings and useful nuclear fusion collision energies (on the rough order of 1000 to 100,000.) So first thing I felt I had to do was write some simulation code to model the nuclei traveling at high energies within some well-known mechanism - such as a proton traveling through an electrostatic focusing lens.

      That was a mistake - at least if I had planned to complete the article in any reasonable time frame. I got a little ways with things, having taken the time-dependent Schrodinger equation (which from a computer programming perspective is really two related equations - one for the real part, one for the imaginary part) and developed a simple program in C and some Python glue code that used the staggered leap-frog algorithm (CTCS) to simulate its time evolution. I found a nice utility to help me generate mpeg movies from a sequence of RBG image files and I managed to put the following initial page together:

      http://www.lugoj.com/NanotechFusion/nanotechfusion.html

      I never got further - realized I was about to embark on an original research project that would take a long time. And the machine I had was no speed demon.

      What annoys me the most, though, is after diligent searching I can't find my old C and Python code anymore. I was sure I had an archive copy of it from the old computer I developed it on, but I've had no luck finding it on the clutch of computers I now have in my office. Of course I could rewrite it, and probably do a better job the second time around, but it annoys me to lose what I considered unfinished work.
       
    • Ah APT and nuclear fusion - an interesting topic!
      Btw: (offtopic) Wendelstein 7-X is starting soon :)

      >> JimL: "... realized I was about to embark on an original research project that would take a long time. ..."
      Yep it's completely uncharted area there.

      >> JimL: "... So first thing I felt I had to do was write some simulation code ... That was a mistake - at least if I had planned to complete the article in any reasonable time frame. ..."
      You indeed picked one of the most difficult topics there are - regarding applications of advanced APM products.

      I’m not sure if it is even in principle possible to archive "shoot and hit" fusion. What I mean with this just invented term is a fusion of a pair* of nuclei with a probability >>50% to archive a successful hit on the first try. (I assume this is what you where trying to investigate here.) I see no possibility for exploratory engineering here - too many missing reliable models.

      IIRC I once heard something along the lines that: "one cannot focus a particle beam (in position space) below what it was at the point of origin because of Liouville's theorem of constant phase space volume (of closed systems?)"**
      https://en.wikipedia.org/wiki/Liouville's_theorem_%28Hamiltonian%29
      I once came in contact with people working on shooting highly charged ions through fine channels.
      I think someone of them said that this could maybe cheat this unfocussability limitation.
      http://www.iap.tuwien.ac.at/www/atomic/surface/capillaries
      (I doubt this is applicable here.)

      I think aforementioned limitation** is a oversimplification though - since laser-cooling & something like evaporation cooling can AFAIK compress phase space in free(?) position space. There seem to be further methods as a quick search just now revealed: See "Conservation of emittance" - this may be related:
      https://en.wikipedia.org/wiki/Beam_emittance#Conservation_of_emittance

      It certainly won't hurt to have the minimal possible volume in phase space (that is planks volume hbar) at the release point from machine phase to free flight.

      Then there is the point that the starting impulse must be incredibly accurate such that you actually accurately hit the target. This equates to compactness in impulse space and consequently wide dispersion in position space.

      The result: nano-scale focussing wont work since you have to start with micro to macro-scale wave functions. You have to start with a super-cool and spatially widely de-localized proton/deuteron/.. and accelerate its whole wave-function in an incredibly noise free way to get it cold and hot at the same time (in different directions - spherically symmetric??).

      It may help simulate the process in reverse (backward in time) to find out what you need to start with.
      The goal situation seems relatively simple: plank constant & target nucleus size -> projectiles minimal necessary impulse uncertainty at the focus ... (don't forget coulomb repulsion + small errors)

      An interesting question regarding this that I found is: Could supercooled ion trap boxes of a size of some microns to centimetres be used to transport only a part of the wave function of an ion? Some method of transport with even lower friction than super-lubrication may be necessary. I'm collecting my thoughts about such levitation/hyper-lubrication here:
      http://apm.bplaced.net/w/index.php?title=Levitation

      If a "shoot-and-hit-fusion" attempt is really successful I see no chance in hell that you'll be able to control the exit trajectory. Catching high entropy exit particles without messing up the super-cool environment seems very difficult. If you're that good at things you may start to think about efficiently producing antimatter - which I today consider 100% Si-Fi.

      Depending on the choice of fusion partners you may need a third partner to receive the released energy in form of impulse and prevent purely radiative energy release (which seems hardest to capture)

      Then there's the point that a static target (e.g. a chemically bond hydrogen atom) is totally unsuitable:
      See what I noted in the comments of this video (~ 6 months ago - citation omitted)
      http://www.youtube.com/watch?v=cdKyf8fsH6w&t=20m30s
      >> Here Ralph merkle sidemotes: "... atoms have nuclei which are point-masses and yeah they blur a little bit but who cares forget about it ..."
      While irrelevant for APM - if we attempts "shoot-and-hit-fusion" we do care.
      I do repeatedly get the classic question why those nano-machines don't quantum disperse and get useless.
      That's a reason for this comment.

      An interesting question related to "shoot-and-hit-fusion" that should also be useful for other things is how to best ionize atoms (e.g. hydrogen) and contain those ions in an advanced APT system.

      All in all I think putting a lot of effort into "shoot-and-hit-fusion" isn't helping speed up development of APM.
      It is super complex and seems far off and thus pulls too much on the suspense of disbelieve. Thus its not on my personal priority list.

      ~~~~

      Beside the yet very speculative "shoot-and-hit-fusion" there will be much more unspeculative possibilities to use APM to boost conventional fusion approaches.
      I'm collecting my thoughts about this here - only a bulleted list yet:
      http://apm.bplaced.net/w/index.php?title=Nuclear_fusion

      I think inertial fusion could be made much more compact (no idea how much exactly) and could go easily beyond break-even. Crashing nuclei with their electron hull makes things much more complicated on the simulation side.
      I'd expect severe limits on the downscalbility because of physical scaling laws though.

      Ater some back on the envelope calculations. I think that stellerator style fusion won't get light enough for e.g. a mobile spaceship (where fusion makes IMO most sense) even with usage of APT materials.


      ~~~~

      >> JimL: "What annoys me the most, though, is ... I can't find my old C and Python code ..."

      I too have lost something APM related once. It was the newest version of this poor little fella:
      Particularly I've lost the work I've done to fit it inside itself in its collapsed state.
      I made this model when I still didn't know the shortcomings of the molecular assembler concept.

      ~~~~

      some remotely related links:
      https://en.wikipedia.org/wiki/Lanthanum_hexaboride --- interesting image
      https://en.wikipedia.org/wiki/Field_electron_emission
      https://en.wikipedia.org/wiki/Electron_gun
      Attached files
    • IIRC I once heard something along the lines that: "one cannot focus a particle beam (in position space) below what it was at the point of origin because of Liouville's theorem of constant phase space volume (of closed systems?)"**

      You bring up many interesting points that I will try to respond to later, but I'll address just the one I quoted:

      The system isn't closed because, classically at least, a charged particle moving through the focussing fields will experience acceleration and thus radiate energy away. If it weren't for quantum mechanics the nuclei would most likely first settle into an ever tighter beam line and then eventually slow to a stop, since there are field potentials along every axis.

    • I think we have a case of "separation of concerns" here:
      A.) phase space volume (PSV) compression
      B.) acceleration
      C.) focussing
      Keeping those apart should make solving them easier.
      I think combining any of these should only be done if a compelling reason is found.
      It seems to make sense to do it in the order A-B-C.


      Regarding A.) PSV compression

      I'm not entirely clear what you where trying to simulate.
      I guess the evolution/propagation of the wave function of one single proton.
      A simple simulation assumes perfect knowledge over the wave function - pure state (is that correct?)
      Thus no matter how you choose your wave function it always has the minimal phase space volume (hbar).
      Then when assuming a certain initial spacial localisation the packet won't spread faster than the minimum speed.

      In reality though you have limited knowledge over the wave function and thus you have a PSV which is bigger than hbar even for a single particle. Thus I guess you have to do a more complex simulation over an ensemble of possible wave-functions. (Is that the right way to simulate the lack of knowledge over the wave function?)
      In other words additionally to the quantum blurriness some knowledge uncertainty adds to it: (Density operator)
      https://en.wikipedia.org/wiki/Density_matrix
      I wonder: Is this operator normally only applied to bunches of particles?
      Annealing e.g. will only work with more than one particle.
      So I’m not really sure how to compress PSV here.


      Regarding B.) acceleration

      While accelerators which are sufficient to boost ions to fusion energies can be relative small** (m scale) in relation to particle accelerators (km scale) I think they'll always remain big relative to the nano-scale.
      [** Neutral Beam Injection for ITER >900tons! - whopping 1000keV though]

      The most compact way to accelerate ions with APT that I currently know of are optical cavity accelerators:
      http://www.quantumday.com/2013/09/ultrafast-laser-accelerator-built-on.html
      Interesting video: https://www.youtube.com/watch?v=LG1kVIIy2Ok
      Basically analogue to these microwave accelerators just finer but still with similar total length.
      https://commons.wikimedia.org/wiki/File:Desy_tesla_cavity01.jpg
      Trouble: the small channel (dx) => big dp in transversal directions :S => B-A-C ??

      Side-note: The energy barriers for fusion are not hard to calculate but I just found that tables for them are somewhat missing on the net. Wikipedia: "... ignition temperature is about 4 keV for the D-T reaction and about 35 keV for the D-D reaction."


      Regarding C.)

      That's the only part of the three (A,B,C) you actually seem to have simulated.
      You seem to do make a choice of some arbitrary initial localisation resulting in an corresponding equally arbitrary (but corresponding) dispersion speed. (Choosing e.g. the size of the proton in its nuclear force "box" 1.7e-15m makes no sense - that should be obvious though.) The only size that I see that’s special here is the radius of the acceleration ring. Widest starting slowest dispersion. (?? output size of an acceleration channel ??)


      >> JimL: "The system isn't closed because, classically at least, a charged particle moving through the focussing fields will experience acceleration and thus radiate energy away. If it weren't for quantum mechanics the nuclei would most likely first settle into an ever tighter beam line and then eventually slow to a stop, since there are field potentials along every axis."

      I'm not entirely sure I get what you're trying to say here.

      While you can increase or decrease a particles energy with external electric or magnetic fields I'm not sure it is possible to make its energy more precise - that is lowering its entropy or in an uncommon formulation quasi cooling it at a hot temperature - (A&C intermixed - bad?). With electromagnetic fields this is surely possible as laser-cooling shows.
      It might have to do with that:
      a.) magnetic fields preserve energy (except synchrotron radiation at high energies)
      b.) electric fields preserve (... what was it again? - darn I forgot).
      (Side-note: I think this is applied to visualize local spots of the table of nucleotides with a Wien filter.)


      ps: The necessary massive parallelism and high frequency for a practical level of power generation will make this endeavour even more difficult.
       
    • Lukas (LSUESS) wrote:

      Then there's the point that a static target (e.g. a chemically bond hydrogen atom) is totally unsuitable:
      See what I noted in the comments of this video (~ 6 months ago - citation omitted)
      http://www.youtube.com/watch?v=cdKyf8fsH6w&t=20m30s
      >> Here Ralph merkle sidemotes: "... atoms have nuclei which are point-masses and yeah they blur a little bit but who cares forget about it ..."
      While irrelevant for APM - if we attempts "shoot-and-hit-fusion" we do care.
      I do repeatedly get the classic question why those nano-machines don't quantum disperse and get useless. That's a reason for this comment.
      Just for completeness in case that youtube comment vanishes in the future:

      Lukas (LSUESS) wrote:

       aka mechadense
      20:30 About quantum blurryness - another take on this is: If you capture a molecule in a tight space (e.g. in a box) you do work against degeneracy pressure which is released in "omnidirectional" kinetic energy when you suddenly lift its spacial constraints completely. The thighter it was compressed in space the faster it's probability distribution will fall apart. This is heisenbergs uncertainty principle in slightly unconventional wording. (small spacial distribution -> wide impulse distribution -> fast wave packet dispersion) Judging from this macroscopic crystals which's average outer positions can (it has been done) be measured down to the femtometer level in space should fall apart instantly because of this extreme sharpness in space. But they don't! Why is an interesting question on itself - it has todo with not yet well understood quantum decoherence. If you strongly bond a small molecule to the crystal (that is you use the crystal as a movement constraining box) the molecule essentially becomes part of the crystal and inherits its sharp and not apart-running position. Actually the macroscopic position of the crystals roughly pins down the positions of the atomic nuclei of the molecule. The exact positions of the nuclei (at 0K temperature) can't be determined as exact as the position of a macroscopic crystal though. The actual size of the probability distribution cloud for a nucleus is maintained through the "chemical bond force box" the size of this cloud is below the size of its host atom but above the size of the nucleus. As a sidenote the size of the nucleus is maintained through its "nuclear force box" and the size of a whole atom (electron shell) is maintained through the "electrostatic core potential box". To theoretically recreate the actual "force-pictures" that have been taken of molecules you have to "add" to the core crystal location that does not run apart the nucleus blurryness, the electron shell blurrieness and finally some thermal blurrieness - the same for the opposing needle tip. (actually mathematically this "adding" is folding)