Just more powerful magnets
Just more powerful magnets
Is the practicality of most fusion designs down to how powerful the available electromagnets are? Smaller gyroradii and longer containment times... If you could somehow make a 200 Tesla magnet (forget if it is possible) would practical fusion plants be popping up as fast as fission designs did in the 50s?
Re: Just more powerful magnets
Sorry if this has been asked before, I was unable to find the answer.
Re: Just more powerful magnets
May be, or not
Simple containment governed by gyro radius in a magnetic field should improve.Both cusp containment and ExB losses should be less. Simple scaling is that density can increase as the square of the B field with fusion as much as the B field to the 4th power. This may apply to stable magnetic containment fields convex towards the higher densities of plasma, which generally mean cusp machines. In Tokamaks with closed fields, the pilonidal B fields weaken as you go out from the center. Stronger fields may help,but instabilities when they occur may be more devastating and efforts to control these instabilities may become more challenging, perhaps in an exponential fashion. Scrape off layers and diverter considerations may be more problematic. And with cusp machines like the Polywell injection of electrons through cusps may become more difficult. This seems to be a major concern with the Polywell currently. High Beta containment may be attractive, but this may also impede electron injection efficiency. Stronger B fields would possibly exacerbate this problem further.
For pinch machines like DPF, things may be more straight forward, or not...
I speculate that things may be represented best as a trend towards improvement till a peak is reached and then efficiency falls off. Where this peak for the various approaches lies may be tricky. Only very well understood modeling or expirement can give an answer. A comparison may be represented by the fusion cross section of DD. It continues to increase at higher temperatures, but once the growth (slope of the curve) becomes less than the growth of Bremsstruhlung radiation, ground is lost. and eventually, at several MeV, atom smashing reactions begin to dominate.
PS: Gyrotron radiation called cyclotron radiation in the accelerators of that name (I think) is a minor energy loss compared to Bremsstruhlung with B fields of a few Tesla. The magnatized plasma at several hundred or thousands of Tesla will eventually exceed Bremsstruhlung radiation. The machines where most of the plasma is not magnatized for most of the particles lifetimes may mostly avoid this problem. The Polywell and Lockheeds approach may be examples of this.
Dan Tibbets
Simple containment governed by gyro radius in a magnetic field should improve.Both cusp containment and ExB losses should be less. Simple scaling is that density can increase as the square of the B field with fusion as much as the B field to the 4th power. This may apply to stable magnetic containment fields convex towards the higher densities of plasma, which generally mean cusp machines. In Tokamaks with closed fields, the pilonidal B fields weaken as you go out from the center. Stronger fields may help,but instabilities when they occur may be more devastating and efforts to control these instabilities may become more challenging, perhaps in an exponential fashion. Scrape off layers and diverter considerations may be more problematic. And with cusp machines like the Polywell injection of electrons through cusps may become more difficult. This seems to be a major concern with the Polywell currently. High Beta containment may be attractive, but this may also impede electron injection efficiency. Stronger B fields would possibly exacerbate this problem further.
For pinch machines like DPF, things may be more straight forward, or not...
I speculate that things may be represented best as a trend towards improvement till a peak is reached and then efficiency falls off. Where this peak for the various approaches lies may be tricky. Only very well understood modeling or expirement can give an answer. A comparison may be represented by the fusion cross section of DD. It continues to increase at higher temperatures, but once the growth (slope of the curve) becomes less than the growth of Bremsstruhlung radiation, ground is lost. and eventually, at several MeV, atom smashing reactions begin to dominate.
PS: Gyrotron radiation called cyclotron radiation in the accelerators of that name (I think) is a minor energy loss compared to Bremsstruhlung with B fields of a few Tesla. The magnatized plasma at several hundred or thousands of Tesla will eventually exceed Bremsstruhlung radiation. The machines where most of the plasma is not magnatized for most of the particles lifetimes may mostly avoid this problem. The Polywell and Lockheeds approach may be examples of this.
Dan Tibbets
To error is human... and I'm very human.
Re: Just more powerful magnets
There comes a point when the magnets would be too powerful and impact the ions excessively and change the behavioral dynamics. Traditionally this is not as much an issue due to mass.
The development of atomic power, though it could confer unimaginable blessings on mankind, is something that is dreaded by the owners of coal mines and oil wells. (Hazlitt)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)
Re: Just more powerful magnets
But only because they refuse to use an XCusp machine. The Polywell has a "funny cusp". Make use of it.D Tibbets wrote:And with cusp machines like the Polywell injection of electrons through cusps may become more difficult. This seems to be a major concern with the Polywell currently. High Beta containment may be attractive, but this may also impede electron injection efficiency. Stronger B fields would possibly exacerbate this problem further.

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Re: Just more powerful magnets
the simulations i did seem to confirm the B^4 scaling law. Controlling the magnetic fields strength was by far the most effective way of controlling the fusion rate.
However, a few caveats, as Dan already pointed out:
* the biggest obstacle my simulations revealed is getting the electrons in through the cusps. like trying to get a bullseye through the eye of a tornado. and of course the higher the field strengh, the harder it is. and like the power scaling law, this scales nonlinearly (though i don't know if it's b^2 or b^3 or what.)
* increasing the B field strength also impacts the average velocity (or KE, rather) through the core. and there's a KE (albeit very high), beyond which the fusion rate starts dropping off. While this'll probably be more than compensated for by the increased density, it remains true that after this point the scaling is going to be a little under B^4. Though not that bad, really. http://s155.photobucket.com/user/MSimon ... 1.jpg.html In fact, before that point you're really getting a boost over basic B^4 scaling because your crosssection is increasing pretty quickly. (unless that was already included in? i don't think so, but i don't know.)
* and finally, my simulation didn't model things like Bremsstruhlung loses, etc. only inertial and electromagnetic. fusion rate was approximated based on density and KE. So finerscale / more subtle things like that, I can't speak to.
But yeah, these caveats aside, the two big factors are size and field strength, and field strength is the much bigger factor. though increasing size means you can increase the field strength more.
However, a few caveats, as Dan already pointed out:
* the biggest obstacle my simulations revealed is getting the electrons in through the cusps. like trying to get a bullseye through the eye of a tornado. and of course the higher the field strengh, the harder it is. and like the power scaling law, this scales nonlinearly (though i don't know if it's b^2 or b^3 or what.)
* increasing the B field strength also impacts the average velocity (or KE, rather) through the core. and there's a KE (albeit very high), beyond which the fusion rate starts dropping off. While this'll probably be more than compensated for by the increased density, it remains true that after this point the scaling is going to be a little under B^4. Though not that bad, really. http://s155.photobucket.com/user/MSimon ... 1.jpg.html In fact, before that point you're really getting a boost over basic B^4 scaling because your crosssection is increasing pretty quickly. (unless that was already included in? i don't think so, but i don't know.)
* and finally, my simulation didn't model things like Bremsstruhlung loses, etc. only inertial and electromagnetic. fusion rate was approximated based on density and KE. So finerscale / more subtle things like that, I can't speak to.
But yeah, these caveats aside, the two big factors are size and field strength, and field strength is the much bigger factor. though increasing size means you can increase the field strength more.
Re: Just more powerful magnets
Does the increase in electron injection difficulty correspond to an equal increase in electron trapping? If so, it sounds (to a layman) like the injection drawback is cancelled out by an electron trapping benefit.

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Re: Just more powerful magnets
I would like to know the same. more specifically i'd like to know the scaling law for injection efficiency, with magnetic field strength. i presume it'd be nonlinear.krenshala wrote:Does the increase in electron injection difficulty correspond to an equal increase in electron trapping? If so, it sounds (to a layman) like the injection drawback is cancelled out by an electron trapping benefit.
but there's another aspect that it can be increased by more precise guns, vibration mitigation, etc.
so, let's say at some reasonable fixed precision, say modeled as guassian noise from perfect, how does the injection efficiency vary with magnetic field strength? with grid bias?
seems like an important question.

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 Joined: Wed Jul 14, 2010 5:27 pm
Re: Just more powerful magnets
It occurs to me that one could do this without calculus that is _too_ advanced.
so basically you simplify to just one coil  and simplify a little further by saying that's a current loop. then you can get a formula for b field by integrating over the current loop. i can probably just look that up in schaum's outline of electromagnetics. same for charge.
now i can take that, and start with a point, h from the center of the loop, perpendicular, displaced by d, with initial forward velocity vf and radial velocity vr. now i'm integrating over a path. i got something like a path integral.
so, not as insurmountable as it first seems. looks like in fact there's a pretty clear way to go about finding the equation to calculate it...
so basically you simplify to just one coil  and simplify a little further by saying that's a current loop. then you can get a formula for b field by integrating over the current loop. i can probably just look that up in schaum's outline of electromagnetics. same for charge.
now i can take that, and start with a point, h from the center of the loop, perpendicular, displaced by d, with initial forward velocity vf and radial velocity vr. now i'm integrating over a path. i got something like a path integral.
so, not as insurmountable as it first seems. looks like in fact there's a pretty clear way to go about finding the equation to calculate it...
happyjack27 wrote:I would like to know the same. more specifically i'd like to know the scaling law for injection efficiency, with magnetic field strength. i presume it'd be nonlinear.krenshala wrote:Does the increase in electron injection difficulty correspond to an equal increase in electron trapping? If so, it sounds (to a layman) like the injection drawback is cancelled out by an electron trapping benefit.
but there's another aspect that it can be increased by more precise guns, vibration mitigation, etc.
so, let's say at some reasonable fixed precision, say modeled as guassian noise from perfect, how does the injection efficiency vary with magnetic field strength? with grid bias?
seems like an important question.

 Posts: 1435
 Joined: Wed Jul 14, 2010 5:27 pm
Re: Just more powerful magnets
some initial google searches for "off axis magnetic field current loop" have proven... discouraging.happyjack27 wrote:It occurs to me that one could do this without calculus that is _too_ advanced.
so basically you simplify to just one coil  and simplify a little further by saying that's a current loop. then you can get a formula for b field by integrating over the current loop. i can probably just look that up in schaum's outline of electromagnetics. same for charge.
now i can take that, and start with a point, h from the center of the loop, perpendicular, displaced by d, with initial forward velocity vf and radial velocity vr. now i'm integrating over a path. i got something like a path integral.
so, not as insurmountable as it first seems. looks like in fact there's a pretty clear way to go about finding the equation to calculate it...
but it occurs to me, if i'm understanding correctly, that the mag field would never imbue any rotational acceleration (concentric with the current loop) to the approaching charged particle. if this is true, then the problem can be reduced to a 2dimensional problem  a flat slice through the center of the current loop.
am i wrong here?
the vector field would then be:
per: x,y coordinate
2vector of mag field at x,y
2vector of egradent at x,y
and then you'd be tracing a particle with coordinates
x,y,
2vector of velocity,
(1vector of particle charge (constant))
(1vector of particle mass(constant))
and combining this would give you a result of:
2vector of acceleration
and then you'd just have to backtrack a particle that barely makes it in. you might have a few dimensions to backtrack. but in any case that would give you your basin of injection success. and then your injection efficiency would just be the probability of having the initial state of an electron starting inside that basin.
agree?
Re: Just more powerful magnets
Ultra strong magnetic fields wouldn't mitigate bremsstrahlung losses unless you were doing something extremely clever. I have some hope with MIT and CO's findings regarding radiation loss concerning electrons. But I'm not holding my breath.