My understanding of the electric fields within a BFR for what its worth, a static analysis.
I understand that the electric field is zero at the center of the wiffle ball, and the electrons have a tendency to congregate in a sheath at the Beta = 1 radius. If there is anything to that understanding, then by using R , or R to any power, we are neglecting the radius of the wiffle ball in the calculations. I guess the thinking is that outside the wiffle ball, the far field assumption holds and the electric field can be treated as from a point source. I believe that inside the wiffle ball, the sheath acts as a Faraday cage so the internal field is everywhere zero.
I think (a mistake there) that it is invalid to treat the electric field as a point source within the near field between the MaGrid and the surface of the sheath. Doesn't the near surface of the sheath block the field of the electrons in the far surface (radially apposed side) of the sheath, just as a metallic Faraday cage would?
I guess what I'm thinking (another mistake, or maybe the same one) is that in order to properly treat the electric field, one must know the radius of the wiffle ball as well as the radius of the MaGrid, and treat the electron sheath and the MaGrid as concentric spheres. Then the answer depends on the ratio of R-sheath / R-MaGrid. Call this ratio R'. If R' nears zero then the far field assumption is OK, but if R' nears one, then the parallel plate assumption would be valid, giving dramatically different answers.
There is another fly in the ointment though, because if the ions do spend most of their time within the interior of sheath of the wiffle ball then there is another field source. That is, the aggregate positive charge of the ions inside the sheath. (Nothing says you can't have an electric field within a Faraday cage, only that fields do not penetrate the surface of the Faraday cage.) Would this aggregate positive charge tend to force the sheath to expand? No, it might cause it to contract, though. Would over driving the BFR (excessive fuel ions) result in forcing the sheath beyond the beta = 1 radius, a blow out, so to speak? No, it might cause it to drop below the beta = 1 operating point, though. I guess the electron and ion guns must be synchronized ... A balance struck. To little fuel is what causes the blow out. ??? Is that right ???
Of course the cusps in the magnetic fields result in lumps or spikes on the surface of the electron sheath, but the exact character of these lumps or spikes is another hotly debated issue.
Bussard's bremsstrahlung calculation
Re: Bussard's bremsstrahlung calculation
The average ion velocity/bulk energy aren't proportional to R to any power, at least not without an offset. Think about it - at the radial point of the turnaround, the average ion velocity is ZERO metres per second, implying a differential residence time (seconds per metre) of...?TheRadicalModerate wrote:What's the proper value? I was on shaky ground with that one and assumed that the kinetic energy had to scale the same way as the potential did. (I fell and couldn't get up trying to convert between time-based parametric equations and position-based force values.) Either way, it still looks like the assertion that the ions are denser at the edge is not correct (i.e. that they're denser in the center, despite moving at maximum velocity).Art Carlson wrote:The analysis is OK, but why would the kinetic energy be proportional to 1/R?TheRadicalModerate wrote:I'm wondering about the max ion density at the edge of the machine. Consider a spherical shell at some distance R from the center of the machine. I'd think that the ion density would be proportional to (relative time to traverse the shell) / (volume of the shell). The kinetic energy of an ion is proportional to 1/R, which means that the time spent in a shell is proportional to sqrt(R). And the volume of the shell is 4*pi*(R^2)*dR, i.e. proportional to R^2. So density is proportional to R^(-3/2), or denser in the center than the edge, isn't it?
To put it another way, if an ion oscillates through the core in a perfectly sinusoidal pattern, it spends about 9% of its time in the outermost 1% of its trajectory in a radial sense, but less than 4% of its time in the next-outermost 1% (which taken as a spherical shell has 98% of the volume of the outermost layer, meaning the average density in this second layer is less than half as high). I'm not proposing that the ion motion is actually sinusoidal, or that it's as locally monoenergetic as implied by this example (the real system will be smeared out somewhat), but it illustrates the point...
The R^-2 density profile only applies near the centre. There's definitely a spike there, subject to thermal smearing of course, but the R^-2 profile assumes that the ions are at full speed, so it's invalid once they get away from the core and start to slow down.
We inject them into a plasma ball that has a net negative charge. They're fast initially, when they first pass the magrid, but they slow down as they approach the core due to the negative potential well. They then speed up again as they move away, having maximum speed at the edge of the wiffleball where they get turned around by the magnetic field and sent back down the well. The exact shape of the potential well and thus the location and rapidity of this slowdown effect appears to be still up in the air...Which brings me to my next point of confusion: We keep saying that the core electrons are cold. If we're injecting them into the center and therefore increasing the electrostatic potential of the virtual cathode, doesn't all of that injection energy wind up heating them up? Seems like they want out of that containment awful bad...
Last edited by 93143 on Wed Jun 24, 2009 1:38 am, edited 1 time in total.
Those are metal tubes. You know. Space bottles. The outside of the tubes is a Faraday cage. There are electric fields inside the tubes.Aero wrote:That's pretty terse Simon. What are you saying?MSimon wrote:Metal 6SN7. Or if you like dinky tubes 6CW4.Nothing says you can't have an electric field within a Faraday cage,
I'm really surprised you fellers aren't up on the 6CW4. State of the art when it was developed. Brand name: nuvistor. Introduced in 1959.
And the 6SN7? It may have actually been a 6SS7. Those have been around even longer.
Engineering is the art of making what you want from what you can get at a profit.
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alexjrgreen
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6SN7 - twin triode, 6CW4 - high mu triodeMSimon wrote:Metal 6SN7. Or if you like dinky tubes 6CW4.Nothing says you can't have an electric field within a Faraday cage,
http://store.triodestore.com/otpopsmaltub.html
Ars artis est celare artem.
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alexjrgreen
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Simulation of the Plasma Meniscus with and without Space Charge using Triode Extraction System
http://www.sbfisica.org.br/bjp/files/v39_44.pdf
http://www.sbfisica.org.br/bjp/files/v39_44.pdf
Ars artis est celare artem.
WARNING- long post (I got carried away) 
People are frequently using density in describing the ion populations in a region. But,keep in mind that density is the number of ions, etc. in a unit of volume (like ml or cc). The numbers of ions in the outer zones of a sphere may be larger, but because the volume of the zones (say a zone of 1 cm width at X cm from the center) decrease at the -3rd power of the radius (I think), the density ( ions/cc) actually increases as you approach the center, unless you are in a completly thermalized system without any dominant radial componet to the motion. And there will always be a radial component so long as there is a powered cathode in a Hirsch Farnsworth type of fusor, or a powered virtual cathode in a Polywell. The questions as I see them is how well you can maintain that virtual cathode and what it costs you in terms of electron and ion energies. It would hurt my brain too much to try to figure out the relative densities based on the volumes and transition times of the ions. Sufice it to say that a IEC fusor may have a ~ 100 fold increase in density in the center. If there is a good focus/ confluence, I' guessing that ratio could be much higher.
The questions with radial inertial electrostatic confinement fusors with central cathodes, or as Bussard prefers- inertial electroDYNAMIC fusors with central virtual cathodes has been the costs of maintaining the easily achievable fusion conditions. With grided fusors this results in an ~ 1 billion short fall in the energy balance. What the Polywell might achieve I don't know. It depends on various facters which seem to boil down to confinement time and thermalization time, along with the potential well properties that might allow ion loses but only after recovering most of the energy from them. There are conflicting viewpoints due to the confusion about the dynamic nature of electrostatics (er.. dynamics) the magnetic cusp properties, the thermalization properties, the radiation properties (x-rays), which theoretical models to apply, etc. Add to that arguments about scaling laws, and critical engeenering questions. It all lends itself to interesting debates and hand waveing. Hopefully for the forums sake hard data will become aviable befor everyone leaves in frustration or anger and returns to thier day job. I don't know of any other place where a topic is discussed by such a wide range of (hopefully) reasoned individuals, with at least some input from insiders, and patient counterarguments.
Concerning the energy of the dense electrons colliding in the center. Using the term cold here reflects the kinetic energy of the individual electrons (thier speed). They have slowed down due to mutual repulsion to almost a standstill befor exiting the other side of the core or reversing and acellerating to the magnetic u-turn, where everything starts over again. If you take the energy per electron times the number of electrons in a zone, the total energy per cc may be greatest in the core(?) but the energy per electron is at a minimum.
This begs the question of the total ion vs electron energies in the core and surrounding areas. The ions acellerate into a smaller volume so there is a net increase in density and speed, thus each ion spends little time in the core; but the electrons decellerate into a smaller volume in the core and spend a longer time there. Add to that the excess total electrons in the machine, and the mass differences ( and charge differences for non hydrogen ions). Plug the numbers into a formula, and I assume this might lead to the predictions of a perabolic well vs a square well(?).
A virtual anode could presumably form in the center with an adiquite focus, Bussard mentions this in several sources. To many ions would potentially'blow out' the well. Too little ions may have little effect except for decreasing the fusion rate. This begs another question. This virtual anode would essentially be a reverse of what is going on in the rest of the wiffleball, except there would be no question of confinement in this portion of the machine. In this case the reaction core would actually be a shell surrounding the anode. I speculate that there could be a lot of variables that might be adjusted to perhaps modify the conditions and volume in which fusion would be taking place. Could it be used as an advantage (for instance effecting the "purity" of the radial ion flow, or have some 'aneling effect') , or would it always be a detriment?
*Bussard mentions acellerating the virgin electrons into the magrid with a strong positive potential on the electron guns, or on the magrid (on the magrid in WB6). If the high potential is on the guns instead of the grids, how would this effect recirculation?
Dan Tibbets
My laymans impression is that people seem to be thinking in terms of electrostatics, but keep in mind that Bussard emphazised the point that this a dynamic machine. The electrons (befor any ions are added- it becomes more complicated then) travel outward due to electrostatic (dynamic?) repulsion from other electrons that have been injected towards the center. They reach the magnetic (Wiffleball) border at maximal speed, where they turn around (like a hyperbolic orbit around a planet). I don't know if this distintion has any significance, but I believe it is more acurate. The electrons would not accumulate in a 'static' shell at the Wiffleball border unless thier speed (KeV) and resultant gyroradius decreased to the point where it can become embeded/traped on a magnetic field line . I don't know how, but I'm assuming these now low energy electrons are quickly transported to the cusps and then the magrid exterior where thy move to the vessel walls, perhaps find an ion to neutralize with in this low energy domain,or are bounced and acellerated back inside with the original energy (speed) thanks to the positive charge on the magrid.* I'm guessing (much as the blind man guesses abut the shape of an elephant) that this dynamic situation impeads the formation of border conditions as described by Art Carlson.Aero wrote:My understanding of the electric fields within a BFR for what its worth, a static analysis...................."
People are frequently using density in describing the ion populations in a region. But,keep in mind that density is the number of ions, etc. in a unit of volume (like ml or cc). The numbers of ions in the outer zones of a sphere may be larger, but because the volume of the zones (say a zone of 1 cm width at X cm from the center) decrease at the -3rd power of the radius (I think), the density ( ions/cc) actually increases as you approach the center, unless you are in a completly thermalized system without any dominant radial componet to the motion. And there will always be a radial component so long as there is a powered cathode in a Hirsch Farnsworth type of fusor, or a powered virtual cathode in a Polywell. The questions as I see them is how well you can maintain that virtual cathode and what it costs you in terms of electron and ion energies. It would hurt my brain too much to try to figure out the relative densities based on the volumes and transition times of the ions. Sufice it to say that a IEC fusor may have a ~ 100 fold increase in density in the center. If there is a good focus/ confluence, I' guessing that ratio could be much higher.
The questions with radial inertial electrostatic confinement fusors with central cathodes, or as Bussard prefers- inertial electroDYNAMIC fusors with central virtual cathodes has been the costs of maintaining the easily achievable fusion conditions. With grided fusors this results in an ~ 1 billion short fall in the energy balance. What the Polywell might achieve I don't know. It depends on various facters which seem to boil down to confinement time and thermalization time, along with the potential well properties that might allow ion loses but only after recovering most of the energy from them. There are conflicting viewpoints due to the confusion about the dynamic nature of electrostatics (er.. dynamics) the magnetic cusp properties, the thermalization properties, the radiation properties (x-rays), which theoretical models to apply, etc. Add to that arguments about scaling laws, and critical engeenering questions. It all lends itself to interesting debates and hand waveing. Hopefully for the forums sake hard data will become aviable befor everyone leaves in frustration or anger and returns to thier day job. I don't know of any other place where a topic is discussed by such a wide range of (hopefully) reasoned individuals, with at least some input from insiders, and patient counterarguments.
Concerning the energy of the dense electrons colliding in the center. Using the term cold here reflects the kinetic energy of the individual electrons (thier speed). They have slowed down due to mutual repulsion to almost a standstill befor exiting the other side of the core or reversing and acellerating to the magnetic u-turn, where everything starts over again. If you take the energy per electron times the number of electrons in a zone, the total energy per cc may be greatest in the core(?) but the energy per electron is at a minimum.
This begs the question of the total ion vs electron energies in the core and surrounding areas. The ions acellerate into a smaller volume so there is a net increase in density and speed, thus each ion spends little time in the core; but the electrons decellerate into a smaller volume in the core and spend a longer time there. Add to that the excess total electrons in the machine, and the mass differences ( and charge differences for non hydrogen ions). Plug the numbers into a formula, and I assume this might lead to the predictions of a perabolic well vs a square well(?).
A virtual anode could presumably form in the center with an adiquite focus, Bussard mentions this in several sources. To many ions would potentially'blow out' the well. Too little ions may have little effect except for decreasing the fusion rate. This begs another question. This virtual anode would essentially be a reverse of what is going on in the rest of the wiffleball, except there would be no question of confinement in this portion of the machine. In this case the reaction core would actually be a shell surrounding the anode. I speculate that there could be a lot of variables that might be adjusted to perhaps modify the conditions and volume in which fusion would be taking place. Could it be used as an advantage (for instance effecting the "purity" of the radial ion flow, or have some 'aneling effect') , or would it always be a detriment?
*Bussard mentions acellerating the virgin electrons into the magrid with a strong positive potential on the electron guns, or on the magrid (on the magrid in WB6). If the high potential is on the guns instead of the grids, how would this effect recirculation?
Dan Tibbets
To error is human... and I'm very human.
DTibbets:
Have you a number or a calculation for the mean free path of the electrons in the field free region in the interior to, and immediately adjacent to, the beta=1 surface?
You seem to be saying that the electrons are behaving as if they are generally in a collisionless gas flow regime, but I don't see why this should be so.
There could be many layers (shells), of a thickness about equal to the local mean free path, and each containing electrons with energies consistent with that "height" in the potential well. Like layers of an onion.
Does this notion of electrons whizzing back and forth unimpeded from the exterior through the center and back out have any basis, experimental or theoretical?
Have you a number or a calculation for the mean free path of the electrons in the field free region in the interior to, and immediately adjacent to, the beta=1 surface?
You seem to be saying that the electrons are behaving as if they are generally in a collisionless gas flow regime, but I don't see why this should be so.
There could be many layers (shells), of a thickness about equal to the local mean free path, and each containing electrons with energies consistent with that "height" in the potential well. Like layers of an onion.
Does this notion of electrons whizzing back and forth unimpeded from the exterior through the center and back out have any basis, experimental or theoretical?
The only indication I am aware of that is available in the open literature is that a fusor seems to have a natural RF frequency. POPS also says that there should be a natural frequency of ions.icarus wrote:DTibbets:
Have you a number or a calculation for the mean free path of the electrons in the field free region in the interior to, and immediately adjacent to, the beta=1 surface?
You seem to be saying that the electrons are behaving as if they are generally in a collisionless gas flow regime, but I don't see why this should be so.
There could be many layers (shells), of a thickness about equal to the local mean free path, and each containing electrons with energies consistent with that "height" in the potential well. Like layers of an onion.
Does this notion of electrons whizzing back and forth unimpeded from the exterior through the center and back out have any basis, experimental or theoretical?
Engineering is the art of making what you want from what you can get at a profit.
MSimon:
Is it your thinking then that the electrons are pulsing radially inwards and outwards in bulk motion (travelling waves) at a certain natural RF?
Well that's pretty tenuous. Natural RF (frequencies) in this system could be from any number of electro-dynamical effects.The only indication I am aware of that is available in the open literature is that a fusor seems to have a natural RF frequency. POPS also says that there should be a natural frequency of ions.
Is it your thinking then that the electrons are pulsing radially inwards and outwards in bulk motion (travelling waves) at a certain natural RF?
Without any solid evidence. Yes.Is it your thinking then that the electrons are pulsing radially inwards and outwards in bulk motion (travelling waves) at a certain natural RF?
I think bunching is a better explanation of annealing than low temperature Maxwellian exchange.
It would be nice to get some evidence.
Engineering is the art of making what you want from what you can get at a profit.
Obviously my description is grossly simplified and would best describe the behavior in a very sparsely populated situation. Randomization in speed and direction would proceed apace with continuous near and distant Coulomb interactions. The question remains how fast this occurs compared to the particle lifetimes in the machine and the continuous injection of mono energetic and radial electrons. Also, need to consider that in a spherical devise the collisions occurring near the dense center can change the speed, but could not change the radial vector much.icarus wrote:DTibbets:
Have you a number or a calculation for the mean free path of the electrons in the field free region in the interior to, and immediately adjacent to, the beta=1 surface?
You seem to be saying that the electrons are behaving as if they are generally in a collisionless gas flow regime, but I don't see why this should be so.
There could be many layers (shells), of a thickness about equal to the local mean free path, and each containing electrons with energies consistent with that "height" in the potential well. Like layers of an onion.
Does this notion of electrons whizzing back and forth unimpeded from the exterior through the center and back out have any basis, experimental or theoretical?
Three references that might be helpful are below.
http://www.lesia.obspm.fr/perso/nicole-meyer/Beck.pdf
http://web.gat.com/conferences/meetings ... a004pr.pdf
really long url that crapped all over the formatting
Dan Tibbets
To error is human... and I'm very human.
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TheRadicalModerate
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Re: Bussard's bremsstrahlung calculation
Are you trying to assert that the residence time doesn't have a limit at R? I'm not buying that one.93143 wrote:The average ion velocity/bulk energy aren't proportional to R to any power, at least not without an offset. Think about it - at the radial point of the turnaround, the average ion velocity is ZERO metres per second, implying a differential residence time (seconds per metre) of...?
I went back and looked at this again. This is basically just the Kepler problem in one dimension (which is where I got the 1/R). But, being pretty much incompetent analytically, I went off and did a cheesy numerical simulation as well. From that I got pretty much the same answer, except it appears that the time in any given shell of dR thickness is proportional to R, not sqrt(R).
(Here's the spreadsheet with the simulation., as an XLS file. Note that, for clarity, I'm not worrying about constants in this. Also note that I'm assuming that the forces on a particle within the wiffle field are 0.)
Sure looks to me like density is considerably higher in the center than it is on the edge.
I'm pretty much assuming that it is monoenergetic, at least for purposes of this analysis. All I'm trying to show is that the "crowded edge" assumption should be re-examined. I agree that the velocity profile is periodic, but it definitely isn't sinusoidal.93143 wrote:To put it another way, if an ion oscillates through the core in a perfectly sinusoidal pattern, it spends about 9% of its time in the outermost 1% of its trajectory in a radial sense, but less than 4% of its time in the next-outermost 1% (which taken as a spherical shell has 98% of the volume of the outermost layer, meaning the average density in this second layer is less than half as high). I'm not proposing that the ion motion is actually sinusoidal, or that it's as locally monoenergetic as implied by this example (the real system will be smeared out somewhat), but it illustrates the point...
That doesn't make any sense to me. Indeed, I'd assert just the opposite: Inside the containment for the electrons, there should be no forces on the ion at all, while outside the containment, Coulomb's Law applies quite nicely.93143 wrote:The R^-2 density profile only applies near the centre. There's definitely a spike there, subject to thermal smearing of course, but the R^-2 profile assumes that the ions are at full speed, so it's invalid once they get away from the core and start to slow down.
More complicated
That doesn't make any sense to me. Indeed, I'd assert just the opposite: Inside the containment for the electrons, there should be no forces on the ion at all, while outside the containment, Coulomb's Law applies quite nicely.
I agree with you on what happens to the ion outside. But as the ion enters the electron containment should it not have a force on it equal to the electrons that still exist in between it and the center? In essence, the force is going to depend on the distribution of electron densities to some extent. If 99% of the electrons are on the outer edge, then the ion will stop experiencing any force from them the moment it cross that barrier. If 99% are pressed up tight to the center, they will continue exerting force on the ion all the way up to that tight inner ring. The reality likely falling some place in between. Or am I just extrapolating to far from conventional electrostatics?
I agree with you on what happens to the ion outside. But as the ion enters the electron containment should it not have a force on it equal to the electrons that still exist in between it and the center? In essence, the force is going to depend on the distribution of electron densities to some extent. If 99% of the electrons are on the outer edge, then the ion will stop experiencing any force from them the moment it cross that barrier. If 99% are pressed up tight to the center, they will continue exerting force on the ion all the way up to that tight inner ring. The reality likely falling some place in between. Or am I just extrapolating to far from conventional electrostatics?