Recovery.Gov Project Tracker
To clear up some misunderstanding (hopefully, not mine). High Beta means approaching but not exceeding one. As stated, greater than one results in the cusps blowing out. High Beta refers to comparisons with other machines, Tokamaks for example might operate in the region of ~ 0.1 Beta. I think I read somewhere that there is a Tokamak variation that might reach 0.4 Beta.
Greater density does not imply greater drive voltage. The pressure inside the magrid is determined by the density * the voltage/ B. This gives the Beta value up to the limit where the 'can explodes' or Beta = 1.
If the density is increased, the voltage would have to be decreased to maintain the same Beta. alternately if the density is reduced...
That they report increased density than expected, suggests that the Wiffleball effect and ion containment is working better than anticipated. This is somewhat confusing if electron losses are greater than expected. In that case they would not have been approaching Beta= one as closely, and that is directly related to the magnitude of the Wiffleball effect and the resultant density obtainable. Also, increasing the heating to me implies increasing the voltage/ KE of the ions, which is the same as saying they wish to increase the potential well to higher voltages. The potential well is by far the driving force that determines the energy of the ions. Since they mention the electron guns, I assume their current efforts do not include microwave heating. Microwaves are very important for heating Tokamak plasmas but not Polywells. My understanding is that if microwaves are used in the Polywell it will be to speed up neutral gas ionization near the Wiffleball border, or to induce POPs like effects.
Thermalization issues are not related to the density, so long as the average temperature is the same. It effects fusion rate, and possible Bremsstrulung, but not the pressure/ density measurement. So I do not think their brief statement gives any hints about thermalization issues- except: With the larger machines, the distance traveled in one pass of a charged particle is greater. At the same MFP this means that there may be more mantle thermalization per pass and this limits the effectiveness of edge annealing. Higher voltages compensates for this (as well as increasing the fusion cross section). Note that increased machine diameter and increased density will result in shorter MFP as a percentage of the machine diameter. So if the drive potential was adiquate for WB8 with predicted densities, the unexpected (?) improved densities would result in MFPs being too short to obtain planned goals regarding the MFP issues. Increased drive voltage would be needed to compensate for this issue alone. Nebel did say that WB6 worked in this thermalization limiting fashion, but that he was uncertain if larger machines would do so. Higher voltages in larger machines (and/or more dense plasma machines) would resolve this question.
Another consideration. Nebel mentioned that the Nubs in WB7 were hot spots, implying that they were more significant for ion and /or electron impacts /loses than anticipated. Going to wall standoffs may have helped due to the removal of cusp repeller effects effects similar to the repellar plates in WB5, which were large loss pathways for ions. With mild magnetic shielding of the nubs, the magrid potential would accumulate electrons here, and these would compromize the central electrostatic ion confinement. Thus lower density would result. The absence of these nubs near the mid plane of the magrid magnets could lead to greater ion confinement and density. Since the resultant ion density is greater, the contained electron density must also be greater, since the plasma is almost neutral. This would require greater electron input current, all other things being equal. I think that this would result in increased capacity electron guns/ magrid potential maintenance being required without invoking poorer electron confinement. Or perhaps not , my reasoning is nebulous here.
If greater densities can be achieved, then particle densities of ~ 10^23/ M^3 may be doable, as opposed to 10^21 or 10^22 particles per M^3. This would allow for smaller machine which would have some advantages. Of course engineering concerns (heat loading) may already be the size limiting factor for D-D Polywells. Even if the physics allowed more compact machines at the same power, the thermal wall loads may not permit it. For P-B11 Polywells this may be a different story. Because of direct conversion, the thermal loads may be less of a problem, so a P-B11 Polywell could actually end up being slightly smaller than a D-D Polywell ( referring to the Magrid diameter, not all the junk outside the Magrid).
Dan Tibbets
Greater density does not imply greater drive voltage. The pressure inside the magrid is determined by the density * the voltage/ B. This gives the Beta value up to the limit where the 'can explodes' or Beta = 1.
If the density is increased, the voltage would have to be decreased to maintain the same Beta. alternately if the density is reduced...
That they report increased density than expected, suggests that the Wiffleball effect and ion containment is working better than anticipated. This is somewhat confusing if electron losses are greater than expected. In that case they would not have been approaching Beta= one as closely, and that is directly related to the magnitude of the Wiffleball effect and the resultant density obtainable. Also, increasing the heating to me implies increasing the voltage/ KE of the ions, which is the same as saying they wish to increase the potential well to higher voltages. The potential well is by far the driving force that determines the energy of the ions. Since they mention the electron guns, I assume their current efforts do not include microwave heating. Microwaves are very important for heating Tokamak plasmas but not Polywells. My understanding is that if microwaves are used in the Polywell it will be to speed up neutral gas ionization near the Wiffleball border, or to induce POPs like effects.
Thermalization issues are not related to the density, so long as the average temperature is the same. It effects fusion rate, and possible Bremsstrulung, but not the pressure/ density measurement. So I do not think their brief statement gives any hints about thermalization issues- except: With the larger machines, the distance traveled in one pass of a charged particle is greater. At the same MFP this means that there may be more mantle thermalization per pass and this limits the effectiveness of edge annealing. Higher voltages compensates for this (as well as increasing the fusion cross section). Note that increased machine diameter and increased density will result in shorter MFP as a percentage of the machine diameter. So if the drive potential was adiquate for WB8 with predicted densities, the unexpected (?) improved densities would result in MFPs being too short to obtain planned goals regarding the MFP issues. Increased drive voltage would be needed to compensate for this issue alone. Nebel did say that WB6 worked in this thermalization limiting fashion, but that he was uncertain if larger machines would do so. Higher voltages in larger machines (and/or more dense plasma machines) would resolve this question.
Another consideration. Nebel mentioned that the Nubs in WB7 were hot spots, implying that they were more significant for ion and /or electron impacts /loses than anticipated. Going to wall standoffs may have helped due to the removal of cusp repeller effects effects similar to the repellar plates in WB5, which were large loss pathways for ions. With mild magnetic shielding of the nubs, the magrid potential would accumulate electrons here, and these would compromize the central electrostatic ion confinement. Thus lower density would result. The absence of these nubs near the mid plane of the magrid magnets could lead to greater ion confinement and density. Since the resultant ion density is greater, the contained electron density must also be greater, since the plasma is almost neutral. This would require greater electron input current, all other things being equal. I think that this would result in increased capacity electron guns/ magrid potential maintenance being required without invoking poorer electron confinement. Or perhaps not , my reasoning is nebulous here.
If greater densities can be achieved, then particle densities of ~ 10^23/ M^3 may be doable, as opposed to 10^21 or 10^22 particles per M^3. This would allow for smaller machine which would have some advantages. Of course engineering concerns (heat loading) may already be the size limiting factor for D-D Polywells. Even if the physics allowed more compact machines at the same power, the thermal wall loads may not permit it. For P-B11 Polywells this may be a different story. Because of direct conversion, the thermal loads may be less of a problem, so a P-B11 Polywell could actually end up being slightly smaller than a D-D Polywell ( referring to the Magrid diameter, not all the junk outside the Magrid).
Dan Tibbets
To error is human... and I'm very human.
Interesting line of thought Dan. I did not run that one out in my first take. If they did go to standoffs, you may be on to a part of it.Another consideration. Nebel mentioned that the Nubs in WB7 were hot spots, implying that they were more significant for ion and /or electron impacts /loses than anticipated. Going to wall standoffs may have helped due to the removal of cusp repeller effects effects similar to the repellar plates in WB5, which were large loss pathways for ions. With mild magnetic shielding of the nubs, the magrid potential would accumulate electrons here, and these would compromize the central electrostatic ion confinement. Thus lower density would result. The absence of these nubs near the mid plane of the magrid magnets could lead to greater ion confinement and density. Since the resultant ion density is greater, the contained electron density must also be greater, since the plasma is almost neutral. This would require greater electron input current, all other things being equal. I think that this would result in increased capacity electron guns/ magrid potential maintenance being required without invoking poorer electron confinement. Or perhaps not , my reasoning is nebulous here.
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)
The two factors need not be directly related. If by "heating" they mean upping the AVERAGE temperature of the electrons, it may be that they wish to flow MORE HOT mono-energetic electrons thru the system to flush out (heat up?) the thermalized electrons.D Tibbets wrote: That they report increased density than expected, suggests that the Wiffleball effect and ion containment is working better than anticipated. This is somewhat confusing if electron losses are greater than expected. In that case they would not have been approaching Beta= one as closely, and that is directly related to the magnitude of the Wiffleball effect and the resultant density obtainable.
Again, heating may not mean such an increase, just a removal (heat up) of anything that has thermalized downward.D Tibbets wrote: Also, increasing the heating to me implies increasing the voltage/ KE of the ions, which is the same as saying they wish to increase the potential well to higher voltages.
If there are more ions per cc, there is a higher chance for collisions which means a greater chance to themalize. Keeping those ions mono-energetic seems likely to be a complex dance of factors, including electron flow rate. Just saying.D Tibbets wrote: Thermalization issues are not related to the density, so long as the average temperature is the same.
Just thinking about this quickly, why are they concerned with the electron velocities at all? Seems to me the electrons can do their job of creating a potential well for the real actors (positively charged ions for fusion) as long as the electrons stay in the magnetic bottle. Are faster electrons more tightly held by the wiffleball?
They create the wiffleball. Otherwise Polywell is just a cusp confinement machine, no?toddzilla wrote:Just thinking about this quickly, why are they concerned with the electron velocities at all? Seems to me the electrons can do their job of creating a potential well for the real actors (positively charged ions for fusion) as long as the electrons stay in the magnetic bottle. Are faster electrons more tightly held by the wiffleball?
Some replies.
EMC2 have used microwaves (from microwave oven magnatrons) , as per Tom Ligon. What they were used for other than possibly trying to ionizing neutrals more quickly in small machines is unknown . I have not heard of any mention of them being used in WB6.
The Polywell is not just a bag to hold ions. It holds them and importantly accelerates them (heats them) to fusion temperatures in a structured potential well- thus some degree of confluence of the ions. I'm not certain (read as I haven't a clue) why the electrons have to have a significant KE to form a deep potential well. I'd think that so long as an ion was born just outside the cloud of electrons it would accelerate the same. But, EMC2 had difficulty obtaining deep wells. They improved considerably with WB5, but was still far short of goals. Bussard thought that increasing the electron current ~ 10 fold would increase the potential well a similar amount. But they only got a ~ 2 fold increase. The leakage of electrons (and ions?) was just too much. This seems strange as the reported ~ 10 fold improvement in containment / recirculation in WB6 over WB4 would seem to to be a similar effect. Perhaps in WB5 the ions leaking out pulled out more electrons- bipolar flow that A. Carlson championed. As mentioned then though, the ions tend to tug the electrons in a modest(?) coupling, but the reverse is not nearly as significant, all due to the momentum/ mass difference between the ions and electrons. Thus the repellers in WB5 (and repeller like nubs in WB6 and WB7?) attracts ions which also attracts weakly coupled electrons*. As I mentioned in the preceding post the nubs may act in this manner, though much (?) weaker than the repeller plates in WB5. Further elimination of this effect (if real) would be a convenient explanation for greater densities within the Wiffleball with the otherwise same conditions.
Changing the thermalization profile could require more heating . Or perhaps not. It might be more an issue of cooling. As the ions thermalize, some will be down scattered to cooler temperatures. I still do not understand their fate. I suppose they get reaccelerated by the hotter ions. The important point is that the hot- up scattered ions can escape, thus carrying away heat and thus cooling the rest of the plasma. These hot ions are not only bad for Brensstrulung considerations, but also because of this net cooling effect. Thus inhibiting this thermalization spread of the above average temperature ions effectively increases the temperature of the rest of the plasma (heating the below average ions through collisions (?). As mentioned above the main method of this inhibition of thermalization (of up scattered ions) is annealing. As pointed out in the paper by King, etel the Coulomb collision frequency has to dominate in the edge region (annealing). This requires that the MFP in most of the machine is greater than the diameter of the machine. As the MFP is 1/ square of the density and ~ temperature ^2, one can off set the other. The diameter (or usually radius is used) is the other variable. With a doubling of the radius, the collision frequency in the mantle (between core and edge) is doubled in proportion to the edge collision frequency. So all three factors need to be considered. My impression from Nebel's statement was that the trad offs in density and temperature in larger machines may not keep up in larger machines. You could reduce the density by decreasing Beta, but this also decreases the fusion rate , while increasing the electron losses. As has been mentioned, the Polywell is a conglomeration of compromises.
As KitemanSA suggested, increasing the heating -voltage to compensate for the plasma cooling by the escaping up scattered hot ions. is not the answer. I think this may have been A. Carlson's point when he said that multiple million volt potential wells would be required to compensate and that is devastating from a Bremsstrulung point of view (at least for P-B11 fusion). The work around is to prevent progressive up scattering through the annealing process, and by allowing the ions that are too hot to escape so long as the quantity lost is not too painful to replace.
* My understanding of coupling is that positive and negative particles interact with each other in a dominate fashion over the space charge, when they are close together. Cold dense plasmas are closely coupled. Hot and less dense plasmas are weakly coupled. Atoms would be the ultimate coupling. Tokamak plasmas are weakly coupled. Polywells may be denser, but also hotter. The hotter the temperature the faster the particles, so the time they are close together is less and thus deflections are smaller. That is why the Coulomb cross section (defined by the MFP increasing) goes down as the temperature (speed) increases. In his Google talk Bussard mentioned that the pure electron potential well has a square shape, but once ions are introduced, the electrons are tugged to a degree by the ions towards the center and a resultant elliptical well forms. This is due to the weak coupling and the low mass/ momentum of the electrons. This is a partial bipolar flow inwards that fights the space charge. In the case of electrons escaping through a cusp due to the space charge, they will also tug on ions, but because of the increased momentum of the ions this effect is several orders of magnitude less significant. At least, this was my argument against A. Carlson's claim that there would be bipolar flow (electrons = ions) out of the cusps.
Except for these mild to slight coupling concerns (depending on whether you are looking from the ions or the electrons perspective) the space charges dominate. This is why a collection of cold electrons dwelling in the cusps are bad (such as in WB5). This local space charge competes with the central potential well, so the coupling contribution becomes more significant, approaching the conditions that A. Carlson championed.
Dan Tibbets
EMC2 have used microwaves (from microwave oven magnatrons) , as per Tom Ligon. What they were used for other than possibly trying to ionizing neutrals more quickly in small machines is unknown . I have not heard of any mention of them being used in WB6.
The Polywell is not just a bag to hold ions. It holds them and importantly accelerates them (heats them) to fusion temperatures in a structured potential well- thus some degree of confluence of the ions. I'm not certain (read as I haven't a clue) why the electrons have to have a significant KE to form a deep potential well. I'd think that so long as an ion was born just outside the cloud of electrons it would accelerate the same. But, EMC2 had difficulty obtaining deep wells. They improved considerably with WB5, but was still far short of goals. Bussard thought that increasing the electron current ~ 10 fold would increase the potential well a similar amount. But they only got a ~ 2 fold increase. The leakage of electrons (and ions?) was just too much. This seems strange as the reported ~ 10 fold improvement in containment / recirculation in WB6 over WB4 would seem to to be a similar effect. Perhaps in WB5 the ions leaking out pulled out more electrons- bipolar flow that A. Carlson championed. As mentioned then though, the ions tend to tug the electrons in a modest(?) coupling, but the reverse is not nearly as significant, all due to the momentum/ mass difference between the ions and electrons. Thus the repellers in WB5 (and repeller like nubs in WB6 and WB7?) attracts ions which also attracts weakly coupled electrons*. As I mentioned in the preceding post the nubs may act in this manner, though much (?) weaker than the repeller plates in WB5. Further elimination of this effect (if real) would be a convenient explanation for greater densities within the Wiffleball with the otherwise same conditions.
Changing the thermalization profile could require more heating . Or perhaps not. It might be more an issue of cooling. As the ions thermalize, some will be down scattered to cooler temperatures. I still do not understand their fate. I suppose they get reaccelerated by the hotter ions. The important point is that the hot- up scattered ions can escape, thus carrying away heat and thus cooling the rest of the plasma. These hot ions are not only bad for Brensstrulung considerations, but also because of this net cooling effect. Thus inhibiting this thermalization spread of the above average temperature ions effectively increases the temperature of the rest of the plasma (heating the below average ions through collisions (?). As mentioned above the main method of this inhibition of thermalization (of up scattered ions) is annealing. As pointed out in the paper by King, etel the Coulomb collision frequency has to dominate in the edge region (annealing). This requires that the MFP in most of the machine is greater than the diameter of the machine. As the MFP is 1/ square of the density and ~ temperature ^2, one can off set the other. The diameter (or usually radius is used) is the other variable. With a doubling of the radius, the collision frequency in the mantle (between core and edge) is doubled in proportion to the edge collision frequency. So all three factors need to be considered. My impression from Nebel's statement was that the trad offs in density and temperature in larger machines may not keep up in larger machines. You could reduce the density by decreasing Beta, but this also decreases the fusion rate , while increasing the electron losses. As has been mentioned, the Polywell is a conglomeration of compromises.
As KitemanSA suggested, increasing the heating -voltage to compensate for the plasma cooling by the escaping up scattered hot ions. is not the answer. I think this may have been A. Carlson's point when he said that multiple million volt potential wells would be required to compensate and that is devastating from a Bremsstrulung point of view (at least for P-B11 fusion). The work around is to prevent progressive up scattering through the annealing process, and by allowing the ions that are too hot to escape so long as the quantity lost is not too painful to replace.
* My understanding of coupling is that positive and negative particles interact with each other in a dominate fashion over the space charge, when they are close together. Cold dense plasmas are closely coupled. Hot and less dense plasmas are weakly coupled. Atoms would be the ultimate coupling. Tokamak plasmas are weakly coupled. Polywells may be denser, but also hotter. The hotter the temperature the faster the particles, so the time they are close together is less and thus deflections are smaller. That is why the Coulomb cross section (defined by the MFP increasing) goes down as the temperature (speed) increases. In his Google talk Bussard mentioned that the pure electron potential well has a square shape, but once ions are introduced, the electrons are tugged to a degree by the ions towards the center and a resultant elliptical well forms. This is due to the weak coupling and the low mass/ momentum of the electrons. This is a partial bipolar flow inwards that fights the space charge. In the case of electrons escaping through a cusp due to the space charge, they will also tug on ions, but because of the increased momentum of the ions this effect is several orders of magnitude less significant. At least, this was my argument against A. Carlson's claim that there would be bipolar flow (electrons = ions) out of the cusps.
Except for these mild to slight coupling concerns (depending on whether you are looking from the ions or the electrons perspective) the space charges dominate. This is why a collection of cold electrons dwelling in the cusps are bad (such as in WB5). This local space charge competes with the central potential well, so the coupling contribution becomes more significant, approaching the conditions that A. Carlson championed.
Dan Tibbets
To error is human... and I'm very human.
Bipolar is the appropriate term. It is the best thing in the world, it is great. In fact I'm the greatest
... perhaps not, it is depressing that I used the wrong word. The world is not what it seemed. sigh... 
(apologies to anyone actually suffering this psychiatric condition )
Ambipolar is indeed the correct term.
Dan Tibbets
To error is human... and I'm very human.
The paper I was referring to in an earlier post was not by Katherine King (she has published various papers) but by Rosenberg and Krall.
http://www.dtic.mil/dtic/tr/fulltext/u2/a257651.pdf
Another paper with perhaps pertinent information:
http://www.askmar.com/Fusion_files/EMC2 ... ration.pdf
Dan Tibbets
http://www.dtic.mil/dtic/tr/fulltext/u2/a257651.pdf
Another paper with perhaps pertinent information:
http://www.askmar.com/Fusion_files/EMC2 ... ration.pdf
Dan Tibbets
To error is human... and I'm very human.