One Figure For The Theory Of the Wiffle Ball

Discuss how polywell fusion works; share theoretical questions and answers.

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mattman
Posts: 459
Joined: Tue May 27, 2008 11:14 pm

One Figure For The Theory Of the Wiffle Ball

Post by mattman »

Looking for feedback

Image


Caption:

This figure shows the development of the purposed “waffle ball” confinement concept [6]. Three rows of figures are shown: the magnetic field, the electron motion and the plasma density inside the polywell. (A) At low beta, the field is the superposition of six rings in a box [2]. In the center is a null point - a zone of no magnetic field. The plasma is magnetized, meaning that the plasma and magnetic field intermix [11]. The electrons and ions feel a Lorentz force [11]. This makes them corkscrew along the magnetic field lines; well their charges interact with one another [10]. The radius of this corkscrew is the gyroradius. The plasma density is low, making the ratio of plasma pressure to magnetic field pressure (the beta number) very low. (B) As plasma is injected, the density rises. The plasma puts more pressure on the surrounding magnetic field, increasing the beta number. (C) At a beta ratio nears 1, this plasma pressure is equal to, or greater than the magnetic field pressure. The pressure pushes the magnetic field outward, starting from the null point [1, 3, 6]. A sharp boundary is formed [3]. A skin current is predicted to form on this boundary layer [4, 5, 8]. Because the magnetic field must be continuous, this forces the surrounding magnetic field density to rise [10]. This tightens the corkscrewing motion outsides the center. (D) As the plasma presses outward, the density of the surrounding field rises. This shrinks the space available for escaping plasma [6]. It causes the plasma outside the field free region to spin in a tighter orbit (with a smaller gyroradius). Meanwhile, the material in the center sees no field from the rings. This means that its’ motion inside the field free radius should be relatively straight or ballistic [2]. (E) This forms two regions: adiabatic and non-adiabatic plasma [2, 8].

Sources:

1. Presentation “Measurement of Enhanced Cusp Confinement at High Beta” Dr. Jaeyoung Park, University of Wisconsin-Madison Madison Wisconsin. June 2014
2. Carr, Matthew, and David Gummersall. "Low Beta Confinement in a Polywell Modeled with Conventional Point Cusp Theories." Physics of Plasmas 18.112501 (2011): n. page. Print
3. Park, Jaeyoung, Nicholas A. Krall, and Paul E. Sieck. "High Energy Electron Confinement in a Magnetic Cusp Configuration." In Submission (2014): 1-12. Http://arxiv.org. Web. 13 June 2014.
4. Tuck, James L. "A New Plasma Confinement Geometry." Nature 187.4740 (1960): 863-64. Nature Publishing Group. Web. 13 June 2014.
5. Berkowitz, J., K.o. Friedrichs, H. Goertzel, H. Grad, J. Killeen, and E. Rubin. "Cusped Geometries." Journal of Nuclear Energy (1954) 7.3-4 (1958): 292-93. Web. 16 June 2014.
6.“The Advent of Clean Nuclear Fusion: Superperformance Space Power and Propulsion” Bussard R, W. 57th International Astronautical Congress (IAC 2006), Valencia, Spain - October 2006
7. Tuszewski, M. "Field Reversed Configurations." Nuclear Fusion 28.11 (1988): 2033-092.
8. Containment in a cusped Plasma System, Dr. Harold Grad, NYO-9496
9. Rogers, Joel. "Steady State Polywell Fusion Device Designed Using 2D Simulation." The 10th Annual US-Japan IEC Conference. Kyoto University, 4 Dec. 2008. Web. 04 Jan. 2014.
10. "Ephi - the Simple Physics Simulator." www.mare.ee. Indrek Mandre, 2007. Web. 08 Apr. 2012.
11. Jackson, John David. Classical Electrodynamics. 2nd ed. N.p.: Jones & Bartlett, n.d. Print.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: One Figure For The Theory Of the Wiffle Ball

Post by D Tibbets »

I have little conflict with your presentation, except...

Beta can approach one, but not exceed it without the plasma pressure being greater than magnetic pressure. This implies several things. The magnetic field can be pushed back to the limits (radius) of the magnet cans, and thus ground on the cans- the KE is lost, and containment is essentially limited to one pass- dismal. Alternatly, and perhaps more significant, the Wiffleball border- plasma/ B field dominate cross over border expands beyond the midplane radius of the magrid and the cusps start opening up again relative to the surface area of the confining wiffleball border. This is essentially a reversal of the situation as Beta approaches one from the low side. Confinement thus rapidly decreases to that at low Beta conditions. This increasingly limits the pressure obtainable because of losses reaching levels similar to low Beta. A Beta of one becomes a self stabilizing condition so long as electron/ plasma input can be maintained very slighly above that needed to make up for losses at an idealized Beta of one. There may be oscillations about this point, and this may even offer opportunities for various electron input manipulations and plasma wave effects/ POPS effects.

Your illistrations shows the expansion in the average radius of the magnetic free zone, but there is no illistrated change in the geometry/ slope of the field lines. I think the fields away from the cusps would be compressed more because they are more perpendicular to the plasma, and the KE of the plasma particles in the vector radial to the center and perpendicular to the B field pushes the most. This tends to push the inward peaks of the B field outward more with the effect that the highly conical surfaces of the quasi spherical plasma glob becomes mopre rounded- spherical with relatively smaller dimples where the cusps are. The B field surfaces are never pushed back beyond convex surfaces, but overall sphericity increases, becomes smoother. This is useful in considering the changes in surface area as the plasma quasi sphere as the plasma expands without a corresponding increase in cusp loss area. It is not that the cusps are shrunken or pinched, but that their loss collecting areas are reduced as the overall surface becomes more spherical . The pool table does not become a same size snooker table with smaller pockets (cusps); rather the pockets remain the same size, but the table becomes much larger.

I admit some ambiguity. The description of the Wiffleball tends to suggest constant size/ volume with shrinkage of the cusp holes, resulting in a increase in maintainable density at constant volume. Alternately, the same effect results if the holes remain the same but the volume increases with constant density. The former implies a change in the surface geometry and, sharp border conditions. The latter to volume expansion. I suspect both apply in an interactive manner.

A current sheath at the Wiffleball border is reasonable with a percentage of the electrons being trapped on B field lines near the border and mirroring back and forth. But with a Beta very close to one and the sharp border described by Grad, the electrons turn with only ~ 1/2 gyroraduis orbit before returning the the B field free interior. The electron dwell time on this border is very short . In this ideal situation, I think there would be no or very minimal sheath current. How close to this idealized conjecture the real system approaches is unknown.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: One Figure For The Theory Of the Wiffle Ball

Post by D Tibbets »

In order to clarify (hopefully) my limited understanding of the surface current sheath. , considerations of the shape of the potentail well needs to be considered. Electrons are injected with a mostly radial vector towards the center. This results in a space charge that slows the electrons in the center and accelerates them towards the edge. This initial elliptical (or parabolic?) potential well quickly relaxes through inter electron collisions into a more peripheral high angular momentum cloud of electrons near the confining Wiffleball border. . This does not have to imply a B field line trapped electron population mirroring back and forth along lines. The sharp border could still deflect the electrons as if from a hard surface, but because the electrons try to get away from each other / space charge effects, they end up in this border region. Bussard implied this in his Google talk when he mentiond the square shape of the potential well. I is more complicated than this though. With the introduction of ions the electrons are tugged along withe the nearby radially traveling ions . This pulls the electrons inward and the shape of the potential well becomes (stabilizes at) a more elliptical configuration. This interplay related to the relative momentum of the ions and electrons results in the final potential well shape and the distributions of ion and electron populations in terms of radial distribution and energy. It has consequences for ion convergence, central virtual anode formation, Bremsstruhlung considerations, etc. It also effects the electron currents in terms of surface current and radial current. A complex situation to say the least. It is not just a matter of the percentage of electrons that are trapped on B field lines just beyond the Wiffleball border (and undergoing ExB diffusion) but also the electrons traveling on high angular momentum paths just inside (and glancing off) of the Wiffleball border. Even this glancing action is complex because the border is not truely spherical , it is always convex, meaning that one glance may deflect the electronat a shallow angle, but the next may deflect it at an acute angle back towards the center, or conversely glance down a cusp cone.

Dan Tibbets
To error is human... and I'm very human.

mattman
Posts: 459
Joined: Tue May 27, 2008 11:14 pm

Re: One Figure For The Theory Of the Wiffle Ball

Post by mattman »

OK,

1. Someone asked: What is causing this expansion? Diamagnetism? Bulk plasma pressure? Grad’s concept? I do not think we know for sure.

2. I do not think anyone has measured the shape. We always talk about the "14-point star". But it's theory. I will leave it intentionally vague.

3. Plasma pressure and B-field pressure will both change as the cloud presses outward.


Below is the refined figure.

===

Image

Caption:

This figure shows the development of the proposed “waffle ball” confinement concept [6]. Three rows of figures are shown: the magnetic field, the electron motion and the plasma density inside the polywell. (A) At low beta, the field is the superposition of six rings in a box [2]. In the center is a null point - a zone of no magnetic field. The plasma is magnetized, meaning that the plasma and magnetic field intermix [11]. The electrons and ions feel a Lorentz force [11]. This makes them corkscrew along the magnetic field lines; while their charges interact with one another [10]. The radius of this corkscrew is the gyroradius. The plasma density is low, making the resulting plasma pressure (density*temp*boltzmann) also low. This means the beta ratio is also low. (B) As plasma is injected, the density rises. The plasma puts more pressure on the surrounding magnetic field, increasing the beta ratio. (C) As the beta ratio reaches and exceeds 1, the plasma pressure overpowers the magnetic field pressure. This pushes the cloud outward, starting from the central null point [1, 3, 6]. As the plasma presses outwards, the density of the surrounding magnetic field rises [10]. This tightens the corkscrewing motion of the particles outsides the center. They move with a smaller gyroradius. A sharp boundary is formed [3]. A skin current is predicted to form on this boundary layer [4, 5, 8]. This may cause the plasma to go diamagnetic, rejecting the external field [6]. (D) If the pressures find equilibrium at a beta of one, this determines the shape of the plasma cloud. The tightening field also shrinks the space available for escaping plasma, forming the “wiffle ball” confinement [6, 12]. (E) In the center, there is no magnetic field from the rings. This means that its’ motion inside the field free radius should be relatively straight or ballistic [2]. This forms two regions: adiabatic and non-adiabatic plasma [2, 8].

Sources:

1. Presentation “Measurement of Enhanced Cusp Confinement at High Beta” Dr. Jaeyoung Park, University of Wisconsin-Madison Madison Wisconsin. June 2014
2. Carr, Matthew, and David Gummersall. "Low Beta Confinement in a Polywell Modeled with Conventional Point Cusp Theories." Physics of Plasmas 18.112501 (2011): n. page. Print
3. Park, Jaeyoung, Nicholas A. Krall, and Paul E. Sieck. "High Energy Electron Confinement in a Magnetic Cusp Configuration." In Submission (2014): 1-12. Http://arxiv.org. Web. 13 June 2014.
4. Tuck, James L. "A New Plasma Confinement Geometry." Nature 187.4740 (1960): 863-64. Nature Publishing Group. Web. 13 June 2014.
5. Berkowitz, J., K.o. Friedrichs, H. Goertzel, H. Grad, J. Killeen, and E. Rubin. "Cusped Geometries." Journal of Nuclear Energy (1954) 7.3-4 (1958): 292-93. Web. 16 June 2014.
6.“The Advent of Clean Nuclear Fusion: Superperformance Space Power and Propulsion” Bussard R, W. 57th International Astronautical Congress (IAC 2006), Valencia, Spain - October 2006
7. Tuszewski, M. "Field Reversed Configurations." Nuclear Fusion 28.11 (1988): 2033-092.
8. Containment in a cusped Plasma System, Dr. Harold Grad, NYO-9496
9. Rogers, Joel. "Steady State Polywell Fusion Device Designed Using 2D Simulation." The 10th Annual US-Japan IEC Conference. Kyoto University, 4 Dec. 2008. Web. 04 Jan. 2014.
10. "Ephi - the Simple Physics Simulator." www.mare.ee. Indrek Mandre, 2007. Web. 08 Apr. 2012.
11. Jackson, John David. Classical Electrodynamics. 2nd ed. N.p.: Jones & Bartlett, n.d. Print.
12. Should Google Go Nuclear? Clean, Cheap, Nuclear Power. 24 minutes, 18 seconds. Perf. Dr. Robert Bussard. Google Tech Talks. YouTube, 9 Nov. 2206. Web. 15 Sept. 2010. http://video.google.com/videoplay?docid ... 6673788606#.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: One Figure For The Theory Of the Wiffle Ball

Post by D Tibbets »

What is the difference between your two posts?

Here is a picture of my appreciation of the approximate shape of the magnetic free plasma expanded to near Beta=one conditions. This is a mathematical model from a web site. The increased current input to the center is interpreted as increased density which pushes out the confining magnetic field.

Image

Second image is before expansion and after, with arbitrary yellow lines drawn to better illustrate the border between the confining electromagnet magnetic field region and the field free interior. Again note that the border is always at least slightly convex to the center, though this illustration does not show that well.

Image

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: One Figure For The Theory Of the Wiffle Ball

Post by D Tibbets »

An additional image created a few years ago. This is again a modeled illustration with a set of internal magnets substituting for the plasma pressure. Ignor my manipulation in the center and only look at the space between the magnet sets to get a picture of the interface between them. This model forced Art Carlson, a highly critical plasma physicist to concede that his anti Wiffleball demand for modeled proof was satisfied. At least he quit using this as an argument against the Polywell.

Image

Dan Tibbets
To error is human... and I'm very human.

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