just plain electrostatic confinement

[ohiovr]

Magnetic fields seem to be the predominant way to confine a plasma. Electric fields can be mighty too, why couldn't they be utilized to confine a plasma of some kind?

if you had a cavity between several highly positively charged plates if you tossed in some protons in the center, would they be repelled by the fields and tend to hang out in the center? Or would the virtue of there still being electrons in the charged plates make those protons flee out like a bat out of hell?

Forget heating it for now. Will it confine or not?

[ladajo]

I think the issue with your idea is mass.

[D Tibbets]

Gauss law may apply to an extent if the plates are large enough. As the proton moves towards one plate the positive charge against it increases, while the positive charge behind it also increases. It sounds counter intuitive but when you assign a bunch of fixed point charges on both plates, the Gauss Law interaction becomes apparent. This means that any proton inside the space between the two plates moves with any momentum they have initially, or that it gains by collisions with other protons. and sooner rather than later it will hit one of the plates. There is no central restoring force in a perfect Gauss Law example, and less than total central restoring force in practically any example of plate dimensions and seperation. If you have just a few protons the collisions would be rare and a selected proton might remain stationary or a long time. But, if you want more than very very rare fusion collisions, you have to have a lot of collisions .

The idea is similar to a Penning trap for containing a few antiparticles. Between the magnetic containment and positive charge on the magnets, the few particles might be contained for a long time. Once the number of contained particles increases though- like from 10^3 particles per cc to 10^9 particles per cc, the coulomb collisions scatters the protons (or positrons) This results in wall collisions. Even with magnetic shielding it still occurs due to collision driven ExB transport across the magnetic field. Confinement decreases as density dependent collisions goes up. And we haven't even talked about cusp losses yet. In the two plate model, this would be equivalent to the edge of the plates.

If you want to contain one particle very close to absolute zero, this would work very well. If you want to contain enough protons to do something like fusion you need a lot a protons,deuterons, etc. and of course speed.

In the Polywell there are two ways to look at ion confinement. You can model a potential well with the greatest negativity in the center and the ions are drawn to the center, becoming the greatest momentum of the ion, they fly past and slow as they climb the potential well on the other side (or same side if collisions knock it back). The cycle repeats. If electrons cluster more towards the edge, the ions above most of them (greater radii) are accelerated centrally. Once past the shell of electrons they continue on towards the center due to their momentum and again Gauss Law considerations. Ideally positive ions could be contained indefinitely but with collisions the ion population moves towards thermalization, which means that some of the ions will be upscattered to energies above the potential well and they will escape electrostatic confinement. The higher the density, the faster this occurs. One modifying effect that delays this is the proposed edge annealing of ions near the top of their potential well. The physics of this is straight forward, but it is uncertain if the dynamics allows for this annealing effect. The positive charge or neutral charge on the Magrid or two seperated flat plates (practically infinite size) does not contribute to the behavior of the charged particles inside/ between them. This is an ideal analysis. Real world Magrids or plates do not provide for perfect Gauss Law interactions, so there is some gray area.

[EDIT] Actually with Gauss Law my discription may suffer, but essentially a charged particle inside a hollow conductive sphere sees no preferential wall charge irregardless of what ever voltage may be applied to the shell, Odd shaped shells or shells stretched to such an extent that it resembles two flat plates to the local charged particle maintains Gauss Law. When holes are punched in the sphere/ plates, things start to change, especially close to the holes.

Dan Tibbets

[hanelyp]

The 2 charged plates sound almost like a 2D Farnsworth fusor, minus a few important detail.

[ohiovr]

[EDIT] Actually with Gauss Law my discription may suffer, but essentially a charged particle inside a hollow conductive sphere sees no preferential wall charge irregardless of what ever voltage may be applied to the shell, Odd shaped shells or shells stretched to such an extent that it resembles two flat plates to the local charged particle maintains Gauss Law. When holes are punched in the sphere/ plates, things start to change, especially close to the holes.

Dan Tibbets

Thanks Dan. I had considered an experiment Faraday did:

http://en.wikipedia.org/wiki/Faraday's_ ... experiment

Where charges tend to hang out on the outside of hollow metal objects. This makes me wonder a little about how the fusor can confine the plasma. Is the Fusor grid's holes so large that this effect doesn't happen?

I had thought then of the worst case scenario. What if you make a spherical cavity out of a bunch of smaller spheres that don't touch but are within a small distance from each other. There would be weaknesses, or would the gauss law apply to that also?

[KitemanSA]

A fusor appears to be a point NEGATIVE charge to an ion which accelerates past the grid, passes THRU the fusor core, exits the grid and is then attracted by that point negative charge again. Thus it slows, accelerates back, passes the grid, thru the fusor core, ad infinitem until it hits another ion and fuses, or hits a grid and is lost, or thermalizes and can't fuse anymore.

[ohiovr]

A fusor appears to be a point NEGATIVE charge to an ion which accelerates past the grid, passes THRU the fusor core, exits the grid and is then attracted by that point negative charge again. Thus it slows, accelerates back, passes the grid, thru the fusor core, ad infinitem until it hits another ion and fuses, or hits a grid and is lost, or thermalizes and can't fuse anymore.

If you can have a core of electrons before you start adding ions, why not just start with a group of ions with no electrons?

[KitemanSA]

A fusor appears to be a point NEGATIVE charge to an ion which accelerates past the grid, passes THRU the fusor core, exits the grid and is then attracted by that point negative charge again. Thus it slows, accelerates back, passes the grid, thru the fusor core, ad infinitem until it hits another ion and fuses, or hits a grid and is lost, or thermalizes and can't fuse anymore.

If you can have a core of electrons before you start adding ions, why not just start with a group of ions with no electrons?

are you talking "fusor" or "Polywell"? There are no electrons in a Farnsworth Fusor, except those on the grid.

[ohiovr]

A fusor appears to be a point NEGATIVE charge to an ion which accelerates past the grid, passes THRU the fusor core, exits the grid and is then attracted by that point negative charge again. Thus it slows, accelerates back, passes the grid, thru the fusor core, ad infinitem until it hits another ion and fuses, or hits a grid and is lost, or thermalizes and can't fuse anymore.

If you can have a core of electrons before you start adding ions, why not just start with a group of ions with no electrons?

are you talking "fusor" or "Polywell"? There are no electrons in a Farnsworth Fusor, except those on the grid.

Ok. So the grid is negatively charged? And it behaves as a point charge?

[ohiovr]

I made a really short video about the idea

http://www.youtube.com/watch?v=7bAc_LwyrzA

[KitemanSA]

Ok. So the grid is negatively charged? And it behaves as a point charge?

Correct.

[hanelyp]

There are 2 major variants of the Farnsworth type device:
- inner grid negative, directly driving ions.
- inner grid positive, driving electrons to produce a virtual cathode which accelerates ions. The polywell more closely follows this pattern.

[ohiovr]

A point at the center of a cage contains a negative charge (without there being any electrons at that point) which attracts ions. Super! If the potential is high enough how could the ions ever gain enough energy to get far enough away from the point charge to collide with the grid?

[D Tibbets]

There are some misconceptions here. A grid or collection of conductive balls arranged at a common radius from the center are essentially the same thing. In the typical glow discharge fusor The grid is negatively charged. This does two interactive things. While the current of electrons flowing through the wire is not enough to heat it much (only perhaps 10-20 milli amps, the negatibe potential of the wire does attract ions ( another topic is how the ions are created). These ions if outside the grid is attracted towards it, If the grid is mostly symmetrical and occupies only a small area of an imaginary sphere at that radius,, it may fly past the wire grid towards the center. Once inside the grid the ion no longer sees the charge on the grid- assuming ideal Gauss Law conditions. As such the internal ion is not accelerated further by the wire cathode grid and continues on momentum alone. They pass through the center and continue the same way until they are outside the radius of the wire grid. Now they are again exposed to a centrally directed negative potential. The ions slow, stop, and return towards the center at the potential energy of the wire grid (Voltage). The ions do interact with each other also and this leads to what is called the central virtual anode, though this is generally only a smaller negative charge up to the point where things break down.

Not all ions miss the wire, those that hit it, generally at full KE heats the grid,this is what causes the grid to glow red hot. This heating leads tomany more electrons being emmited from the wire (thermoionic emmision) and also being sputtered off by the ion impacts. The electrons fly off in all directions, those that fly towards the center can create a virtual cathode which changes the nature of the potential well for the ions somewhat. These electrons though are very quickly though. going to end up hitting the surrounding walls of the vacuum chamber. It is this electron current from the wire cathode, and through the plasma (which the electrons are a part of) to the grounding shell that is the input power of the system. In a glow discharge fusor, the voltage and current measured is mostly this electron current from cathode wire to vacuum vessel shell ( or grounding grid. The ions are mobile charge carriers also so they complicate the picture in a plasma as opposed to a solid wire where only the electrons are generally considered as the charge carrier.

So, in a glow discharge fusor there is both a real cathode wire or mini spheres, etc. and possibly a virtual cathode that is made up of electrons as they pass through the center of the machine. The contributions of these two cathodes may vary, though in a fusor it is mostly the wire cathode.

Electrostatic charge can only contain one species, either positively charged ions or electrons. It cannot do both at the same time. You will always have losses ~ equal to your input power. The electron losses are essentially 100 percent. The ion losses may be ~ 5-10%. This means that any electron in the system will only make one pass before grounding on a surface. The ions may make up to 10-20 passes.

Magnetic fields can contain both species simultaneously, provided they are in motion. The problem is that cusps are leaky. And even if there are no cusps, magnetic fields are leaky due to what is called ExB drift. This is much like diffusion of a gas except the process is quantified to discrete jumps based on the gyroradius of the charged particle. The collisions between particles drives this so the containment worsens as the density increases.

Idea of the Polywell is that you ignore the magnetic containment of the ions as the gyroradius of these particles is painfully wide. It would only require perhaps 10 collisions to transport an ion through the magnetic field. An electron under the same conditions would require more than ~ 600 collisions. The electron confinement is ~ 60 times better (compared to hydrogen ions) from the perspective of ExB. In the Polywell,this means that only electrons need to be contained magnetically. By injecting more electrons than ions , there is an excess of electrons and this creates the virtual cathode. If Gauss Law was perfect in the machine, there would be no ion impact on the real cathodes- electron guns. That is not true, but if it can be made close enough....

This decoupling of the methods of electron containment and ion containment (magnetic and electrostatic) is the what lies at the root of the physics of the machine. The electron excess that creates a non neutral plasma is the tool used for ion containment. Things quickly become more complicated as collision effects, up scattering, annealing, recirculation, electron injection efficiency, shape of the potential well, depth of the potential well in relation to input voltage, confluence, various plasma instabilities, etc are considered. One aspect of the magnetic confinement that is often ignored by critics is the issue of edge instabilities/ macro instabilities. The advantage that the Polywell has due to the always convex magnetic fields towards the plasma is potentially tremendous. This consideration is what is driving tokamaks to huge size and convoluted schemes in order to manage these edge instabilities. It also is what limits the tolerable densities and thus power density of tokamak machines. Driving up densities and thus Beta in tokamaks magnifies the edge instabilities logarithmically.

The Polywell is a leaky machine, but the leakyness does not increase with increased density (up to a limit), it actually decreases(the Wiffleball effect). This changes the machine from an admitted failure into a possible winner, at least based on the physics as scaled from small machines.

Dan Tibbets

[KitemanSA]

There are 2 major variants of the Farnsworth type device:
- inner grid negative, directly driving ions.
- inner grid positive, driving electrons to produce a virtual cathode which accelerates ions. The polywell more closely follows this pattern.

The second is an Elmore-Tuck-Watson machine. Because the well is developed by a flow of electrons, it is not a true electroSTATIC fusor but is an electro-dynamic fusor.