Significance of Electron Recirculation Revisited

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

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Betruger
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Postby Betruger » Fri Apr 02, 2010 7:23 pm

Oops. Thanks.

Art Carlson
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Postby Art Carlson » Fri Apr 02, 2010 7:44 pm

Art Carlson wrote:For a sphere with radius R and a

uniform charge density rho,

the potential difference between the center of the sphere and infinity is Phi

= 0.5*(rho/epsilon_0)*R^2

Take Phi and rho as given, and solve for R:

R = sqrt( 2*(e*Phi) / (rho*e/epsilon_0) )

TallDave wrote: What's the lowest density that could produce macroscropic non-neutral structures?

Art Carlson wrote:Do you know how to plug numbers into a formula?

TallDave wrote:Do you? If so, why haven't you done so to test their meaningfulness? They're your equations, after all, and for those of us who don't encounter rho or T_e on a daily basis they're a tad obscure, esp. when you don't explain what your terms represent.

Where's the problem?

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Postby Art Carlson » Fri Apr 02, 2010 8:20 pm

Indrek wrote:
Art Carlson wrote:Would you mind giving some numbers?
  • n_e
  • n_i
  • the geometry of the structure (smallest dimension, and whether it is more spherical, cylindrical, or slab shaped)
  • the potential difference within the structure
  • WB6 dimensions, 0.1T
  • sphere of uniform charge, 0.1m radius
  • Effective well depth ~4000V
  • <E>=12kV
  • (N_e-N_i)e=5.4e-8C

Art Carlson wrote:Phi = 0.5*(rho/epsilon_0)*R^2

V = (4/3)*pi*R^3 = (4/3)*pi*(0.1 m)^3 = (4.2e-3 m^3)
rho = Q / V = (5.4e-8 C) / (4.2e-3 m^3) = (1.29e-5 C/m^3)
(rho/epsilon_0) = (1.29e-5 C/m^3) / (8.85e-12 F/m) = (1.46e6 V/m^2)
Phi = 0.5*(rho/epsilon_0)*R^2 = 0.5*(1.46e6 V/m^2)*(0.1 m)^2 = (730 V)

This is a factor of 5 or 6 lower than the 4000V you mention, but that is probably well within the uncertainties and approximations we have made.

Can you verify quasineutrality, i.e. that (N_e-N_i) / N_e << 1 ? I assume so.

So where do you see a problem?

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Postby TallDave » Fri Apr 02, 2010 8:54 pm

Well, then you said you didn't mean we couldn't have potential across larger areas, so now I'm not sure we disagree on anything of consequence. My thought was we could test whether this would also prevent a fusor from operating, but clearly the latter doesn't.
Last edited by TallDave on Fri Apr 02, 2010 9:25 pm, edited 1 time in total.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

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Postby Indrek » Fri Apr 02, 2010 9:23 pm

Art Carlson wrote:
Indrek wrote:
Art Carlson wrote:Would you mind giving some numbers?
  • n_e
  • n_i
  • the geometry of the structure (smallest dimension, and whether it is more spherical, cylindrical, or slab shaped)
  • the potential difference within the structure
  • WB6 dimensions, 0.1T
  • sphere of uniform charge, 0.1m radius
  • Effective well depth ~4000V
  • <E>=12kV
  • (N_e-N_i)e=5.4e-8C

Art Carlson wrote:Phi = 0.5*(rho/epsilon_0)*R^2

V = (4/3)*pi*R^3 = (4/3)*pi*(0.1 m)^3 = (4.2e-3 m^3)
rho = Q / V = (5.4e-8 C) / (4.2e-3 m^3) = (1.29e-5 C/m^3)
(rho/epsilon_0) = (1.29e-5 C/m^3) / (8.85e-12 F/m) = (1.46e6 V/m^2)
Phi = 0.5*(rho/epsilon_0)*R^2 = 0.5*(1.46e6 V/m^2)*(0.1 m)^2 = (730 V)

This is a factor of 5 or 6 lower than the 4000V you mention, but that is probably well within the uncertainties and approximations we have made.

Can you verify quasineutrality, i.e. that (N_e-N_i) / N_e << 1 ? I assume so.

So where do you see a problem?

You made an error, it comes at 7300. But now I'm totally confused. Did you not say that non-neutral structures of only microns can appear. But this one here is 0.2m large and satisfies the Gauss law.

Or wait. You are treating quasi-neutral and non-neutral as different things?

In that case. Here's a question: how much does the Gauss law care how the neutral part of the plasma is distributed? I answer: it doesn't at all. So what is it that you are actually saying? We could place about the same amount of charge even outside where there are no ions, no problem, probably, no Gauss laws broken.

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Postby MSimon » Fri Apr 02, 2010 11:44 pm

the way i see it, there is a magnetic equilibrium manifold, an electrostatic equilibrium manifold, offset, and two species differing in inertia, but (almost) balanced in charge. even without various edge and surface effects, that topology spells a multi-mode resonant system to me. so it will 'pump' in various dimensions, hence Maxwell, Coulomb and quasineutrality happily co-reside, within frame.


That is what I think too. I even get visions of it from time to time.

As far as bunching: have a look at the two MIT PhD thesis papers on a gridded machine. I have seen similar results in other (not open) simulations.
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Postby Art Carlson » Sat Apr 03, 2010 1:24 pm

Apparently I used the term "non-neutral structure" without being sufficiently clear on what I meant. (It's implicit in the derivation - but that's a poor excuse.)

What's the easiest way to say this? It's simplest if we only have protons and electrons. Quasi-neutral means the proton density is nearly equal to the electron density. By non-neutral I meant that one of the densities is much larger than the other. Strictly speaking that may be a poor choice of words. Maybe I should have said

As a simple consequence of Coulomb's Law, coupled with an upper limit for the potential and a lower limit for the density, a region in a polywell reactor where the ion density differs substantially from the electron density can never be bigger than a few microns across.

At one time some people were under the impression that there were a lot more electrons in a polywell than there are ions. I think the realisation has taken hold that that cannot be and need not be. Where the misconception is dwelling like a stubborn cough is the cusps. The cusps may be very small, but they are not small enough to allow a significant imbalance of ions and electrons. And yet some people seem to think that electrons can make an excursion out the cusps and back in again without taking ions along as hitchhikers. It's important because it means you can't improve on cusp confinement by applying some clever arrangement of radial electric fields. And cusp confinement by itself isn't good enough.

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Postby Indrek » Sat Apr 03, 2010 3:58 pm

Art Carlson wrote:Apparently I used the term "non-neutral structure" without being sufficiently clear on what I meant. (It's implicit in the derivation - but that's a poor excuse.)

What's the easiest way to say this? It's simplest if we only have protons and electrons. Quasi-neutral means the proton density is nearly equal to the electron density. By non-neutral I meant that one of the densities is much larger than the other. Strictly speaking that may be a poor choice of words. Maybe I should have said

As a simple consequence of Coulomb's Law, coupled with an upper limit for the potential and a lower limit for the density, a region in a polywell reactor where the ion density differs substantially from the electron density can never be bigger than a few microns across.
At one time some people were under the impression that there were a lot more electrons in a polywell than there are ions. I think the realisation has taken hold that that cannot be and need not be. Where the misconception is dwelling like a stubborn cough is the cusps. The cusps may be very small, but they are not small enough to allow a significant imbalance of ions and electrons. And yet some people seem to think that electrons can make an excursion out the cusps and back in again without taking ions along as hitchhikers. It's important because it means you can't improve on cusp confinement by applying some clever arrangement of radial electric fields. And cusp confinement by itself isn't good enough.

I have come to the same conclusion. From the same electrostatics simulations. Allow me to quote myself from a message I posted before in this very thread:
Indrek wrote:Now there has been talk about this all-electron wiffleball. With a description: We send in electrons. Then we puff some deuterum in it and it starts to fuse. How large wiffleball can you have with just that charge that made up the potential well. 5.4e-8C. If you work my image coil derivation in reverse you'll see the wiffleball we would get would be the size of I dunno, less than a millimeter? And that's absurd.

And if we added all those electrons in, all ~1e17 of them, with no ions, we would get a potential well of billion volts. With 12kV electrons. If that worked, Maxwell would start spinning so fast in his grave we could attach magnets to his corpse and solve all the world's energy problems. So can't do that.

Although this is not as clear as yours, I think your statement is also misleading. Rather it should be: At the plasma densities in polywell, the net charge of electrons (N_e-N_i) compared to the density of plasma can be very small (say one part per million), or in math
(N_e - N_i) / N_e << 1. From this follows that the amount of charge that can flow out of the system through the cusps (or whatever) must be miniscule compared to the overall electron population.

And putting your equation into perspective. The electrons get only so much energy (eV) when we put them into the system (say we shoot 12keV electron beams). If we constrain the structures inside the polywell to the same valued potential difference and require them to be non-neutral (large charge density) then they must be miniscule - meaning they can't contain much charge at all compared to the overall electron population.

Ok. Better end this thread here.

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Postby rcain » Sat Apr 03, 2010 10:26 pm

MSimon wrote: ...As far as bunching: have a look at the two MIT PhD thesis papers on a gridded machine. I have seen similar results in other (not open) simulations.


Do you have a link at all? ( I tried search with no success) thanks.

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Postby MSimon » Sat Apr 03, 2010 10:34 pm

rcain wrote:
MSimon wrote: ...As far as bunching: have a look at the two MIT PhD thesis papers on a gridded machine. I have seen similar results in other (not open) simulations.


Do you have a link at all? ( I tried search with no success) thanks.


http://ssl.mit.edu/publications/theses/ ... Thomas.pdf

http://ssl.mit.edu/publications/theses/ ... chCarl.pdf

The sidebar here is full of linky goodness:

http://iecfusiontech.blogspot.com/
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Postby rcain » Sun Apr 04, 2010 4:40 am

thanks for those. i recall now reading them, though now again with renewed interest.

good to see Poincare plots in use. (an intro to the subject here for those interested - http://www.physics.emory.edu/~weeks/res ... ries7.html - Poincaré sections - visualisations of 'self organizing behaviors)

also, use of OOPIC s/w feaures large. i am downloading a free copy now. (Solo had a bash with it a while ago, and DrMike looked at it, anyone else here used it in anger?)

Now, please forgive this massively long post, but I couldnt help but note some key findings as a read, and thougt i'd post them here, rather than lose them:

http://ssl.mit.edu/publications/theses/ ... chCarl.pdf wrote:...
4.3.2. Detection of two-stream instability
A secondary goal of this work was to look for evidence of the two-stream instability that
McGuire had seen in computational experiments with good confinement [357]. The
saturated mode of this instability was generally seen to be either a single or double
bunching of the ions as they “ring” in the well of the IEC system. This growth can be
seen in the raw data of figure 84 and more clearly in figure 85 below.
...
Figure 85 above clearly
illustrates the growth in amplitude of the oscillating signal after the ion injection is
terminated (time 0). While a slug of ions is expected after the ion source is shut down,
this bunching would gradually spread out (decay) over time or stay at roughly the same
amplitude in the worst case, unless there is a collective mode instability. The only
mechanism for an actual amplitude increase after all ion sources have been terminated is
a collective instability. No doubt this instability is excited by the perturbation caused by
the slug of ions as the phase of the signal matches the slug quite well.
--
{2E-4 /10 = 2e-5 secs ring = 100kHz ion bounce freq approx - to 250kHz}
--


and ...
http://ssl.mit.edu/publications/theses/ ... Thomas.pdf wrote:...
p113::
The above figure is characteristic for low levels of constant injection of ions. The
plot shows the potential in the device center as the charge in the system builds. Initially
the value of the potential is that of the background fields and as ions build this value rises
about 140 volts at peak. Initially, the space charge builds steadily, corresponding to the
uniform beams growing in strength. As instability drives the system into the
synchronized state, the space charge oscillates and the maximum and minimum is easily
seen. At steady state, the frequency of this sinusoidal oscillation is the bounce frequency
of individual ions in the system. The synchronization takes some time to develop, but
settles into a steady state behavior at a rate that depends on the level of current injection.
...
One can see that in Figure 3.35 the oscillation envelope is much smaller than in the
lower current case of Figure 3.34. As the current level increases, the ion lifetime
decreases. Eventually the lifetime is short enough that a given ion doesn’t have enough
time to synchronize with the rest of the group before it is lost. Thus a significant portion
of the ions are still in the ‘uniform beam’ state instead of the fully synchronized state.

In the low current case, the oscillation minimum is close to the base background space
charge level, indicating that almost all of the ions are synchronized. At very high
injection currents, synchronization does not occur, but the instabilities violently eject
particles from the system, preventing any recirculation of beam current. This realization
is important for traditional IEC systems which have tried to reach high fusion rates with
extremely high pulsed injection profiles.
...
To understand why the space charge puts a limit on the confinement of the system,
observe the ion maps in Figure 3.36 and Figure 3.37.
...
The ion beams through the center of the device have filamented, so that the ions no longer recirculate through each
other. This ‘two-lane road’ is less efficient at packing charge into the ion channel as the
two filaments push each other apart.
...
Fusion rate estimates, density pulse shapes::
Before a rate can be estimated, the pulsed nature of the core ion population must
be addressed. With operation in the low-pressure regime, beam-beam reactions in the
core will dominate the fusion reaction rate. The steady-state density pulse shapes in the
core for the deuterium cases are shown in Figure 3.39 and Figure 3.40. The core rate
depends on the square of the density.
...
One can see that the power gain increases dramatically as the
current is reduced, with the roughly the same scaling as the ion lifetime. There does not
appear to be any barrier to increasing the ion lifetime and fusion efficiency by reducing
the input current to a mere trickle. This makes sense, since in an ideal system, new ions
would be introduced only as the old ones fuse.
The prospect of a break-even fusion reactor is fabulous, but the fusion rates
shown above are unimpressive. Some improvement could be made by reducing the
overall size of the device as discussed earlier, but this becomes very difficult due to the
complexity of the grids and the high voltage gaps. In order to make useful amount of
fusion however, the densities must be increased.
...
Chapter 54 Synchronization (p124)
...
On a slightly slower time scale, bunches on
each separate beam path become synchronized with all the others.The beams are initially
well-confined and as they reflect and circulate, the density of each beam grows.
As the density grows large enough, the individual uniform beams break up
into many bunches which counter stream through each other. Eventually these coalesce
into 2 opposing bunches for each beam line.
******
If the (ion) injection is terminated, the stable state is then 2 opposed bunches per beam line with all bunches
collapsing into the device center at the same time and reaching the anode at the same time.
{now that, i would like to explore further...the heaviside function.. iirc, it is precisely when Bussard's ion beam stopped that he got his famous neutron count. (Valencia paper)}
****
The amount of time required for this process varies according to the input current level
and can occur as quickly as 25 passes.
...
p126:: Figure 4.1 Progression of synchronization, localized space charge (vertical axis) vs.
equatorial position vs. time. Each tile spans a tenth of a pass in time and plots the space
charge specifically along the equatorial beam line.
...
p128:: Figure 4.2 Progression of synchronization, ion maps. Starting in top left, time runs left
to right, with each slide jumping about 2.5 passes forward, covering 50 passes total.
...
The specific response at harmonics of the bounce frequency suggests that the device size indeed
provides a significant boundary condition on the allowed oscillations in the system.
...
Fourier transform analysis of synchronization (p135 )::
p141::
The harmonics, however, grow over a time but then plateau.
The highest frequency mode, 1 MHz, actually grows the fastest but plateaus at about 40
passes. The 750 kHz harmonic peaks at about 50 passes and is somewhat stronger than
the 1 MHz mode. The 500 kHz reaches its peak at about 60 passes and then fluctuates
somewhat. After 100 passes, the bounce frequency is a full order of magnitude stronger
than the next strongest mode.
...
The important thing to note is that the transient nature of the injection process produces
disturbances at harmonics of the bounce frequency, providing a natural seed from which
instability can grow.
{again - i want to explore this region further. i suspect it maybe something Rick is looking at}
...
From Figure 4.19, one can see that the lifetime ‘constant’ quickly climbs to about
12,000 passes at 10 ms, and then linearly increases with time. The time constant for the
last 10 ms of the run is about 50,000 passes. This is quite an improvement over the 10
passes for a traditional IEC one grid system. This gradual increase in lifetimes suggests 2
scenarios. The first is that there is an initial mix of particle lifetimes, the ions don’t really
mix over time, and the short-lived ones are simply lost earlier. The second is that the
ions mix over time and bunches as a whole grow more stable as they shed particles over
time. In either case, the physical cause of particle removal from the system appears to be
an artifact of the model, not an actual process such as striking the cathode grids or
upscattering in energy and leaving the simulation region. This suggests that if emitters
can be properly designed not to be impinged by the beam, lifetimes of greater than tens of
thousands of passes should be achievable at the modest densities allowed in a nonneutralized
system.
...
While Huygens was developing his sophisticated clocks {circa 1656},
he noticed that the pendula would become in sync with each other,
despite being physically separated. The very same clocks would drift apart if they were
located farther away, say in another building. The slight perturbations caused by each of
the clocks transmitted through the floor and wall was apparently enough to keep them
swinging together. Specifically, the clock pendula were found to oscillate perfectly
asynchronously, so that a disturbance on the connecting wall produced by one would
cancel out the other.
...
Figure 4.20 Schematic view of the Zajfman trap, Figure 1 from Pedersen, et al., 2002 (p150)
...
The kinematic criterion ensures that the more energetic particles will tend to migrate to
the rear of the bunch. This re-organization in phase space forces the collision process to
be a structured process instead of a random one.
...
{ http://www.physics.emory.edu/~weeks/res ... ries7.html - Poincaré sections - visualisations of 'self organizing behaviors }
...
The kinematics of the trap organizes the Coulomb interaction so that collisions
redistribute the ion’s energy so that ions orbit the center of mass of the total ion bunch.
...
p162::
The transition from stable to unstable wave numbers sets a
condition for minimum density at which to expect instability.
...
Smaller wavelengths thus require larger
densities before they become unstable.
...
Thus, the time evolution of the disturbance will increasingly morph into a
global expression of this infinitely extending waveform
...
However, if time is allowed to continue, the entire waveform grows in amplitude so that
the entire device is affected by the localized disturbance.
...
By analyzing the dispersion relation at the anode we can see
how the smaller wavelengths are locally unstable and can produce computed results
...
...we find that the anode region can
support wavelengths an order of magnitude smaller than the center.
...
Thus, short wavelength waves which may be stable in the device center can be unstable near the anode.
...
Based on observations of the anode region in the OOPIC simulations and the
above analysis, it appears that the instability originates as disturbances near the anode.
The unstable waves co-exist with and excite stable traveling waves. Thus, the unstable
anode waves are able to travel across the device as stable waves, become unstable near
the opposite anode and thus continue to build over time. Eventually the disturbance
becomes non-linear as it dominates the original uniform streaming beams. The larger
wavelengths will tend to grow and saturate more slowly than the smaller wavelengths.
The longest wavelength disturbance allowed by the device boundary conditions
eventually dominates and saturates itself to produce the counterstreaming bunches seen in
the simulations.
...
p191 (particle cloud collision model)::
Thus for strong interactions the peak energy transfer collision is only a function of the initial
separation.
...
Now we know that as a bunch gains or loses
energy, its period in the IEC will change. The change in period brings the two bunch
centers physically closer on the next pass. This change in period defines the time
constant for the interaction to bring two bunches into synchrony
...
One can see that at the higher densities of interest for an eventual energy
producing system, the synchronization occurs on very fast time scales. The high strength
of the interaction is ultimately not compatible with a stable, gradual process of small
energy transfers.
{40-50 passes, from earlier treatment of harmonics}
...
The stability of the synchronized state is found to break down at higher bunch
densities due to the high levels of energy exchange between bunches. As the density is
increased, the system will tend to eject a single bunch from the group and as time and/or
density are further increased, more bunches are ejected from the synchronized group.
The overly-large energy exchange destroys the cycling behavior
...
The velocity plot in Figure 4.54 shows that the synchronized bunches start at the
anode with minimal velocity. Two groups immediately emerge, the first accelerated into
the device core and the second delayed at the anode due to the space charge of the first
group. As the first group descends into the core the second group follows it. We know
that these leading particles will gain energy from the delayed particles, and sure enough
this first group emerges from the core with much more energy, and they are carried out
well past the anode. The second group continues on towards the anode after passing
through the center of the device and then diverges in velocity as it approaches the anode.
The process continues with each pass and the system eventually becomes fully
desynchronized
...
Also, the observed ejection mechanism
doesn’t bode well for running the device at these higher densities. The collective
behavior is unstable because too much energy is being exchanged, and this also means
that the excess energy will carry particles out of the device, effectively upscattering them
in energy. This occurs much faster than the classical collisions. Also, in this nonneutralized
IEC, the long range effect of the Coulomb force is not limited by invoking
Debye shielding of the potential.
...
High angle scattering events from the core are
shown to be effectively slower than fusion since most of the deflected ions will be
deflected centrally onto another ion beam path and not be lost.
...
While it is usually thought
to cause thermalization of plasma, in this situation the ion-ion interaction actually
maintains a non-thermal distribution.
{now that should interest Art}
...
As ion density builds from
recirculation or simply high input currents, the collective behavior violently expels
particles from the system. The steady-state peak ion density is found to be only a weak
function of the input current, so that for a given geometry and voltage setting, the
collective behavior sets a space charge limit. The potential associated with this limiting
density is about 10% of the background potential in the device core, for example a 50 kV
will reach steady state when the ion core potential reaches about 5 kV. Thus, while a low
density device may theoretically operate at energy break-even or better, there are serious
problems with scaling up the density to reach useful reaction rates and powers.
...
A hybrid design with magnetic lenses may
allow high levels of space charge to be confined, and it is unclear how this would affect
the synchronization mechanism.
{enter the Busard magrid}
...
The synchronization mechanism provides a concrete
example of how non-Maxwellian, non-neutral plasmas can be maintained by using the
very forces that usually thermalize it.
...


{comments in curly braces are my own}

... i have a strong hunch theres a working solution waiting to be discovered in here somewhere. my guess - pulsed mode only, modulatng the ion injectors at somewhere/some mix between 100kHz and 1Mhz (1st to 3rd harmonics), plus triming phase.

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Postby MSimon » Sun Apr 04, 2010 5:04 am

... i have a strong hunch theres a working solution waiting to be discovered in here somewhere.


That has been my hunch since about May of '07.

Rick says to make the device work it has to be tuned. He talks about "knobs".

Tom Ligon alludes to it in a story he wrote about the early fumblings of IC engine design.

http://powerandcontrol.blogspot.com/200 ... ed-up.html
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Postby rcain » Sun Apr 04, 2010 5:18 am

... perhaps a new picture starts to emerge (also the new Ion injectors in Ricks requisition list, etc).

if it ends up as a pulsed machine, then surely most of Art's aguments against the device, cease being applicable. no?

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Postby MSimon » Sun Apr 04, 2010 5:23 am

rcain wrote:... perhaps a new picture starts to emerge (also the new Ion injectors in Ricks requisition list, etc).

if it ends up as a pulsed machine, then surely most of Art's aguments against the device, cease being applicable. no?


I can't say.

What I did learn from Rick's POPS work is that he was already thinking along such lines in relation to POPS i.e. time varying the injection in order to get the density up.

From what I can tell Doc B did an excellent job in putting a team together with the best mix of skills to see the project through to a successful conclusion (if that is possible).
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Postby rcain » Sun Apr 04, 2010 5:33 am

MSimon wrote:...time varying the injection in order to get the density up.


that sounds the ticket. (though the paper above ascertains a maximum density possible within such a regime, reasons cited).

theres similar theoretical use of phase-space to 'scan' the domain of glancing ion collisions in one of the above papers. POPs however i had understood to be RF modulation of the interior/plasma space (though I suppose it may well involve ion 'shaping' also, ill read up).

re. knocking arguments on the head - i was thinking particularly of cusp neutrality/ambipolarity and thermalisation - both of which are potentially circumventable in a (synchronous) pulsed machine.


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