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mheslep

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I'm pondering the density limits realizable in thermalized plasmas (as in Tokamaks) and it seems that confinement by a rotating electric field (something like a Paul trap) would theoretically allow much higher densities than the current magnetic field techniques. No doubt I'm missing something but I hope Ill be excused for thinking out loud. Here's the reasoning:

Magnetic Limit ----------------------------------------------------------

The confinement limit for a mag. field is the Brillouin density:

[tex]\eta=\frac{\epsilon_{0}B^2}{2Mion}[/tex] in ions per M^3

For deuterons and assuming the highest achievable(?) steady state field:

B=20 Tesla (ITER is 13T last I looked)

Mion=2*AMU in Kg

Gives:

[tex]\eta=10^{12}[/tex]

ions per cm^3

E Field Limit(?) -------------------------------------------------------

Here I'm considering the force to be overcome is the de-focusing effect of the space charge and neglecting and self confining mag. field. To keep it simple I'm using a cylindrical geometry of a non-neutral plasma. In that case the radial E field created by the space charge is found from Poisson:

[tex]\nabla E=\rho / \epsilon_{0}[/tex]

solving in gauss's law form:

[tex]Er = r\eta q_{e} / (2 \epsilon_{0})[/tex]

Then using the density found for the mag limit above at 1M:

Er @ d=1e12cm-3 = 8millivolt / cm

a trivial field. So a confining field producing 8mV/cm at the outside edge is needed to hold a cold(?) plasma. A rotating E-field would be required that produced a time averaged potential well with that Er, something like a Paul trap.

http://en.wikipedia.org/wiki/Paul_trap

I'm guessing that Er could be increased by ~10^8 before running into equipment limits.

Observations:

-The mass variable in the Brillouin limit makes mag. fields a lousy way to contain ions in particular; electrons

would get 2*3600x more density than deuterons, hence Bussard and the Polywell.

-E fields are orders of magnitude better at confinement. So why isn't electric

field confinement of plasma under more investigation?

Magnetic Limit ----------------------------------------------------------

The confinement limit for a mag. field is the Brillouin density:

[tex]\eta=\frac{\epsilon_{0}B^2}{2Mion}[/tex] in ions per M^3

For deuterons and assuming the highest achievable(?) steady state field:

B=20 Tesla (ITER is 13T last I looked)

Mion=2*AMU in Kg

Gives:

[tex]\eta=10^{12}[/tex]

ions per cm^3

E Field Limit(?) -------------------------------------------------------

Here I'm considering the force to be overcome is the de-focusing effect of the space charge and neglecting and self confining mag. field. To keep it simple I'm using a cylindrical geometry of a non-neutral plasma. In that case the radial E field created by the space charge is found from Poisson:

[tex]\nabla E=\rho / \epsilon_{0}[/tex]

solving in gauss's law form:

[tex]Er = r\eta q_{e} / (2 \epsilon_{0})[/tex]

Then using the density found for the mag limit above at 1M:

Er @ d=1e12cm-3 = 8millivolt / cm

a trivial field. So a confining field producing 8mV/cm at the outside edge is needed to hold a cold(?) plasma. A rotating E-field would be required that produced a time averaged potential well with that Er, something like a Paul trap.

http://en.wikipedia.org/wiki/Paul_trap

I'm guessing that Er could be increased by ~10^8 before running into equipment limits.

Observations:

-The mass variable in the Brillouin limit makes mag. fields a lousy way to contain ions in particular; electrons

would get 2*3600x more density than deuterons, hence Bussard and the Polywell.

-E fields are orders of magnitude better at confinement. So why isn't electric

field confinement of plasma under more investigation?

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