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mheslep
Gold Member
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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:
\eta=\frac{\epsilon_{0}B^2}{2Mion} 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:
\eta=10^{12}
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:
\nabla E=\rho / \epsilon_{0}
solving in gauss's law form:
Er = r\eta q_{e} / (2 \epsilon_{0})
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:
\eta=\frac{\epsilon_{0}B^2}{2Mion} 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:
\eta=10^{12}
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:
\nabla E=\rho / \epsilon_{0}
solving in gauss's law form:
Er = r\eta q_{e} / (2 \epsilon_{0})
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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