Question about plasma pressure at low densities.

[RGClark]

Below is a post to sci.physics. It proposes just storing ionized gas for fuel for ion drive engines rather than using the power on board for ionizing the gas as well as accelerating the ions.
My question is what kind of power would you need to contain a fully ionized gas using magnetic or electric fields? If the gas was low density could you just use light weight permanent magnets?


Bob Clark

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Newsgroups: sci.space.policy, sci.astro, sci.physics, sci.physics.relativity, sci.physics.fusion
From: Robert Clark <rgregorycl...@yahoo.com>
Date: Thu, 20 Sep 2007 13:47:28 -0700
Local: Thurs, Sep 20 2007 4:47 pm
Subject: Stored ionized gas for ion drives.

This page gives a formula for the exhaust speed of an ion engine in
terms of the charge on the ions and the voltage driving the ion flow:

Ion thruster.
http://en.wikipedia.org/wiki/Ion_thruster#Energy_usage

The exhaust speed increases with the charge on the ions and decreases
with their mass. You would think then that a light gas like hydrogen
would be ideal since heavier gases even when fully ionized would still
contain approximately equal numbers of neutrons as protons which would
not contribute to the charge but would approximately double the mass.
Yet it is the heavier gases like cesium and more recently xenon that
are used. The explanation is that of the energy it takes to ionize the
gas used as fuel. The figure on this page shows the energy to ionize a
light gas such as hydrogen is relatively high compared to the heavier
gases:

Ionization Energies.
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/ionize.html

The figure gives the energy per mole which is high in itself. It is
even worse when you consider this on a per mass basis since the mass
amount of hydrogen would be so small compared to the amount of energy
needed to ionize it.
So could we instead store the hydrogen or some other light gas
already in ionized form so we would not have to supply power to ionize
the gas, only to accelerate it?
If you used ionized hydrogen, so you would be accelerating protons,
then using 6 x 10^18 protons to make one 1 Coulomb, and a mass of 1.6
x 10^-27 kg for a proton, and V representing the voltage in volts, the
speed on the ions (protons) would be about (10^4)sqrt(2*V) in meters/
second.
If we made the voltage be 5,000 V we would get 1,000,000 m/s speed
much higher than any current ion drive. Also, there are power supplies
that convert low voltage high amperage power into high voltage, low
amperage power, even up to 500,000 V. The we could get 10,000,000 m/s
= 10,000 km/s exhaust speed.
The question is could we get light weight means of storing large
amounts of ionized gas? Note that is this for space based propulsion
not launch from Earth. You would have a possibly large energy
generating station that remained in low Earth orbit to supply the
power to ionize the gas once the spacecraft was placed in orbit. The
power generator would be left behind in orbit. Then the volume of the
gas container could be large to keep the density of the gas low. This
would allow very thin container walls. Note the low density would also
allow the electrostatic repulsion of the positively charged ions to be
more easily constrained.
A possible problem though is the charged ions contacting the walls
could lead to a loss of ionization. You might be able to use a low
level magnetic field to prevent the ions contacting the walls. Low
density of the gas would insure the strength of the magnetic field
required would be low. It might even be accomplished by thin permanent
magnets so you would not need to use extra power.
Some questions: what would be the electrostatic pressure produced by
a low density highly ionized gas? What strength magnetic field would
you need to contain it?
Note that with an exhaust speed of say 10,000 km/s, by the rocket
equation we could get the rocket itself up to relativistic speeds with
acceptable mass ratios.
Then this would provide a means of testing relativistic effects on
macroscopic bodies.

Bob Clark
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[Astronuc]

One does not simply store a plasma for later use. The plasma would lose heat (thermal energy) by conduction and convection if not confined, and even if magnetically confined, still loses energy through radiation (blackbody, brehmstrahlung, cyclotron radiation, recombination, and diffusion of neutrals).

The pressure = (n_i+ n_e)kT assuming the ion and electron temperature are the same.

The magnetic field needs to provide a pressure equal to that of the plasma and is given by B²/2\mu.

500 kV accelerating potential is a little unrealistic, since discharges at HV are difficult to control.

 

[mheslep]

One does not simply store a plasma for later use. ...

Don't forget about Penning or Paul traps. For a non neutral plasma there is no recombination. Neither is useful for long term energy storage as posed by the original poster.

 

[Astronuc]

Don't forget about Penning or Paul traps. For a non neutral plasma there is no recombination. Neither is useful for long term energy storage as posed by the original poster.

And neither can be used to store much energy nor mass. Storing only electrons or just protons is rather impractical.

 

[mheslep]

And neither can be used to store much energy nor mass. Storing only electrons or just protons is rather impractical.

Practicality depending on the application:

...Currently Penning traps are used at CERN to store antiprotons...

 

[RGClark]

One does not simply store a plasma for later use. The plasma would lose heat (thermal energy) by conduction and convection if not confined, and even if magnetically confined, still loses energy through radiation (blackbody, brehmstrahlung, cyclotron radiation, recombination, and diffusion of neutrals).

The pressure = (n_i+ n_e)kT assuming the ion and electron temperature are the same.

The magnetic field needs to provide a pressure equal to that of the plasma and is given by B²/2\mu.

500 kV accelerating potential is a little unrealistic, since discharges at HV are difficult to control.

Thanks for the info. There has been success at storing non neutral plasmas for months in Penning traps. 500,000 V might be difficult, but 5,000 V to achieve 1,000,000 m/s exhaust speed is still quite significant.
I'm expecting that there will have to be some energy input to maintain, contain the plasma, but not the recombination and diffusion of neutrals if maintained as a plasma of only one charge.


Bob Clark

 

[Astronuc]

There has been success at storing non neutral plasmas for months in Penning traps.

What mass? What particle density?

Determine the acceleration one wants to achieve, and assume a spacecraft mass.

That gives thrust, which is a combination of mass flow rate and exhaust velocity.

Where is the energy coming from? What is the specfic energy of the propellant?