Space charge density

[Bond777]

Let say we have a hollow dielectric tube in which a cloud of unipolar charge (electrons) is moved by flowing gases from emitting cathode to anode. Then this charge returns from anode to cathode through an external circuit and a load. Could you help me to calculate at least very approximately what maximal space charge density in the tube and subsequently current density at the load could be achieved, if the gases move charge in the tube with the sonic speed, approximately? And what power density at the loaf (per kg) could we expect from such device very approximately?

[studiot]

7 hours ago, Bond777 said:

Let say we have a hollow dielectric tube in which a cloud of unipolar charge (electrons) is moved by flowing gases from emitting cathode to anode. Then this charge returns from anode to cathode through an external circuit and a load. Could you help me to calculate at least very approximately what maximal space charge density in the tube and subsequently current density at the load could be achieved, if the gases move charge in the tube with the sonic speed, approximately? And what power density at the loaf (per kg) could we expect from such device very approximately?

 

Gosh it's a long time since I looked at this subject.

I think some more information is required.

What do you mean by flowing gases ?

The electron ballistics of vacuum or near vacuum devices and those which have an appreciable gas fill are quite different.

Also relevant is the question of what frequency are you working at D.C. or (ie zero) or some A.C. frequency.

You have mentioned space charge, which normally refers to a particular effect in such tubes, not the charge density of the flowing current.
Please confirm what you actually mean.

I'm guessing but are you referring to this ?

 

Edited March 26, 2021 by studiot

[Bond777]

13 hours ago, studiot said:

What do you mean by flowing gases ?

I'm trying to find what power density could we ever expect from devices like this:

38114997.pdf (iaea.org)

Under condition that emitter electrode will be able to create sufficient charge supply. Gases could be created by burning fuel in a combustion cumber. It is know that unipolar charges have tendency to repel each other quite much. Does it mean we would be never able to have significant current density inside of tube and subsequently power density at the load?

[studiot]

4 hours ago, Bond777 said:

I'm trying to find what power density could we ever expect from devices like this:

38114997.pdf (iaea.org)

Under condition that emitter electrode will be able to create sufficient charge supply. Gases could be created by burning fuel in a combustion cumber. It is know that unipolar charges have tendency to repel each other quite much. Does it mean we would be never able to have significant current density inside of tube and subsequently power density at the load?

 

No it does not mean that at all.

You 40 page document derives analytical conditions for a simplified model in one dimension.

Note this analysis is compatible with my attachment which uses Poisson's equation for the flow.

The simplest model is Laplace's equation

[math]{\nabla ^2}\left( \Phi  \right) = 0[/math]

This does not account for interaction between paticles so for a stream must be replaced by Poisson'r equations

[math]{\nabla ^2}\left( \Phi  \right) = f\left( \Phi  \right)[/math]

Where phi is a suitable flow variable.

Do I understand you are interested in the the method outlined in your eference document here is the summary whihc would have been useful for you to post

Quote

THEORETICAL INVESTIGATION OF AN ELECTROGASDYNAMIC
GENERATOR
by
Sören Palmgren
SUMMARY
In an electrogasdynamic generator a portion of the enthalpy of a
high velocity gas flow is converted directly into electrical energy
through forcing unipolar charge c a r r i e r s against an electric field.
In a first attempt we try to describe this process by use of a onedimensional
mathematical model with an adiabatic flow. An exact
analytic equation is derived for this case. Assuming the interaction
between the charge c a r r i e r s and the gas to be a perturbation of the
first order this equation can be solved analytically. The zero order
perturbation, i. e. constant thermodynamic state of the flow, agrees
with previous analyses. It is found that this is an adequate approximation
for the linear model. A complete analysis of a cylindrical
EGD generator must however take into account the radial electric
field due to the space charge and the losses due to radial diffusion
and mobility. A tentative investigation of a three dimensional axially
symmetric model has therefore been made, including a survey and
c r i t i c i sm of some earlier analyses.

Printed and distributed in 1968

 

I have emboldended the important descriptive sentence.