Most of my articles present here were first posted by me in Lifters
If high voltage applied between two electrodes in dielectric medium, the only current flowing is a very small current due to few ions always present due to ionizing radiation. However, when voltage is increased above ionization threshold, some present ions are accelerated to speeds where each collision with neutral molecule result in its ionization. As result, an avalanche of ionizations occurs and whole medium becomes ionized.
This high field density is difficult to achieve if electrodes are equally sized and far apart. However, if one of the electrodes is very small, thin or sharp (such as wire), field density near its surface is very high and ionization can occur at moderate voltages, while second electrode (collector) has no sharp edges and no ions are generated there. What happens then?
Effect called corona discharge. Ions built near the surface of sharp electrode create a small ionized region (plasma, corona). Bulk medium can not become ionized outside this region as the field density there is not enough. Therefore when some ion leaves this area, it just keeps drifting to the opposite electrode following the electric field, without ionizing other molecules.
Only ions with same sign to that of corona electrode can leave because
ions with opposite sign are attracted to the corona electrode and become
immediately neutralized. As result we have two regions:
One important result is that in mono-polar region all ions are moving _in same direction_ from corona wire to collector. At the other hand, every second ions undergo zillions of collisions with outside air so in fact they are moving only very slowly, much slower then if medium would not be present.
In fact calculations shows that absolute most of momentum obtained by ions from electric field is given away to the medium. It is as if ions are "imbedded" in air as sticks in water, and electric field is "pooling" the entire device forward, "leaning" on this ions-sticks.
In reality ions are not fixed in the air, they are moving a little,
so whole picture is not as much as somebody pooling a rift leaning on a
fixed in water stick, but more similar to a rower dragging an oar through
water to "push" boat in opposite direction. Electric field drags ions from
one electrode to another and due to their viscous interaction with air
Some conclusion related to the form of electrodes of electric propulsion
2) Collector should have a form which provides _minimal_ field intensity
near surface, to prevent any ionization near to it resulting
3) At the other hand, it should not have too large surface departing
from direct line between center of electrode and emitter, because flow
But from point 2 conventional lifter could be improved to reduce counter-current from sharp edge of its collector.
So what is the perfect lifter from this point? It appears to be wire-circle
emitter placed co-axial with a toroidal collector of same
See lots of more detailed explanations, equations and optimizations
elsewhere in this site.
on corona discharge with subsequent interraction of accelerated ions with
Now I am presenting the derivation of ultimate formula of lifter - thrust to current relation.
Starting eqn. for force applied
by electric field to medium with distributed charge q is:
where E is voltage applied between electrodes and d is lenght between wire and collector. This formula is strictly correct only for plate capacitor arrangement (where ion flight path is parallel to force) but difference due to different field form will be small. Obviously due to first law of mechanics, the same force is applied by medium to lifter, so this is our force of interest.
Now, lets calculate amount of
charge q distributed between electrodes at any time when corona discharge
i is current and w is drift velocity of ions . Ions are moving not on straight path because electrically induced motion is overlayed by thermal mothion. During this whole motion ions interract with molecules of enviroment. So drift rate is a net velocity of ions in direction from corona to collector.
Now, drift velocity is related
to fild strengh as
Here k is mobility coefficient
of ion in air. From the web-site of the institute of electrostatic technology
(http://fee.mpei.ac.ru/elstat/lect in russian) I have values for
mobility of positive ions (if wire is positive) and negative ions (if wire
negative). k (+) = 2.1 cm^2/volt*sec k(-) 2.24 cm^2/volt*sec
Now bringing it all together, w from (3) into (2) and than q from (2) into (1) we have our force:
Simplifying we get
Now to be totally exact we have to substract the momentum which ions retain when they hit the collector. F_lost = m`*w. We can easilty calculate mass flow m`=dm/dt knowing current and molecular weight of ions, which is M=19gm/mole.
m` = M*i/(e*Na)
F_lost = M*i*k*E/(d*e*Na)
F_total = F-F_lost
Wow! while current certainly
depends on voltage, the result is that at given current thrust does not
depend on voltage. At given current thrust increases with lenght between
Now the ultimate test - I compare the predicton of this equation with real experimentally observed thrust for lifters 1-4 (data on current, config and experimentaly observed thrust from table in http://jnaudin.free.fr/html/lifter4.htm).
First lifter 1:
WOW! the prediction and experiment differ only 2 times!
Remember that we considered the
straight fligh path of ions, but actually it is curved so in reality less
force is applied because not all force is directed parallely to wire/collector
line. Additional power loss can happen due to "counter-current" of ions
with opposite sign because of small corona formation at collector (if edge
is too sharp)
Anyway, lets see other lifters.
Wow! This is realy close. Note that lifter 4 used rounded-up top of collector to minimize counter-current, so it achieved higher lift efficiency vs. theoretical equation compared to other lifters.
To summarize - Prediction falls quite near to experimental results for all sizes of lifter, and the closes result is in case where minimal counter-current can be expected. Finaly you have an equation to judge lifter efficiency, and additional proof for ion-propulsion mechanism.
Later I will investigate relation between voltage and current. Anway, the main point in improvement of lifter's force/power ratio - how to increase the current and distance between wire and collector without increasing voltage.
The corona onset voltage V0 is given by Peek's equation (links to some chapters of Peek's book are in http://www.ee.vill.edu/ion/p61.html):
where r is radius of corona-wire
in cm, d distance between wires and
At d=30mm and r=0.5 mm we get V0=14.4 kV
Anyway, in my derivation the field strengh E has canceled out because it at one side it increases thrust, and the other side decreases it by decresing number of carriers (charge) inside the interval. So there is no voltage in the equation, only current.
If we want voltage/thrust dependence,
it also can be done.
It has general form:
For the case of wire/parallel
flat plate electrode configuration
e0 - dielectric permittivity of air
Unfortunately wire/paralel plate
approximation is not very good for Lifter.
If we use f_geo (2) it is not
clear what to put as plate witdh W. Intuitivelly it should be less that
foil hight h=40mm (because foil is not parallel to wire) but much more
then thickness of the foil. I found that using empyrical "effective width"
h/7 gives current
Anyway, derivation of strict eqn. for G for lifter electrode configuration is still open.
So what about thrust? From above
eqn and using my previous eqn. for thrust F=i*d/k
Using f_geo (2) with W=h/6 we
get for Lifter 1 where
F=0.069 N which is about twice of experimentally observed 0.032 N probably due to some counter-current. Anyway it is not bad for a raw assesment and considering that counter-current should reduce the thrust.
Let's see what we would get using
50 gauge wire as Tom Ventura recently
So with decreasing wire thickness we get thrust increase of 4.3%.
I will explore later how to optimize
power/thrust relation based on this eqn., and to find form of G which corresponds
exactly to lifter electrode configuration.
>thrusters in atmosphere in terms of N/W?
Speed of single charged particle with mass m and charge e accelerated
between two electrodes with voltage V is: v= sqrt(2*V*e/m)
To calcualte number of particles flying at given power in unit time,
we divide total passed charge by the charge of single particle
Total force applyed is equal to total exchanged momentum per unit time
(assuming all momentum of accelerated particle is used for propulsion,
which is maximal possible estimate).
If you put there m=me=9.1093897E-31kg (electron mass) that gives ~10^-6
But if you put m=14*2=28*mp (N2) or m=16*2=32*mp (02), where mp is mass
Mass of particle required to achieve such thrust is
> It's not clear how this would give a force, (Newton)
That is the easy one. Electromagnetic radiation has momentum,
To calculate the force, F = p/t = W/c.
Recalculating this into "equivalent mass" we get ~10^-5 gm...
However, generated momentum of microwaves is just too small...
I have taken more close look at it as described here
1) There can not be any continuous flow of electrons between electrodes
due to this effect, because there is no way how they can pass electrode/dielectric
boudary. When voltage is switched on, there will be a transient current
due to change of capacitance due to dielectric material redistribution.
When redistribution is finished, capacitance becomes constant and current
2) Correspondingly, from 1 follows that can not be any continous flow of dielectric material, which shows that dielectrophoresis can apply to lifters only for short moment when voltage is switched on.
Now some points not related to lifters (which are DC), but could be relevant to AC-based propulsion devices:
3) When voltage is switched off, material flow is reverse to original
one and the momentum of outflowing material is same as momentum of inflowing
material therefore making net effect of one voltage pulse equal to zero.
4) AC-voltage can be represented as a series of interchanging positive and negative voltage pulses, therefore point 3) applies to them as well. There is no net material flow except that due to differences in friction of in/outflowing material.
That is why application of electrophoresis require some additional material flow to separate more and less polarizable particles, as they say in above cited web-site:
"Selective separation can thus be achieved by applying an additional force such as gravity or fluid flow".
|technical||Top of Page||contact postmaster|