## Lifter theoryby Evgenij Barsoukov

Dedicated to Lifter comunity, see details in http://jnaudin.free.fr/html/lifters.htm
Most of my articles present here were first posted by me in Lifters mailing list
http://groups.yahoo.com/group/Lifters

Contents:

The original document can be found at : http://sudy_zhenja.tripod.com/lifter_theory/main.html

## Effect explanation

Ion thrust occuring during corona discharge due to interraction of ions with medium has following steps :

• 1) Ionization of air molecules near electrode with high field intensity near to it (the small electrode, the wire in the lifter).  Lets call it "emitter" for simplicity.
• 2) Acceleration of ionized molecules by electric field in direction of  wide electrode, let's call it "collector".
• 3) Transmission of momentum from accelerated molecules to outside air

Let's apply all this 3 steps to cases with different polarity. First lets make "emitter" positive.

• 1) We will have ionization of air to cathion-radicals or cations such  as N2+ N2+*.
• 2) Positive particles will be accelerated in direction of negative  electrode (collector)
• 3) Momentum is transmitted from accelerated positive particles in  direction of collector.

Now lets reverse polarity and make "emitter" negative.

• 1) We will have ionization of air to anion-radicals or anions such as  N2- N2-*.
• 2) Negative particles will be accelerated in direction of positive  electrode (collector)
• 3) Momentum is transmitted from accelerated negative particles in  direction of collector.

As you can see, momentum is transmitted in direction of collector.

**** Thrust is applied TO the electrode which has charge carriers  available near to it.
With other words, thrust is directed to electrode with higher field intensity near to it.
Direction of thrust  does not depend on polarity **********

Now, what about magnitude of thrust, depending on polarity? It depend on the ionization energy for particular positive or negative ions.

Energy for reaction N2 + e ->N2- and energy for reaction N2- e->N2+  are different (the second is lower), therefore current and magnitude of thrust with negative emitter is slightly lower than that with positive emitter. This indeed has been observed by some of lifter experimentalist, particularly by Cristian Marinescu
( see http://jnaudin.free.fr/html/lfreplog.htm ).

Second conclusion related to the form of electrodes of electric propulsion devices:

• 1) emitter should be as thin as possible to provide highest field intensity near to it to provide more charge carriers.
• 2) Collector should have a form which provides _minimal_ field intensity near surface, to prevent any ionization near to it resulting in "counter-current" which reduces the thrust. Collector should have no sharp edges and the best configuration is spherical or toroidal. Optimization can be made in electric-field simulators.
• 3) At the other hand, it should not have too large surface departing from direct line between center of electrode and emitter, because flow lines deviating from this direct line contribute less to net thrust. From this point, conventional lifter configuration is best - because all surface is on the axial line.

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
diameter.

## Ionic jet thrust calculation (~10^-7N / 100W)

>Anyone have an idea as to the max (or practical) efficiency of ion wind 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).
At the other hand, momentum of single particle is p=m*v = m*sqrt(2*V*e/m)

To calculate number of particles flying at given power in unit time, we divide total passed charge by the charge of single particle

n=Q/(e*t)=i/e

current i we obtain from power E as i=E/V so n=E/(V*e)

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). As result we have:

F=n*p=m*sqrt(2*V*e/m)*E/(e*V)

If you put there m=me=9.1093897E-31kg (electron mass) that gives ~10^-6 N at E=100Watt, V=30 000Volt.

In experiment with lifter 4 they  ( http://jnaudin.free.fr/html/lifter4.htm ) observed thrust 0.4N at 100W, so number above is way to small.

But if you put m=14*2=28*mp (N2) or m=16*2=32*mp (02), where mp is mass of proton=1.6726231E-27kg, we have better picture (10^-4N) but still way too small compared to 0.4N. Whatever ions are used in this "ion wind", these are not ions taken from the air...

Mass of particle required to achieve such thrust is m = F^2*V*ee/(2*E^2).

For F=0.4N and above voltage and power we have: m~2*10^7*mp (where mp is proton mass) or 3.69*10^-20 kg.

This mass is not too large to be practical - it could be clusters of the electrode material or electrode coating brocken off the surface under very high stress applied by the voltage.

## Radiation pressure (~20^-9 N / 100W)

> 2) Poynting vector has unit of energy/second*m^2. It's not clear how this would give a force, (Newton)

That is the easy one. Electromagnetic radiation has momentum, it has been shown theoretically by Maxwell and experimentally measured by Lebedev.
Momentum of a totally reflected electromagnetic wave, p = 2E/c

To calculate the force, F = p/t = W/c.
For radiation power W=100Watt we have force 2W/c ~20-9 N.

Recalculating this into "equivalent mass" we get ~20^-5 gm... too small... indeed, electrons moving with curved trajectories and speeds around 1/3 c (like they do in lifters)should radiate  short wavelength radiation. There are devices such as reltrons, and x-ray tubes used to generate such short wavelength radiation, which have exactly same  principle, and look very much like lifter immerced in a vacuum tube.

However, generated momentum of radiation pressure compared to the measured lifter thrust shows that radiation pressure is only one of the minor mechanisms providing the final thrust.

## Dielectrophoresis

Dielectrophoresis was mentioned several times here, even by me in relation with lifter operation.

I have taken more close look at it as described here http://www.ibmm.informatics.bangor.ac.uk/pages/science/dep.htm
and suddently realized that it can not possiblly have to do anything with  discussed effect. Why? - because dielectrophoresis is a _transient_ effect.  It is redistribution of particles in inhomogenous electric field depending on their polarizability. Once the redistribution is finished, material flow is also finished, therefore dielectrophoresis is a _transient_ effect resulting in change of material state from "Voltage OFF" to "Voltage ON", it can not have a continuous component.

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 stops. However, electric current (as well as thrust) in lifter are observed continuously as long as voltage is on.

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.
This is true unless there is a difference in medium friction coefficient at high and low flow speed, which could result in some momentum retained by electrode arrangement. This point needs to be investigated separately.

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".

## Ion/air interaction by corona discharge in Lifter - thrust/current relation

In my previous messages I gave basic mechanism of lifter operation based on corona discharge with subsequent interraction of accelerated ions with outside enviroment.
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:
F=q*E/d         (1)

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 is on.
i=q*w/d
so
q=i*d/w            (2)

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
w=k*E/d            (3)

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
I will use k(+) for calculations below.

Now bringing it all together, w from (3) into (2) and than q from (2) into (1) we have our force:

F=i*d*E/(w*d)
F=i*d*E/(k*E*d/d)

Simplifying we get

 F=i*d/k

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)
Na is Avogadro number = 6.0221367E+23 mole^-1, e - electron charge = 1.6*10^-19
so (substituting w from (3))

F_lost = M*i*k*E/(d*e*Na)

F_total =  F-F_lost

 F_total=i*d/k  - M*i*k*E/(d*e*Na)

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 electrodes.
Later we will see that F_lost is negligibly small, so good equation to work with is simply  i*d/k

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 Lifter1:
d= 30mm
k=k (+) = 2.1 cm^2/volt*sec
i=450uA

F1=0.064 N
F_lost = 1.8*10^-7N (so will be neglected in all other calculations)
experimental F1exp=2.3+1gm*g =0.032N

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)
More exact calculation considering exact field configuration might come even closer, but hey - we have our raw equation! Du you think numbers are so close just by chance!?

Anyway, lets see other lifters.
Lifter2 :
d = 30mm
i=570uA
F2=0.077 N
F2exp=6.6+3gm*g=0.094N

Lifter v3.0 :
d=30mm
i=2.46mA
F3=0.351 N
F3exp=16+4gm*g= 0.196 N

Lifter 4.0 :
d=40mm
i=2.01mA
F4=0.383 N
F4exp=32+4gm*g=0.353 N

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.

## Thrust/voltage relation in lifter

This calculation is based on assumptions  that corona is present only on one electrode so the counter-current of ions with opposite to wire sign is negligible. Otherwise counter-current would reduce thrust.

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 ):

V0=g0*r*ln(d/r)
where
g0=30*kV/cm*delta*(1+0.301/sqrt(delat*r))

where r is radius of corona-wire in cm, d distance between wires and
delta is a factor depending on air pressure and temperature as
delta=3.92b/(273+t )
where b is pressure in cm of barometric pressure and
t is temperature in degree C.

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.
The current/voltage characteristic of flat collector / wire combination
is derived by Copperman (see http://www.me.umn.edu/courses/me5115/notes/ESPnotes.pdf
for details).

It has general form:

 I = k*G*V(V-V0)             eqn. 1

where k ion mobility coeficient and V voltage and  G depends on particular electrode configuration.

For the case of wire/parallel flat plate electrode configuration
G = 2*pi*e0*L/(d^2*ln(f_geo/r))

e0 - dielectric permittivity of air
d is the wire-plate spacing;
W plate width
L  plate lenght (should be >> W)
f_geo is the characteristic length of particular electrode geompetry
(1)       f_geo=4d/pi for 2*d/W<= 0.6, and
(2)      f_geo=W/(2*pi exp(pi*d/W))   for 2*d/W>=2.0
First is more near to lifter case, but maybe second case with some effective W can also be used.

Unfortunately wire/paralel plate approximation is not very good for Lifter.
For example for Lifter 1 at 40kV and d=30mm we get
with f_geo(1) and r (30 gauge)=0.1275 mm
I= 1.8mA whereas experiment shows 450uA.

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
I=480 uA which is near to experimental so eqn. can be used in this form.

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
we have voltage/thrust relation:

 F=2*pi*e0*L*V(V-V0)/(d*ln(f_geo/r)))                   eqn.2

Remarkalbe thing is that k canceled out and that d went into denominator which
indicates that it should be kept as small as possible because it decreases current as d^2 but increases thrust only as d^1.

Using f_geo (2) with W=h/6 we get for Lifter 1 where
L=200*3=600mm
V=40kV
r= (assuming 50 gauge = 0.255 mm diameter) = 0.1275 mm

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
tried (quite a cool experiment considering how brittle it should be)
r= (30 gauge = 0.025 mm diameter) = 0.01275
I obtain using eqn. 1
i= 51 uA
F=0.072 N at 40kV

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.

## AC operation of Lifter

> I am thinking: since many experiments have shown that reverse polarity still produce lift force (which kI found out was true with my lifter) then perhaps AC will work as well?

It will depend on frequency you are using. You have to provide that ions which "started" from corona wire reach the collector before you change the polarity. Otherwise you will have in wire/collector interval mix of positive and negative ions flying back and forth and compensating each others thrust.

It is easy to calculate maximal frequency below which you will still have thrust (critical frequency). It will be 1/tau
where tau is flight time of ion between electrodes.

tau = d/w
where w is drift velocity and d is distance between electrodes

w = k*E/d where E is voltage and k mobility coefficient (about 2.1 cm^2/volt*sec). So critical frequency is

f=1/tau = k*E/d^2

for E=40 kV and d=30mm
we have

In you increase AC frequency Above value thrust will rapidly decrease. If you operate at much lower frequcy you will have thrust, but I guess it will be less than tha DC value at the same voltage.

## 3-electrode  AC/DC lifter proposal

Any theory is good only if it allows to improve some technolgoy.
Equation F=i*d/k suggests, that it is desirable to maximaze amount of available charge (and corespondingly current) without increasing d or V.

For this we need to de-couple charge generation from ion-aceleration. This could be achieved by  simple 3-electrode AC-DC lifter design. Instead of corona wire we use two winded together wires, one of which is insulated with sufficiently thick teflon insulation (lets call it "base"). We apply between this 2 electrodes AC voltage sufficient to produce sustained barrier discharge. Because of very small distance between electrodes required AC voltage would be quite small, say 5 kV. It can be further reduced by coating the insulation with ferroelectric material pelets but for preliminary test it is not necessary.

Now, as we already have our plasma, we only need to "suck" out of it ions of one polarity. For this we place with distance d (much larger than usual, say 100 mm, a collector and apply DC voltage between it and not-insulated wire, "emmiter" (which should be +). This way we should achieve noticeable current betwen emmiter and collector at quite large distances d but reasonably small DC and AC voltages applied and those get much higher F=i*d/k at lower power. Is this a way to radically improve thrust/power ratio and escape from the need of magic lifter electrode confuguration and very high voltages needed for initiation of corona? Some cool experimentator is required to answer this question...