Re: coaxial cap and oil in cap

From: 	Jim Monte[SMTP:JDM95003-at-UCONNVM.UCONN.EDU]
Sent: 	Friday, January 09, 1998 3:21 PM
To: 	tesla-at-pupman-dot-com
Cc: 	tom_mcgahee-at-sigmais-dot-com
Subject: 	Re: coaxial cap and oil in cap

Fr. Tom and all,

Nope, no offense at all about your comments or any still to come.
In fact, thank you.  I would much rather find a problem before than
after!  It is much easier to redesign than rebuild.  Below I have a
few follow-up comments/questions interspersed.

Jim Monte

>From: "Thomas McGahee" <tom_mcgahee-at-sigmais-dot-com>
>To: "Tesla List" <tesla-at-pupman-dot-com>
>Subject: Re: Cylinder Cap / Oil Cap
>Date: Fri, 9 Jan 1998 11:23:49 -0500
>> Whil. I'm posting, I would like some feedback regarding a cap I am
>> considering making.  The capacitor will essentially be a cylindrical
>> capacitor with the outer cylinder being 3/4" copper tubing and the inner
>> one being 1/2" copper tubing.  This will be implemented as shown below:
>>                      | + |
>>                      |   |
>>    -- ------ ------ ------ ------ ------ ------ --
>>     | |    | |    | |    | |    | |    | |    | |
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||   stage 1
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||
>>    |   |  |   |  |   |  |   |  |   |  |   |  |   |
>>    -- ------ ------ ------ ------ ------ ------ --
>>               .
>>                 .                                    intermediate
>>                   .                                     stages
>>    -- ------ ------ ------ ------ ------ ------ --
>>     | |    | |    | |    | |    | |    | |    | |
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||
>>    || ||  || ||  || ||  || ||  || ||  || ||  || ||    stage n
>>    |   |  |   |  |   |  |   |  |   |  |   |  |   |
>>    -- ------ ------ ------ ------ ------ ------ --
>>                      |   |
>>                      | - |
>> The tubing would be TIG welded to copper plate and the whole assembly
>> would be submerged in oil.  Each stage would look something like a
>> bed of nails, with the inner stages having nails on both sides.  The
>> holes in the copper plate would be to allow the oil to pass.  Insulating
>> spacers would prevent each stage from shorting.
>> This design seems to have an advantage over using a solid dielectric in
>> that if you did manage to break down the oil, an oil change is all that
>> is needed to bring the cap back to good-as-new condition.  Being copper
>> with fairly short conducting paths, it should be very well-suited for
>> pulse applications, and since copper tubing is mass produced, it should
>> be reasonably cheap.  Disadvantages I see are mainly in the time it will
>> take to weld everything together with sufficient precision.  Any others?
>> I have seen a lot regarding oil dielectric constants and breakdown
>> voltages, but I do not recall seeing anything about losses of various
>> oils.  Can someone supply information on loss tangents for different
>> oils?
>> With oil having a breakdown voltage of approx 200 kV/inch, using 1/2"
>> and 3/4" tubing would give a breakdown voltage of about 25 kV/stage,
>> but I've also read that asking a single cap stage for more than 10 kV
>> is asking for trouble.  Any suggestions on what would be a reasonable
>> rating for this cap per stage?
>> Incidentally, a cylindrical cap has
>>   C= 2*pi*dielectric_permittivity*length / ln(outer_radius/inner_radius).
>'nother snip
>> Jim Monte
>You asked for feedback on your proposed design. I hope that the following
>remarks will be seen as constructive feedback, and not negative
>criticism. Thanks for your post! It is the free flow of ideas that
>makes this Tesla list so very useful to us all.
>The question is not whether your design will work (it will), but rather
>does it have any real advantages over other designs?
>What I see is a capacitor design in which there is a LOT of metal and not
>that much capacitance per pound. I would hate to see you (or anyone else)
>spend a lot of time building such a decice only to find that it involves
>a lot of work and material and doesn't offer much bang for the buck.
>In a flat plate and rolled cap design the surface area of the plates
>is pretty well used. In the above proposed design I see that effectively
>each electrode set comprises only a single useful surface area as far as
>capacitance goes. So right off the bat there is a 50% loss in overall
>plate capacitance. (In regular caps both sides of the plate enter in
>and play a part.)

  For equal surface area, the coaxial cap has about 95-99% of the cap
  of a parallel plate cap for dimensions in the range I was talikng
  about when the distance between the coaxial cylinders is equal
  to the plate separation of the parallel plate cap.  (This gives
  approximately the same E-field strength.)

  The "exact" ratio (neglecting edge effects, etc.) turns out to be
        Ccoax/Cparplate = 2*(r-1)/((r+1)*ln(r)),

  Since rolling effectively doubles the available surface area
  I agree with your 50% estimate.

>There appears to be much wasted space. By this I mean space that does
>not contribute to actual capacitance or HV insulation. Thus the cap
>will be quite bulky. It will require much more oil than a flat cap or
>rolled cap design.

  Again I agree.  Actually I could cap off the inner tubes to reduce
  the oil use.  Then its oil use could be competitive with a parallel
  plate cap if the outer tubes were closely spaced.  (In each stage
  these are all at the same potential.)  As far as the size, well,
  it doesn't bother me -- as long as it will still fit through doorways.

>The only thing it has going for itself is the all-oil aspect.
>But what would you be gaining by this design over a straight-forward
>oil-only flat plate cap?

  This was my first idea.  Comparing the two designs:
    1) Flat plates are very flimsy compared to a formed tube, so much
       thicker plates would be required for a given rigidness.  I would
       guess several times more material would be required just for
       physical support reasons.  Try holding a sheet of paper
       horizontally by only its edge.  It will buckle.  Gravity (or
       accidental tipping if vertical) or even electrostatic forces
       would do the same thing on the cap.

    2) Copper plate is unusual and consequently expensive, at least as
       far as I've seen so far.  Copper tubing is everywhere and can
       even be bought from a scrap dealer at near scrap value to save
       more.  Aluminum plate and steel plate are more common, but
       copper conducts 50% better than Al and nearly 500% better than
       iron.  With skin effect issues, it isn't possible to just make
       the conductors thicker to compensate.  Rolling is even worse
       in this regard since the conduction path is relatively long.

>While all-oil designs are self-healing and easily fixed in case of an
>accident, the bad news is that they become quite bulky. The major
>advantage of poly caps is that the poly can withstand very high
>voltages per mil. With only oil you need much greater distances
>between plate surfaces, and this *reduces* the effective capacitance
>you can attain. A LOT!

  It's essentially an inverse relationship between cap value and
  plate separation for both designs, so yes, the oil cap will be bigger.

>For the time being it appears that it is really hard to beat the
>oil/poly capacitor.

  My criteria for "goodness" in a capacitor is that lower loss, more
  rugged/reliable, and more repairable all make for a better cap.
  I expect everyone agrees on these.  I may differ from some on the size
  issue.  With everything else equal, I don't mind something being
  smaller, but I don't give "smaller" much weight in my "goodness"
  calculations.  I want a cap that I can work very hard and still expect
  it to last "forever".  Poly will probably not do that, and I don't
  think a poly cap is considered repairable.  I would gladly trade
  a lot of size for something that isn't throw-away.  One concern I
  do have is the low-loss issue.  I have not seen a lot on how well
  oil compares to poly.  Ideas, anyone?

>Just a remark concerning using oil of a higher dielectric constant:
>while it is true that the poly will get a higher *percentage* of the
>voltage than the oil, please note that without the oil the poly
>would be getting 100% of the voltage stress. So adding ANY kind
>of oil could not possibly "stress the poly more" if by "more" you
>mean "more than it would get all by itself." Indeed, if there
>is anything to be concerned about it is whether or not the OIL
>can take the stress. Although the oil will get a smaller *percentage*
>of the voltage stress, it is also MUCH THINNER in thickness than
>the intervening poly, and so it's small percentage of voltage has
>to be held back by a very thin layer. THAT is where my own concern
>was originally centered,

  Voltage drop is proportional to thickness in a plate cap since E
  is constant within a dielectric, so the fact that the oil layer may
  be thin is not a problem.

>                         but experiments have shown that the oil
>with a dielectric constant of 4 DOES in fact give a higher total
>capacitance than regular transformer or mineral oil, and it DOES
>stand up to the rigors of the Tesla coil environment. And my own
>personal philosophy on such things is to use whatever has been
>demonstrated to work.

  I was  talking about low-dielectric-constant oil vs a higher-
  dielectric oil, not oil vs dry.  In the oil vs oil case, both
  will have the same thickness, so the voltage drop across each
  will be inversly proportional to its dielectric constant.  In the
  same service the total voltage across the cap will not change, so
  the poly will receive more voltage if the oil has a higher dielectric
  constant.  I have no doubt that adding an oil with a higher dielectric
  constant will raise the cap value.  My comment is that it will
  not do so without more stress on the poly in the cap.

>                      See also Ralph Downs' recent post today on the
>use of high dielectric constant oil. The facts speak for themselves.

  I just read it.  It's hard to argue with facts, and I make a point not
  to.  This was a dry vs oil test that fits well into an extension of
  the simple cap model I gave before.  Here we can model the cap as
  having 3 dielectric layers:  poly, air, and oil, and the corresponding
  C value would be             S=effective surface area
                  S            dp,ep=poly thickness / permittivity
    C = ---------------------  da,ea=air thickness / permittivity
        dp/ep + da/ea + do/eo  do,eo=oil thickness / permittivity
                               dp+da+do=plate separation
   Since oil has a higher dielectric constant than air, replacing
   air by oil will make C larger. Assume constant plate separation and
   that the poly to be incompressible -> da + do = dao = constant.  With
   all air, Cair = S/(dp/ep + dao/ea) and with oil replacing all air,
   Coil = S/(dp/ep + dao/eo).  Taking the ratio of these,
   Coil/Cair = (dp/ep + dao/ea) / (dp/ep + dao/eo)
   Since eo>ea Coil/Cair >1.  Something in between these extremes gives
   an intermediate result.  A partially oil-filled cap will have a C
   value higher than one with only air, but not as high as one with
   only oil.  Making eo larger by using a different oil with a
   higher dielectric constant makes the ratio even larger.

  Something that just occurred to me before I sent this off, is that
  we can estimate the effective oil thickness with the Coil/Cair ratio.
  From Ralph Down's testing,
    Coil/Cair = 859/635, doa+dp=1/16".  This gives 2 linear equations
    in 2 unknowns.  Using epolystyrene=2.55e0, eo=4e0, ea=1e0 (the
    e0, the permittivity of free space, cancels anyhow), and assuming
    no math error, the air/oil thickness is 0.0108 inches.  At least it
    is positive and less than the total 1/16" :), and it sounds fairly
    reasonable.  Playing one last game, now we know all the thicknesses,
    so how much did the oil with a higher dielectric constant buy us
    in capacitance?  Taking the ratio of Coil_with_k=4 and Coil_with_k=2,
    0.69% is what I got.  Comments?
>Hope this helps.
>Fr. Tom McGahee