As I hinted at in an earlier post, we combined high voltage with a vacuum! I drilled a small hole in the side of a glass bottle to run a loop of wire through to the inside. Actually this was the second attempt. The first bottle shattered when I tried to drill the hole. I even used a small triangle shaped bit designed for drilling glass, tile, etc. V suggested I put tape over the spot to drill to help prevent it from cracking. So I put tape on the glass and drilled through the tape, sure enough, it worked. Then I epoxied the hole around the wire to seal the bottle's side back up. For the top cap I drilled a 1/2" hole for a brass hose barb adapter (now I'm thinking of using nylon so it doesn't possibly conduct electricity to the outside) into a plastic aspirin bottle cap (it fit well over the end of the bottle). I also drilled a second smaller hole to pass a wire through for the other side of the high voltage circuit. Then I epoxied around the holes in the cap and the cap to the bottle. After that it was just a matter of pumping it down and firing it up.
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| First attempt |
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| The bottle had specks of some kind of tar-like substance stuck to it, which I tried to remove with rubbing alcohol. |
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| Epoxy is setting over the drilled hole. |
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| It worked better to mix the epoxy on a flat plastic lid then apply it. Here I am sealing the hose connector to the aspirin lid. |
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| An initial attempt. If you look closely you can see some purple glow and sparks. |
I was a bit worried that the electrons might travel down the vacuum in the hose to the pump and ground there, bit it didn't seem to happen.
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| You can see the glow in the space around the lower wire. |
In low air pressure the electrons can jump long distances through the partial vacuum. They are very energized from the voltage potential and moving fast. In the process ions are produced from the low density nitrogen and oxygen atoms remaining, which race in the opposite direction (although this is still AC so particles are oscillating back and fourth). This resulting ion gas is a plasma, like the sun is made from, and it doesn't behave like a gas because it is strongly affected by electromagnetic fields. From time to time electrons will rejoin the ions and emit light, the purple glow. The plasma is not working entirely as I want yet, I want to accelerate the electrons with some amount passing through the center of the wire loop, overshooting and continuing down the bottle, but instead it bent and went for a section of wire that was closest to the cap (it was impossible to get the wire even by passing it through a tiny drilled hole). Next we need a diode bridge rectifier to convert the AC to DC. I also suspect the vacuum needs to be even lower so there is not as much interference from the air that is left. What we made is something like a Geissler tube (invented in 1857). But what I am ultimately going for is a Crooks tube, which was developed from that. Anyway, this is just the first pass.
The peak voltage difference is 12,000 volts, so, in theory, what speed are the electrons accelerated to by the field⸮ The result was surprising to me. In classical mechanics E = 1/2 m v^2 , or kinetic energy is equal to half the mass times the velocity squared. The mass of an electron is a tiny 9.11 x 10^-31 kg. The energy is the charge of a particle multiplied by the voltage, the charge of an electron is -1.60 x 10^19 columb. Multiplying this by 12,000 volts gives a kinetic energy of 1.92 x 10^-15 joule per electron. Now that we have the energy and mass of an electron we can work backward to solve for the velocity. This works out to about 65,000 kilometers per second. To put it into perspective, the speed of light is about 300,000 kilometers per second. In other words, this voltage can accelerate electrons (in a vacuum and full velocity) to 22%, or just over 1/5, the speed of light. I didn't really expect this starting out so I double checked my calculations a few times. This is starting to get fast enough that the results from classical mechanics begin to diverge from predictions under relativity. So the speed will be off by a small amount. However, I did a quick calculation and the Lorentz factor (a measure of how distorted space, time, mass and momentum become due to special relativity effects) at this speed is only gamma=1.02. So, for example, there is only a 2% time dilation (time moves 2% slower for the electrons than for us at these speeds).
Special relativity is funny. Because energy adds mass the faster you move something (adding kinetic energy) the more it weighs, and the harder it becomes to move it faster. As you approach the speed of light most of the mass comes from the energy rather than the object itself. It is not off by much but I wanted to try to calculate the velocity of the electrons under relativity rather than classical mechanics. It took a while but I finally came up with, and found in the literature (to verify), the relationship v = c * sqrt[1-(mc^2/(mc^2+E))^2]. Buried in this you can see the famous E and mc^2. Solving this gave a speed of 63,900 km/s. So the electrons are predicted to be moving at « only » 21% the speed of light due to relativistic effects and not 22% as I calculated above. In the full calculation the numbers are off by only 1.7% between classical mechanics and relativity at this speed.
In the graph above I plotted the electrons predicted speed (under ideal conditions at full acceleration in a vacuum...) as a function of the voltage potential. In classical mechanics, the blue line, the electron's velocity keeps increasing with more voltage in a parabola shape (remember kinetic energy is a function of velocity squared). At a little over a quarter of a million volts the electrons pass the speed of light, the yellow line. Under relativity there is an extra downward bend in the curve, from the mass added by the energy, and the velocity will never exceed the speed of light. However, for small voltages, in other words low velocities, either calculation works fine.
The average speed of movement of particles can also be considered the temperature. This leads to another curious number. Ignoring the ions for a moment and focusing only on the more numerous electrons. The kinetic energy is related to temperature in thermodynamics by E=(2/3)BK, where B is Boltzmann's constant, 1.38 x 10^-23 J/K, and K is the temperature in Kelvins. If we plug in our particle energy estimate of 1.92 x 10^15 J from above, we can solve for the temperature in Kelvins. This gives us a staggering 93 million Kelvin! --if I have not made a mistake somewhere in my assumptions or calculations. Keep in mind the plasma is at a very low pressure, so the particles are rare and spread out, so when they impart their energy to the much much denser atoms in the glass, for example, it has a much smaller effect than we might otherwise expect. (However, the jar was very hot and the copper was glowing red... ) Imagine the point of a pin and the base of an iron skillet heated up to the same 500 degrees. It is the same temperature but there is a huge difference in which one you would rather touch. Room temperature is 296 Kelvin. The surface of the sun is « only » 5,800 Kelvin. Lightning, a plasma at atmospheric pressure, is 28,000 Kelvin. The core of the sun, which is under tremendous pressures, is 15 million Kelvin. It would seem, according to calculations, that we have made something, in a bottle in our house, that has a potential to be six times hotter than the core of the sun, at which time we start to wonder about our fire insurance...(which reminds me of a joke I heard in Kenya; I'll write about that later). However, these are unfair examples; the temperature of electrons in a plasma can easily be several orders of magnitude higher than ions and neutral atoms, because they are so easily accelerated. Temperatures, in a thermodynamic sense, can be misleading when we think about temperature in the everyday sense.
And then just as a final note, what is the relative mass of the electrons to the glass wall⸮ The transformer puts out 0.032 amps of current. A flow of one amp is made up of 6.24 x 10^18 electrons per second. So in this case there are 2 x 10^17 electrons moving along per second. As stated above, an electron's mass is 9.11 x 10^-31 kg. So the mass of electrons moving by each second is 1.82 x 10^10 grams. Regular soda-lime container glass has a density of 2.52g per cubic centimeter. Dividing one by the other we can see that a cubic centimeter of glass is 1.39 x 10^10, or 10 billion, times as dense as the electrons flowing over a second of time. So simplistically ,(and perhaps this is a completely wrong way to think about it but) if we completely and 100% efficiently transferred the 93 million Kelvins of energy from one second of electrons at this voltage and amps to a cubic centimeter of glass, it would add 671 Kelvins after the kinetic energy is diluted 10 billion times out amongst the greater mass.
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