Invictos
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Timing Electrons
This is a follow up Topic to this one: http://www.sciencemadness.org/talk/viewthread.php?tid=72593
Annnyway, that said, here's the 411: We're building an electron accelerator. We have the capability to power the machine up to a 200 KeV differential
at the moment, with plans to build upwards in future (see the other thread for why this is "in future" )
Our end goal is (now) this: We want to be able to detect when electrons reach the end of the chamber, so that we can time their travel time throughout
the pipe. We're going to then take this data, and compare it what we'd expect given basic kinematics. After we have that number, we're going to
calculate the time while taking into account special relativity.
All said and done, we should be able to prove E = MC^2 experimentally. (Or more accurately E^2= (MC^2)^2+(PC)^2)
The knee-jerk idea would be to get a photomultiplier, connect it to an arduino, hook that up to the electron source, and set the timer. However, I'm
sure we're going to be talking about .000...0001th's of a second here. Is this method going to be high enough precision? If not, I've considered
making the tube longer to allow for the difference in accelerations to become more obvious.
Thanks for your time everyone, I've attached some Kinematics math to show how drastic of an effect relativity would have (Assuming I did the math
correctly, relativity would cause the mass of the electron at the final kinematic velocity to have increased by over twice the amount)
[Edited on 3-5-2017 by Invictos]
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phlogiston
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It is equally important that your electron source can produce accurately timed pulses. That may be a more difficult problem than detecting the arrival
of the electrons (which could be done with a PMT).
How does your electron source work?
You need to know exactly when a bunch of electrons takes off.
And you need to consider what impact your definition of 'arrival' of a pulse of electrons will have on your conclusion. Does a pulse arrive at the
first 'edge' of the pulse, or at the peak amplitude (group velocity), or etc?
Group velocities may even appear to be superluminal. If the shape of a pulse changes as it travels (there is some spread in the speed of the electrons
making up the peak), the peak of the pulse may appear to be faster-than-c even if all of the electrons individually never travelled faster than c.
Accurately measuring time is not very difficult. Electronics are really fast. However, you will need to take into account the time needed by signals
to travel through transmission lines, parasitic capacitance/inductance, etc. If you do not understand this already, you should study how fast digital
circuits are build and the techniques used in RF electronics.
[Edited on 6-3-2017 by phlogiston]
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"If a rocket goes up, who cares where it comes down, that's not my concern said Wernher von Braun" - Tom Lehrer |
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Invictos
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Quote: Originally posted by phlogiston  | It is equally important that your electron source can produce accurately timed pulses. That may be a more difficult problem than detecting the arrival
of the electrons (which could be done with a PMT).
How does your electron source work?
You need to know exactly when a bunch of electrons takes off.
And you need to consider what impact your definition of 'arrival' of a pulse of electrons will have on your conclusion. Does a pulse arrive at the
first 'edge' of the pulse, or at the peak amplitude (group velocity), or etc?
Group velocities may even appear to be superluminal. If the shape of a pulse changes as it travels (there is some spread in the speed of the electrons
making up the peak), the peak of the pulse may appear to be faster-than-c even if all of the electrons individually never travelled faster than c.
Accurately measuring time is not very difficult. Electronics are really fast. However, you will need to take into account the time needed by signals
to travel through transmission lines, parasitic capacitance/inductance, etc. If you do not understand this already, you should study how fast digital
circuits are build and the techniques used in RF electronics.
[Edited on 6-3-2017 by phlogiston] |
We are using a Tungsten Filament by Kimball Physics (This one:http://www.kimballphysics.com/tungsten-filaments)
I see what you're saying with pulses...would've never thought of that  ! I can't
find data on how fast the cathode heats up, maybe you'll have better luck. In the event it takes a while, could we let it heat up first before
applying the voltage potential? Essentially it would just be spewing out electrons at 4 eV for a minute or so, which should just fall to the tube
walls, right?
The voltage itself is being applied by Van De Graaff generator, so that could be controlled a bit easier... I think...
EDIT: Forgot to answer the second part~ My circuit knowledge is workable, but that's something I'll have to look into...thanks for the suggestion!
[Edited on 3-6-2017 by Invictos]
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WGTR
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Do you want to time individual x-ray photons? Some newer detectors can distinguish around 1,000,000 counts per second, but in any case there's a
practical limit, and that would present an upper limit for beam current before you start getting a lot of overlapping pulses.
I'm envisioning a scenario where each well-separated count is time stamped, and then as the accelerating voltage increases, watch the statistical
shift in arrival time of the photons, to see if it matches what you expect (if I'm understanding this correctly). It would likely require a very
accurate time base, and I'm probably presenting an oversimplification.
I normally turn the filament voltage up first when working with the SEM, but some filament types require that. I'd think tungsten is fine with full
voltage on a cold filament. The main problem is that tungsten filaments can take several minutes to cool back down under a hard vacuum, and it's
possible to ruin the filament by cracking it to atmosphere too early.
Beam current can be easily adjusted by varying the filament voltage.
[Edited on 3-6-2017 by WGTR]
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Invictos
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| Quote: Originally posted by WGTR | Do you want to time individual x-ray photons? Some newer detectors can distinguish around 1,000,000 counts per second, but in any case there's a
practical limit, and that would present an upper limit for beam current before you start getting a lot of overlapping pulses.
I'm envisioning a scenario where each well-separated count is time stamped, and then as the accelerating voltage increases, watch the statistical
shift in arrival time of the photons, to see if it matches what you expect (if I'm understanding this correctly). It would likely require a very
accurate time base, and I'm probably presenting an oversimplification.
I normally turn the filament voltage up first when working with the SEM, but some filament types require that. I'd think tungsten is fine with full
voltage on a cold filament. The main problem is that tungsten filaments can take several minutes to cool back down under a hard vacuum, and it's
possible to ruin the filament by cracking it to atmosphere too early.
Beam current can be easily adjusted by varying the filament voltage.
[Edited on 3-6-2017 by WGTR] |
That's the dream in terms of precission, but I can't see us managing to change the potential difference smoothly enough to make that work
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wg48
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For a 1 metre tube the flight time for light is 3.3ns. For an electron travelling 1/2c it will be approximately 4x that 13.3ns. Lets assume your
electrons take 10ns and you need 10% accuracy that’s 1ns. You may need 1%. You can measure that with a good oscilloscope (expensive) if you need
0.1ns you will need a very good oscilloscope (very expensive). You could use a counter, which would be cheaper than a oscilloscope but will be more
useful for trouble shooting.
So you need to turn the electrons on and off. You could use a spark gap even a triggered spark gap but that would require triggering some how and an
air gap at 200kV (wide) may be too slow. Perhaps a control grid after your filament but it will need to be supplied by pulses at perhaps 50v (depends
on the grid to cathode separation) with preferably less than 1ns rise time.
Depending on which end of the tube is at 200kV either the electron detector or the electron on and off switch will be at 200kV so communication will
have to be wireless perhaps fiber optics and one of them will have to battery powered.
Delays are not big problem if all signals travel down the same cable and length. Difficult if one is cable and the other is optical fiber. However by
varying the electron travel time you should be able to factor out any differential timing.
So the problem is all the electronics has to have fixed delays with fast edges 0.1ns to 10ns. If you’re into that stuff not a problem if your not it
will be a lot to learn.
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Sulaiman
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Your 1.5 MeV dream machine is going to have a long acceleration tube,
the vacuum required to achieve suitable mean free paths will need turbo and/or ion pumps,
so I suggest that you work out that part first,
then use it so that the longest tube practical can be used in your present setup
as, of course, a longer tube makes measurement errors less significant.
You need a grid for your electron gun,
probably with a fibre-optic link for electrical isolation.
(and an e.h.t. isolated power supply (battery) for the filament power and grid control)
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Invictos
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For the vacuum, we have access to an Edwards two stage rotary pump, so not quite ion pump level, but it's still a few steps above a bicycle pump!
A grid seems like the way to go most likely...is there a way to build that from scratch do you think? It's hypothetically just a bit of metal at ~-50
V, right? Otherwise we may just need to deal with the initial electron cloud in the data...
And wg48, if I hypothetically didn't know how to do that, what would one google to get started learning? I'm set on my Mulitvariable Calc, Computer
Science, Stats, et. cetera so I should be able to handle the Math on that
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Sulaiman
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My two-stage rotary will get to 10 to 50 mm mean free path,
maybe your Edwards is in excellent condition and could give 100 mm mean free path,
but not much more.
if ion- and turbo- pumps are too pricey,
consider a Sprengel pump https://en.wikipedia.org/wiki/Sprengel_pump
I saw it in a Cody'sLab video, https://www.youtube.com/watch?v=viJ3T-1KZqY
read about it, and wondered why it is not more popular in amateur labs
other than the mercury problem
The sprengel pump should be sufficient for your needs
and has good references ... lightbulbs and electronics !
[Edited on 6-3-2017 by Sulaiman]
[Edited on 6-3-2017 by Sulaiman]
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Invictos
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| Quote: Originally posted by Sulaiman | My two-stage rotary will get to 10 to 50 mm mean free path,
maybe your Edwards is in excellent condition and could give 100 mm mean free path,
but not much more.
if ion- and turbo- pumps are too pricey,
consider a Sprengel pump https://en.wikipedia.org/wiki/Sprengel_pump
I saw it in a Cody'sLab video, https://www.youtube.com/watch?v=viJ3T-1KZqY
read about it, and wondered why it is not more popular in amateur labs
other than the mercury problem
The sprengel pump should be sufficient for your needs
and has good references ... lightbulbs and electronics !
[Edited on 6-3-2017 by Sulaiman]
[Edited on 6-3-2017 by Sulaiman] |
Mercury...huh...That's clever
We'll look into that!
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Sulaiman
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An important parameter for the Sprengel pump is the bore of the drop tube,
too large and it does not work, too small and it is too slow,
many articles, little detail, until I found
2.5mm to 2.75mm is recommended in Sprengel's original published paper.
https://books.google.co.uk/books?id=UKIwAAAAYAAJ&pg=PA9&...
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wg48
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| Quote: Originally posted by Invictos | For the vacuum, we have access to an Edwards two stage rotary pump, so not quite ion pump level, but it's still a few steps above a bicycle pump!
A grid seems like the way to go most likely...is there a way to build that from scratch do you think? It's hypothetically just a bit of metal at ~-50
V, right? Otherwise we may just need to deal with the initial electron cloud in the data...
And wg48, if I hypothetically didn't know how to do that, what would one google to get started learning? I'm set on my Mulitvariable Calc, Computer
Science, Stats, et. cetera so I should be able to handle the Math on that
|
When the grid is at a negative potential wrt the cathode/filament it repels electrons from the cathode back to the cathode. In order to do that the
grid must screening the cathode and its space charge (cloud of electrons) from the electrostatic attraction of the anode. Meaning no field line from
the anode can connect with the electron emitting surface of the cathode.
What you will be making is an electron gun. The grid will be a metal thimble that encloses the cathode accept for a single small (about 1mm dia) hole
facing the anode. When the grid is at 0V or a few volts positive wrt to the cathode it allows electrons to exit the hole and get accelerated to the
anode.
I don’t know what you capabilities are but I suspect if you can build everything else the grid will be a minor task.
I suggest search terms such as “construction cathode ray tube”, grid, thermionic valve
If you can find an old big fat television with one of those large lumps of glass in it (lol) you could attempt to remove the electron gun from it
examine its construction.
That’s not an easy task to do safely because it contains a vacuum so be super careful.
Here is some pics
Below is the part of a color or black and white television tube that contains three electron guns or one if its a black and white. Again please be
carefull if you attempt to recover the gun assembly
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wg48
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That works with water too but it makes a much lower vacuum. Even with a one metre drop pipe it can significantly speed up filtration. Low water
consumption means the drop pipe can go straight to the drain which can provide most of the drop (suck) height.
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Invictos
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I see...I used to have relatives who worked with the tubes, so I'll ask them!
As for the vacuum, I'll have to give that paper a read! As vacuums that fine require a decent amount of...precision...hypothetical question: What
would happen if we can't get the vacuum any better than our approximate 0.00075 torr? (I googled a similar pump and pulled that number, so that's
very, very approximate...)
It'll still work, albeit with messier data, right? I'm a data scientist at heart, so noise I can handle!
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Sulaiman
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Based on this Wikipedia article https://en.wikipedia.org/wiki/Mean_free_path
0.00075 Torr = 7.5 10-4 Torr is equivalent to a mean free path of 100 mm !
for a 1m long acceleration tube, that is 10 mean free path lengths,
attenuation = 1/e10 = 4.54 10-5
i.e. 1 in 22,000 electrons would travel an unimpeded path 
Luckily you are not concerned with noise
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Invictos
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| Quote: Originally posted by Sulaiman | Based on this Wikipedia article https://en.wikipedia.org/wiki/Mean_free_path
0.00075 Torr = 7.5 10-4 Torr is equivalent to a mean free path of 100 mm !
for a 1m long acceleration tube, that is 10 mean free path lengths,
attenuation = 1/e10 = 4.54 10-5
i.e. 1 in 22,000 electrons would travel an unimpeded path
Luckily you are not concerned with noise |
That's quite a formuler there...where do you find these things! 
1 in 22,000....that's not noise, that's the entire philharmonic orchestra!
So I ran some numbers...say we go with a .5 meter tube. Thanks to the ever-so-fun compounding effect of integrals and probability, that would be
(1/e5)-1 = 1 in 148 electrons.
Taking that and running with it, let's say the pipe diameter is half an inch (I'm in the US, deal with it  ). Take an electron that starts at the center of the pipe, 0.00635 meters away from the wall. Say it has a
near-collision with a stray molecule in the pipe during transit that changes the trajectory of the molecule by one degree. If I can trig, .5 -
(tan(89) * .00635), the electron will collide with the wall .136 meters before the target. That said, I'd be willing to bet that most of the rouge 147
electrons are not going to make it to the detectors...right? If we place the pump closer to the detector, we could probably maximize on the
strays colliding with the wall.
Of course, that leads to a final kinematics velocity of 1.87x108 m/s rather than 2.65x108 m/s, but I think that's a healthy
trade off!
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WGTR
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My 2 cents for what it's worth:
Write up a proposal, as detailed and impressive as you can, on the usefulness of what you are doing, and go to some local universities to see if they
will pity you and either give or let you borrow some surplus vacuum equipment. With the right approach, maybe someone will take a liking to you.
Another place to check might be commercial research facilities.
Maybe a halfway worn-out ion pump would get you where you need to be. The two-stage roughing pump isn't going to cut it on its own, unfortunately.
[Edited on 3-8-2017 by WGTR]
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WGTR
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Also, a key phrase that you're looking for is "electron optics".
https://en.m.wikipedia.org/wiki/Electron_optics
Many years ago I downloaded a free simulator that would allow you to visualize the effects of different electrode geometries, but I can't locate it
now. At one point I was interested in seeing whether or not you could accelerate an electron to a higher energy level than would be attained by
simply heating the cathode, without drawing current from the acceleration electrode (you can't, and this would violate a law of thermodynamics).
Edit: Actually, I think this is the program that I used:
https://electronoptics.com/Downloads/Index
[Edited on 3-9-2017 by WGTR]
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Invictos
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I see... I'll have to look into that!
P.S. Sorry for the long response delay, work
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