Effective ways of accelerating a 50 picogram particle

[BrandonBerchtold]

TL;DR Summary

Is it possible to accelerate a 50 picogram particle to speeds on the order of 1,000,000 meters per second (or higher) using methods typically used in particle accelerators? If so, which methods would lend themselves most practical?

Would it be practical to accelerate a 50 picogram particle to speeds on the order of 1,000,000 meters per second (in a high vacuum environment) using methods typically used in particle accelerators? 2 methods that come to mind are a series arrangement of parallel pate accelerators and a moving wave microwave cavity linear accelerator.

I am guessing the parallel plate accelerator design would need impractically high voltages to achieve high enough speeds due to the high mass to charge ratio of the particle being accelerated? My rough calculations are below:

Assumptions:
- Particle is charged to same voltage as first accelerator plate
- V = Applied Voltage to charge particle = Parallel plate accelerator total voltage difference between first and last plate
- Particle has diameter of 10 microns
- Particle density is 86 kg/m^3

Charge on sphere = 4 * PI * ε0 * Sphere radius * V
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html

0.5*m*velocity^2 = Charge on sphere * V

V = Sphere radius * velocity * 1,272,342
V = 0.000,005*1,000,000*1,272,342 = 6,361,710 volts

Nearly 7 Megavolts seems pretty high for a parallel plate accelerator right?

My concern with the microwave linear accelerator is that usually electrons enter the accelerator going on the order of 0.4c and match the speed of the wave in order to get caught in the trough between wave peaks before the wave accelerates to relativistic speeds. Could such an accelerator be tuned to capture 50 picogram particles traveling at much much slower speeds and accelerate them to 1,000,000 meters per second? I know close to nothing about how these accelerators work so any input is appreciated.

Are there other types of accelerators that would be better suited for such an application?

 

[mitochan]

Just let me know if you please voltage you need for your case
$$V=\frac{mv^2}{2q}$$

 

[BrandonBerchtold]

Just let me know if you please voltage you need for your case
$$V=\frac{mv^2}{2q}$$

Yes, that is the formula I was using to calculate the required voltage. (Apologies for the messy formatting in my question.)

 

[mitochan]

Thanks and sorry for my careless reading. Now Van de Graaff generator generates 5MV or so. You may take a look at it or current status of other accelerators.

 

[BrandonBerchtold]

Thanks and sorry for my careless reading. Now Van de Graaff generator generates 5MV or so. You may take a look at it or current status of other accelerators.

I think the issue would be more so the breakdown voltage of the dielectric separating the plates as opposed to the generation of high voltages. Extruded teflon can handle on the order of 20 MV/meter before breaking down so at 7 MV that would require a fairly long vacuum chamber. And for larger particles the required voltage gets quite high since voltage is inversely proportional to particle radius.

 

[mfb]

Dust accelerators reach ~100 km/s with the smallest dust particles, that is a good start. They are not designed for higher speeds, they are mainly used for impact studies for spacecraft . They only reach that speed with particles in the femtogram range, however. 50 picogram = 5*10^-14 kg.

You can't charge particles that small to megavolts relative to infinity, they would immediately expel electrons or even ions. From the dust accelerator it looks like the smallest particles are charged with ~10,000 elementary charges. With that charge a "dust synchrotron" with 5 T magnets needs a radius of 6200 km to reach 1000 km/s. That is clearly impractical. With electric fields of 1 kV/mm we need 15000 km acceleration distance.

The electric field at the surface scales with Q/r². Increasing the mass by a factor 50,000 while keeping the density increases the radius by a factor ~40, so we can put a factor 1600 more charge on them. Maybe another factor ~5 because your particle has such a low density, so let's say a factor 10,000 more. Then the electric field accelerator shrinks to 1.5 km. Possible but quite expensive. Better accelerating gradients might be achievable. Similarly, the synchrotron-style device shrinks to 620 m radius. Make it 10 T magnets and the radius goes down to 300 m.

 

[Vanadium 50]

]1,272,342

Significant figures please! And units! And don't just write a wall-of-numbers! I'm trying to figure out how much charge you are talking about and all I can figure out is that it's buried in the 1,272,342. Somewhere.

You want 25,000 joules per particle. This is about 300x more than the LHC does per bunch. Essentially a particle accelerator is a transformer, and you want crazy high energies and currents at the output. This is just not practical.

 

[mfb]

You want 25,000 joules per particle. This is about 300x more than the LHC does per bunch.

Huh? 1.1 * 10¹¹ * 6.5 TeV = 115 kJ has been achieved. We had more protons per bunch but I don't remember the record at 6.5 TeV now. The poor charge to mass ratio makes this so difficult.

 

[Vanadium 50]

I'm using CERN's public number of total energy, and dividing by 2808. Not building up from first principles.

 

[DaveE]

OK, now I'm curious.
Why do you want to do this? What is the application/experiment?

 

[mfb]

I'm using CERN's public number of total energy, and dividing by 2808. Not building up from first principles.

That would be 500-600 MJ or so for both beams, leading to the same result (number of bunches was a bit lower as far as I remember). 700 MJ is the design value.

 

[Vanadium 50]

Fine. I should have Googled better. You got me., Merry Christmas,

 

[trurle]

Summary:: Is it possible to accelerate a 50 picogram particle to speeds on the order of 1,000,000 meters per second (or higher) using methods typically used in particle accelerators? If so, which methods would lend themselves most practical?

Would it be practical to accelerate a 50 picogram particle to speeds on the order of 1,000,000 meters per second (in a high vacuum environment) using methods typically used in particle accelerators? 2 methods that come to mind are a series arrangement of parallel pate accelerators and a moving wave microwave cavity linear accelerator.

I am guessing the parallel plate accelerator design would need impractically high voltages to achieve high enough speeds due to the high mass to charge ratio of the particle being accelerated? My rough calculations are below:

Assumptions:
- Particle is charged to same voltage as first accelerator plate
- V = Applied Voltage to charge particle = Parallel plate accelerator total voltage difference between first and last plate
- Particle has diameter of 10 microns
- Particle density is 86 kg/m^3

Charge on sphere = 4 * PI * ε0 * Sphere radius * V
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html

0.5*m*velocity^2 = Charge on sphere * V

V = Sphere radius * velocity * 1,272,342
V = 0.000,005*1,000,000*1,272,342 = 6,361,710 volts

Nearly 7 Megavolts seems pretty high for a parallel plate accelerator right?

My concern with the microwave linear accelerator is that usually electrons enter the accelerator going on the order of 0.4c and match the speed of the wave in order to get caught in the trough between wave peaks before the wave accelerates to relativistic speeds. Could such an accelerator be tuned to capture 50 picogram particles traveling at much much slower speeds and accelerate them to 1,000,000 meters per second? I know close to nothing about how these accelerators work so any input is appreciated.

Are there other types of accelerators that would be better suited for such an application?

This is basically a question about velocity capability of colloid (electrospray) thruster.
Current state-of-art is 1500-15000 m/s

https://static1.squarespace.com/static/5446faa2e4b025843cfc6731/t/59ce4f211f318d6cc856ca0d/1506692898494/TILE+Product+Family+Data+Sheet.pdf
https://pcos.gsfc.nasa.gov/studies/L3/MicrothrusterOverviewforL3STv1.pdf

 

[zoki85]

That would be 500-600 MJ or so for both beams, leading to the same result (number of bunches was a bit lower as far as I remember). 700 MJ is the design value.

Energy comparisons between processes may be sometimes amusing but I don't find them particularly useful there...Typical CG lightning is estimated in a range 500 -1000 MJ. Is that a lot or little? I can't tell.
Also it wouldn't hurt to mention a very poor efficiency of LHC machine having on mind 40 MW of cryogenic power used while the protons accelerate in marry go round fashion for about half an hour

 

[mfb]

The cryogenics power is not going into the protons. The RF cavities are not even that inefficient, even though it is a minor consideration - they are needed to accelerate the protons for 20 minutes every day or so, the rest of the time with beam they just need to compensate the small synchrotron radiation losses.

What we compared was the energy of a proton bunch with the energy of a solid bunch of atoms in this hypothetical accelerator, that is a relevant comparison.

 

[zoki85]

Still, that power is dissipated in order to LHC work. It is not essential for the principle of acceleration but that's the way how the machine is designed. Similarily my VDG is 1% efficient mostly becouse of the mechanical and frictional losses spent in order to separate and transport charges to HV electrode.

 

[BrandonBerchtold]

OK, now I'm curious.
Why do you want to do this? What is the application/experiment?

I came across this paper and wanted to see if there were some other methods of accelerating particles to the speeds they discussed.

https://www.google.com/url?sa=t&sou...Vaw3LUfVzqBSk61gNLXGoniiH&cshid=1577910227595

 

[BrandonBerchtold]

I came across an interesting blow gun method by the same researchers and it involves firing a particle beam at the projectile to accelerate it by creating a very high localized electric field behind the particle.

https://www.researchgate.net/publication/224408312_Acceleration_of_Macroscopic_Particle_to_Hypervelocity_by_High-Intensity_Beams

 

[mfb]

I came across an interesting blow gun method by the same researchers and it involves firing a particle beam at the projectile to accelerate it by creating a very high localized electric field behind the particle.

Looks like conference proceedings.
I don't share the optimism of the authors to hand-wave away several problems. RF cavities reach their high gradients because the particles flying through are relativistic. A 1 GHz cavity changes its direction of the electric field every 0.5 nanoseconds, a 1000 km/s particle flies only 0.5 mm in that time, getting ~15 kV of acceleration gradient. And that's the best case, at 1000 km/s. Most of the cavity size would be wasted unless they find a method to use several 0.5 mm steps within a single cavity (with some shielding tubes... not impossible, but certainly not trivial). This is independent of the cavity frequency, accelerating track and cavity size scale in the same way.
Anyway, the idea to "push" the particle with an ion beam looks interesting. Would need more research.