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New Accelerator Technique Doubles Particle Energy
ZonkerWilliam writes "Plasma wake particle accelerators are making surprisingly quick advances. It was a just a little while ago we had GeV acceleration in 3cm. Now they are capable of doubling the energy of electrons. 'Imagine a car that accelerates from zero to sixty in 250 feet, and then rockets to 120 miles per hour in just one more inch. That's essentially what a collaboration of accelerator physicists has accomplished, using electrons for their race cars and plasma for the afterburners. Because electrons already travel at near light's speed in an accelerator, the physicists actually doubled the energy of the electrons, not their speed.'"
The kinetic energy is proportional to speed^2 (E=1/2 m v^2), so a car at 120mph has 4 times the energy of a car at 60mph. Thus, doubling in energy is not like doubling in speed.
Unfortunately, these concepts will not be applied to the next generation of high energy accelerators. The International Linear Collider will supplant the Large Hadron Collider some time after 2015, but relies on superconducting static-gap technology and will be 30-40 kilometers long. Perhaps the next generation of experiemnts will employ plasma accelerators?
In terms of solving the relevent math covered in the study of Quantum Mechanics and Molecular Spectroscopy (senior Inorganic Chem II at my alma mater), pumping energy into an electron is computationally similar to accelerating an object of 1000 kg mass to 60 mph over the span of time required to travel 250 feet and then nearly instantaneously pumping enough energy to double the velocity in the span of time represented by the distance travelled in one more inch.
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E=mv^2/2 only for small values of v.
The other formula for E, you might have heard of, is E=mc^2. m = \gamma m_0, where m_0 is the rest mass, \gamma = 1 / sqrt(1 - \beta^2), and beta = v/c. I.e.,
E=m_0 c^2/sqrt(1 - v^2/c^2)
For very small values of v (relative to c), 1/sqrt(1-v^2/c^2) \approx = (1/2)v^2/c^2, which leads back to your formula - but the approximation is only valid for v
Ben Hocking
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I assume you are referencing Dimopoulos and Landsberg's paper http://prola.aps.org/abstract/PRL/v87/i16/e161602 . There is nothing to worry about. These physicists proposed that if certain theories were true (M theory, quantum loop gravity, super symmetry) then the energy densities seen in the RHIC or LHC experiments could produce something "mathematically analogous" to a black hole. There is no possibility under any current theory that an event horizon could form and attract matter.
1/2 mv^2 is the non-relativistic kinetic energy. The mass correction will change the energy rapidly as v approaches c. The mass correction with the Lorentz factor in that expression are needed to get the correct relativistic energy.
The lorentz factor is 1/sqrt(1-(v/c)^2); at 0.99c it will multiply the mass (and energy) by a factor of 7; at 0.999c it will multiply everything by a factor of 22.3.
I actually do some work on this with the PWFA group at USC (i'm an undergrad research assistant). It really is amazing! We can reach acceleration gradients of around 60 GeV/m, compared to something like 40 MeV/m for a normal accelerator. It works like this: .or at least something close to that!
1. The electrons travel down the main linac in carefully spaced "bunches", and get accelerated to around 43 GeV over a course of ~3KM (this is at the main beam at SLAC).
2. A (in the last experiment) 1.2m long Lithium plasma "oven" is at the end of the beam, which the electrons are directed into.
3. The first, or "driving," bunch goes through the plasma, and repels all of the electrons it gets near, leaving an "empty" wake behind it, where only the positively charged ions are.
4. The positive charge behind the driving beam pulls it backwards, causing it to lose energy. At the same time, a "witness" bunch placed strategically within the wakefield gets pulled forward by the positively charged ions. The witness gains energy while the driver loses energy.
5. Voila! One bunch now has twice the energy, and one bunch now has none . .
The main caveat is that you're upward-limited by your entering energy, so you still need a huge Linac to accelerate the bunches to begin with. This will likely get tacked on in the form of a "plasma afterburner" to a normal linac, such as in the setup at SLAC.
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As I understand it, luminosity is one major reason why this technology is not yet ready for prime time (i.e. not in time for the proposed ILC). You can't just accelerate a few particles to high energies and say you are done. You're looking for rare processes, so you need to create many consistent particle collisions per second in a tiny area. This means you need to have a tight, "bright" beam. The Tevatron has a luminosity of ~2e+32 interactions/cm^2/s now, the LHC may eventually reach 1e+34, and the goal for the ILC is more like 2e+34. Plasma wakefield systems are now demonstrating large increases in energy over short distances, but it's very difficult to daisy-chain them together to reach high total energies with any significant luminosity.
Any black hole created in a lab on earth is going to have negligable sucking power, since the mass in them will be tiny. The vision of a black hole forming and swallowing the earth is great sci-fi, but (happily) poor science. At worst, it will hang around, swallowing the odd electron at very rare intervals.
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Even if you generate these at an enormous rate, you'll still end up gobbling up a few protons a year. Heat death of the universe will be an issue before those micro black holes are. Remember that black holes' anomalous effects at close range are due to the *density* of the matter, while the long-range effects are based on their total mass. As for the former, "close range" for a micro black hole is such that one would most likely pass through the earth without a single particle coming within range on the way. As to the latter, the total mass of a micro black hole is so insignificant as to have no meaningful impact on *anything*.
Interestingly, there are some theories that have proposed that a micro black hole might behave as a fundamental particle, since it would be completely described by its spin, charge and mass, one even going so far as to suggest electrons might *be* black holes.