How fast can an accelerator fire an object?

Uncle Al wrote:


A lot sooner than that - (in Newtonian mechanics) at 50,000 g (500 km/s^2) it takes 600 seconds to reach the speed of light, implying a barrel 90 million km long - less than the length of a Golden Ship, iirc.
-- Peter Fairbrother
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Peter Fairbrother wrote:

Now the Pentagon is gonna bother us for specs, estimates, and a PERT chart. First, we're gonna substitute an alloy .223... "8^>)
--
Uncle Al
http://www.mazepath.com/uncleal/
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Elctric fastness F_E works as the product of charges over their separation squarede kqq/ss. The accelerator's capacity, by capacitanse and inductanse, will say how fast that is.
Mhm, this is a good candidar for greater fieldly intensities at the input end: http://wikipedia.org/wiki/Plasma_acceleration http://wikipedia.org/wiki/Wakefield_accelerator

Plug in the gradients at the above links.
-Aut
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Once you get beyond 99% of c, it's easier to keep track of things in terms of energy or momentum rather than speed. While the speed is limited, the energy and momentum are not. Wake field accelerators are achieving energy transfer of about a GeV/m. A 60,000 mile run is about a 100,000,000 meter run, and so this corresponds to an energy of 100,000,000 GeV transfer in principle (though building a 60,000 mile long wave field accelerator would probably consume the GDP of the top 10 economic powers for a decade).
For an electron accelerated, this corresponds to a relativistic gamma of 200 billion. The relationship between the fraction of the speed of light (beta) and gamma is beta=sqrt[1 - 1/(gamma)^2]. In this case, this works out to a decimal point followed by 22 nines, approximately.

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