[ExI] Physical limits of electromagnetic launchers

[Anders Sandberg]

On 02/06/2012 19:53, Kelly Anderson wrote:
> If we take a lesson from the particle accelerator folks, can we run 
> them around a big circle speeding them up for a bit before going to 
> the long straight cannon? What point do you have to be at for the 
> sideways G forces to be too much?

Particle accelerators use charged particles held in place with a 
magnetic field and accelerated using oscillating electical fields. So 
the problem becomes whether one can charge up the payload enough to make 
it couple well with the field, and how big the accelerator has to be.

Looking at the formula for the gyroradius of a particle, 
r=gamma*(v/c)*m*c/qB where gamma is the relativistic factor, m the mass, 
q the charge and B the magnetic field one can see that it scales 
linearly with mass. So accelerating a 30 gram mass like the LHC would, 
would require an accelerator ca 1.6e23 times wider. We are talking 
lightyears here. It can be shrunk by increasing the field strength, but 
probably not many orders of magnitude.

We can certainly increase the charge (one electron charge per 30 gram is 
puny). I'm not sure what the limit is: obviously beyond a certain point 
the surface atoms will start sputtering away. Megavolt potentials are 
however entirely doable (especially in vaccum), and assuming ~cm sized 
spherical payloads and using Coulumbs law, I get q=6e12. That would give 
an accelerator just 2.5e10 times bigger than the LHC. Still too big for 
the solar system (about 1600 AU), but maybe if we are lucky there are 
materials that can handle a few order of magnitude more charge.



-- 
Anders Sandberg,
Future of Humanity Institute
Philosophy Faculty of Oxford University