# Nuclear fusion using electromagnetic fields

I was just thinking about how deuterium and tritium are charged particles and so I couldn't help but wonder why we don't use the same process used in the LHC(electromagnetic fields to accelerate particles) for nuclear fusion?

• This is the basis for the TOKAMAK. – rmhleo Sep 23 '14 at 7:50
• @rmhleo: In tokomaks like JET and ITER the magnetic fields are used to confine the particles, but their energy comes from heating them with a large electric current. The mechanism is completely different to the LHC. – John Rennie Sep 23 '14 at 9:18

Oh, but we do! I'm assuming you mean using the fields to simply collide particles with each other, right? Then that's already being done. For example, take this neat little machine: http://en.wikipedia.org/wiki/Fusor This one runs on the exact same principle you described (though I'm not quite familiar with the inner workings of the LHC).

For energy generation, most current approaches to nuclear fusion here in Europe heat up those exact particles to high temperatures, making them collide into each other due to their high kinetic energies, and then use magnetic fields to steer the particles (en masse in the form of plasma) to keep it confined, to keep it from running into the walls, damaging them and cooling themselves down. It's really hard to execute in practice for now, but we're getting there with projects like JET and ITER. Here you go for some further reading: http://en.wikipedia.org/wiki/Magnetic_confinement_fusion

The energy per proton at the LHC is much larger than what is needed for fusion, protons break up into their constituents easily at this energy and fly away after they interact. In a fusion reactor, one wants the particles to stay within the reactor volume such that the released energy can be transferred to other deuterium/tritium nuclei which then can interact etc.

The beams of the LHC have a typical diameter of 0.05 mm, much too small for a practical fusion reactor (also a lot of energy goes into cooling the bending and focusing magnets to keep the size of the beam so small).

The corresponding section on Wikipedia points out that:

The key problem with accelerator-based fusion (and with cold targets in general) is that fusion cross sections are many orders of magnitude lower than Coulomb interaction cross sections. Therefore the vast majority of ions end up expending their energy on bremsstrahlung and ionization of atoms of the target.

Number of particles: A typical number of protons per LHC beam is $3 \cdot 10^{14}$, which isn't much compared to the number of particles in one mole ($6 \cdot 10^{23}$, about two billions larger). Even with one of the most intense proton beams available today (see also https://physics.stackexchange.com/a/77999/671), at 2.2 mA, this would correspond to about $10^{16}$ particles shot on target per second, taking about $10^7$ seconds (115 days) to shoot a mole on a target. This is much too large compared to typical time scales at which fusion processes occur.