# Difference between Betatron and Synchrotron?

from my current understanding of linear accelerators, both utilise changing magnetic fields to focus and confine accelerating electrons to a constant orbital radius. Then, what are the main differences in operation/functionality between the two? Apologies for my naivety, thank you!

• Why not try and find an answer by looking on the Internet which has many websites which will answer your question? – Farcher Jul 18 '17 at 7:58
• ...this is a website I thought would answer my question? I didn't understand a lot of what was said in other resources, so I took to stackexchange. – user107224 Jul 23 '17 at 2:54
• one of the answers @Farcher was probably referring to is this one – Alf Mar 23 '18 at 20:22

The betatron is rather unique type of accelerator since it accelerates the charged particles exclusively by the use of a magnet via a time change of the magnetical field $$\bf{B}= \nabla \times \bf{A}$$. The time change of the vector potential $$\bf{A}$$ related with the magnetic field $$\bf{B}$$ creates a non-conversative electrical field (here cgs-units are used): $$\bf{E} = -\frac{1}{c} \frac{\partial \bf{A}}{\partial t}$$