I read that in synchrotron, the X-ray is produced whenever the electrons undergo acceleration, in particular at the bending magnet, the wiggler or undulator. Since these three devices all employ magnetic field, does this radiating behavior have anything to do with the interaction of the particle with magnetic field? What if the bending is achieved using electric field? I think electric-field bending will also produce synchrotron radiation, yet there does not seem to be synchrotron facilities that use this method. Is there any downside in bending the particle trajectory with electric field?
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$\begingroup$ You have to realize that strong electric fields are harder to manipulate experimentally than magnetic fields. The reason lies in those pesky electrons, that are strongly affected by the fields (as monopoles) and are ubiquitus in all matter. Magnetic fields as there are no magnetic monopoles can only affect dipole moments of matter, and are much easier to use experimentally. $\endgroup$– anna vCommented Jul 2, 2018 at 6:16
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$\begingroup$ I don't fully understand you explanation but I think you are implying that when the bending electric field is too strong, the electrons inside the material surrounding the bending region (not the electrons in the beam) can be detached and unwantedly contaminate the beam. Is it something in this direction? $\endgroup$– nougakoCommented Jul 2, 2018 at 6:34
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1$\begingroup$ @nougalo that too, the conductors and geometry would have to be sheilded, most probably in vacuum so the air molecules would not get in the game. There are sparks wherever there are strong electric fields, but strong magnetic fields (10tesla) just distorted the old tv displays used for the detectors. $\endgroup$– anna vCommented Jul 2, 2018 at 10:27
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2 Answers
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The bending of the trajectory of the electrons means that they suffer an acceleration (change of direction) no matter how the bending is done.
It is the fact that the electrons change direction which means that they radiate electromagnetic radiation and thus lose energy.
It makes no difference whether the bending is done using a magnetic field or an electric field as to the loss of energy.
There is more about synchrotron radiation here.
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$\begingroup$ Then why are people only using magnetic bending? $\endgroup$– nougakoCommented Jul 2, 2018 at 6:36
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1$\begingroup$ @nougako Because magnetic fields are easier to work with. For one, there's virtually no risk of creating a spark from a strong magnetic field, whereas there's a moderate risk of creating a spark from a strong electric field, due to the fact that it ionizes any residual gas in the vacuum chamber. $\endgroup$ Commented Jul 2, 2018 at 15:07
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The reason magnetic fields are used to accomplish the bending (as opposed to electric fields) is because the corresponding force is much larger due to the fact that it scales with the particle's velocity. The Lorentz force acting on the particle is:
$$ \vec{F} = q\left(\vec{E} + \vec{v}\times\vec{B}\right) $$
So now suppose we want to use an electric field in order to generate the same force that a magnetic field would do (given the fields are properly aligned). Let's look at the ratio of the field strengths (using $F \equiv \left|\vec{F}\right|$):
$$ F_{el} = F_{magn} \Rightarrow \frac{E}{B} = v $$
Now because the electrons are moving close to the speed of light (i.e. $v = c$), for replacing a magnetic field in the order of $[T]$ we would need to use an electric field in the order of $10^8\left[\frac{V}{m}\right]$ which is very unpractical. On the other hand magnets generating fields in the $[T]$ range are easy to manufacture and to operate.
For the same reason Synchrotrons use magnetic instead of electric fields for bending the particles' trajectories along the curved orbit.
