Synchrotron Radiation Interference

[Enthalpy]

Hi everybody!

I wanted to surround a particle beam with a sleeve mirror and coat the inner face of the sleeve mirror with a transparent material to make light as fast as the particle and produce a shorter and stronger light pulse, or a weaker pulse. This dielectric can be thin on a support. But it must be very thin.

Take full-energy Pb ions, 57ppb below c at the LHC, divergence +-10mm over 30m. A N=1+0.5 coating in a D=3mm must be 0.34nm thin, just 2-3 atomic layers, and accurate to shorten the pulse. So the first difficulty is to avoid unwanted adsorbed layers. This implies noble materials cleaned under vacuum.

Here some reflection coefficients at 2.1eV for pure metals, from the Hdbk of Chem and Phys. Grazing incidence will improve over the normal incidence.
Ag 0.94 but oxidises easily
Au 0.93 but drops soon with the energy: 0.78 at 2.32eV
Al 0.92 but oxidises
Rh 0.78 <= Good choice?
Pd 0.71
Pt 0.65

Reflection is also distributed in the metal over some depth that changes with the frequency, introducing a group delay. I don't plan to think more at it.

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A cylindrical sleeve inverts the field sent back to the particle path, so over some length, the emission must be smaller and the synchrotron losses too.

An sleeve with elliptic section adds constructively the field emitted at one focus, as it bounces a second time before focussing at the particle path. All paths have also the same transverse length, a synonym for "focus". That seems favourable to the experiment I propose, if light that passed last by one focus can be separated from the other, maybe by a median mirror.

Longitudinal focussing (at bending magnets too), accuracy of construction, accuracy of lateral beam position, need more thoughts. I have no plan to do it.

Marc Schaefer, aka Enthalpy