# Changing wavelength while preserving geometry?

• jaketodd
In summary, the wavelength of an EM wave can be changed in a dielectric, but not its frequency. The wave retains its coherence and both the E and H amplitudes are perpendicular to the direction of propagation. Electrons can be accelerated by RF waves in traveling wave cavities, but they do not experience refraction in dielectrics. The electron's energy and speed increase as it is accelerated, and it can reach speeds close to the speed of light where its mass also increases. The magnetron tube uses crossed electric and magnetic fields to accelerate electrons and excite resonances in the cavities. The interaction of RF waves with electrons does not collapse the wave into a particle, and it is possible to reflect an electron wave while preserving

#### jaketodd

Gold Member
Are there ways to change the wavelength of an EM wave while still preserving all geometry of the wave (for instance, preserving an interference pattern which has, of course, irregular geometry in between the minima and maxima of the wave)? I've heard some crystals can change the wavelength but I'm thinking that perhaps some geometry would be lost due to parts of the wave running into the molecules and/or atoms that the crystal is made of. Would the wavelength change be a coherency-preserving process?

Is an electron wave the same as an EM wave (besides having a higher frequency)? And if no, is there a way to change an electron wave's wavelength while preserving geometry and coherency as described above?

Thank you!

...And, I forgot to ask: Is there a way to measure the amplitude of an electron wave?

In a dielectric, the wavelength, but not the frequency, of an EM wave is changed. Off normal incidence will change the direction (refraction) and cause reflection. The EM wave still retains its coherence. Both the E and the H amplitudes are perpendicular to the direction of propagation. the Poynting vector, P = E x H gives both the direction and the power. The velocity of propagation is also changed : v = c/n.

An electron is not refracted in dielectrics. At high enough energies, it does not slow down in dielectrics (excepting by radiative processes), and can travel "faster than light" in the dielectric, and as a consequence will radiate Cerenkov light. Electrons can be accelerated by RF voltages, from thermionic emission energies, up to about 100,000,000 volts (100 GeV). Current is measured in amps (=6.24151 x 10^18 electrons/sec), and power by volts times amps.

So an electron's eV is dependent on it's speed? And I read somewhere that eV determines wavelength. So if you slowed down an electron wave, it would change the wavelength? Can this be done without collapsing the wave?/Can this be done while preserving coherency? An electron in an atom is thought to be in wave form, right? And it is changing direction (orbiting) because of the attraction to the proton(s). So I'm thinking that with an EM field or something you could change the speed of an electron wave without collapsing it and preserve its' coherency. I am thinking this partly because you said in your reply that an electron "can be accelerated by RF voltages" and I'm thinking by RF you mean radio frequency which is an EM wave. Is all this correct?

Also, is it possible to reflect an electron wave at an angle while preserving coherency throughout the process?

Thank you!

You are right on. Radio frequency waves in traveling wave cavities, usually 1400 to 10,000 MHz, are used to accelerate electrons (roughly 1 eV or electron volt) from thermionic emission (hot) cathodes, and the energy gain can be as much as 25 MeV (million electron volts) per meter. As the electron gains energy, it gains speed, and when it gets close to the speed of light, it starts gaining mass instead.

In the magnetron, the electron energy is a few thousand electron volts (the cathode is biased negative), and the electric field together with the magnetic field (called a crossed field) bend the electron's trajectory into orbits (based on the Lorentz force). The electrons are bunched as they pass the vanes, and in turn they excite resonances in the cavities. There are no free protons in the magnetron tube. It is just vacuum.

To understand the magnetron tube well, you need to study the differential equations of electrons in crossed fields. There are several books on microwave engineering that go into crossed field tubes and magnetron theory in some detail.