## *  Light generated by Fast Electron : simulated with water waves

### A electron is simulated with a bar down to the water surface from a toy train. The waves produced by the bar simulate the light wave (Electromagnetic wave) emitted from the electron.

Electromagnetic waves are emitted when a high-speed electron follows curved trajectories. The closer the speed of electrons is to the speed of light, the shorter electromagnetic wave is produced. The electromagnetic field (EM field) generated by electrons is compressed by Lorentz contraction in the direction of its travel. The EM field around the electron has a non-zero distance to the electron, so it takes time for the EM field to notice that the electron has changed course, so the electromagnetic wave leaves the electron and travels straight without knowing that the electron has changed course. And finally it becomes a wave of electromagnetic field: "visible light", "x-ray", "radio-wave", "gamma-ray", "infra-red", "UV", ..." The thinner the longitudinal width of the EM field due to compression by the Lorentz contraction, the shorter the wavelength of the light wave produced by the electron. In order to reduce its wavelength to the X-ray region: < 1/1,000,000,000 meters, it is necessary to accelerate the electrons, that is, to give them energy, bringing their speed closer and closer to the speed of light. For this purpose, all synchrotron radiation rings are large devices to produce high energy electrons.
For the electron with straight motion, in the electron's rest frame ( where the electron looks "stop"), the EM field is just the Coulomb isotropic static electric field. For the lab frame ( where the electron is moving ), the EM field is mixture of the electric field and magnetic field.

includes :

- Cherenkov Radiation (0:47 ~ 1:04):

Radiation produced by an electron faster than the light wave in a medium
( not in vacuum !, of course. )
( the same principle as "shock wave" produeced by an ultrasonic plane, or wake waves produced by ships ) .

- Bremsstrahlung (Radiation) ( 1:45 ~ 1:49 ) :

( This time, the electromagnetic field propagating with the electron leaves the electron as a electromagnetic wave because it takes a time for electromagnetic field around the electron to know the sudden "stopping" motion of electron. (There are some distance between a part of the electromagnetic field and the electron, and the speed of light is not infinite. ))

## *  Radio Freqeuqncy Wave for Acceleration: simulated with water waves

### RF Standing Wave Cavity (movie)

EM field of Radio Frequency (MHz to GHz) is mostly used to acceleate charged particles (electron, proton, ions,.. ) to high energy more than tens million electron volts. The EM energy is stored in a cavity to produce large amplitude standing wave, if the frequency of incident waves is matched to the resonant frequency of a cavity.
Such acceleration cavities are ussed for circular accelerators where charged particles are passing it many times for acceleeration as it goes round in a circlular orbit.

### RF Traveling Wave Cavity (movie)

The EM enegy field flowing in cavity cells producing big EM wave of which phase speed is equivalent to the speed of the acceleratred charged particles. For a linear accelerators, each electron passes the accelerator structure just one time,
therefore, high power, but pulsed EM field is supplied to produce high EM wave in cavities

## *  Acceleration by Lorentz Force

### Wheel driven by Lorentz force (movie)

Charged particles such as electrons moving in a magnetic field will experience a force called the Lorentz force.
This force is perpendicular to both the direction of the particle's motion and the direction of the magnetic field. The magnitude of the force is given by the product of the charge of the particle, the magnitude of its velocity, and the strength of the magnetic field. In the case of a conductor carrying a current by the moving electrons, the electrons experience the Lorentz force due to the magnetic field. However, electrons are confined in the conductor, the Lorentz force This force results in the conductor experiencing a mechanical force, which is commonly known as the "magnetic force." In this toy, a voltage between the two rails are applied to create a current flow along the axis of the wheels. The vertical magnetic field created by the electromagnets and NdFeB permanent magnets will then cause the electrons in the conductor to experience the Lorentz force, resulting in a mechanical force on the conductor, which can cause the wheels to move. This phenomenon is the principle behind electric motors, where the interaction between a magnetic field and a current-carrying conductor generates mechanical motion.

### Lorentz force Launcher (movie)

Magnetic field is produced by electromagnets (beam steering magnets).
Origamied aluminum planes are placed between two rails
where voltage is applied, and launched by Lorentz force.
In this movie, the design of the plane is not good for the launcher
(no straight line stability!!! ).
The planes origamied by children hit the left wall (~10m flight distance).